From 5d581a5b7a8372a3c6c2da249e7e62720a31f4cf Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 21 Mar 2024 21:45:28 +0100 Subject: [PATCH 001/180] save WIP --- .../.github/workflows/CI.yml | 85 + .../.github/workflows/CleanupDocPreview.yml | 29 + .../.github/workflows/TagBot.yml | 15 + .../AlgebraicSolving.jl-main/.gitignore | 3 + .../AlgebraicSolving.jl-main/LICENSE.md | 636 +++++++ .../AlgebraicSolving.jl-main/Manifest.toml | 675 +++++++ .../AlgebraicSolving.jl-main/Project.toml | 33 + .../AlgebraicSolving.jl-main/README.md | 22 + .../docs/Project.toml | 11 + .../AlgebraicSolving.jl-main/docs/make.jl | 36 + .../docs/src/groebner-bases.md | 65 + .../docs/src/index.md | 23 + .../docs/src/katsura.md | 34 + .../docs/src/normal-forms.md | 44 + .../docs/src/solvers.md | 57 + .../docs/src/types.md | 53 + .../src/AlgebraicSolving.jl | 21 + .../src/algorithms/groebner-bases.jl | 184 ++ .../src/algorithms/normal-forms.jl | 174 ++ .../src/algorithms/solvers.jl | 432 +++++ .../src/examples/cyclic.jl | 23 + .../src/examples/katsura.jl | 90 + .../AlgebraicSolving.jl-main/src/exports.jl | 4 + .../AlgebraicSolving.jl-main/src/imports.jl | 61 + .../src/interfaces/nemo.jl | 118 ++ .../src/siggb/hashtable.jl | 472 +++++ .../src/siggb/linear_algebra.jl | 156 ++ .../src/siggb/monomials.jl | 127 ++ .../src/siggb/siggb.jl | 256 +++ .../src/siggb/symbolic_pp.jl | 368 ++++ .../src/siggb/typedefs.jl | 109 ++ .../src/siggb/update.jl | 350 ++++ .../AlgebraicSolving.jl-main/src/types.jl | 51 + .../test/algorithms/groebner-bases.jl | 70 + .../test/algorithms/normal-forms.jl | 18 + .../test/algorithms/solvers.jl | 53 + .../test/examples/katsura.jl | 28 + .../test/interfaces/nemo.jl | 16 + .../AlgebraicSolving.jl-main/test/runtests.jl | 10 + src/connectcurves/data.jl | 10 + src/connectcurves/main.ipynb | 486 ++++++ src/connectcurves/main.jl | 155 ++ src/connectcurves/src/resultant/Makefile | 18 + .../__pycache__/bresultant.cpython-310.pyc | Bin 0 -> 3376 bytes src/connectcurves/src/resultant/bresultant | Bin 0 -> 3412328 bytes src/connectcurves/src/resultant/bresultant.jl | 71 + .../src/resultant/bresultant.sage | 85 + src/connectcurves/src/resultant/data.c | 387 ++++ src/connectcurves/src/resultant/data.h | 150 ++ .../src/resultant/flint_euclide.c | 355 ++++ .../src/resultant/flint_resultant.c | 1285 ++++++++++++++ src/connectcurves/src/resultant/io.c | 562 ++++++ src/connectcurves/src/resultant/main.c | 1550 +++++++++++++++++ src/connectcurves/src/resultant/out.txt | 1 + .../src/resultant/ratreconstruct.c | 176 ++ src/connectcurves/src/usolve/usolve | Bin 0 -> 2969640 bytes src/connectcurves/src/usolve/usolve.jl | 63 + src/connectcurves/tools.jl | 84 + 58 files changed, 10450 insertions(+) create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CI.yml create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CleanupDocPreview.yml create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/TagBot.yml create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/.gitignore create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/LICENSE.md create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/Manifest.toml create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/Project.toml create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/README.md create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/Project.toml create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/make.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/src/groebner-bases.md create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/src/index.md create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/src/katsura.md create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/src/normal-forms.md create mode 100644 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create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/linear_algebra.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/monomials.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/siggb.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/symbolic_pp.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/typedefs.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/update.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/types.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/groebner-bases.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/normal-forms.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/solvers.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/examples/katsura.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/interfaces/nemo.jl create mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/runtests.jl create mode 100644 src/connectcurves/data.jl create mode 100644 src/connectcurves/main.ipynb create mode 100644 src/connectcurves/main.jl create mode 100644 src/connectcurves/src/resultant/Makefile create mode 100644 src/connectcurves/src/resultant/__pycache__/bresultant.cpython-310.pyc create mode 100755 src/connectcurves/src/resultant/bresultant create mode 100644 src/connectcurves/src/resultant/bresultant.jl create mode 100644 src/connectcurves/src/resultant/bresultant.sage create mode 100644 src/connectcurves/src/resultant/data.c create mode 100644 src/connectcurves/src/resultant/data.h create mode 100644 src/connectcurves/src/resultant/flint_euclide.c create mode 100644 src/connectcurves/src/resultant/flint_resultant.c create mode 100644 src/connectcurves/src/resultant/io.c create mode 100644 src/connectcurves/src/resultant/main.c create mode 100644 src/connectcurves/src/resultant/out.txt create mode 100644 src/connectcurves/src/resultant/ratreconstruct.c create mode 100755 src/connectcurves/src/usolve/usolve create mode 100644 src/connectcurves/src/usolve/usolve.jl create mode 100644 src/connectcurves/tools.jl diff --git a/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CI.yml b/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CI.yml new file mode 100644 index 0000000..730421f --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CI.yml @@ -0,0 +1,85 @@ +name: Run tests + +on: + push: + branches: + - main + pull_request: + workflow_dispatch: + +concurrency: + # group by workflow and ref; the last slightly strange component ensures that for pull + # requests, we limit to 1 concurrent job, but for the main branch we don't + group: ${{ github.workflow }}-${{ github.ref }}-${{ github.ref != 'refs/heads/main' || github.run_number }} + # Cancel intermediate builds, but only if it is a pull request build. + cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }} + +jobs: + test: + runs-on: ${{ matrix.os }} + timeout-minutes: 120 + continue-on-error: ${{ matrix.julia-version == 'nightly' }} + strategy: + fail-fast: false + matrix: + julia-version: + - '1.6' + - '1.9' + - '~1.10.0-0' + - 'nightly' + julia-arch: + - x64 + os: + - ubuntu-latest + include: + # Add a few macOS jobs (not too many, the number we can run in parallel is limited) + - julia-version: '1.6' + julia-arch: x64 + os: macOS-latest + - julia-version: 'nightly' + julia-arch: x64 + os: macOS-latest + + steps: + - uses: actions/checkout@v2 + with: + # For Codecov, we must also fetch the parent of the HEAD commit to + # be able to properly deal with PRs / merges + fetch-depth: 2 + - name: "Set up Julia" + uses: julia-actions/setup-julia@v1 + with: + version: ${{ matrix.julia-version }} + arch: ${{ matrix.julia-arch }} + - name: "Build package" + uses: julia-actions/julia-buildpkg@latest + - name: "Run tests" + uses: julia-actions/julia-runtest@latest + - name: "Run doctests" + if: ${{ matrix.julia-version == '1.6' }} + run: | + julia --project=docs --color=yes --code-coverage -e ' + using Pkg + Pkg.develop(PackageSpec(path=pwd())) + Pkg.instantiate() + using Documenter: doctest + using AlgebraicSolving + doctest(AlgebraicSolving)' + - name: "Process code coverage" + uses: julia-actions/julia-processcoverage@v1 + with: + directories: src + - name: "Upload coverage data to Codecov" + continue-on-error: true + uses: codecov/codecov-action@v2 + docs: + name: Documentation + runs-on: ubuntu-latest + steps: + - uses: actions/checkout@v2 + - uses: julia-actions/cache@v1 + - uses: julia-actions/julia-buildpkg@latest + - uses: julia-actions/julia-docdeploy@latest + env: + GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} + DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} diff --git a/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CleanupDocPreview.yml b/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CleanupDocPreview.yml new file mode 100644 index 0000000..18be754 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CleanupDocPreview.yml @@ -0,0 +1,29 @@ +name: Cleanup Doc Preview + +on: + pull_request: + types: [closed] + +jobs: + cleanup-doc-preview: + runs-on: ubuntu-latest + steps: + - name: Checkout gh-pages branch + uses: actions/checkout@v2 + with: + ref: gh-pages + - name: Delete preview + run: | + if [ -d "previews/PR$PRNUM" ]; then + git config user.name "Documenter.jl" + git config user.email "documenter@juliadocs.github.io" + git rm -rf "previews/PR$PRNUM" + git commit -m "delete preview for $PRNUM" + git push origin gh-pages:gh-pages + fi + env: + PRNUM: ${{ github.event.number }} + +# adapted from here: +# https://juliadocs.github.io/Documenter.jl/stable/man/hosting/#gh-pages-Branch +# without history cleanup diff --git a/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/TagBot.yml b/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/TagBot.yml new file mode 100644 index 0000000..f49313b --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/TagBot.yml @@ -0,0 +1,15 @@ +name: TagBot +on: + issue_comment: + types: + - created + workflow_dispatch: +jobs: + TagBot: + if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot' + runs-on: ubuntu-latest + steps: + - uses: JuliaRegistries/TagBot@v1 + with: + token: ${{ secrets.GITHUB_TOKEN }} + ssh: ${{ secrets.DOCUMENTER_KEY }} diff --git a/src/connectcurves/AlgebraicSolving.jl-main/.gitignore b/src/connectcurves/AlgebraicSolving.jl-main/.gitignore new file mode 100644 index 0000000..014cf71 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/.gitignore @@ -0,0 +1,3 @@ +*~ +docs/build/* +docs/make-dep.jl diff --git 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"3d5dd08c-fd9d-11e8-17fa-ed2836048c2f" +version = "0.21.65" + +[[deps.Zlib_jll]] +deps = ["Libdl"] +uuid = "83775a58-1f1d-513f-b197-d71354ab007a" +version = "1.2.13+1" + +[[deps.cddlib_jll]] +deps = ["Artifacts", "GMP_jll", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "c25e5fe14395ea7b1d702f4eb90c52bdf50e3450" +uuid = "f07e07eb-5685-515a-97c8-3014f6152feb" +version = "0.94.13+0" + +[[deps.lib4ti2_jll]] +deps = ["Artifacts", "GLPK_jll", "GMP_jll", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "79116185def638e73ea3d88ca6c10e210a1dc183" +uuid = "1493ae25-0f90-5c0e-a06c-8c5077d6d66f" +version = "1.6.10+0" + +[[deps.libblastrampoline_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" +version = "5.8.0+1" + +[[deps.libcxxwrap_julia_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "3d47ce071d272d2cae9d1bc449c261237e9784f7" +uuid = "3eaa8342-bff7-56a5-9981-c04077f7cee7" +version = "0.11.2+0" + +[[deps.libsingular_julia_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Singular_jll", "libcxxwrap_julia_jll"] +git-tree-sha1 = "bcf29726c1c4cd53c0e3c6c093cdca68d0f67beb" +uuid = "ae4fbd8f-ecdb-54f8-bbce-35570499b30e" +version = "0.40.11+0" + +[[deps.msolve_jll]] +deps = ["Artifacts", "CompilerSupportLibraries_jll", "FLINT_jll", "GMP_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl", "MPFR_jll"] +git-tree-sha1 = "6d02a110f583341deea0d249b1a741352631aed6" +uuid = "6d01cc9a-e8f6-580e-8c54-544227e08205" +version = "0.6.3+0" + +[[deps.nghttp2_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" +version = "1.52.0+1" + +[[deps.p7zip_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" +version = "17.4.0+2" diff --git a/src/connectcurves/AlgebraicSolving.jl-main/Project.toml b/src/connectcurves/AlgebraicSolving.jl-main/Project.toml new file mode 100644 index 0000000..631e6dc --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/Project.toml @@ -0,0 +1,33 @@ +name = "AlgebraicSolving" +uuid = "66b61cbe-0446-4d5d-9090-1ff510639f9d" +authors = ["ederc ", "Mohab Safey El Din "] +version = "0.4.6" + +[deps] +BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" +ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" +LoopVectorization = "bdcacae8-1622-11e9-2a5c-532679323890" +Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" +Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" +Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" +Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" +Singular = "bcd08a7b-43d2-5ff7-b6d4-c458787f915c" +StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" +Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" +msolve_jll = "6d01cc9a-e8f6-580e-8c54-544227e08205" + +[compat] +LinearAlgebra = "1.6" +Logging = "1.6" +LoopVectorization = "0.12" +Markdown = "1.6" +Nemo = "0.35.1, 0.36, 0.37, 0.38, 0.39" +Printf = "1.6" +Random = "1.6" +StaticArrays = "1" +Test = "1.6" +julia = "1.6" +msolve_jll = "0.6.3" diff --git a/src/connectcurves/AlgebraicSolving.jl-main/README.md b/src/connectcurves/AlgebraicSolving.jl-main/README.md new file mode 100644 index 0000000..5063df7 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/README.md @@ -0,0 +1,22 @@ +# AlgebraicSolving.jl + +A julia package for algebraically solving multivariate polynomial systems. + +## Installation +AlgebraicSolving requires Julia 1.6 or newer. In principle it can be installed and used +like any other Julia package: + +```julia +julia> using Pkg +julia> Pkg.add("AlgebraicSolving") +julia> using AlgebraicSolving +``` + +## Documentation and Examples + +You can find a detailed documentation including various examples at +https://algebraic-solving.github.io/ . + +# Funding + +The development of `AlgebraicSolving` is supported by the [Forschungsinitiative Rheinland-Pfalz](https://rptu.de/forschung/forschungsinitiative-rlp). diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/Project.toml b/src/connectcurves/AlgebraicSolving.jl-main/docs/Project.toml new file mode 100644 index 0000000..ee69314 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/docs/Project.toml @@ -0,0 +1,11 @@ +[deps] +AlgebraicSolving= "66b61cbe-0446-4d5d-9090-1ff510639f9d" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" +msolve_jll = "6d01cc9a-e8f6-580e-8c54-544227e08205" +Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" +Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" + +[compat] +Documenter = "0.26" +msolve_jll = "0.6.1" diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/make.jl b/src/connectcurves/AlgebraicSolving.jl-main/docs/make.jl new file mode 100644 index 0000000..ab996ee --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/docs/make.jl @@ -0,0 +1,36 @@ +using AlgebraicSolving +using Documenter + +push!(LOAD_PATH, "../src") + +DocMeta.setdocmeta!(AlgebraicSolving, :DocTestSetup, :(using AlgebraicSolving); recursive=true) + +# Build documentation. +# ==================== + +makedocs( + # options + modules = [AlgebraicSolving], + doctest = true, + clean = true, + checkdocs = :none, + sitename = "AlgebraicSolving.jl", + format = Documenter.HTML(), + pages = [ + "index.md", + "types.md", + "Algorithms" => ["groebner-bases.md", + "normal-forms.md", + "solvers.md"], + "Examples" => "katsura.md" + ] +) + +# Deploy built documentation from Travis. +# ======================================= + +deploydocs( + # options + repo = "github.com/algebraic-solving/AlgebraicSolving.jl.git", + target = "build", +) diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/groebner-bases.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/groebner-bases.md new file mode 100644 index 0000000..58792c0 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/groebner-bases.md @@ -0,0 +1,65 @@ +```@meta +CurrentModule = AlgebraicSolving +DocTestSetup = quote + using AlgebraicSolving +end +``` + +```@setup algebraicsolving +using AlgebraicSolving +``` + +```@contents +Pages = ["groebner-bases.md"] +``` + +# Gröbner bases + +## Introduction + +AlgebraicSolving allows to compute Gröbner bases for input generators over finite +fields of characteristic smaller $2^{31}$ w.r.t. the degree reverse +lexicographical monomial order. + +At the moment different variants of Faugère's F4 Algorithm are implemented as +well as a signature based algorithm to compute Gröbner bases. + +## Functionality + +```@docs + groebner_basis( + I::Ideal{T} where T <: MPolyRingElem; + initial_hts::Int=17, + nr_thrds::Int=1, + max_nr_pairs::Int=0, + la_option::Int=2, + eliminate::Int=0, + complete_reduction::Bool=true, + info_level::Int=0 + ) +``` + +The engine supports the elimination of one block of variables considering the +product monomial ordering of two blocks, both ordered w.r.t. the degree +reverse lexicographical order. One can either directly add the number of +variables of the first block via the `eliminate` parameter in the +`groebner_basis` call. We have also implemented an alias for this call: + +```@docs + eliminate( + I::Ideal{T} where T <: MPolyRingElem, + eliminate::Int; + initial_hts::Int=17, + nr_thrds::Int=1, + max_nr_pairs::Int=0, + la_option::Int=2, + complete_reduction::Bool=true, + info_level::Int=0 + ) +``` + +To compute signature Gröbner bases use + +```@docs + sig_groebner_basis(sys::Vector{T}; info_level::Int = 0, degbound::Int = 0) where {T <: MPolyRingElem} +``` diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/index.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/index.md new file mode 100644 index 0000000..4ae0cec --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/index.md @@ -0,0 +1,23 @@ +# Getting Started + +AlgebraicSolving is a computer algebra package for the Julia programming +language, maintained by Christian Eder and Mohab Safey El Din. + +- (Source code) + +The features of AlgebraicSolving include algorithms for computing +Gröbner bases over finite fields and for computing real solutions. +The main workhorse of AlgebraicSolving is the [msolve +library](https://msolve.lip6.fr/) . + +## Installation + +To use Nemo we require Julia 1.6 or higher. Please see + for instructions on +how to obtain julia for your system. + +At the Julia prompt simply type + +``` +julia> using Pkg; Pkg.add("AlgebraicSolving") +``` diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/katsura.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/katsura.md new file mode 100644 index 0000000..fa72c56 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/katsura.md @@ -0,0 +1,34 @@ +```@meta +CurrentModule = AlgebraicSolving +DocTestSetup = quote + using AlgebraicSolving +end +``` + +```@setup algebraicsolving +using AlgebraicSolving +``` + +```@contents +Pages = ["katsura.md"] +``` + +# Examples + +Here we include some well-known example multivariate polynomial systems. + +## Katsura-n + +These systems appeared in a problem of magnetism in physics. +For a given $n$ `katsura(n)` has $2^n$ solutions and is defined in a +polynomial ring with $n+1$ variables. For a given polynomial ring `R` +with $n$ variables `katsura(R)` defines the corresponding system with +$2^{n-1}$ solutions. + +### Functionality + +```@docs + katsura(n::Int) + katsura(R::MPolyRing) +``` + diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/normal-forms.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/normal-forms.md new file mode 100644 index 0000000..bf04482 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/normal-forms.md @@ -0,0 +1,44 @@ +```@meta +CurrentModule = AlgebraicSolving +DocTestSetup = quote + using AlgebraicSolving +end +``` + +```@setup algebraicsolving +using AlgebraicSolving +``` + +```@contents +Pages = ["normal-forms.md"] +``` + +# Normal forms + +## Introduction + +AlgebraicSolving allows to compute normal forms of a polynomial resp. a finite +array of polynomials w.r.t. some given ideal over a finite field of +characteristic smaller $2^{31}$ w.r.t. the degree reverse lexicographical +monomial order. + +**Note:** It therefore might first compute a Gröbner bases for the ideal. +## Functionality + +```@docs + normal_form( + f::T, + I::Ideal{T}; + nr_thrds::Int=1, + info_level::Int=0 + ) where T <: MPolyRingElem +``` + +```@docs + normal_form( + F::Vector{T}, + I::Ideal{T}; + nr_thrds::Int=1, + info_level::Int=0 + ) where T <: MPolyRingElem +``` diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/solvers.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/solvers.md new file mode 100644 index 0000000..0017986 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/solvers.md @@ -0,0 +1,57 @@ +```@meta +CurrentModule = AlgebraicSolving +DocTestSetup = quote + using AlgebraicSolving +end +``` + +```@setup algebraicsolving +using AlgebraicSolving +``` + +```@contents +Pages = ["solvers.md"] +``` + +# Algebraic Systems Solving + +## Introduction + +AlgebraicSolving allows to solve systems for input generators over finite +fields of characteristic smaller $2^{31}$ and over the rationals. + +The underlying engine is provided by msolve. + +## Functionality + +```@docs + rational_parametrization( + I::Ideal{T} where T <: MPolyRingElem; + initial_hts::Int=17, + nr_thrds::Int=1, + max_nr_pairs::Int=0, + la_option::Int=2, + info_level::Int=0, + precision::Int=32 + ) + + real_solutions( + I::Ideal{T} where T <: MPolyRingElem; + initial_hts::Int=17, + nr_thrds::Int=1, + max_nr_pairs::Int=0, + la_option::Int=2, + info_level::Int=0, + precision::Int=32 + ) + rational_solutions( + I::Ideal{T} where T <: MPolyRingElem; + initial_hts::Int=17, + nr_thrds::Int=1, + max_nr_pairs::Int=0, + la_option::Int=2, + info_level::Int=0, + precision::Int=32 + ) +``` + diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/types.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/types.md new file mode 100644 index 0000000..80fcd90 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/types.md @@ -0,0 +1,53 @@ +```@meta +CurrentModule = AlgebraicSolving +DocTestSetup = quote + using AlgebraicSolving +end +``` + +```@setup algebraicsolving +using AlgebraicSolving +``` + +```@contents +Pages = ["types.md"] +``` + +# Data Types + +## Introduction + +AlgebraicSolving handles ideals in multivariate polynomial rings over a prime +field of characteristic $0$ or $p$ where $p$ is a prime number $<2^{31}$. + +## Polynomial Rings + +We use [Nemo](https://www.nemocas.org/index.html)'s multivariate polynomial +ring structures: + +```@repl +using AlgebraicSolving +R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"], ordering=:degrevlex) +``` +The above example defines a multivariate polynomial ring in three variables `x`, +`y`, and `z` over the rationals using the dgree reverse lexicographical ordering +for printing polynomials in the following. One can also define polynomial rings +over finite fields: + +```@repl +using AlgebraicSolving +R, (x,y,z) = polynomial_ring(GF(101), ["x", "y", "z"], ordering=:degrevlex) +``` + +## Ideals + +Ideals can be constructed by giving an array of generators. Ideals cache varies +data structures connected to ideals in order to make computational algebra more +effective: + +```@repl +using AlgebraicSolving +R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"], ordering=:degrevlex) +I = Ideal([x+y+1, y*z^2-13*y^2]) +``` + diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/AlgebraicSolving.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/AlgebraicSolving.jl new file mode 100644 index 0000000..54ddc46 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/AlgebraicSolving.jl @@ -0,0 +1,21 @@ +module AlgebraicSolving + +greet() = print("AlgebraicSolving -- a package for algebraic solving based on msolve") + +#= io =# +include("imports.jl") +include("exports.jl") +#= types =# +include("types.jl") +#= functionality =# +include("interfaces/nemo.jl" ) +include("algorithms/groebner-bases.jl") +include("algorithms/normal-forms.jl") +include("algorithms/solvers.jl") +#= siggb =# +include("siggb/siggb.jl") +#= examples =# +include("examples/katsura.jl") +include("examples/cyclic.jl") + +end # module AlgebraicSolving diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/groebner-bases.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/groebner-bases.jl new file mode 100644 index 0000000..3d2f495 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/groebner-bases.jl @@ -0,0 +1,184 @@ +import msolve_jll: libneogb + +export groebner_basis, eliminate + +@doc Markdown.doc""" + eliminate(I::Ideal{T} where T <: MPolyRingElem, eliminate::Int, ) + +Compute a Groebner basis of the ideal `I` w.r.t. to the product monomial ordering defined by two blocks +w.r.t. the degree reverse lexicographical monomial ordering using Faugère's F4 algorithm. Hereby the first block includes +the first `eliminate` variables. + +At the moment the underlying algorithm is based on variants of Faugère's F4 Algorithm. + +**Note**: At the moment only ground fields of characteristic `p`, `p` prime, `p < 2^{31}` are supported. + +# Arguments +- `I::Ideal{T} where T <: MPolyRingElem`: input generators. +- `initial_hts::Int=17`: initial hash table size `log_2`. +- `nr_thrds::Int=1`: number of threads for parallel linear algebra. +- `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`. +- `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`). +- `complete_reduction::Bool=true`: compute a reduced Gröbner basis for `I` +- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). + +# Examples +```jldoctest +julia> using AlgebraicSolving + +julia> R, (x,y,z) = polynomial_ring(GF(101),["x","y","z"], ordering=:degrevlex) +(Multivariate polynomial ring in 3 variables over GF(101), FqMPolyRingElem[x, y, z]) + +julia> I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y]) +FqMPolyRingElem[x + 2*y + 2*z + 100, x^2 + 2*y^2 + 2*z^2 + 100*x, 2*x*y + 2*y*z + 100*y] + +julia> eliminate(I, 2) +1-element Vector{FqMPolyRingElem}: + z^4 + 38*z^3 + 95*z^2 + 95*z +``` +""" +function eliminate( + I::Ideal{T} where T <: MPolyRingElem, + eliminate::Int; + initial_hts::Int=17, + nr_thrds::Int=1, + max_nr_pairs::Int=0, + la_option::Int=2, + complete_reduction::Bool=true, + info_level::Int=0 + ) + if eliminate <= 0 + error("Number of variables to be eliminated is <= 0.") + else + return groebner_basis(I, initial_hts=initial_hts, nr_thrds=nr_thrds, + max_nr_pairs=max_nr_pairs, la_option=la_option, + eliminate=eliminate, + complete_reduction=complete_reduction, + info_level=info_level) + end +end + +@doc Markdown.doc""" + groebner_basis(I::Ideal{T} where T <: MPolyRingElem, ) + +Compute a Groebner basis of the ideal `I` w.r.t. to the degree reverse lexicographical monomial ordering using Faugère's F4 algorithm. +At the moment the underlying algorithm is based on variants of Faugère's F4 Algorithm. + +**Note**: At the moment only ground fields of characteristic `p`, `p` prime, `p < 2^{31}` are supported. + +# Arguments +- `I::Ideal{T} where T <: MPolyRingElem`: input generators. +- `initial_hts::Int=17`: initial hash table size `log_2`. +- `nr_thrds::Int=1`: number of threads for parallel linear algebra. +- `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`. +- `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`). +- `eliminate::Int=0`: size of first block of variables to be eliminated. +- `complete_reduction::Bool=true`: compute a reduced Gröbner basis for `I` +- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). + +# Examples +```jldoctest +julia> using AlgebraicSolving + +julia> R, (x,y,z) = polynomial_ring(GF(101),["x","y","z"], ordering=:degrevlex) +(Multivariate polynomial ring in 3 variables over GF(101), FqMPolyRingElem[x, y, z]) + +julia> I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y]) +FqMPolyRingElem[x + 2*y + 2*z + 100, x^2 + 2*y^2 + 2*z^2 + 100*x, 2*x*y + 2*y*z + 100*y] + +julia> groebner_basis(I) +4-element Vector{FqMPolyRingElem}: + x + 2*y + 2*z + 100 + y*z + 82*z^2 + 10*y + 40*z + y^2 + 60*z^2 + 20*y + 81*z + z^3 + 28*z^2 + 64*y + 13*z + +julia> groebner_basis(I, eliminate=2) +1-element Vector{FqMPolyRingElem}: + z^4 + 38*z^3 + 95*z^2 + 95*z +``` +""" +function groebner_basis( + I::Ideal{T} where T <: MPolyRingElem; + initial_hts::Int=17, + nr_thrds::Int=1, + max_nr_pairs::Int=0, + la_option::Int=2, + eliminate::Int=0, + complete_reduction::Bool=true, + info_level::Int=0 + ) + + return get!(I.gb, eliminate) do + _core_groebner_basis(I, initial_hts = initial_hts, nr_thrds = nr_thrds, + max_nr_pairs = max_nr_pairs, la_option = la_option, + eliminate = eliminate, + complete_reduction = complete_reduction, + info_level = info_level) + end +end + +function _core_groebner_basis( + I::Ideal{T} where T <: MPolyRingElem; + initial_hts::Int=17, + nr_thrds::Int=1, + max_nr_pairs::Int=0, + la_option::Int=2, + eliminate::Int=0, + complete_reduction::Bool=true, + info_level::Int=0 + ) + + F = I.gens + R = first(F).parent + if F == [R(0)] + return F + end + nr_vars = nvars(R) + nr_gens = length(F) + field_char = Int(characteristic(R)) + + mon_order = 0 + elim_block_size = eliminate + reduce_gb = Int(complete_reduction) + + # convert ideal to flattened arrays of ints + if !(is_probable_prime(field_char)) + error("At the moment we only supports finite fields.") + end + + lens, cfs, exps = _convert_to_msolve(F) + + gb_ld = Ref(Cint(0)) + gb_len = Ref(Ptr{Cint}(0)) + gb_exp = Ref(Ptr{Cint}(0)) + gb_cf = Ref(Ptr{Cvoid}(0)) + + nr_terms = ccall((:export_f4, libneogb), Int, + (Ptr{Nothing}, Ptr{Cint}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cvoid}}, + Ptr{Cint}, Ptr{Cint}, Ptr{Cvoid}, Cint, Cint, Cint, Cint, Cint, Cint, + Cint, Cint, Cint, Cint, Cint, Cint, Cint), + cglobal(:jl_malloc), gb_ld, gb_len, gb_exp, gb_cf, lens, exps, cfs, + field_char, mon_order, elim_block_size, nr_vars, nr_gens, initial_hts, + nr_thrds, max_nr_pairs, 0, la_option, reduce_gb, 0, info_level) + + # convert to julia array, also give memory management to julia + jl_ld = gb_ld[] + jl_len = Base.unsafe_wrap(Array, gb_len[], jl_ld) + jl_exp = Base.unsafe_wrap(Array, gb_exp[], nr_terms*nr_vars) + ptr = reinterpret(Ptr{Int32}, gb_cf[]) + jl_cf = Base.unsafe_wrap(Array, ptr, nr_terms) + + basis = _convert_finite_field_array_to_abstract_algebra( + jl_ld, jl_len, jl_cf, jl_exp, R, eliminate) + + + ccall((:free_f4_julia_result_data, libneogb), Nothing , + (Ptr{Nothing}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}}, + Ptr{Ptr{Cvoid}}, Int, Int), + cglobal(:jl_free), gb_len, gb_exp, gb_cf, jl_ld, field_char) + + I.gb[eliminate] = basis + + return basis +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/normal-forms.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/normal-forms.jl new file mode 100644 index 0000000..36a7913 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/normal-forms.jl @@ -0,0 +1,174 @@ +import msolve_jll: libneogb + +export normal_form + +@doc Markdown.doc""" + normal_form( + f::T, + I::Ideal{T}; + nr_thrds::Int=1, + info_level::Int=0 + ) where T <: MPolyRingElem + +Compute the normal forms of the elements of `F` w.r.t. a degree reverse +lexicographical Gröbner basis of `I`. + +**Note:** If `I` has not already cached a degree reverse lexicographical +Gröbner basis, then this one is first computed. + +# Arguments +- `F::Vector{T} where T <: MPolyRingElem`: elements to be reduced. +- `I::Ideal{T} where T <: MPolyRingElem`: ideal data to reduce with. +- `nr_thrds::Int=1`: number of threads for parallel linear algebra. +- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). + +# Examples +```jldoctest +julia> using AlgebraicSolving + +julia> R, (x,y) = polynomial_ring(GF(101),["x","y"]) +(Multivariate polynomial ring in 2 variables over GF(101), FqMPolyRingElem[x, y]) + +julia> I = Ideal([y*x^3+12-y, x+y]) +FqMPolyRingElem[x^3*y + 100*y + 12, x + y] + +julia> f = 2*x^2+7*x*y +2*x^2 + 7*x*y + +julia> normal_form(f, I) +96*y^2 +``` +""" +function normal_form( + f::T, + I::Ideal{T}; + nr_thrds::Int=1, + info_level::Int=0 + ) where T <: MPolyRingElem + nf = _core_normal_form([f], I; nr_thrds, info_level) + return nf[1] +end + +@doc Markdown.doc""" + normal_form( + F::Vector{T}, + I::Ideal{T}; + nr_thrds::Int=1, + info_level::Int=0 + ) where T <: MPolyRingElem + +Compute the normal forms of the elements of `F` w.r.t. a degree reverse +lexicographical Gröbner basis of `I`. + +**Note:** If `I` has not already cached a degree reverse lexicographical +Gröbner basis, then this one is first computed. + +# Arguments +- `F::Vector{T} where T <: MPolyRingElem`: elements to be reduced. +- `I::Ideal{T} where T <: MPolyRingElem`: ideal data to reduce with. +- `nr_thrds::Int=1`: number of threads for parallel linear algebra. +- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). + +# Examples +```jldoctest +julia> using AlgebraicSolving + +julia> R, (x,y) = polynomial_ring(GF(101),["x","y"]) +(Multivariate polynomial ring in 2 variables over GF(101), FqMPolyRingElem[x, y]) + +julia> I = Ideal([y*x^3+12-y, x+y]) +FqMPolyRingElem[x^3*y + 100*y + 12, x + y] + +julia> F = [2*x^2+7*x*y, x+y] +2-element Vector{FqMPolyRingElem}: + 2*x^2 + 7*x*y + x + y + +julia> normal_form(F,I) +2-element Vector{FqMPolyRingElem}: + 96*y^2 + 0 +``` +""" +function normal_form( + F::Vector{T}, + I::Ideal{T}; + nr_thrds::Int=1, + info_level::Int=0 + ) where T <: MPolyRingElem + return _core_normal_form(F, I; nr_thrds, info_level) +end + +function _core_normal_form( + F::Vector{T}, + I::Ideal{T}; + nr_thrds::Int=1, + info_level::Int=0 + ) where T <: MPolyRingElem + + + if (length(F) == 0 || length(I.gens) == 0) + error("Input data not valid.") + end + + R = first(F).parent + nr_vars = nvars(R) + field_char = Int(characteristic(R)) + + if !(is_probable_prime(field_char)) + error("At the moment we only supports finite fields.") + end + + #= first get a degree reverse lexicographical Gröbner basis for I =# + if !haskey(I.gb, 0) + if field_char > 2^17 + groebner_basis(I, eliminate = 0, la_option = 44, info_level = info_level) + else + groebner_basis(I, eliminate = 0, la_option = 2, info_level = info_level) + end + end + G = I.gb[0] + + if G == [R(0)] + return F + end + + tbr_nr_gens = length(F) + bs_nr_gens = length(G) + is_gb = 1 + + # convert ideal to flattened arrays of ints + tbr_lens, tbr_cfs, tbr_exps = _convert_to_msolve(F) + bs_lens, bs_cfs, bs_exps = _convert_to_msolve(G) + + nf_ld = Ref(Cint(0)) + nf_len = Ref(Ptr{Cint}(0)) + nf_exp = Ref(Ptr{Cint}(0)) + nf_cf = Ref(Ptr{Cvoid}(0)) + + nr_terms = ccall((:export_nf, libneogb), Int, + (Ptr{Nothing}, Ptr{Cint}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cvoid}}, + Cint, Ptr{Cint}, Ptr{Cint}, Ptr{Cvoid}, Cint, Ptr{Cint}, Ptr{Cint}, Ptr{Cvoid}, + Cint, Cint, Cint, Cint, Cint, Cint, Cint), + cglobal(:jl_malloc), nf_ld, nf_len, nf_exp, nf_cf, tbr_nr_gens, tbr_lens, tbr_exps, + tbr_cfs, bs_nr_gens, bs_lens, bs_exps, bs_cfs, field_char, 0, 0, nr_vars, is_gb, + nr_thrds, info_level) + + # convert to julia array, also give memory management to julia + jl_ld = nf_ld[] + jl_len = Base.unsafe_wrap(Array, nf_len[], jl_ld) + jl_exp = Base.unsafe_wrap(Array, nf_exp[], nr_terms*nr_vars) + ptr = reinterpret(Ptr{Int32}, nf_cf[]) + jl_cf = Base.unsafe_wrap(Array, ptr, nr_terms) + + basis = _convert_finite_field_array_to_abstract_algebra( + jl_ld, jl_len, jl_cf, jl_exp, R, 0) + + ccall((:free_f4_julia_result_data, libneogb), Nothing , + (Ptr{Nothing}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}}, + Ptr{Ptr{Cvoid}}, Int, Int), + cglobal(:jl_free), nf_len, nf_exp, nf_cf, jl_ld, field_char) + + return basis +end + diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl new file mode 100644 index 0000000..11cd320 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl @@ -0,0 +1,432 @@ +import msolve_jll: libmsolve + +export inter_solutions, real_solutions, rational_solutions, rational_parametrization + +@doc Markdown.doc""" + _get_rational_parametrization(nr::Int32, lens::Vector{Int32}, cfs::Ptr{BigInt}) + +Construct the rational parametrization of the solution set computed via msolve. + +**Note**: This is an internal function and should only be used inside `msolve()`. +""" +function _get_rational_parametrization( + nr::Int32, + lens::Vector{Int32}, + cfs::Ptr{BigInt}, + cfs_lf::Ptr{BigInt}, + nr_vars::Int32 + ) + if cfs_lf != Ptr{BigInt}(0) + lf = [ZZRingElem(unsafe_load(cfs_lf, i)) for i in 1:nr_vars] + else + lf = ZZRingElem[] + end + C, x = polynomial_ring(QQ,"x") + ctr = 0 + + elim = C([unsafe_load(cfs, i) for i in 1:lens[1]]) + ctr += lens[1] + + denom = C([unsafe_load(cfs, i+ctr) for i in 1:lens[2]]) + ctr += lens[2] + + size = nr-2 + p = Vector{PolyRingElem}(undef, size) + k = 1 + for i in 3:nr + p[k] = C([unsafe_load(cfs, j+ctr) for j in 1:lens[i]-1]) + # multiply parametrization polynomial directly with + # corresponding coefficients + p[k] *= (-1) * ZZRingElem(unsafe_load(cfs, lens[i]+ctr)) + ctr += lens[i] + k += 1 + end + + return lf, elim, denom, p +end + +@doc Markdown.doc""" + _core_msolve(I::Ideal{T} where T <: MPolyRingElem, ) + +Compute a rational parametrization and the real solutions of the ideal `I` via msolve. + +**Note**: This is an internal function. +""" +function _core_msolve( + I::Ideal{T} where T <: MPolyRingElem; # input generators + initial_hts::Int=17, # hash table size, default 2^17 + nr_thrds::Int=1, # number of threads + max_nr_pairs::Int=0, # number of pairs maximally chosen + # in symbolic preprocessing + la_option::Int=2, # linear algebra option + info_level::Int=0, # info level for print outs + precision::Int=32 # precision of the solution set + ) + + F = I.gens + R = first(F).parent + nr_vars = nvars(R) + nr_gens = length(F) + field_char = Int(characteristic(R)) + + variable_names = map(string, R.S) + + #= add new variables and linear forms, =# + genericity_handling = 2 + + reset_ht = 0 + print_gb = 0 + get_param = 1 + + mon_order = 0 + elim_block_size = 0 + use_signatures = 0 + + if field_char != 0 + error("At the moment we only support the rationals as ground field.") + end + # convert Singular ideal to flattened arrays of ints + lens, cfs, exps = _convert_to_msolve(F) + + res_ld = Ref(Cint(0)) + res_nr_vars = Ref(Cint(0)) + res_dim = Ref(Cint(0)) + res_dquot = Ref(Cint(0)) + nb_sols = Ref(Cint(0)) + res_len = Ref(Ptr{Cint}(0)) + res_vnames = Ref(Ptr{Ptr{Cchar}}(0)) + res_cf_lf = Ref(Ptr{Cvoid}(0)) + res_cf = Ref(Ptr{Cvoid}(0)) + sols_num = Ref(Ptr{Cvoid}(0)) + sols_den = Ref(Ptr{Cint}(0)) + + ccall((:msolve_julia, libmsolve), Cvoid, + (Ptr{Nothing}, Ptr{Cint}, Ptr{Cint}, Ptr{Cint}, Ptr{Cint}, Ptr{Ptr{Cint}}, + Ptr{Ptr{Ptr{Cchar}}}, Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cint}, Ptr{Cvoid}, Ptr{Ptr{Cint}}, Ptr{Cint}, + Ptr{Cint}, Ptr{Cvoid}, Ptr{Ptr{Cchar}}, Ptr{Cchar}, Cint, Cint, + Cint, Cint, Cint, Cint, Cint, Cint, Cint, Cint, Cint, Cint, Cint, + Cint, Cint, Cint), + cglobal(:jl_malloc), res_ld, res_nr_vars, res_dim, res_dquot, res_len, res_vnames, + res_cf_lf, res_cf, + nb_sols, sols_num, sols_den, lens, exps, cfs, variable_names, + "/dev/null", field_char, mon_order, elim_block_size, nr_vars, + nr_gens, initial_hts, nr_thrds, max_nr_pairs, reset_ht, la_option, + use_signatures, print_gb, get_param, genericity_handling, precision, + info_level) + # convert to julia array, also give memory management to julia + jl_ld = res_ld[] + jl_rp_nr_vars = res_nr_vars[] + jl_dim = res_dim[] + jl_dquot = res_dquot[] + jl_nb_sols = nb_sols[] + + # set dimension + I.dim = jl_dim + if jl_dim > 0 + error("Dimension of ideal is greater than zero, no solutions provided.") + end + + # get rational parametrization + jl_len = Base.unsafe_wrap(Array, res_len[], jl_ld) + nterms = 0 + + if jl_dquot == 0 + C,x = polynomial_ring(QQ,"x") + I.rat_param = RationalParametrization(Symbol[], ZZRingElem[], C(-1), C(-1), PolyRingElem[]) + I.real_sols = QQFieldElem[] + return I.rat_param, I.real_sols + end + [nterms += jl_len[i] for i=1:jl_ld] + jl_cf = reinterpret(Ptr{BigInt}, res_cf[]) + jl_cf_lf = reinterpret(Ptr{BigInt}, res_cf_lf[]) + + jl_vnames = Base.unsafe_wrap(Array, res_vnames[], jl_rp_nr_vars) + + vsymbols = [Symbol(unsafe_string(jl_vnames[i])) for i in 1:jl_rp_nr_vars] + + rat_param = _get_rational_parametrization(jl_ld, jl_len, + jl_cf, jl_cf_lf, jl_rp_nr_vars) + + I.rat_param = RationalParametrization(vsymbols, rat_param[1],rat_param[2], + rat_param[3], rat_param[4]) + if jl_nb_sols == 0 + I.real_sols = QQFieldElem[] + return rat_param, Vector{QQFieldElem}[] + end + + # get solutions + jl_sols_num = reinterpret(Ptr{BigInt}, sols_num[]) + jl_sols_den = reinterpret(Ptr{Int32}, sols_den[]) + # elseif is_prime(field_char) + # jl_cf = reinterpret(Ptr{Int32}, res_cf[]) + # jl_sols_num = reinterpret(Ptr{Int32}, sols_num[]) + # end + + #= solutions are returned as intervals, i.e. a minimum and a maximum entry for + = the numerator and denominator; thus we sum up and divide by 2 =# + + inter_solutions = Vector{Vector{Vector{QQFieldElem}}}(undef, jl_nb_sols) + solutions = Vector{Vector{QQFieldElem}}(undef, jl_nb_sols) + + len = 2*jl_nb_sols*nr_vars + i = 1 + k = 1 + while i <= len + j = 1 + inter_tmp = Vector{Vector{QQFieldElem}}(undef, nr_vars) + tmp = Vector{QQFieldElem}(undef, nr_vars) + while j <= nr_vars + inter_tmp_coeff = Vector{QQFieldElem}(undef, 2) + inter_tmp_coeff[1] = QQFieldElem(unsafe_load(jl_sols_num, i)) >> Int64(unsafe_load(jl_sols_den, i)) + inter_tmp_coeff[2] = QQFieldElem(unsafe_load(jl_sols_num, i+1)) >> Int64(unsafe_load(jl_sols_den, i+1)) + inter_tmp[j] = inter_tmp_coeff + tmp[j] = sum(inter_tmp_coeff) >> 1 + i += 2 + j += 1 + end + inter_solutions[k] = inter_tmp + solutions[k] = tmp + k += 1 + end + I.inter_sols = inter_solutions + I.real_sols = solutions + + ccall((:free_msolve_julia_result_data, libmsolve), Nothing , + (Ptr{Nothing}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cvoid}}, + Ptr{Ptr{Cvoid}}, Ptr{Ptr{Cint}}, Cint, Cint, Cint), + cglobal(:jl_free), res_len, res_cf, sols_num, sols_den, + jl_ld, jl_nb_sols, field_char) + + return rat_param, solutions +end + +@doc Markdown.doc""" + rational_parametrization(I::Ideal{T} where T <: MPolyRingElem, ) + +Given an ideal `I` with a finite solution set over the complex numbers, return +the rational parametrization of the ideal with a given precision (default 32 bits). + +**Note**: At the moment only QQ is supported as ground field. If the dimension of the ideal +is greater then zero an empty array is returned. + +# Arguments +- `I::Ideal{T} where T <: MPolyRingElem`: input generators. +- `initial_hts::Int=17`: initial hash table size `log_2`. +- `nr_thrds::Int=1`: number of threads for parallel linear algebra. +- `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`. +- `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`). +- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). +- `precision::Int=32`: bit precision for the computed solutions. + +# Examples +```jldoctest +julia> using AlgebraicSolving + +julia> R,(x1,x2,x3) = polynomial_ring(QQ, ["x1","x2","x3"]) +(Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x1, x2, x3]) + +julia> I = Ideal([x1+2*x2+2*x3-1, x1^2+2*x2^2+2*x3^2-x1, 2*x1*x2+2*x2*x3-x2]) +QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2] + +julia> rational_parametrization(I) +AlgebraicSolving.RationalParametrization([:x1, :x2, :x3], ZZRingElem[], 84*x^4 - 40*x^3 + x^2 + x, 336*x^3 - 120*x^2 + 2*x + 1, AbstractAlgebra.PolyRingElem[184*x^3 - 80*x^2 + 4*x + 1, 36*x^3 - 18*x^2 + 2*x]) +``` +""" +function rational_parametrization( + I::Ideal{T} where T <: MPolyRingElem; # input generators + initial_hts::Int=17, # hash table size, default 2^17 + nr_thrds::Int=1, # number of threads + max_nr_pairs::Int=0, # number of pairs maximally chosen + # in symbolic preprocessing + la_option::Int=2, # linear algebra option + info_level::Int=0, # info level for print outs + precision::Int=32 # precision of the solution set + ) + + isdefined(I, :rat_param) || + _core_msolve(I, + initial_hts = initial_hts, + nr_thrds = nr_thrds, + max_nr_pairs = max_nr_pairs, + la_option = la_option, + info_level = info_level, + precision = precision) + + return I.rat_param +end + + +@doc Markdown.doc""" + rational_solutions(I::Ideal{T} where T <: MPolyRingElem, ) + +Given an ideal `I` with a finite solution set over the complex numbers, return +the rational roots of the ideal. + +# Arguments +- `I::Ideal{T} where T <: MPolyRingElem`: input generators. +- `initial_hts::Int=17`: initial hash table size `log_2`. +- `nr_thrds::Int=1`: number of threads for parallel linear algebra. +- `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`. +- `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`). +- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). +- `precision::Int=32`: bit precision for the computed solutions. + +# Examples +```jldoctest +julia> using AlgebraicSolving + +julia> R,(x1,x2,x3) = polynomial_ring(QQ, ["x1","x2","x3"]) +(Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x1, x2, x3]) + +julia> I = Ideal([x1+2*x2+2*x3-1, x1^2+2*x2^2+2*x3^2-x1, 2*x1*x2+2*x2*x3-x2]) +QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2] + +julia> rat_sols = rational_solutions(I) +2-element Vector{Vector{QQFieldElem}}: + [1, 0, 0] + [1//3, 0, 1//3] + +julia> map(r->map(p->evaluate(p, r), I.gens), rat_sols) +2-element Vector{Vector{QQFieldElem}}: + [0, 0, 0] + [0, 0, 0] +``` +""" +function rational_solutions( + I::Ideal{T} where T <: MPolyRingElem; # input generators + initial_hts::Int=17, # hash table size, default 2^17 + nr_thrds::Int=1, # number of threads + max_nr_pairs::Int=0, # number of pairs maximally chosen + # in symbolic preprocessing + la_option::Int=2, # linear algebra option + info_level::Int=0, # info level for print outs + precision::Int=32 # precision of the solution set + ) + isdefined(I, :rat_param) || + _core_msolve(I, + initial_hts = initial_hts, + nr_thrds = nr_thrds, + max_nr_pairs = max_nr_pairs, + la_option = la_option, + info_level = info_level, + precision = precision) + param_t = I.rat_param + + nvars = length(param_t.vars) + lpol = filter(l->degree(l) == 1, keys(factor(param_t.elim).fac)) + nb = length(lpol) + + rat_elim = [-coeff(l, 0)// coeff(l, 1) for l in lpol] + rat_den = map(l->evaluate(param_t.denom, l), rat_elim) + rat_num = map(r->map(l->evaluate(l, r), param_t.param), rat_elim) + + rat_sols = Vector{Vector{QQFieldElem}}(undef, nb) + + if length(param_t.vars) == parent(I).nvars + + for i in 1:nb + rat_sols[i] = Vector{QQFieldElem}(undef, nvars) + for j in 1:(nvars-1) + rat_sols[i][j] = rat_num[i][j] // rat_den[i] + end + rat_sols[i][nvars] = rat_elim[i] + end + + else + + for i in 1:nb + rat_sols[i] = Vector{QQFieldElem}(undef, nvars - 1) + for j in 1:(nvars-1) + rat_sols[i][j] = rat_num[i][j] // rat_den[i] + end + end + + end + + I.rat_sols = rat_sols + + return I.rat_sols +end + + +@doc Markdown.doc""" + real_solutions(I::Ideal{T} where T <: MPolyRingElem, ) + +Given an ideal `I` with a finite solution set over the complex numbers, return +the real roots of the ideal with a given precision (default 32 bits). + +**Note**: At the moment only QQ is supported as ground field. If the dimension of the ideal +is greater than zero an empty array is returned. + +# Arguments +- `I::Ideal{T} where T <: MPolyRingElem`: input generators. +- `initial_hts::Int=17`: initial hash table size `log_2`. +- `nr_thrds::Int=1`: number of threads for parallel linear algebra. +- `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`. +- `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`). +- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). +- `precision::Int=32`: bit precision for the computed solutions. + +# Examples +```jldoctest +julia> using AlgebraicSolving + +julia> R,(x1,x2,x3) = polynomial_ring(QQ, ["x1","x2","x3"]) +(Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x1, x2, x3]) + +julia> I = Ideal([x1+2*x2+2*x3-1, x1^2+2*x2^2+2*x3^2-x1, 2*x1*x2+2*x2*x3-x2]) +QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2] + +julia> real_solutions(I) +4-element Vector{Vector{QQFieldElem}}: + [5416829397//8589934592, 2708414699//8589934592, -2844258330290649520990905062759917788583//21778071482940061661655974875633165533184] + [1, 0, 0] + [1945971683//8589934592, 972985841//8589934592, 744426424910260862653434112767010536665//2722258935367507707706996859454145691648] + [2863311531//8589934592, 0, 3629678580490010276942662479272194255531//10889035741470030830827987437816582766592] +``` +""" +function real_solutions( + I::Ideal{T} where T <: MPolyRingElem; # input generators + initial_hts::Int=17, # hash table size, default 2^17 + nr_thrds::Int=1, # number of threads + max_nr_pairs::Int=0, # number of pairs maximally chosen + # in symbolic preprocessing + la_option::Int=2, # linear algebra option + info_level::Int=0, # info level for print outs + precision::Int=32 # precision of the solution set + ) + + isdefined(I, :real_sols) || + _core_msolve(I, + initial_hts = initial_hts, + nr_thrds = nr_thrds, + max_nr_pairs = max_nr_pairs, + la_option = la_option, + info_level = info_level, + precision = precision) + + return I.real_sols +end + +function inter_solutions( + I::Ideal{T} where T <: MPolyRingElem; # input generators + initial_hts::Int=17, # hash table size, default 2^17 + nr_thrds::Int=1, # number of threads + max_nr_pairs::Int=0, # number of pairs maximally chosen + # in symbolic preprocessing + la_option::Int=2, # linear algebra option + info_level::Int=0, # info level for print outs + precision::Int=32 # precision of the solution set + ) + + isdefined(I, :real_sols) || + _core_msolve(I, + initial_hts = initial_hts, + nr_thrds = nr_thrds, + max_nr_pairs = max_nr_pairs, + la_option = la_option, + info_level = info_level, + precision = precision) + + return I.inter_sols +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/examples/cyclic.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/examples/cyclic.jl new file mode 100644 index 0000000..10c539c --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/examples/cyclic.jl @@ -0,0 +1,23 @@ +@doc Markdown.doc""" + cyclic(R::MPolyRing) + +Return the Cyclic ideal in the variables of `R`. + +# Example +```jldoctest +julia> using AlgebraicSolving + +julia> R, vars = polynomial_ring(QQ, ["x$i" for i in 1:4]) +(Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x1, x2, x3, x4]) + +julia> cyclic(R) +QQMPolyRingElem[x1 + x2 + x3 + x4, x1*x2 + x1*x4 + x2*x3 + x3*x4, x1*x2*x3 + x1*x2*x4 + x1*x3*x4 + x2*x3*x4, x1*x2*x3*x4 - 1] +``` +""" +function cyclic(R::MPolyRing) + vars = gens(R) + n = length(vars) + pols = [sum(prod(vars[j%n+1] for j in k:k+i) for k in 1:n) for i in 0:n-2] + push!(pols, prod(vars[i] for i in 1:n)-1) + return Ideal(pols) +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/examples/katsura.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/examples/katsura.jl new file mode 100644 index 0000000..07b6d0a --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/examples/katsura.jl @@ -0,0 +1,90 @@ +export katsura + +function _get_katsura_exponent(n::Int, m::Int, l::Int) + e = zeros(Int, n + 1) + if abs(l) == abs(m - l) + e[abs(l) + 1] = 2 + else + e[abs(l) + 1] = 1 + e[abs(m - l) + 1] = 1 + end + + return e +end + +@doc Markdown.doc""" + katsura(n::Int) + +Given a natural number `n` returns the Katsura ideal generated by +$u_m - \sum_{l=n}^n u_{l-m} u_l$, $1 - \sum_{l = -n}^n u_l$ +where $u_{-i} = u_i$, and $u_i = 0$ for $i > n$ and $m \in \{-n, \ldots, n\}$. +Also note that indices have been shifted to start from 1. + +# Example +```jldoctest +julia> using AlgebraicSolving + +julia> katsura(2) +QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 + 2*x2^2 + 2*x3^2 - x1, 2*x1*x2 + 2*x2*x3 - x2] +``` +""" +function katsura(log_solutions::Int, characteristic::Int=0) + if characteristic == 0 + R, _ = polynomial_ring(QQ, log_solutions + 1, ordering=:degrevlex) + elseif is_probable_prime(characteristic) + R, _ = polynomial_ring(GF(characteristic), log_solutions + 1, ordering=:degrevlex) + else + error("We only support finite fields or QQ as ground fields.") + end + + return katsura(R) +end + +@doc Markdown.doc""" + katsura(R::MPolyRing) + +Returns the Katsura ideal in the given polynomial ring `R`. + +# Example +```jldoctest +julia> using AlgebraicSolving + +julia> R, _ = QQ["x", "y", "z"] +(Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z]) + +julia> katsura(R) +QQMPolyRingElem[x + 2*y + 2*z - 1, x^2 - x + 2*y^2 + 2*z^2, 2*x*y + 2*y*z - y] +``` +""" +function katsura(R::MPolyRing) + CR = base_ring(R) + polys = elem_type(R)[] + n = nvars(R) - 1 + coeffs_vec = 2 * fill(CR(1), n + 1) + coeffs_vec[1] = CR(1) + mono_exps = Matrix(1I, n+1, n+1) + #= mono_exps = Matrix{Int}(identity_matrix(ZZ, n + 1)) =# + linear_poly = R(coeffs_vec, [mono_exps[:, i] for i in 1:n+1]) + linear_poly -= R(1) + push!(polys, linear_poly) + + for m in 0:n - 1 + polynomial = MPolyBuildCtx(R) + for l in -n:n + if abs(l) > n || abs(m - l) > n + continue + end + e = _get_katsura_exponent(n, m, l) + push_term!(polynomial, CR(1), e) + end + + e = zeros(Int, n + 1) + e[abs(m) + 1] = 1 + push_term!(polynomial, CR(-1), e) + poly = finish(polynomial) + push!(polys, poly) + end + + return Ideal(polys) +end + diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/exports.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/exports.jl new file mode 100644 index 0000000..9346798 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/exports.jl @@ -0,0 +1,4 @@ +export polynomial_ring, MPolyRing, GFElem, MPolyRingElem, finite_field, GF, fpMPolyRingElem, + characteristic, degree, ZZ, QQ, vars, nvars, ngens, ZZRingElem, QQFieldElem, QQMPolyRingElem, + base_ring, coefficient_ring, evaluate, prime_field, sig_groebner_basis, cyclic, leading_coefficient, + FqMPolyRingElem, derivative diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/imports.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/imports.jl new file mode 100644 index 0000000..ccf335a --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/imports.jl @@ -0,0 +1,61 @@ +using Markdown +using Test +using msolve_jll +using Nemo +using LinearAlgebra +using StaticArrays +using LoopVectorization + +import Random: MersenneTwister +import Logging: ConsoleLogger, with_logger, Warn, Info +import Printf: @sprintf + +import Nemo: + bell, + binomial, + degree, + denominator, + divexact, + divides, + divisor_sigma, + euler_phi, + evaluate, + factorial, + fibonacci, + fits, + fpMPolyRingElem, + fqPolyRepFieldElem, + fraction_field, + GF, + height, + is_prime, + is_probable_prime, + is_square, + is_unit, + isqrtrem, + jacobi_symbol, + leading_coefficient, + matrix_space, + moebius_mu, + MPolyRing, + MPolyRingElem, + number_of_partitions, + numerator, + polynomial_ring, + PolyRing, + PolyRingElem, + prime_field, + primorial, + QQ, + QQField, + QQFieldElem, + QQMatrix, + QQMPolyRingElem, + rising_factorial, + root, + unit, + vars, + ZZ, + ZZMatrix, + ZZRing, + ZZRingElem diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/interfaces/nemo.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/interfaces/nemo.jl new file mode 100644 index 0000000..1078047 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/interfaces/nemo.jl @@ -0,0 +1,118 @@ + +@doc Markdown.doc""" + _convert_to_msolve( + F::Vector{T}) where T <: MPolyRingElem + +Convert a vector of polynomials to input data for msolve. + +**Note**: This is an internal function. +""" +function _convert_to_msolve( + F::Vector{T}) where T <: MPolyRingElem + + R = parent(first(F)) + + nr_vars = nvars(R) + nr_gens = length(F) + lens = Int32[length(F[i]) for i in 1:nr_gens] + nr_terms = sum(lens) + field_char = characteristic(R) + + if field_char > 2^31 || degree(base_ring(R)) != 1 + error("At the moment we only support prime fields up to prime characteristic < 2^31.") + end + # get coefficients + if field_char == 0 + cfs = BigInt[] + else + cfs = Int32[] + end + if field_char == 0 + for i in 1:nr_gens + for cf in coefficients(F[i]) + push!(cfs, BigInt(numerator(cf))) + push!(cfs, BigInt(denominator(cf))) + end + end + else + for i in 1:nr_gens + for cf in coefficients(F[i]) + push!(cfs, Int32(lift(Nemo.ZZ, cf))) + end + end + end + + # get exponent vectors + exps = Int32[] + for i in 1:nr_gens + for ev in exponent_vectors(F[i]) + append!(exps, convert(Vector{Int32}, ev)) + end + end + + return lens, cfs, exps +end + +@doc Markdown.doc""" + _convert_finite_field_gb_to_abstract_algebra( + bld::Int32, + blen::Vector{Int32}, + bcf::Vector{Int32}, + bexp::Vector{Int32}, + R::MPolyRing, + eliminate::Int=0 + ) + +Converts a finite Gröbner basis computed internally via msolve +to a vector of polynomials. + +**Note**: This is an internal function. +""" +function _convert_finite_field_array_to_abstract_algebra( + bld::Int32, + blen::Vector{Int32}, + bcf::Vector{Int32}, + bexp::Vector{Int32}, + R::MPolyRing, + eliminate::Int=0 + ) + + if characteristic(R) == 0 + error("At the moment we only support finite fields.") + end + + nr_gens = bld + nr_vars = nvars(R) + CR = coefficient_ring(R) + + basis = (typeof(R(0)))[] + #= basis = Vector{MPolyRingElem}(undef, bld) =# + + len = 0 + + if eliminate > 0 + z = zeros(Int, eliminate) + end + for i in 1:nr_gens + #= check if element is part of the eliminated basis =# + if eliminate > 0 + cmp = convert(Vector{Int}, bexp[(len)*nr_vars+1:(len+1)*nr_vars]) + if cmp[1:eliminate] > z + continue + end + end + g = MPolyBuildCtx(R) + if bcf[len+1] == 0 + g.poly = R(0) + else + for j in 1:blen[i] + push_term!(g, CR(bcf[len+j]), + convert(Vector{Int}, bexp[(len+j-1)*nr_vars+1:(len+j)*nr_vars])) + end + end + len += blen[i] + push!(basis, g.poly) + end + + return basis +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/hashtable.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/hashtable.jl new file mode 100644 index 0000000..3f9d955 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/hashtable.jl @@ -0,0 +1,472 @@ +# TAKEN AND ADJUSTED FROM GROEBNER.JL BY ALEXANDER DEMIN +# MIT License + +# Copyright (c) 2022 Alexander Demin + +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to deal +# in the Software without restriction, including without limitation the rights +# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +# copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: + +# The above copyright notice and this permission notice shall be included in all +# copies or substantial portions of the Software. + +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +# SOFTWARE. + +mutable struct Hashvalue + hash::MonHash + divmask::DivMask +end + +function copy_hashvalue(x::Hashvalue) + Hashvalue(x.hash, x.divmask) +end + +# Hashtable designed to store monomials +mutable struct MonomialHashtable{N} + exponents::Vector{Monomial{N}} + + # for buffering exponent vectors during certain operations + buffer::MVector{N, Exp} + + # maps exponent hash to its position in exponents array + hashtable::Vector{MonIdx} + + # stores hashes, division masks, + # and other valuable info + # for each hashtable enrty + hashdata::Vector{Hashvalue} + + #= Monom divisibility =# + # divisor map to check divisibility faster + divmap::Vector{UInt32} + # bits per div variable + ndivbits::Int + + size::Int + # elements added + load::Int +end + +#------------------------------------------------------------------------------ + +# Returns the next look-up position in the table +function nexthashindex(h::MonHash, j::MonHash, mod::MonHash) + (h + j) & mod + MonHash(1) +end + +#------------------------------------------------------------------------------ + +# initialize and set fields for basis hashtable +function initialize_basis_hash_table(::Val{N}) where N + + # for now at most 32 variables + if N > 32 + error("At most 32 variables currently supported.") + end + + # not necessary to create `initial_size` exponents + exponents = Vector{Monomial{N}}(undef, init_ht_size) + hashdata = Vector{Hashvalue}(undef, init_ht_size) + hashtable = zeros(MonIdx, init_ht_size) + + # exponents[1:load] cover all stored exponents + load = 0 + size = init_ht_size + + # initialize fast divisibility params + int32bits = 32 + ndivbits = div(int32bits, N) + # division mask stores at least 1 bit + # per each of first ndivvars variables + ndivbits == 0 && (ndivbits += 1) + divmap = Vector{DivMask}(undef, N * ndivbits) + + # first stored exponent used as buffer lately + buffer = MVector{N}(zeros(Exp, N)) + + MonomialHashtable{N}(exponents, buffer, hashtable, + hashdata, divmap, ndivbits, + size, load) +end + +# initialize hashtable for `symbolic_preprocessing` +# These are of the same purpose and structure as basis hashtable, +# but are more local oriented +function initialize_secondary_hash_table(basis_ht::MonomialHashtable{N}) where {N} + # 2^6 seems to be the best out of 2^5, 2^6, 2^7 + initial_size = 2^6 + + exponents = Vector{Monomial{N}}(undef, initial_size) + hashdata = Vector{Hashvalue}(undef, initial_size) + hashtable = zeros(MonIdx, initial_size) + + # preserve division info + divmap = basis_ht.divmap + ndivbits = basis_ht.ndivbits + + load = 0 + size = initial_size + + buffer = MVector{N}(zeros(Exp, N)) + + MonomialHashtable(exponents, buffer, hashtable, + hashdata, divmap, ndivbits, + size, load) +end + +function select_tablesize(nvars, syssize) + nvars = ring.nvars + tablesize = 2^10 + if nvars > 4 + tablesize = 2^14 + end + if nvars > 7 + tablesize = 2^16 + end + + if syssize < 3 + tablesize = div(tablesize, 2) + end + if syssize < 2 + tablesize = div(tablesize, 2) + end + + return tablesize +end + +#------------------------------------------------------------------------------ + +ht_resize_threshold() = 0.4 +ht_needs_resize(size, load, added) = (load + added)/size > ht_resize_threshold() + +function check_enlarge_hashtable!(ht::MonomialHashtable, added::Integer) + newsize = ht.size + while ht_needs_resize(newsize, ht.load, added) + newsize *= 2 + end + if newsize != ht.size + ht.size = newsize + @assert ispow2(ht.size) + + resize!(ht.hashdata, ht.size) + resize!(ht.exponents, ht.size) + ht.hashtable = zeros(Int, ht.size) + + mod = MonHash(ht.size - 1) + + for i in 1:ht.load + # hash for this elem is already computed + he = ht.hashdata[i].hash + hidx = he + @inbounds for j in MonHash(1):MonHash(ht.size) + hidx = nexthashindex(he, j, mod) + !iszero(ht.hashtable[hidx]) && continue + ht.hashtable[hidx] = i + break + end + end + end + nothing +end + +#------------------------------------------------------------------------------ + +# if hash collision happened +function ishashcollision(ht::MonomialHashtable{N}, vidx, exps, he) where N + # if not free and not same hash + @inbounds if ht.hashdata[vidx].hash != he + return true + end + # if not free and not same monomial + # TODO: is this shitty? + @inbounds for i in 1:N + if ht.exponents[vidx].exps[i] != exps[i] + return true + end + end + return false +end + +function insert_in_hash_table!(ht::MonomialHashtable{N}, e::Monomial{N}) where {N} + # generate hash + he = Base.hash(e) + + # find new elem position in the table + hidx = he + # power of twoooo + @assert ispow2(ht.size) + mod = MonHash(ht.size - 1) + i = MonHash(1) + hsize = MonHash(ht.size) + + @inbounds while i < hsize + hidx = nexthashindex(he, i, mod) + + vidx = ht.hashtable[hidx] + + # if free + iszero(vidx) && break + + # if not free and not same hash + if ishashcollision(ht, vidx, e.exps, he) + i += MonHash(1) + continue + end + + # already present in hashtable + return vidx + end + + # add its position to hashtable, and insert exponent to that position + vidx = MonIdx(ht.load + 1) + @inbounds ht.hashtable[hidx] = vidx + @inbounds ht.exponents[vidx] = e + divm = divmask(e, ht.divmap, ht.ndivbits) + @inbounds ht.hashdata[vidx] = Hashvalue(he, divm) + + ht.load += 1 + + return vidx +end + +function find_in_hash_table(ht::MonomialHashtable{N}, e::Monomial{N}) where {N} + # generate hash + he = Base.hash(e) + + # find new elem position in the table + hidx = he + # power of twoooo + @assert ispow2(ht.size) + mod = MonHash(ht.size - 1) + i = MonHash(1) + hsize = MonHash(ht.size) + + @inbounds while i < hsize + hidx = nexthashindex(he, i, mod) + + vidx = ht.hashtable[hidx] + + # if free + iszero(vidx) && break + + # if not free and not same hash + if ishashcollision(ht, vidx, e.exps, he) + i += MonHash(1) + continue + end + + # already present in hashtable + return vidx + end + + return zero(MonIdx) +end + +#------------------------------------------------------------------------------ + +#= + Having `ht` filled with monomials from input polys, + computes ht.divmap and divmask for each of already stored monomials +=# +function fill_divmask!(ht::MonomialHashtable{N}) where N + + min_exp = Vector{UInt64}(undef, N) + max_exp = Vector{UInt64}(undef, N) + + e = first(ht.exponents).exps + + @inbounds for i in 1:N + min_exp[i] = e[i] + max_exp[i] = e[i] + end + + @inbounds for i in 1:ht.load + e = ht.exponents[i].exps + for j in 1:N + if e[j] > max_exp[j] + max_exp[j] = e[j] + continue + end + if e[j] < min_exp[j] + min_exp[j] = e[j] + end + end + end + + ctr = 1 + steps = UInt32(0) + @inbounds for i in 1:N + steps = div(max_exp[i] - min_exp[i], UInt32(ht.ndivbits)) + (iszero(steps)) && (steps += UInt32(1)) + for j in 1:ht.ndivbits + ht.divmap[ctr] = steps + steps += UInt32(1) + ctr += 1 + end + end + @inbounds for vidx in 1:ht.load + m = ht.exponents[vidx] + divm = divmask(m, ht.divmap, ht.ndivbits) + hsh = Base.hash(m) + ht.hashdata[vidx] = Hashvalue(hsh, divm) + end + + nothing +end + +#------------------------------------------------------------------------------ + +# add monomials from `poly` multiplied by exponent vector `etmp` +# with hash `htmp` to hashtable `symbol_ht`, +# and substitute hashes in row +function insert_multiplied_poly_in_hash_table!(row::Vector{MonIdx}, + htmp::MonHash, + etmp::Monomial{N}, + poly::Vector{MonIdx}, + ht::MonomialHashtable{N}, + symbol_ht::MonomialHashtable{N}) where N + + # length of poly to add + len = length(poly) + + mod = MonHash(symbol_ht.size - 1) + + bexps = ht.exponents + bdata = ht.hashdata + + sexps = symbol_ht.exponents + sdata = symbol_ht.hashdata + + l = 1 # hardcoding 1 does not seem nice =( + @label Letsgo + @inbounds while l <= len + # we iterate over all monoms of the given poly, + # multiplying them by htmp/etmp, + # and inserting into symbolic hashtable + + # hash is linear, so that + # hash(e1 + e2) = hash(e1) + hash(e2) + h = htmp + bdata[poly[l]].hash + + e = bexps[poly[l]] + + lastidx = symbol_ht.load + 1 + mul!(symbol_ht.buffer, etmp, e) + + # insert into hashtable + k = h + + i = MonHash(1) + ssize = MonHash(symbol_ht.size) + @inbounds while i <= ssize + k = nexthashindex(h, i, mod) + vidx = symbol_ht.hashtable[k] + + # if index is free + iszero(vidx) && break + + if ishashcollision(symbol_ht, vidx, symbol_ht.buffer, h) + i += MonHash(1) + continue + end + + # hit + row[l] = vidx + l += 1 + + @goto Letsgo + end + # miss + + # add multiplied exponent to hash table + sexps[lastidx] = Monomial(etmp.deg + e.deg, + SVector(copy(symbol_ht.buffer))) + symbol_ht.hashtable[k] = lastidx + + divm = divmask(sexps[lastidx], symbol_ht.divmap, symbol_ht.ndivbits) + sdata[lastidx] = Hashvalue(h, divm) + + row[l] = lastidx + l += 1 + symbol_ht.load += 1 + end + + row +end + +function multiplied_poly_to_matrix_row!( + symbolic_ht::MonomialHashtable{N}, basis_ht::MonomialHashtable{N}, + htmp::MonHash, etmp::Monomial{N}, poly::Vector{MonIdx}) where {N} + + row = similar(poly) + check_enlarge_hashtable!(symbolic_ht, length(poly)) + + insert_multiplied_poly_in_hash_table!(row, htmp, etmp, poly, basis_ht, symbolic_ht) +end + +#------------------------------------------------------------------------------ +function insert_in_basis_hash_table_pivots!( + row::Vector{MonIdx}, + ht::MonomialHashtable{N}, + symbol_ht::MonomialHashtable{N}) where {N} + + check_enlarge_hashtable!(ht, length(row)) + + sdata = symbol_ht.hashdata + sexps = symbol_ht.exponents + + mod = MonHash(ht.size - 1) + bdata = ht.hashdata + bexps = ht.exponents + bhash = ht.hashtable + + l = 1 + @label Letsgo + @inbounds while l <= length(row) + hidx = row[l] + + # symbolic hash + h = sdata[hidx].hash + + lastidx = ht.load + 1 + bexps[lastidx] = sexps[hidx] + e = bexps[lastidx] + + k = h + i = MonHash(1) + @inbounds while i <= ht.size + k = nexthashindex(h, i, mod) + hm = bhash[k] + + iszero(hm) && break + + if ishashcollision(ht, hm, e.exps, h) + i += MonHash(1) + continue + end + + row[l] = hm + l += 1 + @goto Letsgo + end + + bhash[k] = pos = lastidx + row[l] = pos + l += 1 + + bdata[pos] = Hashvalue(h, sdata[hidx].divmask) + + ht.load += 1 + end + + nothing +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/linear_algebra.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/linear_algebra.jl new file mode 100644 index 0000000..1178901 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/linear_algebra.jl @@ -0,0 +1,156 @@ +function echelonize!(matrix::MacaulayMatrix, + char::Val{Char}, + shift::Val{Shift}) where {Char, Shift} + + arit_ops = 0 + + col2hash = matrix.col2hash + buffer = zeros(Cbuf, matrix.ncols) + hash2col = Vector{MonIdx}(undef, matrix.ncols) + rev_sigorder = Vector{Int}(undef, matrix.nrows) + pivots = matrix.pivots + + @inbounds for i in 1:matrix.nrows + rev_sigorder[matrix.sig_order[i]] = i + row_ind = matrix.sig_order[i] + end + + @inbounds for i in 1:matrix.ncols + hash2col[col2hash[i]] = MonIdx(i) + end + + @inbounds for i in 1:matrix.nrows + row_ind = matrix.sig_order[i] + + row_cols = matrix.rows[row_ind] + l_col_idx = hash2col[first(row_cols)] + pivots[l_col_idx] == row_ind && continue + + # check if the row can be reduced + does_red = false + for (j, m_idx) in enumerate(row_cols) + colidx = hash2col[m_idx] + pividx = pivots[colidx] + does_red = !iszero(pividx) && rev_sigorder[pividx] < i + does_red && break + end + if !does_red + pivots[l_col_idx] = row_ind + continue + end + + # buffer the row + row_coeffs = matrix.coeffs[row_ind] + @inbounds for (k, j) in enumerate(row_cols) + col_idx = hash2col[j] + buffer[col_idx] = row_coeffs[k] + end + + # do the reduction + @inbounds for j in 1:matrix.ncols + a = buffer[j] % Char + iszero(a) && continue + pividx = pivots[j] + if iszero(pividx) || rev_sigorder[pividx] >= i + continue + end + + # subtract m*rows[pivots[j]] from buffer + pivmons = matrix.rows[pividx] + pivcoeffs = matrix.coeffs[pividx] + + arit_ops_new = critical_loop!(buffer, j, a, hash2col, pivmons, + pivcoeffs, shift) + arit_ops += arit_ops_new + end + + new_row_length = 0 + @inbounds for j in 1:matrix.ncols + iszero(buffer[j]) && continue + buffer[j] = buffer[j] % Char + iszero(buffer[j]) && continue + new_row_length += 1 + end + + # write out matrix row again + j = 1 + inver = one(Coeff) + new_row = Vector{MonIdx}(undef, new_row_length) + new_coeffs = Vector{Coeff}(undef, new_row_length) + @inbounds for k in 1:matrix.ncols + iszero(buffer[k]) && continue + if isone(j) + pivots[k] = row_ind + inver = inv(Coeff(buffer[k]), char) + end + new_row[j] = col2hash[k] + new_coeffs[j] = isone(j) ? one(Coeff) : mul(inver, buffer[k], char) + buffer[k] = zero(Cbuf) + j += 1 + end + + # check if row lead reduced, TODO: dont know if this is reliable + s = matrix.sigs[row_ind] + m = monomial(s) + @inbounds if isempty(new_row) || (matrix.rows[row_ind][1] != new_row[1] && any(!iszero, m.exps)) + matrix.toadd[matrix.toadd_length+1] = row_ind + matrix.toadd_length += 1 + end + + matrix.rows[row_ind] = new_row + matrix.coeffs[row_ind] = new_coeffs + end + if !iszero(arit_ops) + @info "$(arit_ops) submul's" + end +end + +# subtract mult +# TODO: for module tracking we won't be able to assume that mult = buffer[bufind] +@inline function critical_loop!(buffer::Vector{Cbuf}, + bufind::Int, + mult::Cbuf, + hash2col::Vector{MonIdx}, + pivmons::Vector{MonIdx}, + pivcoeffs::Vector{Coeff}, + shift::Val{Shift}) where Shift + + @inbounds buffer[bufind] = zero(Cbuf) + l = length(pivmons) + @turbo warn_check_args=false for k in 2:l + c = pivcoeffs[k] + m_idx = pivmons[k] + colidx = hash2col[m_idx] + buffer[colidx] = submul(buffer[colidx], mult, c, shift) + end + return l-1 +end + +# helper functions +# field arithmetic +function maxshift(::Val{Char}) where Char + bufchar = Cbuf(Char) + return bufchar << leading_zeros(bufchar) +end + +# compute a representation of a - b*c mod char (char ~ Shift) +@inline function submul(a::Cbuf, b::Cbuf, c::Coeff, ::Val{Shift}) where Shift + r0 = a - b*Cbuf(c) + r1 = r0 + Shift + r0 > a ? r1 : r0 +end + +@inline function inv(a::Coeff, ::Val{Char}) where Char + return invmod(Cbuf(a), Cbuf(Char)) % Coeff +end + +@inline function mul(a, b, ::Val{Char}) where Char + return Coeff((Cbuf(a) * Cbuf(b)) % Char) +end + +# for debug helping + +function is_triangular(matrix::MacaulayMatrix) + lms = [first(row) for row in matrix.rows[1:matrix.nrows] if !isempty(row)] + return length(lms) == length(unique(lms)) +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/monomials.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/monomials.jl new file mode 100644 index 0000000..d2aab7d --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/monomials.jl @@ -0,0 +1,127 @@ +#-- Monomial arithmetic --# + +function mul(a::Monomial, b::Monomial) + return Monomial(a.deg + b.deg, a.exps + b.exps) +end + +function mul!(buf::MVector{N, Exp}, a::Monomial{N}, b::Monomial{N}) where N + @inbounds for i in 1:N + buf[i] = a.exps[i] + b.exps[i] + end +end + +function divide(a::Monomial, b::Monomial) + return Monomial(a.deg - b.deg, a.exps - b.exps) +end + +# lcm(a, b) / a +function lcm_div(a::Monomial{N}, b::Monomial{N}) where N + e1 = a.exps + e2 = b.exps + @inbounds exps = SVector{N, Exp}([e1[i] >= e2[i] ? zero(Exp) : e2[i] - e1[i] for i in 1:N]) + return Monomial(sum(exps), exps) +end + +# false if the monomial corresponding to a does not divide +# the monomial corresponding to b +@inline function divch(a::DivMask, b::DivMask) + return iszero(a & (~b)) +end + +@inline function divch(a::Monomial{N}, b::Monomial{N}) where N + if a.deg <= b.deg + @inbounds for i in 1:N + a.exps[i] > b.exps[i] && return false + end + return true + end + return false +end + +@inline function divch(a::Monomial, b::Monomial, + am::DivMask, bm::DivMask) + + return divch(am, bm) && divch(a, b) +end + +# TODO: unroll this loop +@inline function divch!(buf::MVector{N, Exp}, + a::Monomial{N}, + b::Monomial{N}) where N + + @inbounds for i in 1:N + buf[i] = a.exps[i] - b.exps[i] + if buf[i] < 0 + return false + end + end + return true +end + +#-- Monomial Orders --# + +# DRL comparison +@generated function lt_drl(a::Monomial{N}, b::Monomial{N}) where N + quote + a.deg < b.deg && return true + a.deg > b.deg && return false + + ae = a.exps + be = b.exps + $([:(ae[$i] < be[$i] && return false ; ae[$i] > be[$i] && return true) for i in N:-1:1]...) + + return false + end +end + +function lt_pot(a::Sig, b::Sig) + if index(a) == index(b) + return lt_drl(a[2], b[2]) + else + return index(a) < index(b) + end +end + +#---------------------# + +#-- Masking and hashing --# + +# from groebner.jl +# TODO: make this generated? +function divmask(e::Monomial{N}, + divmap, + ndivbits) where N + + ctr = one(DivMask) + res = zero(DivMask) + o = one(DivMask) + for i in N:-1:1 + for j in 1:ndivbits + @inbounds if e.exps[i] >= divmap[ctr] + res |= o << (ctr - 1) + end + ctr += o + end + end + + res +end + +@generated function makehash(::Val{N}, m) where {N} + rng = MersenneTwister(18121987) + hash = :( $(UInt64(0)) ) + for i in 1:N + hash = :($hash + $(rand(rng, MonHash))*(m[$i])) + end + return :($hash % MonHash) +end + +Base.hash(a::Monomial{N}) where N = makehash(Val(N), a.exps) + +#-------------------------# + +# for readibility +index(a::Sig) = a[1] +monomial(a::Sig) = a[2] +index(a::MaskSig) = a[1] +mask(a::MaskSig) = a[2] diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/siggb.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/siggb.jl new file mode 100644 index 0000000..b598352 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/siggb.jl @@ -0,0 +1,256 @@ +# sizes for initialization +const init_ht_size = 2^17 +const init_basis_size = 10000 +const init_syz_size = 1000 +const init_pair_size = 10000 +# default sorting alg +const def_sort_alg = Base.Sort.DEFAULT_UNSTABLE +include("typedefs.jl") +include("monomials.jl") +include("hashtable.jl") +include("update.jl") +include("symbolic_pp.jl") +include("linear_algebra.jl") + +@doc Markdown.doc""" + sig_groebner_basis(sys::Vector{T}; info_level::Int = 0, degbound::Int = 0) where {T <: MPolyRingElem} + +Compute a Signature Gröbner basis of the sequence `sys` w.r.t. to the +degree reverse lexicographical monomial ordering and the degree +position-over-term ordering induced by `sys`. The output is a vector +of `Tuple{Tuple{Int64, T}, T}` where the first element indicates the +signature and the second the underlying polynomial. + +**Note**: At the moment only ground fields of characteristic `p`, `p` prime, `p < 2^{31}` are supported. +**Note**: The input generators must be homogeneous. +**Note**: The algorithms behaviour may depend heavily on how the elements in `sys` are sorted. + +# Arguments +- `sys::Vector{T} where T <: MpolyElem`: input generators. +- `info_level::Int=0`: info level printout: off (`0`, default), computational details (`1`) +- `degbound::Int=0`: degree bound for Gröbner basis computation, compute a full Gröbner basis if `0` (default) or only up to degree `d`. + +# Example +```jldoctest +julia> using AlgebraicSolving + +julia> R, vars = polynomial_ring(GF(17), ["x$i" for i in 1:4]) +(Multivariate polynomial ring in 4 variables over GF(17), FqMPolyRingElem[x1, x2, x3, x4]) + +julia> F = AlgebraicSolving.cyclic(R) +FqMPolyRingElem[x1 + x2 + x3 + x4, x1*x2 + x1*x4 + x2*x3 + x3*x4, x1*x2*x3 + x1*x2*x4 + x1*x3*x4 + x2*x3*x4, x1*x2*x3*x4 + 16] + +julia> Fhom = AlgebraicSolving._homogenize(F.gens) +4-element Vector{FqMPolyRingElem}: + x1 + x2 + x3 + x4 + x1*x2 + x2*x3 + x1*x4 + x3*x4 + x1*x2*x3 + x1*x2*x4 + x1*x3*x4 + x2*x3*x4 + x1*x2*x3*x4 + 16*x5^4 + +julia> sig_groebner_basis(Fhom) +7-element Vector{Tuple{Tuple{Int64, FqMPolyRingElem}, FqMPolyRingElem}}: + ((1, 1), x1 + x2 + x3 + x4) + ((2, 1), x2^2 + 2*x2*x4 + x4^2) + ((3, 1), x2*x3^2 + x3^2*x4 + 16*x2*x4^2 + 16*x4^3) + ((4, 1), x2*x3*x4^2 + x3^2*x4^2 + 16*x2*x4^3 + x3*x4^3 + 16*x4^4 + 16*x5^4) + ((4, x3), x3^3*x4^2 + x3^2*x4^3 + 16*x3*x5^4 + 16*x4*x5^4) + ((4, x2), x2*x4^4 + x4^5 + 16*x2*x5^4 + 16*x4*x5^4) + ((4, x2*x3), x3^2*x4^4 + x2*x3*x5^4 + 16*x2*x4*x5^4 + x3*x4*x5^4 + 15*x4^2*x5^4) +``` +""" +function sig_groebner_basis(sys::Vector{T}; info_level::Int=0, degbound::Int=0) where {T <: MPolyRingElem} + R = parent(first(sys)) + Rchar = characteristic(R) + + # check if input is ok + if Rchar > 2^31 || iszero(Rchar) + error("At the moment we only support finite fields up to prime characteristic < 2^31.") + end + sysl = length(sys) + degs = Vector{Exp}(undef, sysl) + @inbounds for (i, f) in enumerate(sys) + deg = total_degree(f) + if deg > typemax(Exp) + error("input degrees too large.") + end + degs[i] = Exp(deg) + for m in exponent_vectors(f) + if sum(m) != deg + error("input system must be homogeneous.") + end + end + end + + # constants for fast arithmetic + char = Val(Coeff(Rchar.d)) + shift = Val(maxshift(char)) + + # convert to and initialize our data structures + nv = nvars(R) + basis_ht = initialize_basis_hash_table(Val(nv)) + + # initialize basis + sigs = Vector{Sig{nv}}(undef, init_basis_size) + sigmasks = Vector{MaskSig}(undef, init_basis_size) + sigratios = Vector{Monomial{nv}}(undef, init_basis_size) + rewrite_nodes = Vector{Vector{Int}}(undef, init_basis_size+1) + lm_masks = Vector{DivMask}(undef, init_basis_size) + monomials = Vector{Vector{MonIdx}}(undef, init_basis_size) + coeffs = Vector{Vector{Coeff}}(undef, init_basis_size) + is_red = Vector{Bool}(undef, init_basis_size) + syz_sigs = Vector{Monomial{nv}}(undef, init_syz_size) + syz_masks = Vector{MaskSig}(undef, init_syz_size) + basis = Basis(sigs, sigmasks, sigratios, rewrite_nodes, + lm_masks, monomials, coeffs, is_red, + syz_sigs, syz_masks, degs, sysl, + init_basis_size, sysl + 1, 0, init_syz_size) + + # root node + basis.rewrite_nodes[1] = vcat([length(sys)-1, -1], + collect(2:length(sys)+1)) + + # initialize pairset + pairset = Pairset{nv}(Vector{SPair{nv}}(undef, init_pair_size), + sysl, + init_pair_size) + + one_mon = monomial(SVector{nv}(zeros(Exp, nv))) + zero_sig = (zero(SigIndex), one_mon) + # store initial pols in basis and pairset + @inbounds for i in 1:sysl + f = sys[i] + lf = length(f) + + # gather up monomials and coeffs + exps = collect(exponent_vectors(f)) + cfs = collect(coefficients(f)) + mons = Vector{MonIdx}(undef, lf) + coeffs = Vector{Coeff}(undef, lf) + inver = one(Coeff) + @inbounds for j in 1:lf + m = monomial(SVector{nv}((Exp).(exps[j]))) + eidx = insert_in_hash_table!(basis_ht, m) + if isone(j) + inver = inv(Coeff(lift(ZZ, cfs[1])), char) + end + cf = isone(j) ? one(Coeff) : mul(inver, Coeff(lift(ZZ, cfs[j])), char) + mons[j] = eidx + coeffs[j] = cf + end + s = sortperm(mons, by = eidx -> basis_ht.exponents[eidx], + lt = lt_drl, rev = true) + @inbounds mons = mons[s] + @inbounds coeffs = coeffs[s] + + # signatures + sig = (SigIndex(i), one_mon) + lm_exps = SVector{nv}((Exp).(exps[1])) + sigr = monomial(lm_exps) + + # store stuff in basis + basis.sigs[i] = sig + basis.sigratios[i] = sigr + basis.rewrite_nodes[i+1] = [-1, 1] + basis.monomials[i] = mons + basis.coefficients[i] = coeffs + basis.is_red[i] = false + + # add unitvector as pair + pairset.elems[i] = SPair{nv}(sig, zero_sig, zero(DivMask), + zero(DivMask), i, 0, degs[i]) + end + + # compute divmasks + fill_divmask!(basis_ht) + dm_one_mon = divmask(one_mon, basis_ht.divmap, basis_ht.ndivbits) + @inbounds for i in 1:sysl + basis.sigmasks[i] = (SigIndex(i), dm_one_mon) + pairset.elems[i].top_sig_mask = basis.sigmasks[i][2] + basis.lm_masks[i] = basis_ht.hashdata[basis.monomials[i][1]].divmask + end + + logger = ConsoleLogger(stdout, info_level == 0 ? Warn : Info) + with_logger(logger) do + siggb!(basis, pairset, basis_ht, char, shift, degbound = degbound) + end + + # output + eltp = typeof(first(sys)) + outp = Tuple{Tuple{Int, eltp}, eltp}[] + @inbounds for i in basis.basis_offset:basis.basis_load + exps = [basis_ht.exponents[m].exps for m in basis.monomials[i]] + ctx = MPolyBuildCtx(R) + for (e, c) in zip(exps, basis.coefficients[i]) + push_term!(ctx, coefficient_ring(R)(c), Vector{Int}(e)) + end + pol = finish(ctx) + + s = basis.sigs[i] + ctx = MPolyBuildCtx(R) + push_term!(ctx, one(coefficient_ring(R)), Vector{Int}(monomial(s).exps)) + sig = (Int(index(s)), finish(ctx)) + + push!(outp, (sig, pol)) + end + return outp +end + +function siggb!(basis::Basis{N}, + pairset::Pairset, + basis_ht::MonomialHashtable, + char::Val{Char}, + shift::Val{Shift}; + degbound = 0) where {N, Char, Shift} + + while !iszero(pairset.load) + if !iszero(degbound) && first(pairset.elems).deg > degbound + break + end + matrix = initialize_matrix(Val(N)) + symbol_ht = initialize_secondary_hash_table(basis_ht) + + select_normal!(pairset, basis, matrix, basis_ht, symbol_ht) + symbolic_pp!(basis, matrix, basis_ht, symbol_ht) + finalize_matrix!(matrix, symbol_ht) + echelonize!(matrix, char, shift) + + update_basis!(basis, matrix, pairset, symbol_ht, basis_ht) + end +end + + +# miscallaneous helper functions +function sort_pairset_by_degree!(pairset::Pairset, from::Int, sz::Int) + ordr = Base.Sort.ord(isless, p -> p.deg, false, Base.Sort.Forward) + sort!(pairset.elems, from, from+sz, def_sort_alg, ordr) +end + +# homogenize w.r.t. the last variable +function _homogenize(F::Vector{P}) where {P <: MPolyRingElem} + R = parent(first(F)) + S, vars = polynomial_ring(base_ring(R), ["x$i" for i in 1:nvars(R)+1], + ordering = :degrevlex) + res = typeof(first(F))[] + for f in F + ctx = MPolyBuildCtx(S) + d = total_degree(f) + for (e, c) in zip(exponent_vectors(f), coefficients(f)) + enew = push!(e, d - sum(e)) + push_term!(ctx, c, e) + end + push!(res, finish(ctx)) + end + return res +end + +# test against msolve +function _is_gb(gb::Vector{Tuple{Tuple{Int, P}, P}}) where {P <: MPolyRingElem} + gb_pols = [p[2] for p in gb] + gb_msolve = groebner_basis(Ideal(gb_pols), complete_reduction = true) + + lms_gb = (Nemo.leading_monomial).(gb_pols) + lms_msolve = (Nemo.leading_monomial).(gb_msolve) + res1 = all(u -> any(v -> divides(u, v)[1], lms_gb), lms_msolve) + res2 = all(u -> any(v -> divides(u, v)[1], lms_msolve), lms_gb) + return res1 && res2 +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/symbolic_pp.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/symbolic_pp.jl new file mode 100644 index 0000000..d3380da --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/symbolic_pp.jl @@ -0,0 +1,368 @@ +function select_normal!(pairset::Pairset{N}, + basis::Basis{N}, + matrix::MacaulayMatrix, + ht::MonomialHashtable, + symbol_ht::MonomialHashtable) where N + + # sort pairset + sort_pairset_by_degree!(pairset, 1, pairset.load-1) + + # number of selected pairs + npairs = 0 + deg = zero(Exp) + for i in 1:pairset.load + if iszero(deg) + deg = pairset.elems[i].deg + npairs += 1 + continue + end + if pairset.elems[i].deg == deg + npairs += 1 + else + break + end + end + + @info "selected $(npairs) pairs, degree $(deg)" + added_to_matrix = 0 + + # allocate matrix + reinitialize_matrix!(matrix, npairs) + skip = falses(npairs) + + @inbounds for i in 1:npairs + if skip[i] + continue + end + + pair = pairset.elems[i] + # for each unique pair signature + curr_top_sig = pair.top_sig + rewr_ind = find_canonical_rewriter(basis, pair.top_sig, + pair.top_sig_mask) + + pair_with_rewr_ind = 0 + for j in i:npairs + pair2 = pairset.elems[j] + if pair2.top_sig == curr_top_sig + skip[j] = true + if pair2.top_index == rewr_ind + pair_with_rewr_ind = j + end + end + end + + if !iszero(pair_with_rewr_ind) + + # take pair with non-rewr top signature + pair = pairset.elems[pair_with_rewr_ind] + + # add if pair is a unit vector + add_cond = iszero(pair.bot_index) + + # check if we have a pivot already + if !add_cond + mult = divide(monomial(curr_top_sig), + monomial(basis.sigs[rewr_ind])) + lm = mul(mult, leading_monomial(basis, ht, rewr_ind)) + l_idx = find_in_hash_table(symbol_ht, lm) + if !iszero(l_idx) + if !iszero(matrix.pivots[l_idx]) + add_cond = matrix.sigs[matrix.pivots[l_idx]] != curr_top_sig + end + end + end + + # check if there is a non-rewriteable reducer + if !add_cond + mult = divide(monomial(curr_top_sig), + monomial(basis.sigs[rewr_ind])) + lm = mul(mult, leading_monomial(basis, ht, rewr_ind)) + red_sig_mon = similar(symbol_ht.buffer) + @inbounds for j in 1:N + red_sig_mon[j] = zero(Exp) + end + reducer_sig = (zero(SigIndex), monomial(red_sig_mon)) + reducer_ind = zero(SigIndex) + + @inbounds for j in 1:npairs + pair2 = pairset.elems[j] + pair2.bot_sig == curr_top_sig && continue + if iszero(reducer_ind) || lt_pot(pair2.bot_sig, reducer_sig) + !lt_pot(pair2.bot_sig, curr_top_sig) && continue + new_red = false + if !iszero(pair2.bot_index) + rewriteable_basis(basis, pair2.bot_index, + pair2.bot_sig, + pair2.bot_sig_mask) && continue + ind = pair2.bot_index + mult = divide(monomial(pair2.bot_sig), + monomial(basis.sigs[ind])) + lm2 = mul(mult, leading_monomial(basis, ht, ind)) + new_red = lm2 == lm + end + if new_red + reducer_sig = pair2.bot_sig + reducer_ind = pair2.bot_index + end + end + end + + add_cond = !iszero(reducer_ind) + if add_cond + mult = divide(monomial(reducer_sig), + monomial(basis.sigs[reducer_ind])) + lead_idx = write_to_matrix_row!(matrix, basis, + reducer_ind, + symbol_ht, ht, mult, + reducer_sig) + # set pivot + resize_pivots!(matrix, symbol_ht) + matrix.pivots[lead_idx] = matrix.nrows + end + end + + # add row to matrix if any of the add conds is true + if add_cond + mult = divide(monomial(curr_top_sig), + monomial(basis.sigs[rewr_ind])) + l_idx = write_to_matrix_row!(matrix, basis, rewr_ind, + symbol_ht, ht, mult, + curr_top_sig) + added_to_matrix += 1 + if iszero(pair.bot_index) + matrix.toadd[matrix.toadd_length+1] = matrix.nrows + matrix.toadd_length += 1 + end + end + end + end + + if !iszero(added_to_matrix) + @info "$(added_to_matrix) non-rewriteable critical signatures added to matrix" + end + + # remove selected pairs from pairset + @inbounds for i in 1:(pairset.load-npairs) + pairset.elems[i] = pairset.elems[i+npairs] + end + pairset.load -= npairs + resize_pivots!(matrix, symbol_ht) +end + +function symbolic_pp!(basis::Basis{N}, + matrix::MacaulayMatrix, + ht::MonomialHashtable, + symbol_ht::MonomialHashtable) where N + + i = one(MonIdx) + mult = similar(ht.buffer) + mult2 = similar(ht.buffer) + red_sig_mon = similar(ht.buffer) + + # iterate over monomials in symbolic ht + @inbounds while i <= symbol_ht.load + found_reducer = false + # skip if reducer already exists + if !iszero(matrix.pivots[i]) + # exp = symbol_ht.exponents[i] + # println("mon: $(exp.exps)") + # println("reducer exists") + i += one(MonIdx) + continue + end + + red_ind = 0 + @inbounds for j in 1:N + red_sig_mon[j] = zero(Exp) + end + mul_red_sig = (zero(SigIndex), monomial(red_sig_mon)) + + # realloc matrix if necessary + if matrix.size == matrix.nrows + matrix.size *= 2 + resize!(matrix.rows, matrix.size) + resize!(matrix.sigs, matrix.size) + resize!(matrix.parent_inds, matrix.size) + resize!(matrix.coeffs, matrix.size) + resize!(matrix.toadd, matrix.size) + end + + exp = symbol_ht.exponents[i] + divm = symbol_ht.hashdata[i].divmask + + j = basis.basis_offset + @label target + # find element in basis which divmask divides divmask of monomial + @inbounds while j <= basis.basis_load && !divch(basis.lm_masks[j], divm) + j += 1 + end + + if j <= basis.basis_load + @inbounds red_exp = leading_monomial(basis, ht, j) + + # actual divisibility check + if !(divch!(mult2, exp, red_exp)) + j += 1 + @goto target + end + # found_reducer = true + + # check if new reducer sig is smaller than possible previous + if !iszero(red_ind) && lt_pot(mul_red_sig, mul_cand_sig) + j += 1 + @goto target + end + + # check if reducer is rewriteable + cand_sig = basis.sigs[j] + mul_cand_sig = (index(cand_sig), + mul(monomial(mult2), monomial(cand_sig))) + cand_sig_mask = divmask(monomial(mul_cand_sig), ht.divmap, + ht.ndivbits) + if rewriteable(basis, ht, j, mul_cand_sig, cand_sig_mask) + j += 1 + @goto target + end + + # set reducer + red_ind = j + mul_red_sig = mul_cand_sig + j += 1 + @inbounds for k in 1:N + mult[k] = mult2[k] + end + @goto target + end + + # write to matrix + if !iszero(red_ind) + mm = monomial(SVector(mult)) + @inbounds lead_idx = write_to_matrix_row!(matrix, basis, + red_ind, symbol_ht, + ht, mm, + mul_red_sig) + resize_pivots!(matrix, symbol_ht) + matrix.pivots[lead_idx] = matrix.nrows + end + i += one(MonIdx) + end +end + +function finalize_matrix!(matrix::MacaulayMatrix, + symbol_ht::MonomialHashtable) + + # store indices into hashtable in a sorted way + ncols = symbol_ht.load + matrix.ncols = ncols + + col2hash = Vector{ColIdx}(undef, ncols) + @inbounds for i in 1:ncols + col2hash[i] = i + end + exps = symbol_ht.exponents + function cmp(h1, h2) + @inbounds e1 = exps[h1] + @inbounds e2 = exps[h2] + return !lt_drl(e1, e2) + end + sort!(col2hash, lt = cmp) + matrix.col2hash = col2hash + nc = matrix.ncols + @inbounds matrix.pivots[1:nc] = matrix.pivots[1:nc][col2hash] + + if !iszero(matrix.nrows) + @info "matrix of size $((matrix.nrows, matrix.ncols)), density $(@sprintf "%.2f" 100*sum((length).(matrix.rows[1:matrix.nrows]))/(matrix.nrows * matrix.ncols))%" + end + matrix.sig_order = Vector{Int}(undef, matrix.nrows) + # sort signatures + sortperm!(matrix.sig_order, matrix.sigs[1:matrix.nrows], + lt = (sig1, sig2) -> lt_pot(sig1, sig2)) +end + +# TODO: later to optimize: mem allocations for matrix +# helper functions +function initialize_matrix(::Val{N}) where {N} + rows = Vector{Vector{MonIdx}}(undef, 0) + pivots = Vector{Int}(undef, 0) + pivot_size = 0 + sigs = Vector{Sig{N}}(undef, 0) + parent_inds = Vector{Int}(undef, 0) + sig_order = Vector{Int}(undef, 0) + col2hash = Vector{ColIdx}(undef, 0) + coeffs = Vector{Vector{Coeff}}(undef, 0) + toadd = Vector{Int}(undef, 0) + + size = 0 + nrows = 0 + ncols = 0 + toadd_length = 0 + + return MacaulayMatrix(rows, pivots, pivot_size, + sigs, parent_inds, sig_order, + col2hash, coeffs, size, nrows, + ncols, toadd, toadd_length) +end + +# Refresh and initialize matrix for `npairs` elements +function reinitialize_matrix!(matrix::MacaulayMatrix, npairs::Int) + matrix.size = 2 * npairs + matrix.pivot_size = 2 * npairs + resize!(matrix.rows, matrix.size) + resize!(matrix.pivots, matrix.pivot_size) + for i in 1:matrix.pivot_size + matrix.pivots[i] = 0 + end + resize!(matrix.sigs, matrix.size) + resize!(matrix.parent_inds, matrix.size) + resize!(matrix.coeffs, matrix.size) + resize!(matrix.toadd, matrix.size) + for i in 1:npairs + matrix.toadd[i] = 0 + end + return matrix +end + +# resize pivots array if needed +@inline function resize_pivots!(matrix::MacaulayMatrix, + symbol_ht::MonomialHashtable) + if matrix.pivot_size < symbol_ht.load + pv_size = matrix.pivot_size + new_pv_size = 2 * (symbol_ht.load) + resize!(matrix.pivots, new_pv_size) + @inbounds for j in pv_size+1:new_pv_size + matrix.pivots[j] = 0 + end + matrix.pivot_size = new_pv_size + end +end + +# helper function to write row to matrix +function write_to_matrix_row!(matrix::MacaulayMatrix, + basis::Basis, + basis_idx::Int, + symbol_ht::MonomialHashtable, + ht::MonomialHashtable, + mult::Monomial, + sig::Sig, + row_ind=matrix.nrows+1) + + hsh = Base.hash(mult) + poly = basis.monomials[basis_idx] + row = similar(basis.monomials[basis_idx]) + check_enlarge_hashtable!(symbol_ht, length(basis.monomials[basis_idx])) + + s = basis.sigs[basis_idx] + lm = mul(mult, leading_monomial(basis, ht, basis_idx)) + + @inbounds matrix.rows[row_ind] = + insert_multiplied_poly_in_hash_table!(row, hsh, mult, poly, + ht, symbol_ht) + @inbounds matrix.coeffs[row_ind] = basis.coefficients[basis_idx] + @inbounds matrix.sigs[row_ind] = sig + @inbounds matrix.parent_inds[row_ind] = basis_idx + if row_ind == matrix.nrows + 1 + matrix.nrows += 1 + end + return first(matrix.rows[row_ind]) +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/typedefs.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/typedefs.jl new file mode 100644 index 0000000..c8b064e --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/typedefs.jl @@ -0,0 +1,109 @@ +# type for signature indices +const SigIndex = UInt16 +# type for exponents in monomials +# ints because sigratios may require negative exponents +const Exp = Int16 +# types for hashvalue, ht index and divisor mask of a monomial +const MonIdx = Int32 +const MonHash = UInt32 +const DivMask = UInt32 +# stuff for matrix +const ColIdx = UInt32 +const Coeff = UInt32 +# 64 bit buffer +const Cbuf = UInt64 + +struct Monomial{N} + deg::Exp + exps::SVector{N, Exp} +end +function monomial(exps::SV) where {N, SV <: StaticArray{Tuple{N}}} + return Monomial{N}(sum(exps), exps) +end +const Sig{N} = Tuple{SigIndex, Monomial{N}} +const MaskSig = Tuple{SigIndex, DivMask} + +mutable struct Basis{N} + sigs::Vector{Sig{N}} + sigmasks::Vector{MaskSig} + + sigratios::Vector{Monomial{N}} + + # tree structure: + # - length of data for i is rewrite_nodes[i][1] + # - parent of i is rewrite_nodes[i][2] + # - children of i are rewrite_nodes[i][3:end] + # careful: indices are shifted by + 1 compared to basis indices + rewrite_nodes::Vector{Vector{Int}} + + lm_masks::Vector{DivMask} + + monomials::Vector{Vector{MonIdx}} + coefficients::Vector{Vector{Coeff}} + + is_red::Vector{Bool} + + syz_sigs::Vector{Monomial{N}} + syz_masks::Vector{MaskSig} + + # degrees of input elements + degs::Vector{Exp} + + basis_load::Int + basis_size::Int + # for storing the initial polynomials from 1 to offset-1 + basis_offset::Int + syz_load::Int + syz_size::Int +end + +# TODO: should these be stored in a more vectorized way? +mutable struct SPair{N} + top_sig::Sig{N} + bot_sig::Sig{N} + top_sig_mask::DivMask + bot_sig_mask::DivMask + # top index = 0 -> pair is redundant + top_index::Int + bot_index::Int + deg::Exp +end + +mutable struct Pairset{N} + elems::Vector{SPair{N}} + load::Int + size::Int +end + +mutable struct MacaulayMatrix{N} + + # stored as vectors of corresponding exponents (already hashed and sorted) + rows::Vector{Vector{MonIdx}} + + # pivot row index for colidx is pivots[colidx] + pivots::Vector{Int} + pivot_size::Int + + sigs::Vector{Sig{N}} + parent_inds::Vector{Int} + # sig(row[i]) < sig(row[j]) <=> sig_order[i] < sig_order[j] + sig_order::Vector{Int} + + # maps column index to corresponding hash index + col2hash::Vector{ColIdx} + + # row coefficients + coeffs::Vector{Vector{Coeff}} + + #= sizes info =# + # total number of allocated rows + size::Int + # number of filled rows, nrows <= size + nrows::Int + # number of columns + ncols::Int + + # for each i in toadd rows[i] should be added to basis/syzygies + toadd::Vector{Int} + toadd_length::Int +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/update.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/update.jl new file mode 100644 index 0000000..bdb3428 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/update.jl @@ -0,0 +1,350 @@ +# updating the pairset and basis + +# add new reduced rows to basis/syzygies +# TODO: make a new symbol ht everytime? +function update_basis!(basis::Basis, + matrix::MacaulayMatrix, + pairset::Pairset{N}, + symbol_ht::MonomialHashtable, + basis_ht::MonomialHashtable) where N + + new_basis_c = 0 + new_syz_c = 0 + + # TODO: this can be done more optimally + toadd = matrix.toadd[1:matrix.toadd_length] + # sort!(toadd, by = i -> matrix.sigs[i], lt = lt_pot) + + @inbounds for i in toadd + # determine if row is zero + row = matrix.rows[i] + new_sig = matrix.sigs[i] + new_idx = index(new_sig) + new_sig_mon = monomial(new_sig) + new_sig_mask = (new_idx, divmask(new_sig_mon, basis_ht.divmap, + basis_ht.ndivbits)) + if isempty(row) + new_syz_c += 1 + + # make sure we have enough space + if basis.syz_load == basis.syz_size + basis.syz_size *= 2 + resize!(basis.syz_sigs, basis.syz_size) + resize!(basis.syz_masks, basis.syz_size) + end + + # add new syz sig + l = basis.syz_load + 1 + basis.syz_sigs[l] = monomial(new_sig) + basis.syz_masks[l] = new_sig_mask + basis.syz_load += 1 + + # kill pairs with known syz signature + @inbounds for j in 1:pairset.load + p = pairset.elems[j] + cond = index(p.top_sig) == new_idx + if cond && divch(new_sig_mon, monomial(p.top_sig), + new_sig_mask[2], p.top_sig_mask) + pairset.elems[j].top_index = 0 + end + cond = index(p.bot_sig) == new_idx + if cond && divch(new_sig_mon, monomial(p.bot_sig), + new_sig_mask[2], p.bot_sig_mask) + pairset.elems[j].top_index = 0 + end + end + + # remove pairs that became rewriteable in previous loop + remove_red_pairs!(pairset) + else + new_basis_c += 1 + + # make sure we have enough space + if basis.basis_load == basis.basis_size + basis.basis_size *= 2 + resize!(basis.sigs, basis.basis_size) + resize!(basis.sigmasks, basis.basis_size) + resize!(basis.sigratios, basis.basis_size) + resize!(basis.rewrite_nodes, basis.basis_size) + resize!(basis.lm_masks, basis.basis_size) + resize!(basis.monomials, basis.basis_size) + resize!(basis.coefficients, basis.basis_size) + resize!(basis.is_red, basis.basis_size) + end + + # add to basis hashtable + insert_in_basis_hash_table_pivots!(row, basis_ht, symbol_ht) + lm = basis_ht.exponents[first(row)] + s = new_sig + + # add everything to basis + l = basis.basis_load + 1 + basis.sigs[l] = new_sig + basis.sigmasks[l] = new_sig_mask + new_sig_ratio = divide(lm, new_sig_mon) + basis.sigratios[l] = new_sig_ratio + + parent_ind = matrix.parent_inds[i] + tree_data = basis.rewrite_nodes[parent_ind+1] + insind = 3 + @inbounds for j in insind:insind+tree_data[1] + child_ind = tree_data[j] + rat = basis.sigratios[child_ind-1] + if lt_drl(new_sig_ratio, rat) + break + end + insind += 1 + end + insert!(tree_data, insind, l+1) + tree_data[1] += 1 + basis.rewrite_nodes[l+1] = [-1, parent_ind+1] + + basis.lm_masks[l] = divmask(lm, basis_ht.divmap, + basis_ht.ndivbits) + basis.monomials[l] = row + basis.coefficients[l] = matrix.coeffs[i] + basis.basis_load = l + + # build new pairs + update_pairset!(pairset, basis, basis_ht, l) + end + end + if new_basis_c != 0 || new_syz_c != 0 + @info "$(new_basis_c) new, $(new_syz_c) zero" + end +end + + +# construct all pairs with basis element at new_basis_idx +# and perform corresponding rewrite checks +# assumes DPOT +function update_pairset!(pairset::Pairset{N}, + basis::Basis, + basis_ht::MonomialHashtable, + new_basis_idx::Int) where N + + + new_sig_mon = monomial(basis.sigs[new_basis_idx]) + new_sig_idx = index(basis.sigs[new_basis_idx]) + + # check existing pairs for rewriteability against element + # at new_basis_idx + @inbounds bmask = basis.sigmasks[new_basis_idx] + @inbounds parent_ind = basis.rewrite_nodes[new_basis_idx+1][2] + @inbounds for i in 1:pairset.load + p = pairset.elems[i] + if p.top_index == parent_ind-1 + if divch(new_sig_mon, monomial(p.top_sig), + mask(bmask), p.top_sig_mask) + pairset.elems[i].top_index = 0 + continue + end + end + if p.bot_index == parent_ind-1 + if divch(new_sig_mon, monomial(p.bot_sig), + mask(bmask), p.bot_sig_mask) + pairset.elems[i].top_index = 0 + end + end + end + + # kill pairs that became rewriteable in the previous round + remove_red_pairs!(pairset) + + # resize pairset if needed + num_new_pairs = new_basis_idx - 1 + if pairset.load + num_new_pairs >= pairset.size + resize!(pairset.elems, max(2 * pairset.size, + pairset.load - num_new_pairs)) + pairset.size *= 2 + end + + new_sig_ratio = basis.sigratios[new_basis_idx] + new_lm = leading_monomial(basis, basis_ht, new_basis_idx) + # pair construction loop + @inbounds for i in basis.basis_offset:(new_basis_idx - 1) + basis_lm = leading_monomial(basis, basis_ht, i) + basis_sig_idx = index(basis.sigs[i]) + + mult_new_elem = lcm_div(new_lm, basis_lm) + new_pair_sig_mon = mul(mult_new_elem, new_sig_mon) + + mult_basis_elem = lcm_div(basis_lm, new_lm) + basis_pair_sig_mon = mul(mult_basis_elem, monomial(basis.sigs[i])) + + new_pair_sig = (new_sig_idx, new_pair_sig_mon) + basis_pair_sig = (basis_sig_idx, basis_pair_sig_mon) + + # check if S-pair is singular + new_pair_sig == basis_pair_sig && continue + + new_pair_sig_mask = divmask(new_pair_sig_mon, + basis_ht.divmap, + basis_ht.ndivbits) + basis_pair_sig_mask = divmask(basis_pair_sig_mon, + basis_ht.divmap, + basis_ht.ndivbits) + + # check both pair sigs against non-trivial syzygies + rewriteable_syz(basis, new_pair_sig, + new_pair_sig_mask) && continue + rewriteable_syz(basis, basis_pair_sig, + basis_pair_sig_mask) && continue + + # check both pair signatures against koszul syzygies + rewriteable_koszul(basis, basis_ht, new_pair_sig, + new_pair_sig_mask) && continue + rewriteable_koszul(basis, basis_ht, basis_pair_sig, + basis_pair_sig_mask) && continue + + top_sig, top_sig_mask, top_index, + bot_sig, bot_sig_mask, bot_index = begin + if lt_pot(basis_pair_sig, new_pair_sig) + new_pair_sig, new_pair_sig_mask, new_basis_idx, + basis_pair_sig, basis_pair_sig_mask, i + else + basis_pair_sig, basis_pair_sig_mask, i, + new_pair_sig, new_pair_sig_mask, new_basis_idx + end + end + + pair_deg = new_pair_sig_mon.deg + basis.degs[new_sig_idx] + new_pair = SPair(top_sig, bot_sig, + top_sig_mask, bot_sig_mask, + top_index, bot_index, + pair_deg) + pairset.elems[pairset.load + 1] = new_pair + pairset.load += 1 + end +end + +@inline function rewriteable_syz(basis::Basis, + sig::Sig, + sigmask::DivMask) + + ind = index(sig) + + @inbounds for i in 1:basis.syz_load + if index(basis.syz_masks[i]) == ind + is_rewr = divch(basis.syz_sigs[i], monomial(sig), + basis.syz_masks[i][2], sigmask) + is_rewr && return true + end + end + return false +end + +@inline function rewriteable_basis(basis::Basis, + idx::Int, + sig::Sig, + sigmask::DivMask) + + k = find_canonical_rewriter(basis, sig, sigmask) + return k != idx +end + +# @inline function rewriteable_basis(basis::Basis, +# idx::Int, +# sig::Sig, +# sigmask::DivMask) + +# ind = index(sig) + +# @inbounds for i in basis.basis_load:-1:basis.basis_offset +# i == idx && continue +# i_sig_idx = index(basis.sigmasks[i]) +# i_sig_idx != ind && continue +# i_sig_mask = mask(basis.sigmasks[i]) +# if divch(monomial(basis.sigs[i]), monomial(sig), +# i_sig_mask, sigmask) +# is_rewr = comp_sigratio(basis, i, idx) +# is_rewr && return true +# end +# end +# return false +# end + +function find_canonical_rewriter(basis::Basis, + sig::Sig, + sigmask::DivMask) + + node_ind = 1 + while true + @inbounds node = basis.rewrite_nodes[node_ind] + @inbounds node[1] == -1 && break + found_div = false + @inbounds for i in 3:3+node[1] + ch = node[i] + basis_sig = basis.sigs[ch - 1] + basis_sigmask = basis.sigmasks[ch - 1] + index(basis_sig) != index(sig) && continue + if divch(monomial(basis_sig), monomial(sig), + mask(basis_sigmask), sigmask) + node_ind = ch + found_div = true + break + end + end + !found_div && break + end + return node_ind - 1 +end + +@inline function rewriteable_koszul(basis::Basis, + basis_ht::MonomialHashtable, + sig::Sig, + sigmask::DivMask) + + @inbounds for i in basis.basis_offset:basis.basis_load + if index(basis.sigs[i]) < index(sig) + if divch(basis.lm_masks[i], sigmask) + if divch(leading_monomial(basis, basis_ht, i), monomial(sig)) + return true + end + end + end + end + return false +end + +function rewriteable(basis::Basis, + basis_ht::MonomialHashtable, + idx::Int, + sig::Sig, + sigmask::DivMask) + + rewriteable_syz(basis, sig, sigmask) && return true + rewriteable_basis(basis, idx, sig, sigmask) && return true + rewriteable_koszul(basis, basis_ht, sig, sigmask) && return true + return false +end + +# helper functions for readability +function leading_monomial(basis::Basis, + basis_ht::MonomialHashtable, + i) + + return basis_ht.exponents[first(basis.monomials[i])] +end + +@inline function comp_sigratio(basis::Basis, ind1::Int, ind2::Int) + + rat1 = basis.sigratios[ind1] + rat2 = basis.sigratios[ind2] + if rat1 == rat2 + return lt_drl(monomial(basis.sigs[ind1]), monomial(basis.sigs[ind2])) + end + return lt_drl(rat1, rat2) +end + +# remove pairs that are rewriteable +function remove_red_pairs!(pairset::Pairset) + iszero(pairset.load) && return + j = 0 + @inbounds for i in 1:pairset.load + iszero(pairset.elems[i].top_index) && continue + j += 1 + pairset.elems[j] = pairset.elems[i] + end + pairset.load = j +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/types.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/types.jl new file mode 100644 index 0000000..d193d6d --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/types.jl @@ -0,0 +1,51 @@ +export Ideal + +mutable struct RationalParametrization + vars::Vector{Symbol} + lf_cfs::Vector{ZZRingElem} + elim::QQPolyRingElem + denom::QQPolyRingElem + param::Vector{PolyRingElem} + + function RationalParametrization( + vars::Vector{Symbol}, + lf_cfs::Vector{ZZRingElem}, + elim::QQPolyRingElem, + denom::QQPolyRingElem, + param::Vector{PolyRingElem} + ) + rp = new() + rp.vars = vars + rp.lf_cfs = lf_cfs + rp.elim = elim + rp.denom = denom + rp.param = param + + return rp + end +end + +mutable struct Ideal{T <: MPolyRingElem} + gens::Vector{T} + dim::Int + gb::Dict{Int, Vector{T}} + inter_sols::Vector{Vector{Vector{QQFieldElem}}} + real_sols::Vector{Vector{QQFieldElem}} + rat_sols::Vector{Vector{QQFieldElem}} + rat_param::RationalParametrization + + function Ideal(F::Vector{T}) where {T <: MPolyRingElem} + I = new{T}() + I.gens = F + I.dim = -1 + I.gb = Dict() + + return I + end +end + +Base.parent(I::Ideal) = Nemo.parent(I.gens[1]) + +Base.show(io::IO, I::Ideal) = print(io, I.gens) + +Base.getindex(I::Ideal, idx::Int) = I.gens[idx] diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/groebner-bases.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/groebner-bases.jl new file mode 100644 index 0000000..f26122f --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/groebner-bases.jl @@ -0,0 +1,70 @@ +@testset "Algorithms -> Gröbner bases" begin + R, (x,y,z) = polynomial_ring(QQ,["x","y","z"], ordering=:degrevlex) + F = [x^2+1-3, x*y-z, x*z^2-3*y^2] + #= not a finite field =# + @test_throws ErrorException groebner_basis(Ideal(F)) + R, (x,y,z) = polynomial_ring(GF(101),["x","y","z"], ordering=:degrevlex) + I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y]) + G = groebner_basis(I) + H = MPolyRingElem[ + x + 2*y + 2*z + 100 + y*z + 82*z^2 + 10*y + 40*z + y^2 + 60*z^2 + 20*y + 81*z + z^3 + 28*z^2 + 64*y + 13*z + ] + @test G == H + @test I.gb[0] == H + + G = groebner_basis(I, eliminate=2) + H = MPolyRingElem[ + z^4 + 38*z^3 + 95*z^2 + 95*z + ] + @test G == H + + @test_throws ErrorException eliminate(I,0) + L = eliminate(I,2) + @test L == H + @test I.gb[2] == H + + I = Ideal([R(0)]) + G = groebner_basis(I) + @test G == [R(0)] +end + +@testset "Algorithms -> Sig Gröbner bases" begin + R, (x,y,z) = polynomial_ring(QQ,["x","y","z"], ordering=:degrevlex) + F = [x^2+1-3, x*y-z, x*z^2-3*y^2] + #= not a finite field =# + @test_throws ErrorException sig_groebner_basis(F) + R, (x,y,z) = polynomial_ring(GF(17),["x","y","z"], ordering=:degrevlex) + F = [x^2+1-3, x*y-z, x*z^2-3*y^2] + #= not homogeneous =# + @test_throws ErrorException sig_groebner_basis(F) + + #= GB test 1 =# + Fhom = AlgebraicSolving._homogenize(F) + sgb = sig_groebner_basis(Fhom) + @test AlgebraicSolving._is_gb(sgb) + + #= GB test 2 =# + R, (x,y,z,w) = polynomial_ring(GF(65521),["x","y","z","w"], ordering=:degrevlex) + F = cyclic(R).gens + Fhom = AlgebraicSolving._homogenize(F) + sgb = sig_groebner_basis(Fhom) + @test AlgebraicSolving._is_gb(sgb) + + #= GB test 3 =# + F = katsura(R).gens + Fhom = AlgebraicSolving._homogenize(F) + sgb = sig_groebner_basis(Fhom) + @test AlgebraicSolving._is_gb(sgb) + + #= GB test 4 (pivot setting bug) =# + R, (x1, x2, x3, x4) = polynomial_ring(GF(65521), ["x1", "x2", "x3", "x4"], ordering=:degrevlex) + F = [11523*x1^4 + 30378*x1^3*x2 + 30154*x1^2*x2^2 + 10157*x1*x2^3 - 28136*x2^4 - 4771*x1^3*x3 - 21056*x1^2*x2*x3 + 15696*x1*x2^2*x3 - 16144*x2^3*x3 - 1553*x1^2*x3^2 - 30379*x1*x2*x3^2 - 12735*x2^2*x3^2 + 18058*x1*x3^3 + 24670*x2*x3^3 - 16379*x3^4 + 24196*x1^3*x4 - 19411*x1^2*x2*x4 + 17610*x1*x2^2*x4 - 5715*x2^3*x4 - 21186*x1^2*x3*x4 - 22865*x1*x2*x3*x4 - 1939*x2^2*x3*x4 - 5685*x1*x3^2*x4 + 8508*x2*x3^2*x4 + 21819*x3^3*x4 - 24868*x1^2*x4^2 - 18233*x1*x2*x4^2 - 14116*x2^2*x4^2 + 28291*x1*x3*x4^2 - 9068*x2*x3*x4^2 - 15138*x3^2*x4^2 + 8921*x1*x4^3 - 18808*x2*x4^3 - 3005*x3*x4^3 + 7368*x4^4, + 31703*x1^4 + 23616*x1^3*x2 + 20696*x1^2*x2^2 - 7125*x1*x2^3 + 15334*x2^4 + 26619*x1^3*x3 + 2173*x1^2*x2*x3 - 31312*x1*x2^2*x3 - 31386*x2^3*x3 - 25244*x1^2*x3^2 - 28729*x1*x2*x3^2 + 27244*x2^2*x3^2 - 24892*x1*x3^3 + 2046*x2*x3^3 + 2516*x3^4 - 18588*x1^3*x4 + 9980*x1^2*x2*x4 - 10104*x1*x2^2*x4 + 21688*x2^3*x4 - 1315*x1^2*x3*x4 - 17824*x1*x2*x3*x4 + 14919*x2^2*x3*x4 - 568*x1*x3^2*x4 - 22509*x2*x3^2*x4 + 18494*x3^3*x4 + 25947*x1^2*x4^2 - 28652*x1*x2*x4^2 - 25547*x2^2*x4^2 + 1637*x1*x3*x4^2 - 20130*x2*x3*x4^2 + 19739*x3^2*x4^2 + 3742*x1*x4^3 + 25425*x2*x4^3 + 6342*x3*x4^3 - 3004*x4^4, + 2857*x1^4 + 8898*x1^3*x2 + 16959*x1^2*x2^2 - 28026*x1*x2^3 - 25631*x2^4 + 11030*x1^3*x3 + 29101*x1^2*x2*x3 + 30359*x1*x2^2*x3 + 27330*x2^3*x3 + 19126*x1^2*x3^2 - 26603*x1*x2*x3^2 + 2510*x2^2*x3^2 + 7575*x1*x3^3 - 25033*x2*x3^3 - 21024*x3^4 + 30501*x1^3*x4 + 23834*x1^2*x2*x4 - 1858*x1*x2^2*x4 - 10862*x2^3*x4 + 30320*x1^2*x3*x4 + 19705*x1*x2*x3*x4 + 28359*x2^2*x3*x4 + 17590*x1*x3^2*x4 + 11929*x2*x3^2*x4 + 22830*x3^3*x4 + 13501*x1^2*x4^2 - 24860*x1*x2*x4^2 + 12598*x2^2*x4^2 - 9409*x1*x3*x4^2 - 2827*x2*x3*x4^2 - 8608*x3^2*x4^2 + 30938*x1*x4^3 - 12892*x2*x4^3 + 9165*x3*x4^3 - 5202*x4^4, + -23687*x1^4 + 32692*x1^3*x2 + 20539*x1^2*x2^2 - 27327*x1*x2^3 + 3928*x2^4 - 13018*x1^3*x3 - 13583*x1^2*x2*x3 - 30594*x1*x2^2*x3 - 12584*x2^3*x3 - 9819*x1^2*x3^2 + 14542*x1*x2*x3^2 + 30297*x2^2*x3^2 + 15188*x1*x3^3 + 28438*x2*x3^3 + 13512*x3^4 + 13327*x1^3*x4 + 14335*x1^2*x2*x4 - 15128*x1*x2^2*x4 - 21922*x2^3*x4 - 22104*x1^2*x3*x4 - 23535*x1*x2*x3*x4 - 4393*x2^2*x3*x4 - 20398*x1*x3^2*x4 + 14310*x2*x3^2*x4 - 4426*x3^3*x4 - 23087*x1^2*x4^2 - 21281*x1*x2*x4^2 + 13831*x2^2*x4^2 - 23378*x1*x3*x4^2 + 18852*x2*x3*x4^2 - 11968*x3^2*x4^2 - 31181*x1*x4^3 + 20091*x2*x4^3 - 14043*x3*x4^3 - 10677*x4^4] + sgb = sig_groebner_basis(F) + @test AlgebraicSolving._is_gb(sgb) +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/normal-forms.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/normal-forms.jl new file mode 100644 index 0000000..6ad4ce7 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/normal-forms.jl @@ -0,0 +1,18 @@ +@testset "Algorithms -> Normal forms" begin + R, (x,y) = polynomial_ring(GF(101),["x","y"]) + I = Ideal([y*x+17-y, x+13*y]) + f = x^4+y + @test normal_form(f, I) == 100*y+77 + F = [x+13*y, x*y-4] + @test normal_form(F, I) == [0, y + 80] + R, (x,y) = polynomial_ring(GF(536870923),["x","y"]) + I = Ideal([y*x+17-y, x+13*y]) + F = [x+13*y, x*y-4] + @test normal_form(F, I) == [0, y + 536870902] + R, (x,y) = polynomial_ring(GF(65521),["x","y"]) + I = Ideal([y*x+17-y, x+13*y]) + F = [x+13*y, x*y+16] + @test normal_form(F, I) == [0, y + 65520] + I = Ideal([R(0)]) + @test normal_form(F, I) == F +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/solvers.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/solvers.jl new file mode 100644 index 0000000..ed113e4 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/solvers.jl @@ -0,0 +1,53 @@ +@testset "Algorithms -> Solvers" begin + R, (x1,x2,x3,x4) = polynomial_ring(QQ,["x1","x2","x3","x4"], ordering=:degrevlex) + I = Ideal([x1 + 2*x2 + 2*x3 + 2*x4 - 1, + x1^2 + 2*x2^2 + 2*x3^2 + 2*x4^2 - x1, + 2*x1*x2 + 2*x2*x3 + 2*x3*x4 - x2, + x2^2 + 2*x1*x3 + 2*x2*x4 - x3]) + sols = Vector{QQFieldElem}[ + [4862548775//8589934592, 1281562925//8589934592, 2195068207//8589934592, -32714273694608759819673593948262790419337//174224571863520493293247799005065324265472], + [3779635503//8589934592, 2638476131//8589934592, 908473689//8589934592, -92633843493479102248442236077889080803361//696898287454081973172991196020261297061888], + [1, 0, 0, 0], + [6410479475//8589934592, 2005530653//8589934592, -1585770177//8589934592, 55658687714722201275489356321691134094555601//713623846352979940529142984724747568191373312], + [1611414365//8589934592, 673053615//8589934592, 632173751//8589934592, 708759148891639684402860468800417934359477//2787593149816327892691964784081045188247552], + [2863311531//8589934592, 0, 0, 14518714321960041107770649917088777022123//43556142965880123323311949751266331066368] + ] + rat_sols = Vector{QQFieldElem}[[49, 0, 0, 0], [49//3, 0, 0, 1//3]] + + @test sols == real_solutions(I) + @test rat_sols == rational_solutions(I) + @test I.real_sols == real_solutions(I) + + C, x = polynomial_ring(QQ, "x") + elim = 128304*x^8 - 93312*x^7 + 15552*x^6 + 3144*x^5 - 1120*x^4 + 36*x^3 + 15*x^2 - x + denom = 1026432*x^7 - 653184*x^6 + 93312*x^5 + 15720*x^4 - 4480*x^3 + 108*x^2 + 30*x - 1 + p1 = -3872448*x^7 + 2607552*x^6 - 408528*x^5 - 63088*x^4 + 20224*x^3 - 540*x^2 - 172*x + 7 + p2 = -303264*x^7 + 314928*x^6 - 113544*x^5 + 9840*x^4 + 3000*x^3 - 564*x^2 + 12*x + p3 = -699840*x^7 + 449712*x^6 - 74808*x^5 - 1956*x^4 + 1308*x^3 - 174*x^2 + 18*x + p1 *= -7 + p2 *= -7 + p3 *= -7 + + param = rational_parametrization(I) + + @test param.vars == [:x1, :x2, :x3, :x4] + @test param.lf_cfs == ZZRingElem[] + @test param.elim == elim + @test param.denom == denom + @test param.param[1] == p1 + @test param.param[2] == p2 + @test param.param[3] == p3 + @test I.rat_param.elim == elim + @test I.rat_param.denom == denom + @test I.rat_param.param[1] == p1 + @test I.rat_param.param[2] == p2 + @test I.rat_param.param[3] == p3 + + I = Ideal([x1^2-x2, x1*x3-x4, x2*x4-12, x4^3-x3^2]) + real_solutions(I) + @test I.rat_param.vars == Symbol[] + + I = Ideal([x1^2-x2, x1*x3, x2-12]) + @test_throws ErrorException real_solutions(I) + @test_throws ErrorException rational_solutions(I) +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/examples/katsura.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/examples/katsura.jl new file mode 100644 index 0000000..7e5127f --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/test/examples/katsura.jl @@ -0,0 +1,28 @@ +@testset "Examples -> Katsura" begin + I = katsura(3) + R, x = first(I.gens).parent, vars(first(I.gens)) + G = [x[1] + 2*x[2] + 2*x[3] + 2*x[4] - 1, + x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 - x[1], + 2*x[1]*x[2] + 2*x[2]*x[3] + 2*x[3]*x[4] - x[2], + x[2]^2 + 2*x[1]*x[3] + 2*x[2]*x[4] - x[3]] + + @test I.gens == G + + I = katsura(4, 101) + R, x = first(I.gens).parent, vars(first(I.gens)) + G = [x[1] + 2*x[2] + 2*x[3] + 2*x[4] + 2*x[5] + 100, + x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 + 2*x[5]^2 + 100*x[1], + 2*x[1]*x[2] + 2*x[2]*x[3] + 2*x[3]*x[4] + 2*x[4]*x[5] + 100*x[2], + x[2]^2 + 2*x[1]*x[3] + 2*x[2]*x[4] + 2*x[3]*x[5] + 100*x[3], + 2*x[2]*x[3] + 2*x[1]*x[4] + 2*x[2]*x[5] + 100*x[4]] + + @test I.gens == G + + R, (x,y,z) = polynomial_ring(QQ, ["x","y","z"]) + I = katsura(R) + G = [x + 2*y + 2*z - 1, + x^2 - x + 2*y^2 + 2*z^2, + 2*x*y + 2*y*z - y] + + @test I.gens == G +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/interfaces/nemo.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/interfaces/nemo.jl new file mode 100644 index 0000000..d3ffdcc --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/test/interfaces/nemo.jl @@ -0,0 +1,16 @@ +@testset "Interfaces -> Nemo" begin + R, (x,y,z) = polynomial_ring(QQ,["x","y","z"], ordering=:degrevlex) + F = [x^2+1-3, x*y-z, x*z^2-3*y^2] + cmp = (Int32[2, 2, 2], BigInt[1, 1, -2, 1, 1, 1, -1, 1, 1, 1, -3, 1], Int32[2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0]) + @test AlgebraicSolving._convert_to_msolve(F) == cmp + for _GF in [GF, AlgebraicSolving.Nemo.Native.GF] + R, (x,y,z) = polynomial_ring(_GF(2147483659),["x","y","z"], ordering=:degrevlex) + F = [x^2+1-3, x*y-z, x*z^2-3*y^2] + # prime is bigger than 2^31, should throw an error + @test_throws ErrorException AlgebraicSolving._convert_to_msolve(F) + R, (x,y,z) = polynomial_ring(_GF(101),["x","y","z"], ordering=:degrevlex) + F = [x^2+1-3, x*y-z, x*z^2-3*y^2] + res = AlgebraicSolving._convert_to_msolve(F) + @test AlgebraicSolving._convert_finite_field_array_to_abstract_algebra(Int32(3), res..., R) == F + end +end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/runtests.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/runtests.jl new file mode 100644 index 0000000..11a1d92 --- /dev/null +++ b/src/connectcurves/AlgebraicSolving.jl-main/test/runtests.jl @@ -0,0 +1,10 @@ +using AlgebraicSolving +using Test + +@testset verbose = true "AlgebraicSolving Tests" begin +include("interfaces/nemo.jl") +include("algorithms/groebner-bases.jl") +include("algorithms/normal-forms.jl") +include("algorithms/solvers.jl") +include("examples/katsura.jl") +end diff --git a/src/connectcurves/data.jl b/src/connectcurves/data.jl new file mode 100644 index 0000000..c1533c4 --- /dev/null +++ b/src/connectcurves/data.jl @@ -0,0 +1,10 @@ +#using Nemo +R, (x,y) = Nemo.polynomial_ring(Nemo.QQ, [:x, :y]) + +f = 1594627541097114368612385*x^16 + 24126594979283487048484560*x^15*y - 648897523515553246784074808*x^14*y^2 + 9227671981881181765203810480*x^13*y^3 + 775388988595641728298874736332*x^12*y^4 + 10787151407096126900712389934720*x^11*y^5 + 77139559828286619230682855993096*x^10*y^6 + 452145503210946168432702707056320*x^9*y^7 + 1603450939087454055697523432885078*x^8*y^8 + 472422761323888641034023872620080*x^7*y^9 + 69254293553970771431091788378664*x^6*y^10 + 8171004998268972015374643672912*x^5*y^11 + 486748426688048642456485687660*x^4*y^12 - 12064621488868591078399181568*x^3*y^13 - 1468208821458887902925840024*x^2*y^14 + 12892282240123223587086528*x*y^15 + 1551343473382248651380209*y^16 - 7416582067989458752697004*x^14 - 86407846455606538783280976*x^13*y + 2644747193988832166794696620*x^12*y^2 + 4962811393512179992436546328*x^11*y^3 - 852556155710875435151137729948*x^10*y^4 - 9006223258524272797865687202672*x^9*y^5 - 37408868951040006789841449492372*x^8*y^6 - 96029136974599596104658658159536*x^7*y^7 - 25805546034923632520724584708244*x^6*y^8 - 5242437191813955076157431442064*x^5*y^9 - 409699928605220782678759186860*x^4*y^10 + 39375118017080555511082417752*x^3*y^11 + 4414478650057190403833967932*x^2*y^12 - 62266637085710610417717552*x*y^13 - 7665646840583710272384908*y^14 + 14233446085691566995553618*x^12 + 132571431253302115292123136*x^11*y - 3677320627079906075667837422*x^10*y^2 - 28335523591694036134043888352*x^9*y^3 + 186478273436442358105601202678*x^8*y^4 + 979680543110585521095162296976*x^7*y^5 - 2082167356121156563744172163572*x^6*y^6 - 30539225710419394554664076544*x^5*y^7 + 25429103844006118137220734342*x^4*y^8 - 40056866529454773916181059488*x^3*y^9 - 4741918132209313788162640030*x^2*y^10 + 120063392649421566997191792*x*y^11 + 15453863115268541628254722*y^12 - 14508062550440954802512688*x^10 - 115292786706841839957190896*x^9*y + 2178406370189758736513057100*x^8*y^2 + 17911006599365461837132806264*x^7*y^3 + 18721721306068791970712906740*x^6*y^4 + 140144222573062968441350663256*x^5*y^5 + 15151268277268342933019382004*x^4*y^6 + 14388997206020218965816744888*x^3*y^7 + 2181175955893013097832336108*x^2*y^8 - 116823607901494850142791760*x*y^9 - 16262571151436698863824960*y^10 + 8412196412628079801200763*x^8 + 60038503306269383516796672*x^7*y - 526872554079154536701276538*x^6*y^2 - 2627205980235442180204133952*x^5*y^3 + 1415955761616170935932891503*x^4*y^4 - 1207248891865676270007025776*x^3*y^5 - 411102077811099614734692666*x^2*y^6 + 59338125380312133254699856*x*y^7 + 9471776668272238878375147*y^8 - 2755131867388737857954960*x^6 - 16865677220581290594690288*x^5*y + 37152628773628751552853580*x^4*y^2 - 32454665768852564904473352*x^3*y^3 + 31405824474395795210222812*x^2*y^4 - 14499431708247069028795056*x*y^5 - 2982642484703489520084064*y^6 + 476197729395824935891282*x^4 + 1850003538678786657657456*x^3*y - 861756868723874605906006*x^2*y^2 + 1328290412641467896291664*x*y^3 + 466653249763538900703730*y^4 - 37550891878150349195068*x^2 - 32144769403583975845728*x*y - 33575411625230211328108*y^2 + 864999024811562109121 + +params = [[122052108945321231460815317670274232129992226114393994453269787251191586772999998478131397177313291168794930288045095160607171215109769903956555756352425696420971136000*x^64 - 959032695327466028896923007278462984351139470332688180556285108098088661529598320753396670253784301046095380112992662697008888935637597834208399524065939904172979990400*x^62 + 3394978440692000014057928614441958536159991996524914295852869400764921537705344371827178578116630227593461086898603789268227871843165040143533225447517362520002264974800*x^60 - 7151371831353663495035969461496662107369926971805594266199814693934146824218470195335493405697799780940541485521905675079385537261608449869138456973383228166236613263400*x^58 + 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76093196872372578373119402591542924336595309825576292045515391246379464763158228784639574310982195640136389028170516631428420420489719956379967145212728402543856172428301827720835720619511746291529555478771232044026977196487380606051408105650931853037339102824546133136096406879899656252503263781924026226251779704232683941753426157396355555386426406923634579674802667468556932278540083239541771095586953543174979462316844522007563225998088037858674707962626971083428228623682979720860644003550437215307280073434204980445128604856611045119274229393897316722277964178023092238372341675934924661369445149897548641019617913507175210877932947651340271616]] diff --git a/src/connectcurves/main.ipynb b/src/connectcurves/main.ipynb new file mode 100644 index 0000000..e74f544 --- /dev/null +++ b/src/connectcurves/main.ipynb @@ -0,0 +1,486 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading libraries and data..\n" + ] + }, + { + "data": { + "text/plain": [ + "subresultants_seq_biv (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "println(\"Loading libraries and data..\")\n", + "using Oscar\n", + "include(\"tools.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "usolve (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "include(\"data.jl\")\n", + "include(\"src/usolve/usolve.jl\")\n", + "#using Arblib" + ] + }, + { + "cell_type": "code", + "execution_count": 316, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "evaluate_Arb (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "function order_permut2d(L)\n", + " # Create a list of tuples with elements and their corresponding indices\n", + " LL = [(L[i][j], (i, j)) for i in eachindex(L) for j in eachindex(L[i])]\n", + " # Sort the enumerated list based on the values\n", + " sorted_LL = sort(LL, by = x -> x[1])\n", + " # Extract the sorted values and their corresponding indices\n", + " sorted_L = [pair[1] for pair in sorted_LL]\n", + " sorted_ind = [pair[2] for pair in sorted_LL]\n", + " \n", + " return sorted_L, sorted_ind\n", + "end\n", + "\n", + "function isolate(f; prec = 32, software=\"usolve\")\n", + " @assert Nemo.is_univariate(f) \"Not univariate polynomial\"\n", + "\tif software == \"usolve\"\n", + "\t\treturn usolve(f, precision = prec, uspath=\"src/usolve/usolve\")\n", + " end\n", + "end\n", + "\n", + "function isolate_eval(f, ivar, val; prec=64)\n", + " sols = real_solutions(ideal(R, [f, gens(R)[ivar] - val]), precision=prec)[1]\n", + " return [ s[ivar%2+1] for s in sols ]\n", + "end\n", + "\n", + "function Arb_to_rat(x)\n", + "\tr = radius(x)\n", + "\treturn map(simplest_rational_inside, [x-2*r, x+2*r])\n", + "end\n", + "\n", + "function rat_to_Arb(x)\n", + " x1,x2 = x\n", + " xm, xd = RR((x1+x2)/2), RR(x2-x1)\n", + " return ball(xm,xd)\n", + "end\n", + "\n", + "function evaluate_Arb(f, x)\n", + "\tcf = coefficients_of_univariate(f)\n", + "\treturn evalpoly(RR(x), cf) \n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 283, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Isolating critical values..\n" + ] + } + ], + "source": [ + "println(\"Isolating critical values..\")\n", + "xcrit = [ isolate(first(p), prec=150) for p in params ]\n", + "xcrit_usolve = getindex.(xcrit, 1)\n", + "xcrit = getindex.(xcrit, 2)\n", + "xcritorder, xcritpermut = order_permut2d(xcrit);" + ] + }, + { + "cell_type": "code", + "execution_count": 284, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Computing isolating critical boxes using Arb..\n" + ] + } + ], + "source": [ + "println(\"Computing isolating critical boxes using Arb..\")\n", + "#RR(x) = Arb(x, prec=120)\n", + "RR = ArbField(150)\n", + "Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ]\n", + "LBcrit = [ [ [ map(AbstractAlgebra.QQ, pc[1]), map(AbstractAlgebra.QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ];\n", + "Pcrit = [ [ [ rat_to_Arb(pc[1]), pc[2] ] for pc in pcrit] for pcrit in Pcrit ];" + ] + }, + { + "cell_type": "code", + "execution_count": 317, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "intersect_box (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# To try/do : isolate with usolve, call msolve with only one variable\n", + "function intersect_box(f, B)\n", + " L = Array{Any}(undef, 4)\n", + " for i in 1:2\n", + " # Lxi\n", + " L[i] = Array{Any}(undef,2)\n", + " L[i][1] = isolate_eval(f, 2, B[2][i], prec=150)\n", + " L[i][2] = [ j for (j, l) in pairs(L[i][1]) if (l> B[1][1] && l B[1][1] && l 2\n", + " @assert false \"\\nRefine extreme boxes along x-axis\"\n", + " #refine_xboxes(QQ[\"x\"](params[1][1]), LBcrit[1])\n", + " #i = 0\n", + " #j = 1\n", + " #break\n", + " elseif i > 1 && sum(npcside[1:2]) != 0\n", + " @assert false \"\\nRefine singular boxes along x-axis\"\n", + " #refine_xboxes(QQ[\"x\"](params[2][1]), LBcrit[2])\n", + " #i -= 1\n", + " #break\n", + " end\n", + " LPCside[i][j] = pcside\n", + " push!(Ltm, time() - tm)\n", + " end\n", + " i += 1\n", + " println(\"\")\n", + "end\n", + "LnPCside = [ [[length(indI) for (L, indI) in PB] for PB in lpcside] for lpcside in LPCside ] \n", + "println(\"Average time for one point: $(mean(Ltm))s\")\n", + "println(\"Elapsed time to compute critical boxes: $(time()-ts)s\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 334, + "metadata": {}, + "outputs": [], + "source": [ + "for j in eachindex(LBcrit[1])\n", + " # If the curve does not intersect the box only on vertical sides or not at all\n", + " if !(LnPCside[1][j][1:2] == [0, 0]) || sum(LnPCside[1][j])==0\n", + " PCside, nPCside = LPCside[1][j], LnPCside[1][j]\n", + " I = [ l[1] for l in PCside[3:end] ]\n", + " nI = [ l[2] for l in PCside[3:end] ]\n", + " # Locate the orientation of the extreme point\n", + " # s is the index on the side where there are more branches\n", + " # s=1: left; s=2: right\n", + " s = argmax([length(I[1]), length(I[2])])\n", + " # Ordinate range of the extreme point\n", + " ycrit = Pcrit[1][j][2]\n", + " # If it intersects on the bottom side\n", + " if nPCside[1] == 1\n", + " # yinf: the intersection with the vertical side just below the extreme point\n", + " yinf = maximum([i for (i, yy) in pairs(I[s]) if yy < ycrit])\n", + " # We vertically enlarge the box until it intersects on the horizontal side\n", + " push!(LPCside[1][j][s + 2][2], yinf)\n", + " LPCside[1][j][1][2] = []\n", + " # We update the intersection numbers\n", + " LnPCside[1][j][s + 2] += 1\n", + " LnPCside[1][j][1] = 0\n", + " end\n", + " # If it intersects on the top side\n", + " if nPCside[2] == 1 \n", + " # ymax: the intersection with the vertical side just above the extreme point\n", + " ymax = minimum([i for (i, yy) in pairs(I[s]) if yy > ycrit])\n", + " # We vertically enlarge the box until it intersects on the horizontal side\n", + " push!(LPCside[1][j][s + 2][2], ymax)\n", + " LPCside[1][j][2][2] = []\n", + " # We update the intersection numbers\n", + " LnPCside[1][j][s + 2] += 1\n", + " LnPCside[1][j][2] = 0\n", + " end\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 340, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Graph computation" + ] + }, + { + "ename": "BoundsError", + "evalue": "BoundsError: attempt to access 0-element Vector{Int64} at index [1]", + "output_type": "error", + "traceback": [ + "BoundsError: attempt to access 0-element Vector{Int64} at index [1]\n", + "\n", + "Stacktrace:\n", + " [1] getindex(A::Vector{Int64}, i1::Int64)\n", + " @ Base ./essentials.jl:13\n", + " [2] top-level scope\n", + " @ ~/Documents/gittravail/curves/main.ipynb:23" + ] + } + ], + "source": [ + "print(\"Graph computation\")\n", + "# Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot\n", + "# And even remove this fiber for the graph\n", + "Vert = []\n", + "Edg = []\n", + "Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ]\n", + "Viso = []\n", + "ite = 1\n", + "\n", + "for ind in 1:length(xcritpermut)\n", + " i, j = xcritpermut[ind]\n", + " if ind > 1\n", + " i1, j1 = xcritpermut[ind - 1]\n", + " end\n", + " if ind < length(xcritpermut)\n", + " i2, j2 = xcritpermut[ind + 1]\n", + " I2L, nI2L = LPCside[i2][j2][2]\n", + " end\n", + "\n", + " PCside, nPCside = LPCside[i][j], LnPCside[i][j]\n", + " I = [ l[1] for l in PCside[3:end] ]\n", + " nI = [ l[2] for l in PCside[3:end] ]\n", + " ymincrit = min(nI[1][1] + nI[1][2] + [length(I[1][1])])\n", + "\n", + " # Construct vertices\n", + " ###########################\n", + " # On the vertical left side\n", + " if ind > 1\n", + " for k in 1:length(I[1][1])\n", + " push!(Corr[i][j][1][1], Corr[i1][j1][3][k])\n", + " end\n", + " else\n", + " for k in 1:length(I[1][1])\n", + " push!(Vert, (xcrit[i][j].lower() - exp, I[1][1][k]))\n", + " push!(Corr[i][j][1][1], ite)\n", + " ite += 1\n", + " end\n", + " end\n", + " ###########################\n", + " # On the vertical right side\n", + " if ind < length(xcritpermut)\n", + " for k in 1:length(I[1][2])\n", + " push!(Vert, ((xcrit[i][j] + xcrit[i2][j2]).lower() / 2 + exp, (I[1][2][k] + I2L[k]).lower() / 2))\n", + " push!(Corr[i][j][3], ite)\n", + " ite += 1\n", + " end\n", + " else\n", + " for k in 1:length(I[1][2])\n", + " push!(Vert, (xcrit[i][j].upper() + exp, I[1][2][k]))\n", + " push!(Corr[i][j][3], ite)\n", + " ite += 1\n", + " end\n", + " end\n", + " ###########################\n", + " # Below the critical point\n", + " for k in 1:ymincrit\n", + " push!(Vert, (xcrit[i][j], (I[1][1][k] + I[1][2][k]) / 2))\n", + " push!(Corr[i][j][2][1], ite)\n", + " push!(Edg, (Corr[i][j][1][1][k], ite)) # left\n", + " push!(Edg, (ite, Corr[i][j][3][k])) # right\n", + " ite += 1\n", + " end\n", + " ###########################\n", + " # The critical point\n", + " ##########################\n", + " # if it is an isolated point\n", + " if isempty(nI[1][1]) && isempty(nI[1][2])\n", + " #pass\n", + " # We can add the isolated vertex\n", + " # push!(Vert, Pcrit[i][j])\n", + " # push!(Corr[i][j][2][1], ite)\n", + " # We will subsequently add the vertex in the graph\n", + " # push!(Viso, ite)\n", + " # ite += 1\n", + " ############################################\n", + " ## TO BE REPLACED BY APPSING IDENTIFICATOR ##\n", + " ## works for space curves without nodes ##\n", + " ############################################\n", + " # If we are dealing with a node\n", + " elseif i == 1\n", + " # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2\n", + " push!(Edg, (Corr[i][j][1][1][nI[1][1][1]], Corr[i][j][3][nI[1][2][2]]))\n", + " push!(Edg, (Corr[i][j][1][1][nI[1][1][2]], Corr[i][j][3][nI[1][2][1]]))\n", + " else\n", + " # We can add the vertex\n", + " push!(Vert, Pcrit[i][j])\n", + " push!(Corr[i][j][2][1], ite)\n", + " # We connect to the vertical left side of the critical box\n", + " for k in nI[1][1]\n", + " push!(Edg, (Corr[i][j][1][1][k], ite))\n", + " end\n", + " # We connect to the vertical right side of the critical box\n", + " for k in nI[1][2]\n", + " push!(Edg, (ite, Corr[i][j][3][k]))\n", + " end\n", + " ite += 1\n", + " end\n", + " ###########################\n", + " # Above the critical point\n", + " for k in length(I[1][1]) - length(nI[1][1]) - ymincrit:-1:1\n", + " push!(Vert, (xcrit[i][j], (I[1][1][end - k + 1] + I[1][2][end - k + 1]) / 2))\n", + " push!(Corr[i][j][2][3], ite)\n", + " push!(Edg, (Corr[i][j][1][1][end - k + 1], ite)) # left\n", + " push!(Edg, (ite, Corr[i][j][3][end - k + 1])) # right\n", + " ite += 1\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 329, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sum(LnPCside[1][1])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.10.1", + "language": "julia", + "name": "julia-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/src/connectcurves/main.jl b/src/connectcurves/main.jl new file mode 100644 index 0000000..6aed3b6 --- /dev/null +++ b/src/connectcurves/main.jl @@ -0,0 +1,155 @@ +println("Loading libraries and data..") +using Oscar +include("data.jl") +include("src/usolve/usolve.jl") +#include("tools.jl") + +#using Arblib + +function order_permut2d(L) + # Create a list of tuples with elements and their corresponding indices + LL = [(L[i][j], (i, j)) for i in eachindex(L) for j in eachindex(L[i])] + # Sort the enumerated list based on the values + sorted_LL = sort(LL, by = x -> x[1]) + # Extract the sorted values and their corresponding indices + sorted_L = [pair[1] for pair in sorted_LL] + sorted_ind = [pair[2] for pair in sorted_LL] + + return sorted_L, sorted_ind +end + +function isolate(f; prec = 32, software="usolve") + if software == "usolve" + return usolve(f, precision = prec, uspath="src/usolve/usolve") + end +end + +function Arb_to_rat(x) + r = radius(x) + return map(simplest_rational_inside, [x-2*r, x+2*r]) +end + +function evaluate_Arb(f, x) + cf = coefficients_of_univariate(f) + return evalpoly(RR(x), cf) +end + +println("Isolating critical values..") +xcrit = [ isolate(first(p), prec=32) for p in params ] +xcrit_usolve = getindex.(xcrit, 1) +xcrit = getindex.(xcrit, 2) +xcritorder, xcritpermut = order_permut2d(xcrit) + +println("Computing isolating critical boxes using Arb..") +#RR(x) = Arb(x, prec=120) +RR = ArbField(120) +Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ] + +LBcrit = [ [ [ pc[1], Arb_to_rat(pc[2]) ] for pc in pcrit] for pcrit in Pcrit ] + +printstep("Graph computation") +# Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot +# And even remove this fiber for the graph +Vert = [] +Edg = [] +Corr = [[[[], [[], [], []], []] for _ in xcrit[i] ] for _ in xcrit ] +Viso = [] +ite = 1 + +for ind in 1:length(xcritpermut) + i, j = xcritpermut[ind] + if ind > 1 + i1, j1 = xcritpermut[ind - 1] + end + if ind < length(xcritpermut) + i2, j2 = xcritpermut[ind + 1] + I2L, nI2L = LPCside[i2][j2][2] + end + + PCside, nPCside = LPCside[i][j], LnPCside[i][j] + I, nI = unzip(PCside[2:end]) + ymincrit = min(nI[1][1] + nI[1][2] + [length(I[1][1])]) + + # Construct vertices + ########################### + # On the vertical left side + if ind > 1 + for k in 1:length(I[1][1]) + push!(Corr[i][j][1][1], Corr[i1][j1][3][k]) + end + else + for k in 1:length(I[1][1]) + push!(Vert, (xcrit[i][j].lower() - exp, I[1][1][k])) + push!(Corr[i][j][1][1], ite) + ite += 1 + end + end + ########################### + # On the vertical right side + if ind < length(xcritpermut) + for k in 1:length(I[1][2]) + push!(Vert, ((xcrit[i][j] + xcrit[i2][j2]).lower() / 2 + exp, (I[1][2][k] + I2L[k]).lower() / 2)) + push!(Corr[i][j][3], ite) + ite += 1 + end + else + for k in 1:length(I[1][2]) + push!(Vert, (xcrit[i][j].upper() + exp, I[1][2][k])) + push!(Corr[i][j][3], ite) + ite += 1 + end + end + ########################### + # Below the critical point + for k in 1:ymincrit + push!(Vert, (xcrit[i][j], (I[1][1][k] + I[1][2][k]) / 2)) + push!(Corr[i][j][2][1], ite) + push!(Edg, (Corr[i][j][1][1][k], ite)) # left + push!(Edg, (ite, Corr[i][j][3][k])) # right + ite += 1 + end + ########################### + # The critical point + ########################## + # if it is an isolated point + if isempty(nI[1][1]) && isempty(nI[1][2]) + #pass + # We can add the isolated vertex + # push!(Vert, Pcrit[i][j]) + # push!(Corr[i][j][2][1], ite) + # We will subsequently add the vertex in the graph + # push!(Viso, ite) + # ite += 1 + ############################################ + ## TO BE REPLACED BY APPSING IDENTIFICATOR ## + ## works for space curves without nodes ## + ############################################ + # If we are dealing with a node + elseif i == 1 + # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 + push!(Edg, (Corr[i][j][1][1][nI[1][1][1]], Corr[i][j][3][nI[1][2][2]])) + push!(Edg, (Corr[i][j][1][1][nI[1][1][2]], Corr[i][j][3][nI[1][2][1]])) + else + # We can add the vertex + push!(Vert, Pcrit[i][j]) + push!(Corr[i][j][2][1], ite) + # We connect to the vertical left side of the critical box + for k in nI[1][1] + push!(Edg, (Corr[i][j][1][1][k], ite)) + end + # We connect to the vertical right side of the critical box + for k in nI[1][2] + push!(Edg, (ite, Corr[i][j][3][k])) + end + ite += 1 + end + ########################### + # Above the critical point + for k in length(I[1][1]) - length(nI[1][1]) - ymincrit:-1:1 + push!(Vert, (xcrit[i][j], (I[1][1][end - k + 1] + I[1][2][end - k + 1]) / 2)) + push!(Corr[i][j][2][3], ite) + push!(Edg, (Corr[i][j][1][1][end - k + 1], ite)) # left + push!(Edg, (ite, Corr[i][j][3][end - k + 1])) # right + ite += 1 + end +end \ No newline at end of file diff --git a/src/connectcurves/src/resultant/Makefile b/src/connectcurves/src/resultant/Makefile new file mode 100644 index 0000000..4711740 --- /dev/null +++ b/src/connectcurves/src/resultant/Makefile @@ -0,0 +1,18 @@ +CC = gcc + +CPP = g++ + +GMP_INC_DIR=. +GMP_LIB_DIR=. + +LIB_PATHS = -L/usr/local/lib/ -L/opt/OpenBLAS/lib +INC_PATHS = -I/usr/local/include -I/opt/OpenBLAS/include + +CFLAGS = -std=c99 -O3 -msse -mavx -Wall -pedantic -funroll-loops --param max-unroll-times=2 -fomit-frame-pointer -fexpensive-optimizations + +LDFLAGS = $(DEBUG) $(LIB_PATHS) -static-libgcc -fopenmp -lgmp -lmpfr -lflint -lm -lopenblas -lpthread +LDFLAGS0 = -Wall $(DEBUG) $(LIB_PATHS) -lgmp -lmpfr -lflint -lm + +flint: + $(CC) -O3 -static main.c -o bresultant $(LDFLAGS) /usr/lib/x86_64-linux-gnu/libmpfr.a /usr/lib/x86_64-linux-gnu/libgmp.a /usr/lib/x86_64-linux-gnu/libflint.a + diff --git a/src/connectcurves/src/resultant/__pycache__/bresultant.cpython-310.pyc b/src/connectcurves/src/resultant/__pycache__/bresultant.cpython-310.pyc new file mode 100644 index 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"", ":" => "", ";" => "") + L = eval(Meta.parse(s)) + close(ff) + return L +end + +function Bresultant(f, g; fname1="/tmp/in.bs", fname2="/tmp/out.bs", bspath="./bresultant", v=0) + ToBresultant(f, g, fname1) + out = run(pipeline(`$bspath -f $fname1 -o $fname2`, stderr="/tmp/err.log.bs")) + if v > 0 + ff = open("/tmp/err.log.bs", "r") + println(read(ff, String)) + close(ff) + end + #if v == 1 + # println(split(stderr(out), '\n')[end - 1] |> x -> split(x, ": ")[end] * "s") + #elseif v == 2 + # println(stderr(out)) + #end + return FromBresultant(fname2) +end + +#using Nemo +#R, (x,y) = Nemo.polynomial_ring(Nemo.ZZ, [:x,:y]) +#f = x^2+4*x+x*y-y^2+3*y-4 +#g = derivative(f,y) diff --git a/src/connectcurves/src/resultant/bresultant.sage b/src/connectcurves/src/resultant/bresultant.sage new file mode 100644 index 0000000..697a10d --- /dev/null +++ b/src/connectcurves/src/resultant/bresultant.sage @@ -0,0 +1,85 @@ +""" +25/02/2023 +""" + +import os +import subprocess + +def PolyToBRstring(f): + fc, fe = f.coefficients(), f.exponents() + s = "{} 2\n".format(len(fc)) + M = [ "{} {} {}".format(fc[i], fe[i][1], fe[i][0]) for i in range(len(fc)) ] + s += "\n".join(M) + return s + +def BRstringToPoly(s): + Ls = s.split("\n") + Ls = [ ls.split(" ") for ls in Ls] + Ls = [ [int(l) for l in ls] for ls in Ls ] + + A. = ZZ[] + F, i = [], 0 + while i = ZZ[] + f = open(foutput,'r') + s = f.read() + s = s.replace("\n","").replace(":","").replace(";","") + L = sage_eval(s, locals={'x': x, 'y': y}) + return L + +def Bresultant(f, g, fname1="/tmp/in.bs", fname2="/tmp/out.bs", bspath="./bresultant", v=0): + ToBresultant(f, g, fname1) + out = subprocess.run([bspath, "-f", fname1, "-o", fname2], capture_output=True,text=True) + if v==1: + print((out.stderr).split('\n')[-2].split(': ')[-1]+'s') + if v==2: + print(out.stderr) + return FromBresultant(fname2) + +#A. = ZZ[] +#f=A.random_element() +#g=diff(f,y) +#Bresultant(f,g,v=2) +#FromBresultant("p") diff --git a/src/connectcurves/src/resultant/data.c b/src/connectcurves/src/resultant/data.c new file mode 100644 index 0000000..2cd5744 --- /dev/null +++ b/src/connectcurves/src/resultant/data.c @@ -0,0 +1,387 @@ +#include "data.h" + +//alloue ce qu'il faut, connaissant le degree deg de la param. +static fmpz_param_t *allocate_degree_sepelem_fmpz_param(ulong deg, + mp_ptr sepelem, + int nvars){ + fmpz_param_t *param = malloc(sizeof(fmpz_param_t)); + + param->recons = 0; + param->nvars = nvars; + param->degree = deg; + param->sepelem = sepelem; + param->coords = malloc(sizeof(fmpz_poly_t) * param->nvars); + param->coords_num = malloc(sizeof(fmpz_poly_t) * param->nvars); + param->coords_den = malloc(sizeof(fmpz_poly_t) * param->nvars); + param->coords_lcm = malloc(sizeof(fmpz_t) * param->nvars); + for(ulong i = 0; i < param->nvars; i++){ + fmpz_poly_init2(param->coords[i], deg); + fmpz_poly_init2(param->coords_num[i], deg); + fmpz_poly_init2(param->coords_den[i], deg); + fmpz_init(param->coords_lcm[i]); + fmpz_one(param->coords_lcm[i]); + for(ulong j = 0; j < deg; j++){ + fmpz_poly_set_coeff_ui(param->coords[i], j, 1); + fmpz_poly_set_coeff_ui(param->coords_num[i], j, 1); + fmpz_poly_set_coeff_ui(param->coords_den[i], j, 1); + } + } + + fmpz_poly_init2(param->denom, deg + 1); + fmpz_poly_init2(param->elim, deg + 1); + + fmpz_poly_init2(param->elim_num, deg + 1); + fmpz_poly_init2(param->denom_num, deg + 1); + + fmpz_poly_init2(param->elim_den, deg + 1); + fmpz_poly_init2(param->denom_den, deg + 1); + + fmpz_init(param->elim_lcm); + fmpz_init(param->denom_lcm); + + fmpz_one(param->elim_lcm); + fmpz_one(param->denom_lcm); + + for(ulong j = 0; j <= deg; j++){ + fmpz_poly_set_coeff_ui(param->denom, j, 1); + fmpz_poly_set_coeff_ui(param->elim, j, 1); + + fmpz_poly_set_coeff_ui(param->denom_num, j, 1); + fmpz_poly_set_coeff_ui(param->elim_num, j, 1); + + fmpz_poly_set_coeff_ui(param->denom_den, j, 1); + fmpz_poly_set_coeff_ui(param->elim_den, j, 1); + } + param->rec_elim = 0; + param->rec_denom = 0; + param->rec_coords = malloc(sizeof(ulong)*nvars); + for(int i = 0; i < nvars; i++){ + param->rec_coords[i] = 0; + } + return param; +} + + +static void allocate_degrees_sepelem_fmpz_all_params(fmpz_all_params_t * fmpz_all_params, + data_heap_t *heap, + mp_ptr sepelem, + int nb_params, int nvars){ + + fmpz_all_params->nparams = nb_params; + fmpz_all_params->params = malloc(sizeof(fmpz_param_t *) * fmpz_all_params->nparams); + for(int i = 0; i < fmpz_all_params->nparams; i++){ + fmpz_all_params->params[i] = + allocate_degree_sepelem_fmpz_param((heap->sqf_part->p + i)->length - 1, sepelem, nvars); + } + +} + + +static nmod_param_t *allocate_nmod_param(int nvars, mp_limb_t prime){ + nmod_param_t *param = malloc(sizeof(nmod_param_t)); + param->nvars = nvars; + param->degree = 0; + param->sepelem = NULL; + param->coords = malloc(sizeof(nmod_poly_t) * param->nvars); + for(int i = 0; i < param->nvars; i++){ + nmod_poly_init(param->coords[i], prime); + } + nmod_poly_init(param->denom, prime); + nmod_poly_init(param->elim, prime); + + return param; +} + +static nmod_param_t *allocate_degree_sepelem_nmod_param(ulong deg, mp_ptr sepelem, + int nvars, mp_limb_t prime){ + nmod_param_t *param = malloc(sizeof(nmod_param_t)); + param->nvars = nvars; + param->degree = deg; + param->sepelem = sepelem; + param->coords = malloc(sizeof(nmod_poly_t) * param->nvars); + for(int i = 0; i < param->nvars; i++){ + nmod_poly_init2(param->coords[i], prime, deg); + } + nmod_poly_init2(param->denom, prime, deg); + nmod_poly_init2(param->elim, prime, deg + 1); + + return param; +} + + +static nmod_all_params_t *allocate_nmod_all_params(int nb_params, int nvars, + mp_limb_t prime){ + nmod_all_params_t *nmod_all_params = malloc(sizeof(nmod_all_params_t)); + nmod_all_params->nparams = nb_params; + nmod_all_params->params = malloc(sizeof(nmod_param_t *) * nmod_all_params->nparams); + for(int i = 0; i < nmod_all_params->nparams; i++){ + nmod_all_params->params[i] = allocate_nmod_param(nvars, prime); + } + return nmod_all_params; +} + +static nmod_all_params_t *allocate_degrees_sepelem_nmod_all_params(data_heap_t *heap, + mp_ptr sepelem, + int nb_params, int nvars, + mp_limb_t prime){ + nmod_all_params_t *nmod_all_params = malloc(sizeof(nmod_all_params_t)); + nmod_all_params->nparams = nb_params; + nmod_all_params->params = malloc(sizeof(nmod_param_t *) * nmod_all_params->nparams); + for(int i = 0; i < nmod_all_params->nparams; i++){ + nmod_all_params->params[i] = + allocate_degree_sepelem_nmod_param((heap->sqf_part->p+i)->length - 1, + sepelem, + nvars, prime); + } + return nmod_all_params; +} + +static void free_bsolve_fmpz_param(bsolve_fmpz_param_t *param){ + fmpz_poly_clear(param->elim); + fmpz_poly_clear(param->denom); + for(int i = 0; i < param->nvars; i++){ + fmpz_poly_clear(param->coords[i]); + fmpz_clear(param->cfs[i]); + } + free(param->sepelem); + free(param->coords); + free(param->cfs); + free(param); +} + +static void free_bsolve_fmpz_all_params(bsolve_fmpz_all_params_t *allpars){ + for(int i = 0; i < allpars->nparams; i++ ){ + free_bsolve_fmpz_param(allpars->params[i]); + } + free(allpars); +} + +static void free_nmod_param(nmod_param_t *param){ + for(int i = 0; i < param->nvars; i++){ + nmod_poly_clear(param->coords[i]); + } + nmod_poly_clear(param->denom); + nmod_poly_clear(param->elim); + + free(param); +} + +static void free_nmod_all_params(nmod_all_params_t *nmod_all_params){ + for(int i = 0; i < nmod_all_params->nparams; i++){ + free_nmod_param(nmod_all_params->params[i]); + } + free(nmod_all_params); +} + +static void free_fmpz_param(fmpz_param_t *param){ + for(int i = 0; i < param->nvars; i++){ + fmpz_poly_clear(param->coords[i]); + } + fmpz_poly_clear(param->denom); + fmpz_poly_clear(param->elim); + free(param->rec_coords); + free(param); +} + +static void free_fmpz_all_params(fmpz_all_params_t *fmpz_all_params){ + for(int i = 0; i < fmpz_all_params->nparams; i++){ + free_fmpz_param(fmpz_all_params->params[i]); + } + free(fmpz_all_params); +} + +/* + + tdeg = total degree + mdeg = main degree + sdeg = degree in the other variable + +*/ +static data_heap_t *allocate_data_heap(slong tdegA, slong tdegB, + slong mdegA, slong mdegB, + slong sdegA, slong sdegB, + int size_mod_array){ + if(mdegA < mdegB){ + fprintf(stderr, "Bad call to allocator (error in degrees)\n"); + exit(1); + } + + data_heap_t * heap_bsolve = (data_heap_t *)(malloc(sizeof(data_heap_t))); + heap_bsolve->size_mod_array = size_mod_array; + heap_bsolve->nmod_coeffs_array = _nmod_vec_init(3 * (mdegA + 1)); + + heap_bsolve->npts = MIN(tdegA * tdegB + 1, mdegB * sdegA + mdegA * sdegB + 1); + + heap_bsolve->primes_array = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_mod_array)); + + mp_limb_t prime = n_nextprime(1152921504606847009, 0); + heap_bsolve->a_mod_eval_all = malloc(sizeof(mp_ptr) * (mdegA + 1)); + for(ulong i = 0; i<=mdegA; i++){ + heap_bsolve->a_mod_eval_all[i] = malloc(sizeof(mp_limb_t) * heap_bsolve->npts); + } + + heap_bsolve->b_mod_eval_all = malloc(sizeof(mp_ptr) * (mdegB + 1)); + for(ulong i = 0; i<=mdegB; i++){ + heap_bsolve->b_mod_eval_all[i] = malloc(sizeof(mp_limb_t) * heap_bsolve->npts); + } + + + nmod_poly_init2(heap_bsolve->a_mod_eval, prime, mdegA + 1); + heap_bsolve->a_mod_eval->length = mdegA + 1; + nmod_poly_init2(heap_bsolve->b_mod_eval, prime, mdegB + 1); + heap_bsolve->b_mod_eval->length = mdegB + 1; + + heap_bsolve->res_mod_eval = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * 2 * heap_bsolve->npts)); + heap_bsolve->ev_pts = heap_bsolve->res_mod_eval + heap_bsolve->npts; + + heap_bsolve->par_h_mod_eval = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * 2 * heap_bsolve->npts)); + heap_bsolve->par_t_mod_eval = heap_bsolve->par_h_mod_eval + heap_bsolve->npts; + + heap_bsolve->tree = _nmod_poly_tree_alloc(heap_bsolve->npts); + + heap_bsolve->a_mod = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * (mdegA + 1 + mdegB + 1))); + heap_bsolve->b_mod = heap_bsolve->a_mod + mdegA + 1; + + for(ulong i = 0; i <= mdegA; i++){ + nmod_poly_init(heap_bsolve->a_mod[i], prime); + } + for(ulong i = 0; i <= mdegB; i++){ + nmod_poly_init(heap_bsolve->b_mod[i], prime); + } + heap_bsolve->res_mod_array = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * ( 1 + size_mod_array ))); + for(ulong i = 0; i <= size_mod_array; i++){ + nmod_poly_init(heap_bsolve->res_mod_array[i], prime); + } + heap_bsolve->res_mod = heap_bsolve->res_mod_array + size_mod_array; + + heap_bsolve->res_mod_prime_array = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * ( size_mod_array ))); + for(ulong i = 0; i < size_mod_array; i++){ + nmod_poly_init(heap_bsolve->res_mod_prime_array[i], prime); + } + + heap_bsolve->par_h_mod_array = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * ( size_mod_array ))); + for(ulong i = 0; i < size_mod_array; i++){ + nmod_poly_init(heap_bsolve->par_h_mod_array[i], prime); + } + + heap_bsolve->par_t_mod_array = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * ( size_mod_array ))); + for(ulong i = 0; i < size_mod_array; i++){ + nmod_poly_init(heap_bsolve->par_t_mod_array[i], prime); + } + + heap_bsolve->GCDINV = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * ( size_mod_array ))); + for(ulong i = 0; i < size_mod_array; i++){ + nmod_poly_init(heap_bsolve->GCDINV[i], prime); + } + + heap_bsolve->prod_primes = (fmpz_t *)(malloc(sizeof(fmpz_t)*(size_mod_array + 1))); + + for(int i = 0; i <= size_mod_array; i++){ + fmpz_init(heap_bsolve->prod_primes[i]); + fmpz_one(heap_bsolve->prod_primes[i]); + } + + nmod_poly_factor_init(heap_bsolve->sqf_part); + + heap_bsolve->nmod_lparams_array = malloc(sizeof(nmod_all_params_t *) * size_mod_array); + for(int i = 0; i < size_mod_array; i++){ + heap_bsolve->nmod_lparams_array[i] = allocate_nmod_all_params(1, 2, prime); + } + + heap_bsolve->coef = malloc(sizeof(mpz_rat_t)); + fmpz_init(heap_bsolve->coef->numer); + fmpz_init(heap_bsolve->coef->denom); + + fmpz_init(heap_bsolve->h_prod); + + fmpz_init(heap_bsolve->lcm); + fmpz_one(heap_bsolve->lcm); + + heap_bsolve->prod_mod = malloc(sizeof(fmpz_t)); + fmpz_init(heap_bsolve->prod_mod[0]); + //allocation si besoin dans la fonction de calcul de parametrisation + //square-free (quand le resultant ne l'est pas) + return heap_bsolve; +} + + +static void free_data_heap(slong mdegA, slong mdegB, + int size_mod_array, data_heap_t *heap_bsolve){ + + _nmod_vec_clear(heap_bsolve->nmod_coeffs_array); + nmod_poly_factor_clear(heap_bsolve->sqf_part); + _nmod_poly_tree_free(heap_bsolve->tree, heap_bsolve->npts); + + free(heap_bsolve->primes_array); + + for(ulong i = 0; i<=mdegA; i++){ + free(heap_bsolve->a_mod_eval_all[i]); + } + free(heap_bsolve->a_mod_eval_all); + + for(ulong i = 0; i<=mdegB; i++){ + free(heap_bsolve->b_mod_eval_all[i]); + } + free(heap_bsolve->b_mod_eval_all); + + nmod_poly_clear(heap_bsolve->a_mod_eval); + nmod_poly_clear(heap_bsolve->b_mod_eval); + + free(heap_bsolve->res_mod_eval); + free(heap_bsolve->par_h_mod_eval); + + for(ulong i = 0; i <= mdegA; i++){ + nmod_poly_clear(heap_bsolve->a_mod[i]); + } + for(ulong i = 0; i <= mdegB; i++){ + nmod_poly_clear(heap_bsolve->b_mod[i]); + } + free(heap_bsolve->a_mod); + + for(ulong i = 0; i <= size_mod_array; i++){ + nmod_poly_clear(heap_bsolve->res_mod_array[i]); + } + free(heap_bsolve->res_mod_array); + + for(ulong i = 0; i < size_mod_array; i++){ + nmod_poly_clear(heap_bsolve->res_mod_prime_array[i]); + } + free(heap_bsolve->res_mod_prime_array); + + for(ulong i = 0; i < size_mod_array; i++){ + nmod_poly_clear(heap_bsolve->par_h_mod_array[i]); + } + free(heap_bsolve->par_h_mod_array); + + for(ulong i = 0; i < size_mod_array; i++){ + nmod_poly_clear(heap_bsolve->par_t_mod_array[i]); + } + free(heap_bsolve->par_t_mod_array); + + for(ulong i = 0; i < size_mod_array; i++){ + nmod_poly_clear(heap_bsolve->GCDINV[i]); + } + free(heap_bsolve->GCDINV); + + for(int i = 0; i <= size_mod_array; i++){ + fmpz_clear(heap_bsolve->prod_primes[i]); + } + + fmpz_clear(heap_bsolve->coef->numer); + fmpz_clear(heap_bsolve->coef->denom); + free(heap_bsolve->coef); + + fmpz_clear(heap_bsolve->h_prod); + fmpz_clear(heap_bsolve->lcm); + fmpz_clear(heap_bsolve->prod_mod[0]); + free(heap_bsolve->prod_mod); + + //attention : ecrire une fonction speciale pour desallouer ces zones car elles + //ne sont allouees que quand c'est necessaire (resultant non square-free et + //calcul de parametrisation) + + /* for(int i = 0; i < size_mod_array; i++){ */ + /* free_nmod_all_params(heap_bsolve->nmod_lparams_array[i]); */ + /* } */ + free(heap_bsolve->nmod_lparams_array); +} diff --git a/src/connectcurves/src/resultant/data.h b/src/connectcurves/src/resultant/data.h new file mode 100644 index 0000000..70fba5a --- /dev/null +++ b/src/connectcurves/src/resultant/data.h @@ -0,0 +1,150 @@ +typedef struct{ + fmpz_t numer; + fmpz_t denom; +} mpz_rat_t; + + +typedef struct{ + int nvars; + mp_ptr sepelem; + fmpz_poly_t * coords; + fmpz_poly_t denom; + fmpz_poly_t elim; + fmpz_t *cfs; +} bsolve_fmpz_param_t; + + +typedef struct{ + int nparams; + bsolve_fmpz_param_t **params; +} bsolve_fmpz_all_params_t; + +typedef struct{ + int recons; + int nvars; + int degree; + mp_ptr sepelem; + fmpz_poly_t * coords; // numerateurs des parametrisations + fmpz_poly_t denom; //denominateur + fmpz_poly_t elim; //polynome eliminant + fmpz_poly_t * coords_num; // numerateurs des parametrisations + fmpz_poly_t denom_num; //denominateur + fmpz_poly_t elim_num; //polynome eliminant + fmpz_poly_t * coords_den; // numerateurs des parametrisations + fmpz_poly_t denom_den; //denominateur + fmpz_poly_t elim_den; //polynome eliminant + fmpz_t * coords_lcm; // numerateurs des parametrisations + fmpz_t denom_lcm; //denominateur + fmpz_t elim_lcm; //polynome eliminant + ulong *rec_coords; + ulong rec_denom; + ulong rec_elim; +} fmpz_param_t; + + +typedef struct{ + int nvars; //nvars est le nbre de variables initiales. + ulong degree; // degre de la parametrisation + mp_ptr sepelem; + nmod_poly_t * coords; // numerateurs des parametrisations + //on en a autant que de coordonnees initiales + nmod_poly_t denom; // polynome denomninateur + nmod_poly_t elim; // polynome eliminant +} nmod_param_t; +// donc au total on a exactement nvars + 1 polynomes + + +typedef struct{ + int nparams; // nombre de parametrisations + fmpz_param_t **params; // tableau de parametrisations +} fmpz_all_params_t; + + +typedef struct{ + int nparams; + nmod_param_t **params; +} nmod_all_params_t; + + +typedef struct{ + int verb ; + int task ; // 0 -> parametrisation + // 1 -> square-free resultant + // 2 -> resultant + int binary ; // 1 -> output file in binary format + char *input_file ; + char *output_file ; +} bsolve_flags; + +/* + + Zone memoire pour donnees intermediaires. + + Le but est de calculer le resultant de A et B qui sont des polynomes bivaries. + (ou bien de calculer une parametrisation rationnelle des solutions) + +*/ +typedef struct +{ + ulong size_mod_array; + mp_ptr nmod_coeffs_array; // tableau pour suite des restes euclidiens + ulong npts; // nbre de points pour l'evaluation interpolation + + mp_ptr primes_array; // tableau de premiers utilises pour les calculs + // multi-modulaires + mp_ptr ev_pts; // tableau contenant les points d'evaluation utilises pour + // l'interpolation + mp_ptr *tree; // arbre pour l'evaluation rapide multi-point + mp_ptr *a_mod_eval_all; // tableau qui recevra les coeffs de A mod prime + // dont on a specialise une variable aux entrees + // de ev_pts + mp_ptr *b_mod_eval_all; // tableau qui recevra les coeffs de B mod prime + // dont on a specialise une variable aux entrees + // de ev_pts + nmod_poly_t a_mod_eval; // evaluation de a_mod + nmod_poly_t b_mod_eval; // evaluation de b_mod + + nmod_poly_t * a_mod; // image modulare de A + nmod_poly_t * b_mod; // image modulaire de B + + + mp_ptr res_mod_eval; // tableau recevant les specialisations du resultant de + // A mod prime et B mod prime + + nmod_poly_t * res_mod_array; // tableau contenant les images modulaires du resultant + nmod_poly_t * res_mod_prime_array; // tableau contenant les images modulaires + // de la derivee du resultant + nmod_poly_t * res_mod; // tableau contenant une image modulaire du resultant ; + // sera utilise pour verifier qu'on a fini le calcul + + // la longueur de ces tableaux est la meme que celle de res_mod_eval + mp_ptr par_h_mod_eval; // tableau recevant les coeffs dominants de + // sous-resultants (univaries) de degre 1 + // ici on a evalue une variable + mp_ptr par_t_mod_eval; // tableau recevant les coeffs constants de + // sous-resultants (univaries) de degre 1 + // ici on a evalue une variable + + nmod_poly_t * par_h_mod_array; // tableau contenant les images modulaires du + // coeff dominant du sous-resultant de degre 1 + nmod_poly_t * par_t_mod_array; // tableau contenant les images modulaires du + // coeff constant du sous-resultant de degre 1 + + nmod_poly_t * GCDINV; // quand le GCD du coeff de dom. du + // sous-resultant de degre 1 avec le resultant est = 1 on inverse le coeff + // dominant modulo le resultant + + nmod_all_params_t **nmod_lparams_array; //tableau contenant des images + //modulaires des parametrisations + + fmpz_t *prod_primes; // contiendra des produits de nbre premiers + nmod_poly_factor_t sqf_part; // contiendra la partie square-free + + //data pour les reconstructions. + fmpz_t *prod_mod; + mpz_rat_t *coef; + fmpz_t h_prod; + fmpz_t lcm; + fmpz_t *coef_num_array; + fmpz_t *coef_den_array; +} data_heap_t; diff --git a/src/connectcurves/src/resultant/flint_euclide.c b/src/connectcurves/src/resultant/flint_euclide.c new file mode 100644 index 0000000..df86f74 --- /dev/null +++ b/src/connectcurves/src/resultant/flint_euclide.c @@ -0,0 +1,355 @@ +/* + Functions below are very slight modifications of FLINT file + resultant_euclidean.c which is part of FLINT. + + Copyright (C) 2007, 2008 William Hart + Copyright (C) 2011 Sebastian Pancratz + FLINT is free software: you can redistribute it and/or modify it under + the terms of the GNU Lesser General Public License (LGPL) as published + by the Free Software Foundation; either version 2.1 of the License, or + (at your option) any later version. See . +*/ + +//taken from FLINT +#define MYMPN_NORM(a, an) \ + do { \ + while ((an) != 0 && (a)[(an) - 1] == 0) \ + (an)--; \ + } while (0) + +static void _my_nmod_vec_scalar_mul_nmod_large(mp_ptr res, mp_srcptr vec, + slong len, mp_limb_t c, nmod_t mod){ + for (slong i = 0; i < len; i++) + { + mp_limb_t hi, lo; + umul_ppmm(hi, lo, vec[i], c); + NMOD_RED2(res[i], hi, lo, mod); /* hi already reduced mod n */ + } +} + + +static void _my_nmod_poly_rem_q1(mp_ptr R, + mp_srcptr A, slong lenA, mp_srcptr B, slong lenB, + nmod_t mod) +{ + const mp_limb_t invL = (B[lenB-1] == 1) ? 1 : n_invmod(B[lenB-1], mod.n); + + if (lenB > 1) + { + mp_limb_t t, q0, q1; + + q1 = n_mulmod2_preinv(A[lenA-1], invL, mod.n, mod.ninv); + t = n_mulmod2_preinv(q1, B[lenB-2], mod.n, mod.ninv); + t = n_submod(A[lenA-2], t, mod.n); + q0 = n_mulmod2_preinv(t, invL, mod.n, mod.ninv); + + if (FLINT_BITS + 2 <= 2 * mod.norm) + { + mpn_mul_1(R, B, lenB - 1, q0); + if (lenB > 2) + mpn_addmul_1(R + 1, B, lenB - 2, q1); + _nmod_vec_reduce(R, R, lenB - 1, mod); + } + else + { + _my_nmod_vec_scalar_mul_nmod_large(R, B, lenB - 1, q0, mod); + if (lenB > 2) + _nmod_vec_scalar_addmul_nmod(R + 1, B, lenB - 2, q1, mod); + } + + _nmod_vec_sub(R, A, R, lenB - 1, mod); + } +} + +static void _my_nmod_poly_rem(mp_ptr R, mp_srcptr A, slong lenA, + mp_srcptr B, slong lenB, nmod_t mod) +{ + TMP_INIT; + + if (lenA - lenB == 1) + { + _my_nmod_poly_rem_q1(R, A, lenA, B, lenB, mod); + } + else if (lenA < FMPZ_POLY_SQRTREM_DIVCONQUER_CUTOFF) + { + mp_ptr W; + + TMP_START; + W = TMP_ALLOC(NMOD_DIVREM_BC_ITCH(lenA, lenB, mod)*sizeof(mp_limb_t)); + + _nmod_poly_rem_basecase(R, W, A, lenA, B, lenB, mod); + TMP_END; + } + else + { + mp_ptr Q = _nmod_vec_init(lenA - lenB + 1); + + _nmod_poly_divrem(Q, R, A, lenA, B, lenB, mod); + _nmod_vec_clear(Q); + } +} + +//Les coefficients sont ranges dans le tableau par degres croissants. +//dans param on se retrouvera avec les coefficients de la parametrisation +//attention si il n'y a pas de polynome de degre 1 dans la suite des sous-resultants +//le contenu de param reste inchange (c'est pour ca qu'il faut l'initialiser a 0) +static mp_limb_t +_nmod_poly_param_euclidean_allocated(mp_srcptr poly1, slong len1, + mp_srcptr poly2, slong len2, + nmod_t mod, mp_ptr w, + mp_ptr head, + mp_ptr tail) +{ + if(DEBUG>3){ + fprintf(stderr, "lengths = [%ld, %ld], prime = %ld\n", len1, len2, mod.n); + } + if (poly1 == poly2) + { + return 0; + } + else if (len2 == 1) + { + if (len1 == 1) + { + return 1; + } + else if (len1 == 2) + { + head[0] = poly1[1]; + tail[0] = poly1[0]; + return poly2[0]; + } + else + { + return n_powmod2_ui_preinv(poly2[0], len1 - 1, mod.n, mod.ninv); + } + } + else{ /* len1 >= len2 >= 2 */ + if(len2 == 2){ + head[0] = poly2[1]; + tail[0] = poly2[0]; + } + mp_limb_t res = 1; + + mp_ptr u, v, r, t; + slong l0, l1, l2; + mp_limb_t lc; + + u = w; + v = w + len1; + r = v + len1; + //u == poly1 + _nmod_vec_set(u, poly1, len1); + //v == poly2 + _nmod_vec_set(v, poly2, len2); + l1 = len1; + l2 = len2; + + if(DEBUG>5){ + fprintf(stderr, "Affichage de u\n"); + nmod_vec_print(stderr, u, len1); + fprintf(stderr, "Affichage de v\n"); + nmod_vec_print(stderr, v, len2); + } + + do + { + l0 = l1; + l1 = l2; + //coefficient dominant de v + lc = v[l1 - 1]; + + if(DEBUG>5){ + fprintf(stderr, "u = "); + nmod_vec_print(stderr, u, l0); + fprintf(stderr, "v = "); + nmod_vec_print(stderr, v, l1); + } + //u est de longueur l0, v est de longueur l1 + //r = remainder(u, v) + _my_nmod_poly_rem(r, u, l0, v, l1, mod); + // _nmod_poly_rem(r, u, l0, v, l1, mod); + l2 = l1 - 1; + //determine la longueur de r (decremente l2 tant que le top coeff == 0) + //r est de degre l2 - 1 + MYMPN_NORM(r, l2); + if(DEBUG>5){ + fprintf(stderr, "r = "); + nmod_vec_print(stderr, r, l2); + fprintf(stderr, "l0 = %ld\n", l0); + fprintf(stderr, "l1 = %ld\n", l1); + fprintf(stderr, "l2 = %ld\n", l2); + fprintf(stderr, "lc = %ld\n", lc); + fprintf(stderr, "res = %ld\n", res); + } + //mise a jour + { + t = u; + u = v; + v = r; + r = t; + } + if (l2 >= 1){ + lc = n_powmod2_preinv(lc, l0 - l2, mod.n, mod.ninv); + res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); + + if (((l0 | l1) & 1) == 0) + { + if(DEBUG>5){ + fprintf(stderr, "[%ld, %ld] ", l0, l1); + } + res = nmod_neg(res, mod); + } + if(l2==2){ /* degree of the remainder -- which is now stored in v -- is 1 */ + mp_limb_t hi, lo; //, c; + umul_ppmm(hi, lo, v[0], res); + NMOD_RED2(tail[0], hi, lo, mod); /* hi already reduced mod n */ + hi = 0; lo = 0; + umul_ppmm(hi, lo, v[1], res); + NMOD_RED2(head[0], hi, lo, mod); /* hi already reduced mod n */ + } + if(l2==1){/* degree of the remainder -- which is now stored in v -- is 0 */ + /* head[0] = u[1]; */ + /* tail[0] = u[0]; */ + /* fprintf(stderr, "--> head = %ld\n", head[0]); */ + /* fprintf(stderr, "--> tail = %ld\n", tail[0]); */ + } + } + else /* l2 == 0 */ + { + if (l1 == 1) + { + lc = n_powmod2_preinv(lc, l0 - 1, mod.n, mod.ninv); + res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); + /* head[0] = u[1]; */ + /* tail[0] = u[0]; */ + } + else + { + if(l1==2){ + fprintf(stderr, "l1 == 2 et lc = %ld\n", lc); + lc = n_powmod2_preinv(lc, l0 - 1, mod.n, mod.ninv); + fprintf(stderr, "et maintenant lc = %ld\n", lc); + res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); + fprintf(stderr, "et res = %ld\n", res); + head[0] = u[1]; + tail[0] = u[0]; + /* mp_limb_t hi, lo; //, c; */ + /* umul_ppmm(hi, lo, u[0], res); */ + /* NMOD_RED2(tail[0], hi, lo, mod); /\* hi already reduced mod n *\/ */ + /* hi = 0; lo = 0; */ + /* umul_ppmm(hi, lo, u[1], res); */ + /* NMOD_RED2(head[0], hi, lo, mod); /\* hi already reduced mod n *\/ */ + } + else{ + head[0] = 0; + tail[0] = 0; + } + res = 0; + } + } + } + while (l2 > 0); + + return res; + } +} + + +//Les coefficients sont ranges dans le tableau par degre croissant. +static mp_limb_t +_nmod_poly_resultant_euclidean_allocated(mp_srcptr poly1, slong len1, + mp_srcptr poly2, slong len2, nmod_t mod, mp_ptr w) +{ + if (poly1 == poly2) + { + return 0; + } + else if (len2 == 1) + { + if (len1 == 1) + { + return 1; + } + else if (len1 == 2) + { + return poly2[0]; + } + else + { + return n_powmod2_ui_preinv(poly2[0], len1 - 1, mod.n, mod.ninv); + } + } + else /* len1 >= len2 >= 2 */ + { + mp_limb_t res = 1; + + mp_ptr u, v, r, t; + slong l0, l1, l2; + mp_limb_t lc; + + u = w; + v = w + len1; + r = v + len1; + //u == poly1 + _nmod_vec_set(u, poly1, len1); + //v == poly2 + _nmod_vec_set(v, poly2, len2); + l1 = len1; + l2 = len2; + + do + { + l0 = l1; + l1 = l2; + //coefficient dominant de v + lc = v[l1 - 1]; + + //u est de longueur l0, v est de longueur l1 + //r = remainder(u, v) + _my_nmod_poly_rem(r, u, l0, v, l1, mod); + l2 = l1 - 1; + //determine la longueur de r (decremente l2 tant que le top coeff == 0) + //r est de degre l2 - 1 + MYMPN_NORM(r, l2); + //mise a jour + { + t = u; + u = v; + v = r; + r = t; + } + + if (l2 >= 1) + { + lc = n_powmod2_preinv(lc, l0 - l2, mod.n, mod.ninv); + res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); + + if (((l0 | l1) & 1) == 0) + { + res = nmod_neg(res, mod); + } + } + else + { + if (l1 == 1) + { + lc = n_powmod2_preinv(lc, l0 - 1, mod.n, mod.ninv); + res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); + } + else + { + res = 0; + } + } + } + while (l2 > 0); + + return res; + } +} + + +/* + END OF FLINT modified resultant_euclidean.c + */ diff --git a/src/connectcurves/src/resultant/flint_resultant.c b/src/connectcurves/src/resultant/flint_resultant.c new file mode 100644 index 0000000..ba9535c --- /dev/null +++ b/src/connectcurves/src/resultant/flint_resultant.c @@ -0,0 +1,1285 @@ +/** +Author: Mohab Safey El Din + + + + **/ + +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include "flint/flint.h" +#include "flint/ulong_extras.h" +#include "flint/fmpz.h" +#include "flint/fmpz_poly.h" +#include "flint/nmod_poly.h" + +#define LOG2(X) ((unsigned) (8*sizeof (unsigned long long) - __builtin_clzll((X)) - 1)) + +#define MPN_NORM(a, an) \ + do { \ + while ((an) != 0 && (a)[(an) - 1] == 0) \ + (an)--; \ + } while (0) + + +void fmpz_poly_random_dense(fmpz_poly_t pol, slong deg, mp_bitcnt_t bits, flint_rand_t state){ + + fmpz_t coeff; + fmpz_init(coeff); + + // flint_randseed(state, (ulong) time(NULL), (ulong) clock()); + + long i; + flint_randseed(state, (ulong) clock(), (ulong)(10000*clock())); + + for(i=0;i<=deg;i++){ + fmpz_randbits(coeff, state, bits); + fmpz_poly_set_coeff_fmpz(pol, i, coeff); + flint_randseed(state, (ulong) (i), (ulong)(10000*clock()*(i+1))); + } + fmpz_clear(coeff); +} + +void fmpz_poly_random_dense_old(fmpz_poly_t pol, slong deg, mp_bitcnt_t bits){ + + fmpz_t coeff; + fmpz_init(coeff); + + flint_rand_t state; + flint_randinit(state); + // flint_randseed(state, (ulong) time(NULL), (ulong) clock()); + + long i; + + for(i=0;i<=deg;i++){ + fmpz_randbits(coeff, state, bits); + fmpz_poly_set_coeff_fmpz(pol, i, coeff); + // flint_randseed(state, (ulong) (i), (ulong)(10000*time(NULL)*(i+1))); + } + fmpz_clear(coeff); +} + +void make_mod_poly(nmod_poly_t a_mod, fmpz_poly_t A, mp_limb_t prime){ + for(unsigned long int i=0; ilength; i++){ + nmod_poly_set_coeff_ui(a_mod, i, fmpz_fdiv_ui(A->coeffs+i, prime)); + } +} + + +void run_res_flint(unsigned long int deg, flint_rand_t state){ + + unsigned long int newdeg = deg; + + puts("FLINT resultant functions (nbits = deg / 2)"); + + while(newdeg<=8090){ + unsigned long int deg1 = newdeg, deg2 = deg1; + unsigned int nbits = deg1 / 2; + + fmpz_poly_t A, B; + fmpz_poly_init2(A, deg1+1); + fmpz_poly_init2(B, deg2+1); + fmpz_poly_random_dense(A, deg1, nbits, state); + fmpz_poly_random_dense(B, deg2, nbits, state); + + fmpz_t res_normal; + fmpz_init(res_normal); + + double e_normal = 0, t; + t = omp_get_wtime(); + fmpz_poly_resultant(res_normal, A, B); + e_normal = omp_get_wtime() - t; + + fprintf(stdout, "Degree: %lu\n", newdeg); + fprintf(stdout, "Elapsed time (normal): %f\n\n", e_normal); + + if(fmpz_cmp_ui(res_normal, 0)==0){ + puts("Resultant was 0\n"); + } + newdeg = 2*newdeg; + + fmpz_poly_clear(A); + fmpz_poly_clear(B); + + } +} + +void myresultantold(fmpz_t res, fmpz_poly_t A, fmpz_poly_t B, int nthreads){ + + mp_limb_t myprime; + + unsigned long bound ; //= (deg1+deg2) * nbits + 2 * LOG2( (deg1 + deg2) ) ; + bound = (A->length + B->length - 1)*FLINT_BIT_COUNT((10*(A->length + B->length - 1) + 26)/27) + 3; + + mp_bitcnt_t bits1 = FLINT_ABS(_fmpz_vec_max_bits(A->coeffs, A->length)); + mp_bitcnt_t bits2 = FLINT_ABS(_fmpz_vec_max_bits(B->coeffs, B->length)); + + /* Upper bound Hadamard bound */ + bound += (A->length - 1)*bits1 + (B->length - 1)*bits2; + + unsigned int PRIMESIZE = 32; + + myprime = n_nextprime(1152921504606847009, 0); + // myprime = n_nextprime(4611686018427388039, 0); + fprintf(stdout,"LOG2(prime) = %d\n", LOG2(myprime)); + + unsigned int nbits_prime = 0; //LOG2(myprime); + long count = 1; + long count_primes = 0; + + double e_crt = 0, e_modular = 0, t = omp_get_wtime(); + long size_table = (bound / PRIMESIZE) + 2; + mp_limb_t * primes_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; + mp_limb_t * res_mod_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; + + while(nbits_prime < bound){ + myprime = n_nextprime(myprime, 0); + + if(fmpz_divisible_si(fmpz_poly_lead(A), myprime)==0 && + fmpz_divisible_si(fmpz_poly_lead(B), myprime)==0){ + nbits_prime += LOG2(myprime); + primes_table[count_primes] = myprime; + count_primes++; + } + else{ + fprintf(stdout, "! %ld\n", count); + } + count++; + } + fprintf(stdout, "count = %ld\n", count); + fflush(stdout); + + nmod_poly_t a, b; + nmod_poly_init2(a, myprime, A->length); + nmod_poly_init2(b, myprime, B->length); + + double t_in = 0, e_in = 0; + + omp_set_num_threads(nthreads); +#pragma omp parallel for num_threads(nthreads) + for(long i = 0; i < count_primes; i++){ + mp_limb_t res_mod; + mp_limb_t prime = primes_table[i]; + a->mod.n = prime; + a->mod.ninv = n_preinvert_limb(prime); + count_leading_zeros(a->mod.norm, prime); + + b->mod.n = myprime; + b->mod.ninv = n_preinvert_limb(prime); + count_leading_zeros(b->mod.norm, prime); + + make_mod_poly(a, A, prime); + make_mod_poly(b, B, prime); + t_in = omp_get_wtime(); + res_mod = _nmod_poly_resultant(a->coeffs, A->length, b->coeffs, B->length, a->mod); + e_in += omp_get_wtime() - t_in; + res_mod_table[i] = res_mod; + } + e_modular = omp_get_wtime() - t; + + //utilisation de fmpz_CRT pour recuperer le resultant + fmpz_t prod; + fmpz_init(prod); + fmpz_zero(res); + fmpz_one(prod); + + puts("CRT starts"); + t = omp_get_wtime() ; + for(long i = 0; i < count_primes; i++){ + fmpz_CRT_ui(res, res, prod, res_mod_table[i], primes_table[i], 1); + fmpz_mul_ui(prod, prod, primes_table[i]); + } + e_crt = omp_get_wtime() - t; + + + fprintf(stdout, "Elapsed time (multi-mod resultant): %f (%f + %f)\n", e_modular + e_crt, e_modular, e_crt); + fprintf(stdout, "Elapsed time MM in %f\n", e_in); + fprintf(stdout, "Elapsed time per mod comp. %f\n", e_in / count); + + if (fmpz_cmp_ui(res, 0)==0){ + puts("\nResultant was 0\n"); + } + fmpz_clear(prod); + + free(primes_table); + nmod_poly_clear(a); + nmod_poly_clear(b); + +} + + + +//ce resultant est parallelisable mais consomme trop de memoire (et ca nuit a ses performances) +void myresultant_mem_not_eff(fmpz_t res, fmpz_poly_t A, fmpz_poly_t B, int nthreads){ + + mp_limb_t myprime; + + unsigned long bound ; //= (deg1+deg2) * nbits + 2 * LOG2( (deg1 + deg2) ) ; + bound = (A->length + B->length - 1)*FLINT_BIT_COUNT((10*(A->length + B->length - 1) + 26)/27) + 3; + + mp_bitcnt_t bits1 = FLINT_ABS(_fmpz_vec_max_bits(A->coeffs, A->length)); + mp_bitcnt_t bits2 = FLINT_ABS(_fmpz_vec_max_bits(B->coeffs, B->length)); + + /* Upper bound Hadamard bound */ + bound += (A->length - 1)*bits1 + (B->length - 1)*bits2; + + unsigned int PRIMESIZE = 32; + + myprime = n_nextprime(1152921504606847009, 0); + // myprime = n_nextprime(4611686018427388039, 0); + fprintf(stdout,"LOG2(prime) = %d\n", LOG2(myprime)); + + unsigned int nbits_prime = 0; //LOG2(myprime); + long count = 1; + long count_primes = 0; + + double e_crt = 0, e_modular = 0, t = omp_get_wtime(); + long size_table = (bound / PRIMESIZE) + 2; + mp_limb_t * primes_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; + mp_limb_t * res_mod_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; + + fmpz * leadA = fmpz_poly_lead(A); + fmpz * leadB = fmpz_poly_lead(B); + while(nbits_prime < bound){ + myprime = n_nextprime(myprime, 0); + + if(fmpz_divisible_si(leadA, myprime)==0 && + fmpz_divisible_si(leadB, myprime)==0){ + nbits_prime += LOG2(myprime); + primes_table[count_primes] = myprime; + count_primes++; + } + else{ + fprintf(stdout, "! %ld\n", count); + } + count++; + } + fprintf(stdout, "count = %ld\n", count); + fflush(stdout); + + nmod_poly_t *amod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * count_primes)); + nmod_poly_t *bmod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * count_primes)); + + for(long i = 0 ; i < count_primes; i++){ + mp_limb_t prime = primes_table[i]; + nmod_poly_init2(amod_table[i], prime, A->length); + nmod_poly_init2(bmod_table[i], prime, A->length); + + make_mod_poly(amod_table[i], A, prime); + make_mod_poly(bmod_table[i], B, prime); + + } + double t_in = 0, e_in = 0; + + omp_set_num_threads(nthreads); +#pragma omp parallel for num_threads(nthreads) + for(long i =0 ; i < count_primes ; i++){ + + t_in = omp_get_wtime(); + mp_limb_t res_mod = _nmod_poly_resultant(amod_table[i]->coeffs, A->length, bmod_table[i]->coeffs, B->length, amod_table[i]->mod); + e_in += omp_get_wtime() - t_in; + res_mod_table[i] = res_mod; + + } + + e_modular = omp_get_wtime() - t; + + //utilisation de fmpz_CRT pour recuperer le resultant + fmpz_t prod; + fmpz_init(prod); + fmpz_zero(res); + fmpz_one(prod); + + t = omp_get_wtime() ; + for(long i = 0; i < count_primes; i++){ + fmpz_CRT_ui(res, res, prod, res_mod_table[i], primes_table[i], 1); + fmpz_mul_ui(prod, prod, primes_table[i]); + } + e_crt = omp_get_wtime() - t; + + + fprintf(stdout, "Elapsed time (multi-mod resultant): %f (%f + %f)\n", e_modular + e_crt, e_modular, e_crt); + fprintf(stdout, "Elapsed time MM in %f\n", e_in); + fprintf(stdout, "Elapsed time per mod comp. %f\n", e_in / count); + + if (fmpz_cmp_ui(res, 0)==0){ + puts("\nResultant was 0\n"); + } + fmpz_clear(prod); + + free(primes_table); + //nettoyage memoire a terminer + +} + +unsigned long int compute_bsize_norm(fmpz *l, unsigned long int s){ + fmpz_t sum, sq; + fmpz_init_set_ui(sum, 0); + fmpz_init(sq); + for(unsigned long int i = 0; i < s; i++){ + fmpz_pow_ui(sq, l+i, 2); + fmpz_add(sum, sum, sq); + } + return fmpz_bits(sum) / 2; +} + +//l1 et l2 sont 2 tableaux de coefficients de taille respectives l1 et l2 +unsigned long int compute_bsize_bound_resultant(fmpz *l1, fmpz *l2, unsigned long int s1, unsigned long int s2){ + unsigned long int b1 = compute_bsize_norm(l1, s1); + unsigned long int b2 = compute_bsize_norm(l2, s2); + return (unsigned long int) ( (s1-1) * b2 + (s2-1) * b1 ); +} + + + +static mp_limb_t +_nmod_poly_dth_resultant(mp_srcptr poly1, slong len1, + mp_srcptr poly2, slong len2, + nmod_t mod, + mp_ptr head, + slong sdeg + ) +{ + if (poly1 == poly2) + { + return 0; + } + else if (len2 == 1) + { + if (len1 == 1) + { + return 1; + } + else if (len1 == 2) + { + return poly2[0]; + } + else + { + return n_powmod2_ui_preinv(poly2[0], len1 - 1, mod.n, mod.ninv); + } + } + else /* len1 >= len2 >= 2 */ + { + mp_limb_t res = 1; + + mp_ptr u, v, r, t, w; + slong l0, l1, l2; + mp_limb_t lc; + w = _nmod_vec_init(3 * len1); + + u = w; + v = w + len1; + r = v + len1; + //u == poly1 + _nmod_vec_set(u, poly1, len1); + //v == poly2 + _nmod_vec_set(v, poly2, len2); + l1 = len1; + l2 = len2; + + do + { + l0 = l1; + l1 = l2; + //coefficient dominant de v + lc = v[l1 - 1]; + + /* if(DEBUG>3){ */ + /* fprintf(stderr, "Affichage de v\n"); */ + /* nmod_vec_print(stderr, v, l1); */ + /* } */ + + //u est de longueur l0, v est de longueur l1 + //r = remainder(u, v) + _nmod_poly_rem(r, u, l0, v, l1, mod); + l2 = l1 - 1; + //determine la longueur de r (decremente l2 tant que le top coeff == 0) + //r est de degre l2 - 1 + MPN_NORM(r, l2); + //mise a jour + { + t = u; + u = v; + v = r; + r = t; + } + + if (l2 >= 1) + { + lc = n_powmod2_preinv(lc, l0 - l2, mod.n, mod.ninv); + res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); + + if (((l0 | l1) & 1) == 0) + { + res = nmod_neg(res, mod); + } + if(l2==sdeg+1){ + mp_limb_t hi, lo; + // umul_ppmm(hi, lo, v[0], res); + // NMOD_RED2(tail[0], hi, lo, mod); /* hi already reduced mod n */ + umul_ppmm(hi, lo, v[sdeg], res); + NMOD_RED2(head[0], hi, lo, mod); /* hi already reduced mod n */ + _nmod_vec_clear(w); + return res; + } + } + else + { + if (l1 == 1) + { + lc = n_powmod2_preinv(lc, l0 - 1, mod.n, mod.ninv); + res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); + } + else + { + res = 0; + } + } + } + while (l2 > 0); + _nmod_vec_clear(w); + return res; + } +} + + + +//Calcul du resultant de A et B +//nthreads est le nombre de threads utilises +void my_dth_subresultant(fmpz_t res, fmpz_poly_t A, fmpz_poly_t B, + slong sdeg, int nthreads){ + if(A->lengthlength){ + fprintf(stderr, "Warning: polynomials have been given with increasing degree ; possible sign variation\n"); + my_dth_subresultant(res, B, A, sdeg, nthreads); + return; + } + + mp_limb_t myprime; + + unsigned long bound ; //= (deg1+deg2) * nbits + 2 * LOG2( (deg1 + deg2) ) ; + bound = (A->length + B->length - 1)*FLINT_BIT_COUNT((10*(A->length + B->length - 1) + 26)/27) + 3; + + mp_bitcnt_t bits1 = FLINT_ABS(_fmpz_vec_max_bits(A->coeffs, A->length)); + mp_bitcnt_t bits2 = FLINT_ABS(_fmpz_vec_max_bits(B->coeffs, B->length)); + + /* Upper bound Hadamard bound */ + bound += (A->length - 1)*bits1 + (B->length - 1)*bits2; + + // fprintf(stderr, "Old bound %lu\n", bound); + + bound = compute_bsize_bound_resultant(A->coeffs, B->coeffs, A->length, B->length); + + fprintf(stderr, "Output bit size bound %lu\n", bound); + + //4611686018427388039 + //1152921504606847009 + + myprime = n_nextprime(4611686018427388039, 0); + unsigned int PRIMESIZE = LOG2(myprime); + // myprime = n_nextprime(4611686018427388039, 0); + fprintf(stderr,"LOG2(prime) = %d\n", LOG2(myprime)); + + unsigned int nbits_prime = 0; //LOG2(myprime); + long count = 1; + long count_primes = 0; + + double e_end, e_start; + long size_table = (bound / PRIMESIZE) + 2; + mp_limb_t * primes_table_init = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; + mp_limb_t * primes_table = primes_table_init; + mp_limb_t * res_mod_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * nthreads)) ; + + fmpz * leadA = fmpz_poly_lead(A); + fmpz * leadB = fmpz_poly_lead(B); + e_start = omp_get_wtime(); + while(nbits_prime < bound){ + myprime = n_nextprime(myprime, 0); + if(fmpz_divisible_si(leadA, myprime)==0 && + fmpz_divisible_si(leadB, myprime)==0){ + nbits_prime += LOG2(myprime); + primes_table_init[count_primes] = myprime; + count_primes++; + } + else{ + fprintf(stderr, "! %ld\n", count); + } + count++; + } + fprintf(stderr, "count = %ld / count_primes = %ld\n", count, count_primes); + // fflush(stdout); + + nmod_poly_t *amod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * nthreads)); + nmod_poly_t *bmod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * nthreads)); + + //Il faut les initialiser + for(int i =0; i < nthreads; i++){ + mp_limb_t prime = primes_table[i]; + nmod_poly_init2(amod_table[i], prime, A->length); + nmod_poly_init2(bmod_table[i], prime, A->length); + } + mp_ptr head = malloc(sizeof(mp_limb_t)*size_table); + fprintf(stderr, "First initialization done\n\n"); + unsigned long int nblocks = count_primes / nthreads; + + // double t_in = 0, e_in = 0; + fmpz_t prod; + fmpz_init(prod); + fmpz_zero(res); + fmpz_one(prod); + int index = 0; + omp_set_num_threads(nthreads); + double e_in = 0; + + for(unsigned long int block = 0; block < nblocks; block++){ + // unsigned long int index = block*nthreads; +#pragma omp parallel for num_threads(nthreads) + for(int i =0; i < nthreads; i++){ + + mp_limb_t prime = primes_table[i]; + // fprintf(stderr, "prime = %lu\n", prime); + amod_table[i]->mod.n = prime; + amod_table[i]->mod.ninv = n_preinvert_limb(prime); + count_leading_zeros(amod_table[i]->mod.norm, prime); + + bmod_table[i]->mod.n = prime; + bmod_table[i]->mod.ninv = n_preinvert_limb(prime); + count_leading_zeros(bmod_table[i]->mod.norm, prime); + + make_mod_poly(amod_table[i], A, prime); + make_mod_poly(bmod_table[i], B, prime); + + double t_in = omp_get_wtime(); + _nmod_poly_dth_resultant(amod_table[i]->coeffs, + A->length, + bmod_table[i]->coeffs, + B->length, + amod_table[i]->mod, + head+i+index, + sdeg); + if(e_in==0){ + e_in = omp_get_wtime() - t_in; + fprintf(stderr, "\nRun time modp comp. = %f\n",e_in); + } + res_mod_table[i+index] = head[i+index]; + + } + + if(fmpz_fdiv_ui(res, primes_table[0])==res_mod_table[index]){ + // fprintf(stderr, "Probabilistic stop\n"); + break; + } + else{ + for(int i =0; i < nthreads; i++){ + // unsigned long int index = block*nthreads; + // fprintf(stderr, "Ici: %lu (%d)\n", primes_table[i+index], i); + fmpz_CRT_ui(res, res, prod, res_mod_table[i+index], primes_table[i+index], 1); + // fprintf(stderr, "La?\n"); + fmpz_mul_ui(prod, prod, primes_table[i+index]); + // fprintf(stderr, "On incremente\n"); + // fprintf(stderr, "%lu, %lu, %lu\n", primes_table_init[0], primes_table_init[1], primes_table_init[2]); + } + primes_table+=nthreads; + } + } + /* // fprintf(stderr, "after loops\n"); */ + /* // unsigned long int index = nblocks*nthreads; */ + /* for(unsigned long int i = 0; i < count_primes - index; i++){ */ + /* mp_limb_t prime = primes_table[0]; */ + + /* amod_table[i]->mod.n = prime; */ + /* amod_table[i]->mod.ninv = n_preinvert_limb(prime); */ + /* count_leading_zeros(amod_table[i]->mod.norm, prime); */ + + /* bmod_table[i]->mod.n = prime; */ + /* bmod_table[i]->mod.ninv = n_preinvert_limb(prime); */ + /* count_leading_zeros(bmod_table[i]->mod.norm, prime); */ + + /* make_mod_poly(amod_table[i], A, prime); */ + /* make_mod_poly(bmod_table[i], B, prime); */ + + + /* // t_in = omp_get_wtime(); */ + /* mp_limb_t res_mod = _nmod_poly_dth_resultant( */ + /* amod_table[i]->coeffs, */ + /* A->length, */ + /* bmod_table[i]->coeffs, */ + /* B->length, */ + /* amod_table[i]->mod, */ + /* head+i+index, */ + /* sdeg); */ + /* // e_in += omp_get_wtime() - t_in; */ + + /* res_mod_table[i+index] = head[i+index]; */ + + /* if(fmpz_fdiv_ui(res, primes_table[0])==res_mod_table[i+index]){ */ + /* break; */ + /* } */ + /* else{ */ + /* fmpz_CRT_ui(res, res, prod, res_mod_table[i+index], primes_table[i+index], 1); */ + /* fmpz_mul_ui(prod, prod, primes_table[i+index]); */ + /* primes_table++; */ + /* } */ + /* } */ + e_end = omp_get_wtime() - e_start; + + + //utilisation de fmpz_CRT pour recuperer le resultant + //Obsolete + + /* t = omp_get_wtime() ; */ + /* for(long i = 0; i < count_primes; i++){ */ + /* fmpz_CRT_ui(res, res, prod, res_mod_table[i], primes_table[i], 1); */ + /* fmpz_mul_ui(prod, prod, primes_table[i]); */ + /* } */ + /* e_crt = omp_get_wtime() - t; */ + fprintf(stderr, "Bit size of the result = %ld\n", fmpz_bits(res)); + fprintf(stderr, "Elapsed time (multi-mod resultant): %f\n", e_end); + // fprintf(stderr, "Elapsed time MM in %f\n", e_in); + // fprintf(stderr, "Elapsed time per mod comp. %f\n", e_in / count); + + if (fmpz_cmp_ui(res, 0)==0){ + fprintf(stderr,"\nResultant was 0\n"); + } + fmpz_clear(prod); + + free(primes_table_init); + + for(int i = 0; i < nthreads; i++){ + nmod_poly_clear(amod_table[i]); + nmod_poly_clear(bmod_table[i]); + } + + free(res_mod_table); + free(amod_table); + free(bmod_table); + + //nettoyage memoire a terminer + +} + + +//Calcul du resultant de A et B +//nthreads est le nombre de threads utilises +void myresultant(fmpz_t res, fmpz_poly_t A, fmpz_poly_t B, int nthreads){ + if(A->lengthlength){ + fprintf(stderr, "Warning: polynomials have been given with increasing degree ; possible sign variation\n"); + myresultant(res, B, A, nthreads); + return; + } + + mp_limb_t myprime; + + unsigned long bound ; //= (deg1+deg2) * nbits + 2 * LOG2( (deg1 + deg2) ) ; + bound = (A->length + B->length - 1)*FLINT_BIT_COUNT((10*(A->length + B->length - 1) + 26)/27) + 3; + + mp_bitcnt_t bits1 = FLINT_ABS(_fmpz_vec_max_bits(A->coeffs, A->length)); + mp_bitcnt_t bits2 = FLINT_ABS(_fmpz_vec_max_bits(B->coeffs, B->length)); + + /* Upper bound Hadamard bound */ + bound += (A->length - 1)*bits1 + (B->length - 1)*bits2; + + bound = compute_bsize_bound_resultant(A->coeffs, B->coeffs, A->length, B->length); + + fprintf(stderr, "Output bit size bound %lu\n", bound); + + //4611686018427388039 + myprime = n_nextprime(1152921504606847009, 0); + unsigned int PRIMESIZE = LOG2(myprime); + // myprime = n_nextprime(4611686018427388039, 0); + fprintf(stderr,"LOG2(prime) = %d\n", LOG2(myprime)); + + unsigned int nbits_prime = 0; //LOG2(myprime); + long count = 1; + long count_primes = 0; + + double e_end, e_start; //= omp_get_wtime(); + long size_table = (bound / PRIMESIZE) + 2; + mp_limb_t * primes_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; + mp_limb_t * res_mod_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; + + fmpz * leadA = fmpz_poly_lead(A); + fmpz * leadB = fmpz_poly_lead(B); + e_start = omp_get_wtime(); + while(nbits_prime < bound){ + myprime = n_nextprime(myprime, 0); + if(fmpz_divisible_si(leadA, myprime)==0 && + fmpz_divisible_si(leadB, myprime)==0){ + nbits_prime += LOG2(myprime); + primes_table[count_primes] = myprime; + count_primes++; + } + else{ + fprintf(stderr, "! %ld\n", count); + } + count++; + } + fprintf(stderr, "count = %ld / count_primes = %ld\n", count, count_primes); + // fflush(stdout); + + nmod_poly_t *amod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * nthreads)); + nmod_poly_t *bmod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * nthreads)); + + //Il faut les initialiser + for(int i =0; i < nthreads; i++){ + mp_limb_t prime = primes_table[i]; + nmod_poly_init2(amod_table[i], prime, A->length); + nmod_poly_init2(bmod_table[i], prime, A->length); + } + fprintf(stderr, "First initialization done\n\n"); + unsigned long int nblocks = count_primes / nthreads; + + // double t_in = 0, e_in = 0; + fmpz_t prod; + fmpz_init(prod); + fmpz_zero(res); + fmpz_one(prod); + + omp_set_num_threads(nthreads); + for(unsigned long int block = 0; block < nblocks; block++){ + unsigned long int index = block*nthreads; +#pragma omp parallel for num_threads(nthreads) + for(int i =0; i < nthreads; i++){ + + mp_limb_t prime = primes_table[i+index]; + + amod_table[i]->mod.n = prime; + amod_table[i]->mod.ninv = n_preinvert_limb(prime); + count_leading_zeros(amod_table[i]->mod.norm, prime); + + bmod_table[i]->mod.n = prime; + bmod_table[i]->mod.ninv = n_preinvert_limb(prime); + count_leading_zeros(bmod_table[i]->mod.norm, prime); + + make_mod_poly(amod_table[i], A, prime); + make_mod_poly(bmod_table[i], B, prime); + + + // t_in = omp_get_wtime(); + mp_limb_t res_mod = _nmod_poly_resultant( + amod_table[i]->coeffs, + A->length, + bmod_table[i]->coeffs, + B->length, + amod_table[i]->mod); + // e_in += omp_get_wtime() - t_in; + + res_mod_table[i+index] = res_mod; + + } + if(fmpz_fdiv_ui(res, primes_table[index])==res_mod_table[index]){ + // fprintf(stderr, "Probabilistic stop\n"); + break; + } + else{ + for(int i =0; i < nthreads; i++){ + unsigned long int index = block*nthreads; + + // mp_limb_t prime = primes_table[i+index]; + fmpz_CRT_ui(res, res, prod, res_mod_table[i+index], primes_table[i+index], 1); + fmpz_mul_ui(prod, prod, primes_table[i+index]); + } + } + } + // fprintf(stderr, "after loops\n"); + unsigned long int index = nblocks*nthreads; + for(unsigned long int i = 0; i < count_primes - index; i++){ + mp_limb_t prime = primes_table[i+index]; + + amod_table[i]->mod.n = prime; + amod_table[i]->mod.ninv = n_preinvert_limb(prime); + count_leading_zeros(amod_table[i]->mod.norm, prime); + + bmod_table[i]->mod.n = prime; + bmod_table[i]->mod.ninv = n_preinvert_limb(prime); + count_leading_zeros(bmod_table[i]->mod.norm, prime); + + make_mod_poly(amod_table[i], A, prime); + make_mod_poly(bmod_table[i], B, prime); + + + // t_in = omp_get_wtime(); + mp_limb_t res_mod = _nmod_poly_resultant( + amod_table[i]->coeffs, + A->length, + bmod_table[i]->coeffs, + B->length, + amod_table[i]->mod); + // e_in += omp_get_wtime() - t_in; + + res_mod_table[i+index] = res_mod; + + if(fmpz_fdiv_ui(res, primes_table[i+index])==res_mod_table[i+index]){ + break; + } + else{ + fmpz_CRT_ui(res, res, prod, res_mod_table[i+index], primes_table[i+index], 1); + fmpz_mul_ui(prod, prod, primes_table[i+index]); + } + } + e_end = omp_get_wtime() - e_start; + + + //utilisation de fmpz_CRT pour recuperer le resultant + //Obsolete + + /* t = omp_get_wtime() ; */ + /* for(long i = 0; i < count_primes; i++){ */ + /* fmpz_CRT_ui(res, res, prod, res_mod_table[i], primes_table[i], 1); */ + /* fmpz_mul_ui(prod, prod, primes_table[i]); */ + /* } */ + /* e_crt = omp_get_wtime() - t; */ + fprintf(stderr, "Bit size of the result = %ld\n", fmpz_bits(res)); + fprintf(stderr, "Elapsed time (multi-mod resultant): %f \n", e_end); + // fprintf(stderr, "Elapsed time MM in %f\n", e_in); + // fprintf(stderr, "Elapsed time per mod comp. %f\n", e_in / count); + + if (fmpz_cmp_ui(res, 0)==0){ + fprintf(stderr,"\nResultant was 0\n"); + } + fmpz_clear(prod); + + free(primes_table); + for(int i = 0; i < nthreads; i++){ + nmod_poly_clear(amod_table[i]); + nmod_poly_clear(bmod_table[i]); + } + + free(res_mod_table); + free(amod_table); + free(bmod_table); + + //nettoyage memoire a terminer + +} + +//Compares FLINT resultant with a hand-made multi-mod resultant +//(still using FLINT basics) +void run_compare(unsigned long int deg, flint_rand_t state){ + + unsigned long int deg1 = deg, deg2 = deg1; + unsigned int nbits = deg1 ; + + fmpz_poly_t A, B; + fmpz_poly_init2(A, deg1+1); + fmpz_poly_init2(B, deg2+1); + fmpz_poly_random_dense(A, deg1, nbits, state); + fmpz_poly_random_dense(B, deg2, nbits, state); + + /* fmpz_poly_random_dense_old(A, deg1, nbits); */ + /* fmpz_poly_random_dense_old(B, deg2, nbits); */ + + fmpz_t res_normal, res; + fmpz_init(res_normal); + fmpz_init(res); + + double e_normal = 0, t; + t = omp_get_wtime(); + fmpz_poly_resultant(res_normal, A, B); + e_normal = omp_get_wtime() - t; + fprintf(stderr, "Elapsed time (FLINT resultant): %f\n\n", e_normal); + + t = omp_get_wtime(); + myresultant(res, A, B, 1); + e_normal = omp_get_wtime() - t; + fprintf(stderr, "Elapsed time (my resultant): %f\n", e_normal); + + if(fmpz_cmp(res, res_normal)!=0){ + puts("\n\t BUG BUG BUG\n"); + } + + puts(""); + + /* if(fmpz_cmp_ui(res, 0)==1){ */ + /* puts("Positive"); */ + /* } */ + /* else{ */ + /* puts("Negative"); */ + /* } */ + fmpz_clear(res); + fmpz_clear(res_normal); + +} + +//runs modular FLINT resultant modulo 32 bits prime +void run_modular16(flint_rand_t state, int ntimes){ + + unsigned long int deg = 64; + mp_limb_t myprime = 65537; + + puts("\nFLINT resultant modulo 16 bits prime\n"); + while(deg<=2*8192){ + + fmpz_poly_t A, B; + fmpz_poly_init2(A, deg+1); + fmpz_poly_init2(B, deg+1); + fmpz_poly_random_dense(A, deg, deg / 2, state); + fmpz_poly_random_dense(B, deg, deg / 2, state); + + nmod_poly_t a_mod,b_mod; + nmod_poly_init2(a_mod,myprime, deg+1); + nmod_poly_init2(b_mod,myprime, deg+1); + //attention a la gestion des coefficients negatifs + // nmod_poly_set_coeff_ui(x,3,9002); + // nmod_poly_set_coeff_ui(x,0,6); + + make_mod_poly(a_mod, A, myprime); + make_mod_poly(b_mod, B, myprime); + + fprintf(stdout,"Degree = %lu\n", deg); + + // nmod_poly_print(x);flint_printf("\n"); + // nmod_poly_print(y);flint_printf("\n"); + double e = 0, t = omp_get_wtime(); + int j; + for(int i = 1; i<=ntimes; i++){ + // res = nmod_poly_resultant_hgcd(a_mod, b_mod); + nmod_poly_resultant(a_mod, b_mod); //combine gcd et euclide en fonction du degre + j = j+i; + } + e = omp_get_wtime() - t; + // fprintf(stdout,"%lu \n", res); + fprintf(stdout, "Elapsed time Half gcd resultant = %f\n", e); + + double e2 = 0, t2 = omp_get_wtime(); + for(int i =1 ; i <=ntimes; i++){ + nmod_poly_resultant_euclidean(a_mod, b_mod); + j = j+i; + } + e2 = omp_get_wtime() - t2; + fprintf(stdout, "Elapsed time Euclidean resultant = %f\n", e2); + puts(""); + + nmod_poly_clear(a_mod); + nmod_poly_clear(b_mod); + + fmpz_poly_clear(A); + fmpz_poly_clear(B); + + deg = 2*deg; + } +} + +//runs modular FLINT resultant modulo 32 bits prime +void run_modular32(flint_rand_t state, int ntimes){ + + unsigned long int deg = 30; + mp_limb_t myprime = 4294967311; + + puts("\nFLINT resultant modulo 32 bits prime\n"); + while(deg<=2*8192){ + + fmpz_poly_t A, B; + fmpz_poly_init2(A, deg+1); + fmpz_poly_init2(B, deg+1); + fmpz_poly_random_dense(A, deg, deg / 2, state); + fmpz_poly_random_dense(B, deg, deg / 2, state); + + nmod_poly_t a_mod,b_mod; + nmod_poly_init2(a_mod,myprime, deg+1); + nmod_poly_init2(b_mod,myprime, deg+1); + //attention a la gestion des coefficients negatifs + // nmod_poly_set_coeff_ui(x,3,9002); + // nmod_poly_set_coeff_ui(x,0,6); + + make_mod_poly(a_mod, A, myprime); + make_mod_poly(b_mod, B, myprime); + + fprintf(stdout,"Degree = %lu\n", deg); + + double e = 0, t = omp_get_wtime(); + int j; + for(int i = 1; i<=ntimes; i++){ + // res = nmod_poly_resultant_hgcd(a_mod, b_mod); + nmod_poly_resultant_hgcd(a_mod, b_mod); //combine gcd et euclide en fonction du degre + j = j+i; + } + e = omp_get_wtime() - t; + fprintf(stdout, "Elapsed time Half gcd resultant = %f\n", e); + + double e2 = 0, t2 = omp_get_wtime(); + for(int i =1 ; i <=ntimes; i++){ + nmod_poly_resultant_euclidean(a_mod, b_mod); + j = j+i; + } + e2 = omp_get_wtime() - t2; + fprintf(stdout, "Elapsed time Euclidean resultant = %f\n", e2); + puts(""); + + nmod_poly_clear(a_mod); + nmod_poly_clear(b_mod); + + fmpz_poly_clear(A); + fmpz_poly_clear(B); + + deg = 2*deg; + } +} + +//runs modular FLINT resultant modulo 60 bits fftprime +void run_modular60fftprime(flint_rand_t state, int ntimes){ + + unsigned long int deg = 64; + mp_limb_t myprime = 1945555039024054273; + + puts("\nFLINT resultant modulo 60 bits FFT prime\n"); + while(deg<=8192){ + + fmpz_poly_t A, B; + fmpz_poly_init2(A, deg+1); + fmpz_poly_init2(B, deg+1); + fmpz_poly_random_dense(A, deg, deg / 2, state); + fmpz_poly_random_dense(B, deg, deg / 2, state); + + nmod_poly_t a_mod,b_mod; + nmod_poly_init2(a_mod,myprime, deg+1); + nmod_poly_init2(b_mod,myprime, deg+1); + //attention a la gestion des coefficients negatifs + // nmod_poly_set_coeff_ui(x,3,9002); + // nmod_poly_set_coeff_ui(x,0,6); + + make_mod_poly(a_mod, A, myprime); + make_mod_poly(b_mod, B, myprime); + + fprintf(stdout,"Degree = %lu\n", deg); + + double e = 0, t = omp_get_wtime(); + int j; + for(int i = 1; i<=ntimes; i++){ + // res = nmod_poly_resultant_hgcd(a_mod, b_mod); + nmod_poly_resultant(a_mod, b_mod); //combine gcd et euclide en fonction du degre + j = j+i; + } + e = omp_get_wtime() - t; + + fprintf(stdout, "Elapsed time Half gcd resultant = %f\n", e); + + double e2 = 0, t2 = omp_get_wtime(); + for(int i =1 ; i <=ntimes; i++){ + nmod_poly_resultant_euclidean(a_mod, b_mod); + j = j+i; + } + e2 = omp_get_wtime() - t2; + fprintf(stdout, "Elapsed time Euclidean resultant = %f\n", e2); + puts(""); + + nmod_poly_clear(a_mod); + nmod_poly_clear(b_mod); + + fmpz_poly_clear(A); + fmpz_poly_clear(B); + + deg = 2*deg; + } +} + +//runs modular FLINT resultant modulo 60 bits prime +void run_modular60prime(flint_rand_t state, int ntimes){ + + unsigned long int deg = 256; + mp_limb_t myprime = 1152921504606847009; + + puts("\nFLINT resultant modulo 60 bits prime\n"); + while(deg<=8192){ + + fmpz_poly_t A, B; + fmpz_poly_init2(A, deg+1); + fmpz_poly_init2(B, deg+1); + fmpz_poly_random_dense(A, deg, deg / 2, state); + fmpz_poly_random_dense(B, deg, deg / 2, state); + + nmod_poly_t a_mod,b_mod; + nmod_poly_init2(a_mod,myprime, deg+1); + nmod_poly_init2(b_mod,myprime, deg+1); + //attention a la gestion des coefficients negatifs + // nmod_poly_set_coeff_ui(x,3,9002); + // nmod_poly_set_coeff_ui(x,0,6); + + make_mod_poly(a_mod, A, myprime); + make_mod_poly(b_mod, B, myprime); + + fprintf(stdout,"Degree = %lu\n", deg); + + double e = 0, t = omp_get_wtime(); + int j; + for(int i = 1; i<=ntimes; i++){ + // res = nmod_poly_resultant_hgcd(a_mod, b_mod); + nmod_poly_resultant_hgcd(a_mod, b_mod); //combine gcd et euclide en fonction du degre + j = j+i; + } + e = omp_get_wtime() - t; + + fprintf(stdout, "Elapsed time Half gcd resultant = %f\n", e/ntimes); + + double e2 = 0, t2 = omp_get_wtime(); + for(int i =1 ; i <=ntimes; i++){ + nmod_poly_resultant_euclidean(a_mod, b_mod); + j = j+i; + } + e2 = omp_get_wtime() - t2; + fprintf(stdout, "Elapsed time Euclidean resultant = %f\n", e2/ntimes); + puts(""); + + nmod_poly_clear(a_mod); + nmod_poly_clear(b_mod); + + fmpz_poly_clear(A); + fmpz_poly_clear(B); + + deg = deg * 2; + } +} + +void display_help(){ + fprintf(stdout, "Basic Flint based C program for computing resultant and subresultant in Z[x]\n"); + fprintf(stdout, "Implemented by M. Safey El Din (Sorbonne Univ./CNRS/Inria), mohab.safey@lip6.fr\n"); + fprintf(stdout, "Provided without any guarantee for ** academic use only ** by students, teachers and researchers hosted in high-schools, universities or academic (non-industtrial) research institutes\n"); + fprintf(stdout, "Any kind of other use requires formal agreement from the author\n\n"); + + fprintf(stdout, "-h \t diplays this help\n"); + fprintf(stdout, "-r \t generates random dense polynomials of degree d and runs the resultant computation\n"); + fprintf(stdout, "-f \t reads polynomials in filename and computes the resultant of those polynomials\n"); + fprintf(stdout, "\n Format file: \nFiles provide 2 polynomials encoded as follows \ndegree\ncoef_0\n...\ncoef_degree\n"); + + fprintf(stdout, "\n\nTODO:\n"); + fprintf(stdout, "Main difference with FLINT functions are in memory management+multi-threading\n"); + fprintf(stdout, "Lifting is not that efficient - can be improved\n"); + fprintf(stdout, "Use of fast reductions still needs to be implemented\n"); +} + + + +static char *getoptions(int argc, char **argv, char ** input_file, + ulong *deg, slong *sdeg, int *nthreads){ + int optch, errflag = 0, fflag = 1; + extern int opterr; + + char options[] = "hf:r:d:t:"; + char *filename = NULL; + opterr = 1; + + while ((optch = getopt(argc, argv, options)) != -1) + switch (optch) { + case 'f': + fflag = 0; + *input_file = optarg; + optind--; + break; + case 'h': + display_help(); + exit(1); + case 'r': + *deg = strtol(optarg, NULL, 10); + optind--; + break; + case 'd': + *sdeg = strtol(optarg, NULL, 10); + optind--; + break; + case 't': + *nthreads = strtol(optarg, NULL, 10); + optind--; + break; + default: + errflag++; + break; + } + if(fflag==1){ + fprintf(stderr, "No given file\n"); + *input_file = NULL; + } + if(errflag){ + fprintf(stderr,"Invalid usage\n"); + fprintf(stderr,"%s -f file_name\n", argv[0]); + exit(1); + } + return filename; +} + +void get_input_polynomials(FILE *file, ulong *degA, ulong *degB, + fmpz_poly_t A, fmpz_poly_t B){ + fmpz_t c; + fmpz_init(c); + if(fscanf(file, "%lu", degA)){ + fprintf(stderr, "Degree %lu\n", *degA); + for(ulong i=0; i <= *degA; i++){ + fmpz_fread(file, c); + fmpz_poly_set_coeff_fmpz(A, i, c); + } + } + if(fscanf(file, "%lu", degB)){ + fprintf(stderr, "Degree %lu\n", *degB); + for(ulong i=0; i <= *degB; i++){ + fmpz_fread(file, c); + fmpz_poly_set_coeff_fmpz(B, i, c); + } + } + fmpz_clear(c); +} + +int main(int argc, char *argv[]){ + char **input_file = malloc(sizeof(char**)); + ulong deg = 0; + slong sdeg = -1; + int nthreads = 1; + getoptions(argc, argv, input_file, °, &sdeg, &nthreads); + + if(*input_file!=NULL){ + fprintf(stderr, "Reading file...\n"); + FILE *file = fopen(*input_file,"r"); + ulong degA = 0, degB = 0; + fmpz_poly_t A; + fmpz_poly_t B; + fmpz_poly_init(A); + fmpz_poly_init(B); + get_input_polynomials(file, °A, °B, A, B); + fprintf(stderr, "Done.\n\n"); + fmpz_t res; + fmpz_init(res); + if(sdeg>0){ + my_dth_subresultant(res, A, B, sdeg, nthreads); + } + else{ + myresultant(res, A, B, nthreads); + } + // fmpz_zero(res); + fmpz_fprint(stdout, res); + fmpz_poly_clear(A); + fmpz_poly_clear(B); + fmpz_clear(res); + free(input_file); + return 0; + } + + fprintf(stdout, "\nRunning resultant computations for random dense polynomials in Z[x]\n\n"); + // run_modular(); + flint_rand_t state; + flint_randinit(state); + run_compare(deg, state); + + //FLINT resultant sur les entiers + // run_res_flint(64, state); + + //FLINT resultant modulo premier 16 bits + // run_modular16(state, 100); + + //FLINT resultant modulo premier 32 bits + // run_modular32(state, 10000); + + //FLINT resultant modulo premier 60 bits + run_modular60prime(state, 400); + + //FLINT resultant modulo premier fft 60 bits + // run_modular60fftprime(state, 100); + + flint_randclear(state); + return 0; +} diff --git a/src/connectcurves/src/resultant/io.c b/src/connectcurves/src/resultant/io.c new file mode 100644 index 0000000..c1ee6b3 --- /dev/null +++ b/src/connectcurves/src/resultant/io.c @@ -0,0 +1,562 @@ +static void print_nmod_param(FILE * file, nmod_param_t *param){ + char str[2]={"x"}; + fprintf(file, "%d\n", param->nvars); + fprintf(file, "["); + + for(int i = 0; i < param->nvars; i++){ + nmod_poly_fprint_pretty(file, param->coords[i], str); + } + fprintf(file, "]\n"); + nmod_poly_fprint_pretty(file, param->denom, str); + fprintf(file, "\n"); + nmod_poly_fprint_pretty(file, param->elim, str); + fprintf(stderr, "\n"); +} + + +static inline void print_nmod_all_params_pretty(FILE *file, nmod_all_params_t *all_params){ + fprintf(file, "\n"); + for(int i = 0; i < all_params->nparams; i++){ + print_nmod_param(file, (all_params->params)[i]); + } +} + +static inline void fmpz_poly_fprint_bin(FILE *file, const fmpz_poly_t poly){ + slong len = poly->length; + fprintf(file, "%ld\n", len); + fprintf(stderr, "LENGTH = %ld\n", len); + for(slong i = 0; i < len; i++){ + fmpz_out_raw(file, poly->coeffs + i); + } +} + +static inline void print_fmpz_param_bin(FILE *file, fmpz_param_t *param){ + fprintf(file, "%d\n", param->nvars); + for(int i = 0; i < param->nvars-1; i++){ + fmpz_poly_fprint_bin(file, param->coords[i]); + } + fmpz_poly_fprint_bin(file, param->denom); + fmpz_poly_fprint_bin(file, param->elim); +} + +static inline void print_fmpz_param_pretty(FILE *file, fmpz_param_t *param){ + char stra[2] = {"x"}; + fprintf(file, "%d\n", param->nvars); + fprintf(file, "["); + + for(int i = 0; i < param->nvars; i++){ + fmpz_poly_fprint_pretty(file, param->coords[i], stra); + fprintf(file, ",\n"); + } + fmpz_poly_fprint_pretty(file, param->coords[param->nvars-1], stra); + fprintf(file, "]\n"); + fmpz_poly_fprint_pretty(file, param->denom, stra); + fprintf(file, "\n"); + fmpz_poly_fprint_pretty(file, param->elim, stra); + fprintf(stderr, "\n"); +} + +static inline void print_bs_fmpz_param_bin(FILE *file, bsolve_fmpz_param_t *param){ + fprintf(stderr, "ELIM -> "); + fmpz_poly_fprint_bin(file, param->elim); + fprintf(stderr, "DENOM -> "); + fmpz_poly_fprint_bin(file, param->denom); + int nv = param->nvars + 1; + fprintf(stderr, "NVARS = %d\n", nv); + fprintf(file, "%d\n", nv); + for(int i = 0; i < param->nvars; i++){ + fprintf(stderr, "COORD -> "); + fmpz_poly_fprint_bin(file, param->coords[i]); + fmpz_out_raw(file, param->cfs[i]); + } +} + +static inline void print_bs_fmpz_param_pretty(FILE *file, bsolve_fmpz_param_t *param){ + char stra[2] = {"x"}; + fprintf(file, "["); + fmpz_poly_fprint_pretty(file, param->elim, stra); + fprintf(file, ",\n"); + fmpz_poly_fprint_pretty(file, param->denom, stra); + fprintf(file, ",\n"); + for(int i = 0; i < param->nvars-1; i++){ + fmpz_poly_fprint_pretty(file, param->coords[i], stra); + fprintf(file, ",\n"); + } + fmpz_poly_fprint_pretty(file, param->coords[param->nvars-1], stra); + fprintf(file, "]"); +} + +static inline void print_fmpz_all_params_bin(FILE *file, fmpz_all_params_t *all_params){ + fprintf(file, "%d\n", all_params->nparams); + + for(int i = 0; i < all_params->nparams; i++){ + print_fmpz_param_bin(file, all_params->params[i]); + } +} + + +static inline void print_fmpz_all_params_pretty(FILE *file, fmpz_all_params_t *all_params){ + fprintf(file, "\n"); + for(int i = 0; i < all_params->nparams; i++){ + print_fmpz_param_pretty(file, all_params->params[i]); + } +} + +static inline void print_bs_fmpz_all_params_bin(FILE *file, + bsolve_fmpz_all_params_t *all_params){ + fprintf(file, "%d\n", all_params->nparams); + + for(int i = 0; i < all_params->nparams-1; i++){ + fprintf(stderr, "Display PARAM %d\n", i); + print_bs_fmpz_param_bin(file, all_params->params[i]); + fprintf(file, "\n"); + } + fprintf(stderr, "Display PARAM %d\n", all_params->nparams-1); + print_bs_fmpz_param_bin(file, all_params->params[all_params->nparams-1]); + fprintf(file, "\n"); +} + +static inline void print_bs_fmpz_all_params_pretty(FILE *file, + bsolve_fmpz_all_params_t *all_params){ + fprintf(file, "[\n"); + for(int i = 0; i < all_params->nparams-1; i++){ + print_bs_fmpz_param_pretty(file, all_params->params[i]); + fprintf(file, ",\n"); + } + print_bs_fmpz_param_pretty(file, all_params->params[all_params->nparams-1]); + fprintf(file, "\n];\n"); +} + +static void nmod_vec_print(FILE *file, mp_srcptr vec, slong len){ + if(len==1) { + fprintf(file, "%lu ; \n", vec[0]); + return; + } + fprintf(file, "%lu + ", vec[0]); + for(slong i = 1; i < len - 1; i++){ + fprintf(file, "%lu * x^%ld + ", vec[i], i); + } + fprintf(file, "%lu * x^%ld; \n", vec[len-1], len-1); +} + +/* + Input: +*/ + +static void fmpz_bpoly_fprint_pretty(FILE *file, fmpz_poly_t *A, ulong deg){ + char strx[1]={"x"}; + for(slong i=deg; i >=1 ; i--){ + fprintf(file, "("); + fmpz_poly_fprint_pretty(file, A[i], strx); + fprintf(file, ")*y^%lu+", i); + } + fprintf(file, "("); + fmpz_poly_fprint_pretty(file, A[0], strx); + fprintf(file, ");"); + fprintf(file, "\n"); +} + +static ulong nbits_bound_fmpz_bvar_poly(fmpz_poly_t *A, ulong deg){ + ulong nbits = 0; + fmpz_t sum, sumtmp, tmp; + fmpz_init(sum); + fmpz_init(sumtmp); + fmpz_init(tmp); + fmpz_zero(sum); + for(ulong i = 0; i <= deg; i++){ + fmpz_zero(sumtmp); + for(ulong j = 0; j < A[i]->length; j++){ + fmpz_abs(tmp, A[i]->coeffs+j); + fmpz_add(sumtmp, sumtmp, tmp); + } + fmpz_mul(sumtmp, sumtmp, sumtmp); + fmpz_add(sum, sum, sumtmp); + } + nbits = fmpz_bits(sum) + 1; + fmpz_clear(sumtmp); + fmpz_clear(sum); + fmpz_clear(tmp); + return nbits / 2; +} + +static void crt_lift_resultant(fmpz_poly_t res, nmod_poly_t *res_mod_table, mp_limb_t *primes_table, ulong size, fmpz_t *prod_mod){ + slong maxdegree = -1; + ulong i; + for(i = 0; i < size; i++){ + if(res_mod_table[i]->length - 1 > maxdegree){ + maxdegree = res_mod_table[i]->length - 1; + } + } + if(res->length-1!=maxdegree){ + res->coeffs = malloc(sizeof(fmpz_t) * (maxdegree + 1)); + for(i = 0; i <= maxdegree; i++){ + fmpz_poly_set_coeff_ui(res, i, 1); + } + } + + fmpz_t prod_primes; + fmpz_init(prod_primes); + fmpz_one(prod_primes); + + for(i = 0; i < size; i++){ + for(ulong j = 0; j <= maxdegree; j++){ + myfmpz_CRT_ui((res->coeffs)+j, (res->coeffs)+j, + prod_primes, (res_mod_table[i]->coeffs)[j], + primes_table[i], 1, + prod_mod); + } + fmpz_mul_ui(prod_primes, prod_primes, primes_table[i]); + } + fmpz_clear(prod_primes); +} + + + +static slong get_total_degree(fmpz_poly_t *A, slong degA){ + slong total_degree = -1; + + for(slong i = 0; i <= degA; i++){ + if(A[i]->length - 1 + i > total_degree){ + total_degree = A[i]->length - 1 + i; + } + } + return total_degree; +} + +static slong get_partial_degree(fmpz_poly_t *A, slong degA){ + slong degAx = -1; + for(slong i = 0; i <= degA ; i++){ + if(A[i]->length - 1 > degAx){ + degAx = A[i]->length -1; + } + } + return degAx; +} + + +static void get_exponent(FILE *file, ulong *exp, ulong nvars){ + for(ulong i = 0; i < nvars-1; i++){ + if(fscanf(file, "%lu ", exp+i)){ + } + } + if(fscanf(file, "%lu\n", exp+nvars-1)){ + } +} + +static void get_mpoly_from_file(FILE *file, fmpz_mpoly_t A, fmpz_mpoly_ctx_t ctx){ + ulong nterms, nvars; + if(fscanf(file, "%lu", &nterms)){ + } + else{ + fprintf(stderr, "Error when reading file\n"); + } + if(fscanf(file, "%lu", &nvars)){ + } + else{ + fprintf(stderr, "Error when reading file\n"); + } + if(nvars!=2){ + fprintf(stderr, "Bad number of variables\n"); + exit(1); + } + fmpz_mpoly_fit_length(A, nterms, ctx); + fmpz_t coeff; + fmpz_init(coeff); + ulong * exp = malloc(sizeof(ulong)*nvars); + for(ulong i=0; i < nterms; i++){ + fmpz_fread(file, coeff); + get_exponent(file, exp, nvars); + // _fmpz_mpoly_emplacebackterm_fmpz_ui(A, coeff, exp, ctx); + fmpz_mpoly_push_term_fmpz_ui(A, coeff, exp, ctx); + } + fmpz_mpoly_sort_terms(A, ctx); + fmpz_mpoly_combine_like_terms(A, ctx); + free(exp); + fmpz_clear(coeff); +} + + +/* + +Input: A et B dependent de deux variables (x1,x2) +L'ordre utilise est l'ordre lex x1 > x2 + +On renvoie un pointeur sur les coefficients de A suivis de +ceux de B vus comme un polynome de Z[x2][x1] + +main_degree_A et main_degree_B sont les degres en x1 de A et B + +*/ +static fmpz_poly_t *make_bpoly_from_mpoly2(fmpz_mpoly_t A, fmpz_mpoly_t B, fmpz_mpoly_ctx_t ctx, + slong *main_degree_A, slong *main_degree_B){ + + *main_degree_A = fmpz_mpoly_degree_si(A, 0, ctx); + *main_degree_B = fmpz_mpoly_degree_si(B, 0, ctx); + + fmpz_poly_t *A_univ = (fmpz_poly_t *)(malloc(sizeof(fmpz_poly_t) * + (*main_degree_A + 1 + *main_degree_B + 1))); + for(ulong i = 0; i <= (*main_degree_A) + (*main_degree_B) + 1; i++){ + fmpz_poly_init(A_univ[i]); + fmpz_poly_zero(A_univ[i]); + } + fmpz_mpoly_t Term; + fmpz_mpoly_init(Term, ctx); + slong deg_mainvar_term = 0, old_deg_mainvar_term = -1; + slong deg_var2; + fmpz_t c; + fmpz_init(c); + for(ulong i = 0; i < A->length; i++){ + fmpz_mpoly_get_term(Term, A, i, ctx); + fmpz_mpoly_get_term_coeff_fmpz(c, Term, 0, ctx); + + deg_mainvar_term = fmpz_mpoly_degree_si(Term, 0, ctx); + deg_var2 = fmpz_mpoly_degree_si(Term, 1, ctx); + if(old_deg_mainvar_term != deg_mainvar_term){ + fmpz_poly_fit_length(A_univ[deg_mainvar_term], deg_var2 + 1); + } + fmpz_poly_set_coeff_fmpz(A_univ[deg_mainvar_term], deg_var2, c); + old_deg_mainvar_term = deg_mainvar_term; + } + for(ulong i = 0; i < B->length; i++){ + fmpz_mpoly_get_term(Term, B, i, ctx); + fmpz_mpoly_get_term_coeff_fmpz(c, Term, 0, ctx); + + deg_mainvar_term = fmpz_mpoly_degree_si(Term, 0, ctx); + deg_var2 = fmpz_mpoly_degree_si(Term, 1, ctx); + if(old_deg_mainvar_term!=deg_mainvar_term){ + fmpz_poly_fit_length(A_univ[*main_degree_A + 1 + deg_mainvar_term], deg_var2 + 1); + } + fmpz_poly_set_coeff_fmpz(A_univ[*main_degree_A + 1 + deg_mainvar_term], deg_var2, c); + old_deg_mainvar_term = deg_mainvar_term; + } + + fmpz_mpoly_clear(Term, ctx); + fmpz_clear(c); + return A_univ; +} + +#ifdef TESTDENSE +static void test_dense(slong deg, ulong nbits, flint_rand_t state){ + fmpz_poly_t *A = (fmpz_poly_t *)(malloc(sizeof(fmpz_poly_t) * (deg + 1))); + fmpz_poly_t *B = (fmpz_poly_t *)(malloc(sizeof(fmpz_poly_t) * (deg + 1))); + for(ulong i = 0; i <= deg; i++){ + fmpz_poly_init(A[i]); + fmpz_poly_init(B[i]); + } + + fmpz_bpoly_random_dense(A, deg, nbits, state); + fmpz_bpoly_random_dense(B, deg, nbits, state); + + fmpz_poly_t res; + fmpz_poly_init(res); + fmpz_poly_t res2; + fmpz_poly_init(res2); + fmpz_poly_t res3; + fmpz_poly_init(res3); + + fmpz_bpoly_resultant_deterministic(res, A, deg, B, deg); + fprintf(stderr, "\n\nStarts probabilistic implem.\n\n"); + fmpz_bpoly_resultant_probabilistic(res2, A, deg, B, deg, 0); + // fmpz_bpoly_sqfree_resultant_probabilistic(res2, A, deg, B, deg, 0); + fprintf(stderr, "\n\nStarts SQRFREE probabilistic implem.\n\n"); + fmpz_bpoly_sqfree_resultant_probabilistic(res2, A, deg, B, deg); + + + /* fprintf(stdout,"R:=PolynomialRing(Rationals());\n"); */ + /* fprintf(stdout,"P:=PolynomialRing(R);\n"); */ + /* fprintf(stdout, "A := "); */ + /* fmpz_bpoly_fprint_pretty(A, deg); */ + /* fprintf(stdout, "\nB := "); */ + /* fmpz_bpoly_fprint_pretty(B, deg); */ + /* char str[1]={"x"}; */ + /* fprintf(stdout, "\nmyres := "); */ + /* fmpz_poly_fprint_pretty(stdout, res2, str); */ + /* fprintf(stdout, ";\n"); */ + /* fprintf(stdout, "\ntime res := Resultant(A, B);\n"); */ + /* fprintf(stdout, "res-myres;"); */ + /* fprintf(stdout, "\n"); */ + + for(ulong i = 0; i <= deg; i++){ + fmpz_poly_clear(A[i]); + fmpz_poly_clear(B[i]); + } + fmpz_poly_clear(res); + fmpz_poly_clear(res2); + fmpz_poly_clear(res3); + free(A); + free(B); +} +#endif + +static void display_help(char **argv){ + fprintf(stdout, "Basic usage\n\n%s -f file_in\n\n", argv[0]); + fprintf(stdout, "Whenever it is possible, by default, it returns\n"); + fprintf(stdout, "a finite sequence of zero-dimensional parametrizations\n"); + fprintf(stdout, "of the set of common complex solutions to the input polynomials\n\n"); + + fprintf(stdout, "Each parametrization corresponds to distinct multiplicities \n"); + fprintf(stdout, "of the resultant of the input polynomials w.r.t. the first variable\n\n"); + + fprintf(stdout, "Additional options: \n"); + fprintf(stdout, "-r \t Computes the resultant\n"); + fprintf(stdout, "-q \t Computes the square-free part of the resultant\n"); + fprintf(stdout, "-b \t Output file will be in binary format\n"); + fprintf(stdout, "-o \t output file \n"); + fprintf(stdout, "-h \t displays this help\n\n"); + + fprintf(stdout, "\n\n file_in must have the following format: \n"); + fprintf(stdout, "First line looks like\nnt n\nwhere nt is the number of terms and n the number of variables\n"); + fprintf(stdout, "Next lines look like \ncoeff e1 e2\n where coeff is an integer coefficient to the monomial x1^e1...xn^en\n"); + fprintf(stdout, "And a next polynomial should be given with the same format\n"); + fprintf(stdout, "\nThe variable which is eliminated is the first one (the one whose exponent comes at first)\n"); +} + + +static fmpz_poly_t *get_input_polynomials(FILE *file, slong *degA, slong *degB){ + fmpz_mpoly_ctx_t ctx; + ordering_t ord = ORD_LEX; + fmpz_mpoly_t A, B; + fmpz_mpoly_ctx_init(ctx, 2, ord); + fmpz_mpoly_init(A, ctx); + fmpz_mpoly_init(B, ctx); + + get_mpoly_from_file(file, A, ctx); + get_mpoly_from_file(file, B, ctx); + + fmpz_poly_t *bA = make_bpoly_from_mpoly2(A, B, ctx, degA, degB); + + fmpz_mpoly_clear(A, ctx); + fmpz_mpoly_clear(B, ctx); + fmpz_mpoly_ctx_clear(ctx); + return bA; +} + +static void display_fmpz_poly_to_usolve(FILE *file, fmpz_poly_t res){ + fprintf(file, "%ld\n", res->length-1); + fmpz_t c; + fmpz_init(c); + if(res->length==0){ + fprintf(file,"%d\n", 0); + return; + } + for(ulong i=0; i < res->length; i++){ + fmpz_poly_get_coeff_fmpz(c, res, i); + fmpz_fprint(file, c); + fprintf(file, "\n"); + } + fmpz_clear(c); +} + +static void display_fmpz_poly_binary_to_usolve(FILE *file, fmpz_poly_t res){ + return; + /* const long length = res->length; */ + /* if(res->length==0){ */ + /* mpz_t * tab = (mpz_t *)(malloc(sizeof(mpz_t) )); */ + /* mpz_init(tab[0]); */ + /* mpz_set_ui(tab[0], 0); */ + /* mpz_t p; */ + /* binary_write_INT(file, p);//cette fonction fait un mpz_clear(p) */ + /* binary_write(file, tab, length); */ + /* mpz_clear(tab[0]); */ + /* free(tab); */ + /* return; */ + /* } */ + /* mpz_t * tab = (mpz_t *)(malloc(sizeof(mpz_t) * length)); */ + /* for(long i=0; i < length; i++){ */ + /* mpz_init(tab[i]); */ + /* fmpz_get_mpz(tab[i], res->coeffs+i); */ + /* } */ + /* mpz_t p; */ + /* binary_write_INT(file, p);//cette fonction fait un mpz_clear(p) */ + /* binary_write(file, tab, length); */ + /* for(long i=0; i < length; i++){ */ + /* mpz_clear(tab[i]); */ + /* } */ + /* free(tab); */ +} + + +static char *getoptions(int argc, char **argv, bsolve_flags * flags){ + int optch, errflag = 0, fflag = 1; + extern int opterr; + + char options[] = "rqhbf:o:v:"; + char *filename = NULL; + opterr = 1; + + while ((optch = getopt(argc, argv, options)) != -1) + switch (optch) { + case 'b': + flags->binary = 1; + break; + case 'f': + fflag = 0; + flags->input_file = optarg; + optind--; + break; + case 'h': + display_help(argv); + exit(1); + case 'o': + flags->output_file = optarg; + optind--; + break; + case 'q': + flags->task = 2; + break; + case 'r': + flags->task = 1; + break; + case 'v': + flags->verb = strtol(optarg, NULL, 10); + optind--; + break; + default: + errflag++; + break; + } + if(fflag){ + fprintf(stderr,"No given file\n"); + fprintf(stderr,"%s -f file_name\n", argv[0]); + exit(1); + } + if(errflag){ + fprintf(stderr,"Invalid usage\n"); + fprintf(stderr,"%s -f file_name\n", argv[0]); + exit(1); + } + return filename; +} + +static bsolve_flags *allocate_initialize_flags(){ + bsolve_flags *flags = malloc(sizeof(bsolve_flags)); + flags->verb=0; + flags->task = 0; + flags->binary = 0; + flags->input_file = NULL; + flags->output_file = NULL; + + return flags; +} + +static void free_flags(bsolve_flags * flags){ + free(flags); +} + +static inline void display_resutant(fmpz_poly_t res, bsolve_flags *flags, + int binary_format){ + if(flags->output_file!=NULL){ + FILE *outputfile = fopen(flags->output_file,"w"); + if(binary_format==0){ + display_fmpz_poly_to_usolve(outputfile, res); + } + else{ + display_fmpz_poly_binary_to_usolve(outputfile, res); + } + fclose(outputfile); + } + else{ + display_fmpz_poly_to_usolve(stdout, res); + } +} + diff --git a/src/connectcurves/src/resultant/main.c b/src/connectcurves/src/resultant/main.c new file mode 100644 index 0000000..4f39f54 --- /dev/null +++ b/src/connectcurves/src/resultant/main.c @@ -0,0 +1,1550 @@ +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include "flint/flint.h" +#include "flint/ulong_extras.h" +#include "flint/mpn_extras.h" +#include "flint/fmpz.h" +#include "flint/fmpz_poly.h" +#include "flint/nmod_vec.h" +#include "flint/nmod_poly.h" +#include "flint/fmpz_mpoly.h" + +#define nthreads 1 + +#define LOG2(X) ((unsigned) (8*sizeof (unsigned long long) - __builtin_clzll((X)) - 1)) +#define MIN(a,b) (((a)<(b))?(a):(b)) + +#define DEBUG 2 + +#include "data.c" +#include "ratreconstruct.c" +#include "io.c" +#include "flint_euclide.c" + +//taken from FLINT +typedef unsigned int UDItype __attribute__ ((mode(DI))); +#define umul_ppmm2(w1, w0, u, v) \ + __asm__ ("mul{q} %3" \ + : "=a" ((UDItype) (w0)), \ + "=d" ((UDItype) (w1)) \ + : "%0" ((UDItype) (u)), \ + "rm" ((UDItype) (v))) + +#define NMOD_DIVREM_DIVCONQUER_CUTOFF 300 + + +/* +Input: Les coeffs des polynomes sont stockes du plus petit au plus grand degre + +pol devient un polynome de degre deg, coeffs de taille bits aleatoires + +*/ +static void fmpz_poly_random_dense(fmpz_poly_t pol, slong deg, mp_bitcnt_t bits, flint_rand_t state){ + + fmpz_t coeff; + fmpz_init(coeff); + + // flint_randseed(state, (ulong) time(NULL), (ulong) clock()); + + long i; + flint_randseed(state, (ulong) clock(), (ulong)(10000*clock())); + + for(i=0;i<=deg;i++){ + fmpz_randbits(coeff, state, bits); + fmpz_poly_set_coeff_fmpz(pol, i, coeff); + flint_randseed(state, (ulong) (i), (ulong)(10000*clock()*(i+1))); + } + fmpz_clear(coeff); +} + +/* +bivarpol est un tableau de taille degmain + 1 et dont les elements sont +des pointeurs sur tableau de taille degvar + 1 + +Les coefficients sont donnes du plus petit au plus grand degre +*/ +static void fmpz_bpoly_random_dense(fmpz_poly_t *bivarpol, + slong degmain, + mp_bitcnt_t bits, flint_rand_t state){ + for(slong i = 0; i <= degmain; i++){ + fmpz_poly_random_dense(bivarpol[i], degmain - i, bits, state); + } +} + +/* + +A est un polynome a coefficients dans Z et prime est un nbre premier (qui tient sur un mot-machine) + +a_mod contiendra A mod prime + +*/ +static void make_nmod_poly(nmod_poly_t a_mod, fmpz_poly_t A, mp_limb_t prime){ + a_mod->mod.n = prime; + a_mod->mod.ninv = n_preinvert_limb(prime); + flint_clz(a_mod->mod.norm); + a_mod->length = 0; + for(unsigned long int i=0; ilength; i++){ + nmod_poly_set_coeff_ui(a_mod, i, fmpz_fdiv_ui(A->coeffs+i, prime)); + } +} + +//On calcule A mod prime qu'on met dans a (a est suppose deja alloue) +static void make_nmod_bpoly(nmod_poly_t *a, fmpz_poly_t *A, unsigned long int deg, mp_limb_t prime){ + for(unsigned long int i = 0; i <= deg; i++){ + make_nmod_poly(a[i], A[i], prime); + } +} + + +static void nmod_bpoly_fast_eval_nmod_2_pols(mp_ptr *a_s_ptr, mp_ptr *b_s_ptr, + nmod_poly_t *a, const slong degA, + nmod_poly_t *b, const slong degB, + const mp_ptr eval_points, const ulong n, + mp_ptr * tree){ + nmod_t mod = a[0]->mod; + _nmod_poly_tree_build(tree, eval_points, n, mod); + + for(ulong i = 0; i <= degA; i++){ + _nmod_poly_evaluate_nmod_vec_fast_precomp(a_s_ptr[i], a[i]->coeffs, a[i]->length, tree, n, mod); + } + for(ulong i = 0; i <= degB; i++){ + _nmod_poly_evaluate_nmod_vec_fast_precomp(b_s_ptr[i], b[i]->coeffs, b[i]->length, tree, n, mod); + } + +} + + +static void nmod_bpoly_eval_nmod(nmod_poly_t a_s, + nmod_poly_t *a, const slong degmain, + const mp_limb_t eval_point){ + for(ulong i = 0; i <=degmain; i++){ + a_s->coeffs[i] = nmod_poly_evaluate_nmod(a[i], eval_point); + } + a_s->length = degmain + 1; +} + + +/* +res contiendra le resultat +a et b sont des pointeurs sur tableaux de nmod_poly_t de longueur degmain+1 +(degmain = degre de la variable principale) + +Chaque nmod_poly_t est de degre degvar + +numpoints est le nombre de points d'interpolation dont on a besoin ; il doit etre precalcule + */ +static void nmod_bpoly_resultant(nmod_poly_t res, nmod_poly_t *a, const slong degA, nmod_poly_t *b, + const slong degB, const ulong numpoints, + nmod_poly_t *a_s_ptr, nmod_poly_t *b_s_ptr, + mp_ptr restable, mp_ptr eval_points){ + + ulong count_points = 0, i = 0; + while(count_points < numpoints){ + if(nmod_poly_evaluate_nmod(a[degA], i) != 0){ + eval_points[count_points] = i; + count_points++; + i++; + } + else{ + i++; + } + } + mp_limb_t prime = a[0]->mod.n; + + mp_limb_t ninv = n_preinvert_limb(prime); + + a_s_ptr[0]->mod.n = prime; + a_s_ptr[0]->mod.ninv = ninv; + flint_clz(a_s_ptr[0]->mod.norm); + a_s_ptr[0]->length = 0; + + b_s_ptr[0]->mod.n = prime; + b_s_ptr[0]->mod.ninv = ninv; + flint_clz(b_s_ptr[0]->mod.norm); + b_s_ptr[0]->length = 0; + + // nmod_poly_init2(a_s, prime, degA+1); + // nmod_poly_init2(b_s, prime, degB+1); + // mp_limb_t * restable = (mp_limb_t *)(malloc(sizeof(mp_limb_t)*numpoints)); + // nmod_poly_evaluate_nmod_vec(); + + for(i = 0; i < numpoints; i++){ + nmod_bpoly_eval_nmod(a_s_ptr[0], a, degA, eval_points[i]); + nmod_bpoly_eval_nmod(b_s_ptr[0], b, degB, eval_points[i]); + restable[i] = nmod_poly_resultant(a_s_ptr[0], b_s_ptr[0]); + } + + nmod_poly_interpolate_nmod_vec(res, eval_points, restable, numpoints); +#ifdef DEBUG + char str[1]= {"x"}; + nmod_poly_fprint_pretty(stderr, res, str);fprintf(stderr, "\n"); +#endif + return; +} + + +static inline void get_coeffs_from_eval(nmod_poly_t a_s, mp_ptr *a_s_ptr, ulong deg, slong n){ + for(ulong i=0; i <= deg; i++){ + a_s->coeffs[i] = a_s_ptr[i][n]; + } +} + + + +//calcul du resultant par evaluation interpolation. +//on suppose que le tableau des points d'evaluation ne contient pas que des 0 et est deja alloue +//les donnees necessaires au calcul sont deja allouees egalement. +static void nmod_bpoly_resultant_allocated_feval(data_heap_t *heap, + slong mdegA, slong mdegB, + int pos){ + //a ameliorer + ulong count_points = 0, i = 0; + while(count_points < heap->npts){ + if(nmod_poly_evaluate_nmod(heap->a_mod[mdegA], i) != 0 && nmod_poly_evaluate_nmod(heap->b_mod[mdegB], i) != 0){ + heap->ev_pts[count_points] = i; + count_points++; + i++; + } + else{ + i++; + } + } + + nmod_bpoly_fast_eval_nmod_2_pols(heap->a_mod_eval_all, heap->b_mod_eval_all, + heap->a_mod, mdegA, heap->b_mod, mdegB, + heap->ev_pts, heap->npts, heap->tree); + + for(ulong i = 0; i < heap->npts; i++){ + //On ne peut pas paralleliser a cause de w qui est partage. Il faudra modifier ca. + + get_coeffs_from_eval(heap->a_mod_eval, heap->a_mod_eval_all, mdegA, i); + get_coeffs_from_eval(heap->b_mod_eval, heap->b_mod_eval_all, mdegB, i); + heap->res_mod_eval[i] = _nmod_poly_resultant_euclidean_allocated(heap->a_mod_eval->coeffs, + heap->a_mod_eval->length, + heap->b_mod_eval->coeffs, + heap->b_mod_eval->length, + heap->a_mod_eval->mod, + heap->nmod_coeffs_array); + } + + nmod_poly_interpolate_nmod_vec(heap->res_mod_array[pos], heap->ev_pts, heap->res_mod_eval, heap->npts); + + return; +} + +//Fonction qui renvoie la partie square-free d'un polynome pol + +static void square_free_part_nmod_poly(nmod_poly_t pol, nmod_poly_factor_t sqf){ + + sqf->num = 0; + mp_limb_t lc = pol->coeffs[pol->length-1]; + + nmod_poly_factor_squarefree(sqf, pol); + nmod_poly_set(pol, sqf->p); + + for(ulong count = 1; count < sqf->num; count++){ + nmod_poly_mul(pol, pol, sqf->p+count); + } + + nmod_poly_scalar_mul_nmod(pol, pol, lc); + sqf->num = 0; +} + +static inline void nmod_poly_init_copy(nmod_poly_t *poly1, nmod_poly_t *poly2){ + (*poly1)->length = (*poly2)->length; + (*poly1)->alloc = (*poly2)->alloc; + (*poly1)->coeffs = (*poly2)->coeffs; +} + +static inline void nmod_poly_copy(nmod_poly_t poly1, nmod_poly_t poly2){ + (poly1)->length = (poly2)->length; + for(ulong i = 0; i < (poly1)->length; i++){ + (poly1)->coeffs[i] = (poly2)->coeffs[i]; + } +} + +//calcul d'une param rationnelle par evaluation interpolation. +//on suppose que le tableau des points d'evaluation ne contient pas que des 0 et est deja alloue +//les donnees necessaires au calcul sont deja allouees egalement. +//On renvoie 0 si il y a un probleme +//Notamment, on suppose que le resultant est square-free. +//Du coup, une seule parametrisation est construite dans nmod_all_params_table+pos +static int nmod_bpoly_param_allocated_feval_sqfree(data_heap_t *heap, + slong mdegA, slong mdegB, + int pos){ + + ulong count_points = 0, i = 0; + while(count_points < heap->npts){ + if(nmod_poly_evaluate_nmod(heap->a_mod[mdegA], i) != 0 && + nmod_poly_evaluate_nmod(heap->b_mod[mdegB], i) != 0){ + heap->ev_pts[count_points] = i; + count_points++; + i++; + } + else{ + i++; + } + } + + nmod_bpoly_fast_eval_nmod_2_pols(heap->a_mod_eval_all, + heap->b_mod_eval_all, + heap->a_mod, mdegA, + heap->b_mod, mdegB, + heap->ev_pts, + heap->npts, heap->tree); + for(ulong i = 0; i < heap->npts; i++){ + //On ne peut pas paralleliser a cause de w qui est partage. Il faudra modifier ca. + + get_coeffs_from_eval(heap->a_mod_eval, heap->a_mod_eval_all, mdegA, i); + get_coeffs_from_eval(heap->b_mod_eval, heap->b_mod_eval_all, mdegB, i); + + if(DEBUG > 3){ + fprintf(stderr, "ev_pt = %ld\n", heap->ev_pts[i]); + char str[1] = {"x"}; + nmod_poly_fprint_pretty(stderr, heap->a_mod_eval, str); + fprintf(stderr, "\n"); + nmod_poly_fprint_pretty(stderr, heap->b_mod_eval, str); + fprintf(stderr, "\n"); + } + heap->res_mod_eval[i] = + _nmod_poly_param_euclidean_allocated(heap->a_mod_eval->coeffs, + heap->a_mod_eval->length, + heap->b_mod_eval->coeffs, + heap->b_mod_eval->length, + heap->a_mod_eval->mod, + heap->nmod_coeffs_array, + heap->par_h_mod_eval + i, + heap->par_t_mod_eval + i); + if(DEBUG > 3){ + fprintf(stderr, "Computed resultant = %ld\n", + heap->res_mod_eval[i]); + fprintf(stderr, "head -> %ld\n", + heap->par_h_mod_eval[i]); + fprintf(stderr, "tail -> %ld\n", + heap->par_t_mod_eval[i]); + } + } + + nmod_poly_interpolate_nmod_vec(heap->nmod_lparams_array[pos]->params[0]->elim, + heap->ev_pts, heap->res_mod_eval, heap->npts); + + nmod_poly_interpolate_nmod_vec(heap->nmod_lparams_array[pos]->params[0]->denom, + heap->ev_pts, heap->par_h_mod_eval, heap->npts); + + nmod_poly_interpolate_nmod_vec(heap->nmod_lparams_array[pos]->params[0]->coords[0], + heap->ev_pts, heap->par_t_mod_eval, heap->npts); + //On suppose que le resultant est square-free. + + if(DEBUG > 3){ + for(ulong k = 0; k < heap->npts; k++){ + fprintf(stderr, "%lu ", heap->par_t_mod_eval[k]); + } + fprintf(stderr, "\n"); + for(ulong k = 0; k < heap->npts; k++){ + fprintf(stderr, "%lu ", heap->ev_pts[k]); + } + fprintf(stderr, "\n"); + char str[1] = {"x"}; + fprintf(stderr, "degree = %ld\n", heap->par_t_mod_array[pos]->length - 1); + nmod_poly_fprint_pretty(stderr, heap->par_t_mod_array[pos], str); + fprintf(stderr,"\n"); + fprintf(stderr, "degree = %ld\n", heap->par_h_mod_array[pos]->length - 1); + nmod_poly_fprint_pretty(stderr, heap->par_h_mod_array[pos], str); + fprintf(stderr,"\n\n"); + nmod_poly_fprint_pretty(stderr, heap->nmod_lparams_array[pos]->params[0]->coords[0], str); + fprintf(stderr,"\n"); + } + + if(DEBUG > 4){ + fprintf(stderr, "\nParametrization mod %ld\n", heap->primes_array[pos]); + print_nmod_param(stderr, heap->nmod_lparams_array[pos]->params[0]); + fprintf(stderr, "prime in param struct = \n%ld, \n%ld\n", + heap->nmod_lparams_array[pos]->params[0]->denom->mod.n, + heap->nmod_lparams_array[pos]->params[0]->coords[0]->mod.n); + } + + return 1; +} + + +//calcul d'une param rationnelle par evaluation interpolation. +//on suppose que le tableau des points d'evaluation ne contient pas que des 0 et est deja alloue +//les donnees necessaires au calcul sont deja allouees egalement. +//On renvoie 0 si il y a un probleme +//Ici, on suppose que le resultant n'est pas square-free. + +static int nmod_bpoly_param_allocated_feval_nonsqfree(data_heap_t *heap, + slong mdegA, slong mdegB, + int pos){ + + ulong count_points = 0, i = 0; + while(count_points < heap->npts){ + if(nmod_poly_evaluate_nmod(heap->a_mod[mdegA], i) != 0 && + nmod_poly_evaluate_nmod(heap->b_mod[mdegB], i) != 0){ + heap->ev_pts[count_points] = i; + count_points++; + i++; + } + else{ + i++; + } + } + + nmod_bpoly_fast_eval_nmod_2_pols(heap->a_mod_eval_all, heap->b_mod_eval_all, + heap->a_mod, mdegA, heap->b_mod, mdegB, + heap->ev_pts, heap->npts, heap->tree); + for(ulong i = 0; i < heap->npts; i++){ + //On ne peut pas paralleliser a cause de w qui est partage. Il faudra modifier ca. + + get_coeffs_from_eval(heap->a_mod_eval, heap->a_mod_eval_all, mdegA, i); + get_coeffs_from_eval(heap->b_mod_eval, heap->b_mod_eval_all, mdegB, i); + + heap->res_mod_eval[i] = + _nmod_poly_param_euclidean_allocated(heap->a_mod_eval->coeffs, + heap->a_mod_eval->length, + heap->b_mod_eval->coeffs, + heap->b_mod_eval->length, + heap->a_mod_eval->mod, + heap->nmod_coeffs_array, + heap->par_h_mod_eval + i, + heap->par_t_mod_eval + i); + + } + + nmod_poly_interpolate_nmod_vec(heap->res_mod_array[pos], heap->ev_pts, heap->res_mod_eval, heap->npts); + nmod_poly_interpolate_nmod_vec(heap->par_h_mod_array[pos], + heap->ev_pts, heap->par_h_mod_eval, heap->npts); + nmod_poly_interpolate_nmod_vec(heap->par_t_mod_array[pos], + heap->ev_pts, heap->par_t_mod_eval, heap->npts); + + heap->sqf_part->num = 0; + nmod_poly_factor_squarefree(heap->sqf_part, heap->res_mod_array[pos]); + + for(ulong i = 0; i < heap->sqf_part->num; i++){ + nmod_poly_copy(heap->nmod_lparams_array[pos]->params[i]->elim, + heap->sqf_part->p+i); + + if(nmod_poly_invmod(heap->GCDINV[pos], + heap->par_h_mod_array[pos], + heap->nmod_lparams_array[pos]->params[i]->elim)){ + + nmod_poly_derivative(heap->nmod_lparams_array[pos]->params[i]->denom, + heap->nmod_lparams_array[pos]->params[i]->elim); + + nmod_poly_mul(heap->nmod_lparams_array[pos]->params[i]->coords[0], + heap->par_t_mod_array[pos], + heap->GCDINV[pos]); + + nmod_poly_rem(heap->nmod_lparams_array[pos]->params[i]->coords[0], + heap->nmod_lparams_array[pos]->params[i]->coords[0], + heap->nmod_lparams_array[pos]->params[i]->elim); + nmod_poly_mul(heap->nmod_lparams_array[pos]->params[i]->coords[0], + heap->nmod_lparams_array[pos]->params[i]->coords[0], + heap->nmod_lparams_array[pos]->params[i]->denom + ); + + nmod_poly_rem(heap->nmod_lparams_array[pos]->params[i]->coords[0], + heap->nmod_lparams_array[pos]->params[i]->coords[0], + heap->nmod_lparams_array[pos]->params[i]->elim); + } + else{ + fprintf(stderr, "Pas d'inversion possible\n"); + return 0; + } + } + + if(DEBUG>2){ + fprintf(stderr, "Prime = %ld\n", heap->primes_array[pos]); + print_nmod_all_params_pretty(stderr, heap->nmod_lparams_array[pos]); + } + + return 1; +} + +static void fmpz_bpoly_resultant_deterministic(fmpz_poly_t res, + fmpz_poly_t *A, slong degA, + fmpz_poly_t *B, slong degB){ + slong totaldegA = get_total_degree(A, degA); + slong totaldegB = get_total_degree(B, degB); + + fprintf(stderr, "Total degrees : %ld %ld\n", totaldegA, totaldegB); + //maximum degree in the variable that is not eliminated + slong degAx = get_partial_degree(A, degA); + slong degBx = get_partial_degree(B, degB); + + ulong numpoints = MIN(totaldegA * totaldegB + 1, degB * degAx + degA * degBx + 1); + ulong nbitsA = nbits_bound_fmpz_bvar_poly(A, degA); + ulong nbitsB = nbits_bound_fmpz_bvar_poly(B, degB); + fprintf(stderr, "Max nbits : %lu %lu\n", nbitsA, nbitsB); + ulong i; + + //Hadamard-type bound (Goldstein-Graham) + ulong bound_nbits = nbitsA*(degB) + nbitsB*(degA); + fprintf(stderr, "Bound (nbits) = %lu\n", bound_nbits); + + mp_limb_t prime = 1073741827; + prime = n_nextprime(1152921504606847009, 0); + // prime = n_nextprime(prime, 0); + ulong nbits_prime = LOG2(prime); + + nmod_poly_t *a = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * (degA + 1))); + nmod_poly_t *b = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * (degB + 1))); + + for(i = 0; i <= degA; i++){ + nmod_poly_init(a[i], prime); + make_nmod_poly(a[i], A[i], prime); + } + for(i = 0; i <= degB; i++){ + nmod_poly_init(b[i], prime); + make_nmod_poly(b[i], B[i], prime); + } + + //data for calling nmod_bpoly_resultant + //a_s_ptr contiendra la specialisation des coefficients de a en un point. + nmod_poly_t *a_s_ptr = malloc(sizeof(nmod_poly_t)); + nmod_poly_init2(a_s_ptr[0], prime, degA+1); + + nmod_poly_t *b_s_ptr = malloc(sizeof(nmod_poly_t)); + nmod_poly_init2(b_s_ptr[0], prime, degB+1); + + //contiendra les valeurs des resultants modulo des premiers + mp_limb_t * restable = (mp_limb_t *)(malloc(sizeof(mp_limb_t)*numpoints)); + //contiendra les points d'evaluation + mp_limb_t * eval_points = (mp_limb_t *)(malloc(sizeof(mp_limb_t)*numpoints)); + ////////////////////////////////// + + ulong count_nprimes = 1; + + nmod_poly_t *res_mod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * (bound_nbits / nbits_prime + 1) )); + mp_limb_t *primes_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * (bound_nbits / nbits_prime + 1))); + double e = omp_get_wtime(); + nbits_prime = 0; + + fmpz_t *prod_mod = malloc(sizeof(fmpz_t)); + fmpz_init(prod_mod[0]); + while(nbits_prime < bound_nbits){ + for(i = 0; i <= degA; i++){ + make_nmod_poly(a[i], A[i], prime); + } + for(i = 0; i <= degB; i++){ + make_nmod_poly(b[i], B[i], prime); + } + if(a[degA]->length>0 && b[degB]->length>0){ + nmod_poly_init(res_mod_table[count_nprimes-1], prime); + primes_table[count_nprimes-1] = prime; + nmod_bpoly_resultant(res_mod_table[count_nprimes-1], a, degA, b, degB, numpoints, + a_s_ptr, b_s_ptr, restable, eval_points); + prime = n_nextprime(prime, 0); + nbits_prime += LOG2(prime); + count_nprimes++; + } + else{ + prime = n_nextprime(prime, 0); + } + } + count_nprimes--; + fprintf(stderr, "Number of used primes = %lu\n", count_nprimes); + fprintf(stderr, "Elapsed time (mod comp.): %f\n", omp_get_wtime() - e); + + e=omp_get_wtime(); + crt_lift_resultant(res, res_mod_table, primes_table, count_nprimes, prod_mod); + fprintf(stderr, "Elapsed time (CRT comp.): %f\n", omp_get_wtime() - e); + fprintf(stderr, "Final size coeffs: %ld\n", FLINT_ABS(_fmpz_vec_max_bits(res->coeffs, res->length))); + fprintf(stderr, "Degree of the output: %ld\n", res->length-1); + + fmpz_clear(prod_mod[0]); + free(prod_mod); + nmod_poly_clear(a_s_ptr[0]); + nmod_poly_clear(b_s_ptr[0]); + free(a_s_ptr); + free(b_s_ptr); + free(eval_points); + + for(i = 0; i< count_nprimes; i++){ + nmod_poly_clear(res_mod_table[i]); + } + for(i = 0; i <= degA; i++){ + nmod_poly_clear(a[i]); + } + for(i = 0; i <= degB; i++){ + nmod_poly_clear(b[i]); + } + free(res_mod_table); + free(restable); + free(primes_table); + free(a); + free(b); + return; +} + +/* + Input: dans res_mod_table on a N = size_table images modulaires de resultant + (modulo les premiers de primes_table). + + On vĂ©rifie que res modulo ces premiers correspond aux elements de res_mod_table +*/ +/* static int check_modular_images_old(fmpz_poly_t res, nmod_poly_t res_mod, nmod_poly_t *res_mod_table, */ +/* mp_limb_t *primes_table, int size_table, slong *max_degree){ */ +/* for(int i = 0; i < size_table; i++){ */ +/* if(*max_degree < res_mod_table[i]->length - 1){ */ +/* *max_degree = res_mod_table[i]->length - 1; */ +/* } */ +/* } */ +/* for(int i = 0; i < size_table; i++){ */ +/* make_nmod_poly(res_mod, res, primes_table[i]); */ +/* if(!nmod_poly_equal(res_mod, res_mod_table[i])){ */ +/* return 0; */ +/* } */ +/* } */ +/* return 1; */ +/* } */ + +/* + Input: dans res_mod_table on a N = size_table images modulaires de resultant + (modulo les premiers de primes_table). + + On vĂ©rifie que res modulo ces premiers correspond aux elements de res_mod_table +*/ +static int check_modular_images(fmpz_poly_t res, + data_heap_t *heap, + int size_table, slong *max_degree){ + for(int i = 0; i < size_table; i++){ + if(*max_degree < heap->res_mod_array[i]->length - 1){ + *max_degree = heap->res_mod_array[i]->length - 1; + } + } + for(int i = 0; i < size_table; i++){ + make_nmod_poly(heap->res_mod[0], res, heap->primes_array[i]); + if(!nmod_poly_equal(heap->res_mod[0], heap->res_mod_array[i])){ + return 0; + } + } + return 1; +} + + +static void update_poly_tables_with_prime(data_heap_t *heap, + int pos, mp_limb_t prime){ + mp_limb_t p = n_preinvert_limb(prime); + heap->primes_array[pos] = prime; + + heap->GCDINV[pos]->mod.n = prime; + heap->GCDINV[pos]->mod.ninv = p; + flint_clz(heap->GCDINV[pos]->mod.norm); + + heap->res_mod_array[pos]->mod.n = prime; + heap->res_mod_array[pos]->mod.ninv = p; + flint_clz(heap->res_mod_array[pos]->mod.norm); + + heap->par_t_mod_array[pos]->mod.n = prime; + heap->par_t_mod_array[pos]->mod.ninv = p; + flint_clz(heap->par_t_mod_array[pos]->mod.norm); + + heap->par_h_mod_array[pos]->mod.n = prime; + heap->par_h_mod_array[pos]->mod.ninv = p; + flint_clz(heap->par_h_mod_array[pos]->mod.norm); + + heap->a_mod_eval->mod.n = prime; + heap->a_mod_eval->mod.ninv = p; + flint_clz(heap->a_mod_eval->mod.norm); + + heap->b_mod_eval->mod.n = prime; + heap->b_mod_eval->mod.ninv = p; + flint_clz(heap->b_mod_eval->mod.norm); + +} + +static void update_nmod_param_with_prime(nmod_all_params_t *lparams, + mp_limb_t prime){ + mp_limb_t p = n_preinvert_limb(prime); + + for(int i = 0; i nparams; i++){ + nmod_param_t *param = lparams->params[i]; + param->denom->mod.n = prime; + param->denom->mod.ninv = p; + flint_clz(param->denom->mod.norm); + + param->elim->mod.n = prime; + param->elim->mod.ninv = p; + flint_clz(param->elim->mod.norm); + + for(int j = 0; j < param->nvars; j++){ + param->coords[j]->mod.n = prime; + param->coords[j]->mod.ninv = p; + flint_clz(param->coords[j]->mod.norm); + } + } +} + + +//Fonction qui teste si pol est square-free +//renvoie 0 si pol est square-free, un entier >= 1 sinon +static slong is_non_square_free(nmod_poly_t pol, nmod_poly_factor_t sqf){ + nmod_poly_factor_squarefree(sqf, pol); + int nf = sqf->num ; + sqf->num = 0; + return nf - 1; +} + + +static void get_degrees_and_nbits(fmpz_poly_t *A, slong mdegA, + fmpz_poly_t *B, slong mdegB, + slong *tdegA, slong *tdegB, + slong *sdegA, slong *sdegB, + ulong *nbitsA, ulong *nbitsB){ + //total degrees + *tdegA = get_total_degree(A, mdegA); + *tdegB = get_total_degree(B, mdegB); + + //maximum degree in the variable that is not eliminated + *sdegA = get_partial_degree(A, mdegA); + *sdegB = get_partial_degree(B, mdegB); + + *nbitsA = nbits_bound_fmpz_bvar_poly(A, mdegA); + *nbitsB = nbits_bound_fmpz_bvar_poly(B, mdegB); +} + +//renvoie 0 si on a encore besoin de lifter les coefficients +static inline int check_param_modular_images(fmpz_param_t *param, + data_heap_t *heap, int size){ + for(ulong i = 0; i < size; i++){ + //on verifie le polynome eliminant + make_nmod_poly(heap->res_mod[0], param->elim, heap->primes_array[i]); + if(!nmod_poly_equal(heap->res_mod[0], + heap->nmod_lparams_array[i]->params[0]->elim)){ + return 0; + } + make_nmod_poly(heap->res_mod[0], param->denom, heap->primes_array[i]); + //on verifie le polynome denominateur + if(!nmod_poly_equal(heap->res_mod[0], + heap->nmod_lparams_array[i]->params[0]->denom)){ + return 0; + } + //on verifie les coordonnees + make_nmod_poly(heap->res_mod[0], param->coords[0], heap->primes_array[i]); + if(!nmod_poly_equal(heap->res_mod[0], + heap->nmod_lparams_array[i]->params[0]->coords[0])){ + return 0; + } + } + return 1; +} + + +//renvoie 0 si on a encore besoin de lifter les coefficients +static inline int check_all_params_modular_image(fmpz_all_params_t *all_params, + data_heap_t *heap, int size){ + int nparams = all_params->nparams; + for(int i = 0; i < nparams; i++){ + if(!check_param_modular_images(all_params->params[i], heap, size)){ + return 0; + } + } + return 1; +} + +static inline void integer_param_crt_lifting_all_params(fmpz_all_params_t *all_params, + data_heap_t *heap, int size){ + slong maxdegree = -1; + fmpz_param_t *param = all_params->params[0]; + for(ulong i = 0; i < size; i++){ + if(heap->nmod_lparams_array[0]->params[0]->elim->length - 1 > maxdegree){ + maxdegree = heap->nmod_lparams_array[0]->params[0]->elim->length - 1; + } + } + if((param)->elim->length-1!=maxdegree){ + fprintf(stderr, "Error with degree estimates in integer_param_crt_lifting\n"); + fprintf(stderr, "maxdegree = %ld\n", maxdegree); + fprintf(stderr, "First param of degree = %ld\n", (param)->elim->length-1); + exit(1); + } + + if(DEBUG>=5){ + for(int i = 0; i < size; i++){ + fprintf(stderr, "prime = %ld\n", heap->primes_array[i]); + print_nmod_param(stderr, (heap->nmod_lparams_array[i]->params[0])); + fprintf(stderr, "\n"); + } + } + + for(ulong j = 0; j <= maxdegree; j++){ + for(ulong i = 0; i < size; i++){ + + fmpz_CRT_ui(((param)->elim->coeffs)+j, ((param)->elim->coeffs)+j, + heap->prod_primes[i], + (heap->nmod_lparams_array[i]->params[0]->elim->coeffs)[j], + heap->primes_array[i], 1); + + fmpz_CRT_ui(((param)->denom->coeffs)+j, ((param)->denom->coeffs)+j, + heap->prod_primes[i], + (heap->nmod_lparams_array[i]->params[0]->denom->coeffs)[j], + heap->primes_array[i], 1); + + fmpz_CRT_ui(((param)->coords[0]->coeffs)+j, ((param)->coords[0]->coeffs)+j, + heap->prod_primes[i], + (heap->nmod_lparams_array[i]->params[0]->coords[0]->coeffs)[j], + heap->primes_array[i], 1); + + } + } + +} + +static inline int rational_param_lifting(fmpz_param_t *param, + data_heap_t *heap, + int size, int mul){ + int b = 1; + + ulong deg = heap->nmod_lparams_array[0]->params[mul]->elim->length - 1; + if(param->rec_elim < deg){ + for(ulong j = 0; j <= deg; j++){ + for(ulong i = 0; i < size; i++){ + fmpz_CRT_ui(((param)->elim->coeffs)+j, ((param)->elim->coeffs)+j, + heap->prod_primes[i], + (heap->nmod_lparams_array[i]->params[mul]->elim->coeffs)[j], + heap->primes_array[i], 1); + } + } + fprintf(stderr, "Lifting the elimination polynomial\n"); + if(rat_recon(param->elim, param->elim_num, param->elim_den, param->elim_lcm, + heap, deg, &(param->rec_elim)) == 0){ + b = 0; + } + } + + deg = (heap->nmod_lparams_array[0]->params[mul]->coords[0]->length) - 1; + if(param->rec_coords[0] < deg){ + for(ulong j = 0; j <= deg; j++){ + for(ulong i = 0; i < size; i++){ + fmpz_CRT_ui(((param)->coords[0]->coeffs)+j, ((param)->coords[0]->coeffs)+j, + heap->prod_primes[i], + (heap->nmod_lparams_array[i]->params[mul]->coords[0]->coeffs)[j], + heap->primes_array[i], 1); + } + } + if(b==0){ + return b; + } + fprintf(stderr, "Lifting of the parametrization\n"); + if(rat_recon(param->coords[0], param->coords_num[0], param->coords_den[0], + param->coords_lcm[0], + heap, deg, param->rec_coords) == 0){ + b = 0; + } + } + fprintf(stderr, "LCM = "); + fmpz_fprint(stderr, param->coords_lcm[0]); + fprintf(stderr, "\n"); + + return b; +} + +//attention : ici le denominateur sera de tout de maniere la derivee du polynome +//eliminant +static inline int rational_param_lifting_all_params(fmpz_all_params_t *all_params, + data_heap_t *heap, int size){ + int b = 1; + for(ulong i = 0; i < all_params->nparams; i++){ + fmpz_param_t *param = all_params->params[i]; + if(param->recons == 0){ + if(rational_param_lifting(param, heap, size, i)==0){ + b = 0; + } + else{ + param->recons = 1; + } + } + } + return b; +} + + +static inline void copy_coeffs_poly(fmpz_poly_t poly1, fmpz_poly_t poly2){ + + for(ulong i = 0; i < poly2->length; i++){ + fmpz_poly_set_coeff_fmpz(poly1, i, poly2->coeffs + i); + } +} + +static inline bsolve_fmpz_param_t *copy_to_final_parametrization(fmpz_param_t *param){ + bsolve_fmpz_param_t *bs_param = malloc(sizeof(bsolve_fmpz_param_t)); + bs_param->nvars = param->nvars; + bs_param->sepelem = malloc(sizeof(mp_limb_t) * 2); + bs_param->cfs = malloc(sizeof(fmpz_t) * param->nvars); + + for(int i = 0; i < 2; i++){ + bs_param->sepelem[i] = param->sepelem[i]; + } + fmpz_poly_init2(bs_param->elim, param->elim_num->length); + + copy_coeffs_poly(bs_param->elim, param->elim_num); + + bs_param->coords = malloc(sizeof(fmpz_poly_t) * param->nvars); + + for(int i = 0; i < param->nvars; i++){ + fmpz_poly_init2(bs_param->coords[i], param->coords_num[i]->length); + copy_coeffs_poly(bs_param->coords[i], param->coords_num[i]); + fmpz_init(bs_param->cfs[i]); + fmpz_set(bs_param->cfs[i], param->coords_lcm[i]); + fprintf(stderr, "Warning: changing cfs\n"); + fmpz_set_ui(bs_param->cfs[i], 1); + } + fmpz_poly_init2(bs_param->denom, param->elim_num->length - 1); + + for(ulong i = 0; i < param->elim_num->length - 1; i++){ + fmpz_poly_set_coeff_ui(bs_param->denom, i, 1); + fmpz_mul_ui(bs_param->denom->coeffs + i, bs_param->elim->coeffs + (i+1), i+1); + } + return bs_param; +} + +static inline void copy_to_final_all_params(bsolve_fmpz_all_params_t *bs_params, + fmpz_all_params_t *params){ + bs_params->nparams = params->nparams; + fprintf(stderr, "Number of parametrizations = %d\n", params->nparams); + bs_params->params = malloc(sizeof(bsolve_fmpz_param_t *) * params->nparams); + for(int i = 0; i < params->nparams; i++){ + bs_params->params[i] = copy_to_final_parametrization(params->params[i]); + } +} + +//retourne 1 si il y a une param. rat. des solutions +//sinon retourne 0 + +/* output parametrization will be stored in bs_param */ +static int _fmpz_bpoly_param_probabilistic(bsolve_fmpz_all_params_t *bs_param, + fmpz_poly_t *A, slong mdegA, + fmpz_poly_t *B, slong mdegB){ + slong tdegA, tdegB, sdegA, sdegB; + ulong nbitsA, nbitsB; + int size_table = 8; + /* + tdegA and degB will be the total degrees of A and B + + sdegA and sdegB will be the partial degrees of A and B + in the variable that is kept. + + nbitsA and nbitsB are the max bit size coeffs of A and B + */ + get_degrees_and_nbits(A, mdegA, + B, mdegB, + &tdegA, &tdegB, + &sdegA, &sdegB, + &nbitsA, &nbitsB); + + data_heap_t *heap = allocate_data_heap(tdegA, tdegB, + mdegA, mdegB, + sdegA, sdegB, + size_table); + + fprintf(stderr, "Total degrees : %ld %ld\n", tdegA, tdegB); + fprintf(stderr, "Main degrees : %ld %ld\n", mdegA, mdegB); + fprintf(stderr, "Bit sizes : %lu %lu\n", nbitsA, nbitsB); + fprintf(stderr, "numpoints = %lu\n", heap->npts); + + /*Hadamard-type (Goldstein-Graham) to obtain a bound on the + bit size of the resultant + */ + ulong bound_nbits = nbitsA*(mdegB) + nbitsB*(mdegA); + + fprintf(stderr, "Bound (nbits) = %lu\n", bound_nbits); + + mp_limb_t prime = 1073741827; + prime = n_nextprime(1152921504606847009, 0); + ulong nbits_prime = LOG2(prime); + + ulong count_nprimes = 1; + + double e = omp_get_wtime(); + nbits_prime = 0; + + + double e_mod = 0; + + //On teste si le resultant est square-free + make_nmod_bpoly(heap->a_mod, A, mdegA, prime); + make_nmod_bpoly(heap->b_mod, B, mdegB, prime); + + update_poly_tables_with_prime(heap, 0, prime); + nmod_bpoly_param_allocated_feval_sqfree(heap, + mdegA, mdegB, 0); + + fprintf(stderr, "Degree of the resultant is %ld\n", heap->nmod_lparams_array[0]->params[0]->elim->length - 1); + + /* resultant is a non-zero constant -> no solution */ + if(heap->nmod_lparams_array[0]->params[0]->elim->length == 1){ +#if(DEBUG > 3) + char str[1] = {"x"}; + fprintf(stderr, "elim = "); + nmod_poly_fprint_pretty(stderr, + heap->nmod_lparams_array[0]->params[0]->elim, + str); + fprintf(stderr, "\n"); + fprintf(stderr, "denom = "); + nmod_poly_fprint_pretty(stderr, + heap->nmod_lparams_array[0]->params[0]->denom, + str); + fprintf(stderr, "\n"); +#endif + bs_param->nparams = 1; + bs_param->params = malloc(sizeof(bsolve_fmpz_param_t *)); + bs_param->params[0] = malloc(sizeof(bsolve_fmpz_param_t)); + bs_param->params[0]->nvars = 1; + + bs_param->params[0]->sepelem = malloc(sizeof(mp_limb_t) * 2); + bs_param->params[0]->sepelem[0] = 0; + bs_param->params[0]->sepelem[1] = 1; + + bs_param->params[0]->coords = malloc(sizeof(fmpz_poly_t) ); + + fmpz_poly_init2(bs_param->params[0]->elim, 1); + fmpz_poly_set_ui(bs_param->params[0]->elim, 1); + fmpz_poly_init2(bs_param->params[0]->coords[0], 1); + fmpz_poly_set_ui(bs_param->params[0]->coords[0], 0); + return 1; + } + if(DEBUG>3){ + char str[1] = {"x"}; + nmod_poly_fprint_pretty(stderr, *heap->res_mod_array, str); + fprintf(stderr, "\n"); + fprintf(stderr, "RESULTANT = "); + nmod_poly_fprint_pretty(stderr, heap->nmod_lparams_array[0]->params[0]->elim, str); + fprintf(stderr, "\n"); + } + + heap->sqf_part->num = 0; + nmod_poly_factor_squarefree(heap->sqf_part, heap->nmod_lparams_array[0]->params[0]->elim); + + int nb_sqfree = heap->sqf_part->num; + int is_sqf = 0; + if(nb_sqfree==1 && (heap->sqf_part->p)->length == heap->nmod_lparams_array[0]->params[0]->elim->length) + { + fprintf(stderr, "Resultant is square-free\n"); + is_sqf = 1; + } + else{ + fprintf(stderr, "Resultant is not square-free\n"); + fprintf(stderr, "Array of degree/multiplicity is ["); + for(int i = 0; i < nb_sqfree-1; i++){ + fprintf(stderr, "[%lu, %lu], ", (heap->sqf_part->p+i)->length - 1, (heap->sqf_part->exp[i])); + } + fprintf(stderr, "[%lu, %lu]]\n", (heap->sqf_part->p+(nb_sqfree-1))->length - 1, (heap->sqf_part->exp[nb_sqfree-1])); + } + + if(nmod_poly_invmod(heap->GCDINV[0], + heap->nmod_lparams_array[0]->params[0]->denom, + heap->nmod_lparams_array[0]->params[0]->elim) + == 0){ + + fprintf(stderr, "The input system is not in generic position\n"); + + return 0; + } + mp_ptr sepelem = malloc(sizeof(mp_limb_t) * 2); + sepelem[0]=0; + sepelem[1]=1; + + for(int i = 0; i < size_table; i++){ + heap->nmod_lparams_array[i] = allocate_degrees_sepelem_nmod_all_params(heap, sepelem, + nb_sqfree, 1, + prime); + } + + fmpz_all_params_t *param = malloc(sizeof(fmpz_all_params_t)); + allocate_degrees_sepelem_fmpz_all_params(param, heap, sepelem, + nb_sqfree, 1); + fprintf(stderr, "Allocation done\n"); + fprintf(stderr, "First param of degree = %ld\n", param->params[0]->elim->length-1); + + prime = n_nextprime(prime, 0); + int boo = 1; + while(boo){ + int pos = 0; + + while(pos < size_table){ + + make_nmod_bpoly(heap->a_mod, A, mdegA, prime); + make_nmod_bpoly(heap->b_mod, B, mdegB, prime); + + if(heap->a_mod[mdegA]->length>0 && heap->b_mod[mdegB]->length>0){ + + double start_mod = omp_get_wtime(); + update_poly_tables_with_prime(heap, pos, prime); + //Ici on met a jour nmod_all_primes_table avec prime + update_nmod_param_with_prime(heap->nmod_lparams_array[pos], prime); + + if(is_sqf==1){ + nmod_bpoly_param_allocated_feval_sqfree(heap, + mdegA, mdegB, pos); + } + else{ + if(nmod_bpoly_param_allocated_feval_nonsqfree(heap, + mdegA, mdegB, pos)==0){ + return 0; + } + } + +#if(DEBUG>2) + char str[1] = {"x"}; + fprintf(stderr, "prime = %ld\n", prime); + fprintf(stderr, "RESULTANT = "); + nmod_poly_fprint_pretty(stderr, heap->nmod_lparams_array[pos]->params[0]->elim, str); + fprintf(stderr, "\n"); +#endif + e_mod += (omp_get_wtime() - start_mod); + pos++; + fmpz_mul_ui(heap->prod_primes[pos], heap->prod_primes[pos - 1], prime); + + nbits_prime += LOG2(prime); + prime = n_nextprime(prime, 0); + count_nprimes++; + } + else{ + prime = n_nextprime(prime, 0); + } + } + + if(nb_sqfree==1){ + if(check_all_params_modular_image(param, heap, size_table) == 0){ + //Il faut continuer la construction + integer_param_crt_lifting_all_params(param, heap, + size_table); + fmpz_set(heap->prod_primes[0], heap->prod_primes[size_table]); + if(DEBUG>1){ + if(check_all_params_modular_image(param, heap, size_table)==0){ + fprintf(stderr, "Error in lifting\n"); + exit(1); + } + } + } + else{ + boo = 0; + } + } + else{ + if(rational_param_lifting_all_params(param, heap, size_table) == 0){ + fmpz_set(heap->prod_primes[0], heap->prod_primes[size_table]); + } + else{ + boo = 0; + } + } + } + copy_to_final_all_params(bs_param, param); + count_nprimes--; + fprintf(stderr, "Number of used primes = %lu\n", count_nprimes); + fprintf(stderr, "Elapsed time (modp): %f\n", e_mod); + fprintf(stderr, "Elapsed time (total): %f\n", omp_get_wtime() - e); + + free(sepelem); +// free_fmpz_all_params(all_params); + free_data_heap(mdegA, mdegB, size_table, heap); + + return 1; +} + +static int fmpz_bpoly_param(bsolve_fmpz_all_params_t *bs_param, + fmpz_poly_t *A, slong mdegA, + fmpz_poly_t *B, slong mdegB){ + if(mdegA < mdegB){ + return _fmpz_bpoly_param_probabilistic(bs_param, + B, mdegB, + A, mdegA); + } + else{ + return _fmpz_bpoly_param_probabilistic(bs_param, + A, mdegA, + B, mdegB); + } +} + + + +static void _fmpz_bpoly_resultant_probabilistic(fmpz_poly_t res, + fmpz_poly_t *A, slong mdegA, + fmpz_poly_t *B, slong mdegB){ + slong tdegA, tdegB, sdegA, sdegB; + ulong nbitsA, nbitsB; + int size_table = 4; + fprintf(stderr, "ici on est la\n"); + get_degrees_and_nbits(A, mdegA, + B, mdegB, + &tdegA, &tdegB, + &sdegA, &sdegB, + &nbitsA, &nbitsB); + fprintf(stderr, "allocation starts\n"); + data_heap_t *heap = allocate_data_heap(tdegA, tdegB, + mdegA, mdegB, + sdegA, sdegB, + size_table); + fprintf(stderr, "allocation done\n"); + + fprintf(stderr, "Total degrees : %ld %ld\n", tdegA, tdegB); + fprintf(stderr, "numpoints = %lu\n", heap->npts); + + //Hadamard-type (Goldstein-Graham) + ulong bound_nbits = nbitsA*(mdegB) + nbitsB*(mdegA); + + fprintf(stderr, "Bound (nbits) = %lu\n", bound_nbits); + + mp_limb_t prime = 1073741827; + prime = n_nextprime(1152921504606847009, 0); + // prime = 4611686018427388039; // prime = n_nextprime(prime, 0); + ulong nbits_prime = LOG2(prime); + + ulong count_nprimes = 1; + + //max degree reached during multi-mod computation + slong maxdegree = -1; + + + double e = omp_get_wtime(); + nbits_prime = 0; + + fmpz_t coeff; + fmpz_init(coeff); + + double e_mod = 0; + + //On teste si le resultant est square-free + make_nmod_bpoly(heap->a_mod, A, mdegA, prime); + make_nmod_bpoly(heap->b_mod, B, mdegB, prime); + + update_poly_tables_with_prime(heap, 0, prime); + nmod_bpoly_resultant_allocated_feval(heap, mdegA, mdegB, 0); + + fprintf(stderr, "prime = %lu\n", prime); + fprintf(stderr, "Degree of the resultant is %ld\n", heap->res_mod_array[0]->length - 1); + prime = n_nextprime(prime, 0); + double e_res = 0; + int boo = 1; + while(nbits_prime < bound_nbits && boo){ + int pos = 0; + + while(pos < size_table){ + make_nmod_bpoly(heap->a_mod, A, mdegA, prime); + make_nmod_bpoly(heap->b_mod, B, mdegB, prime); + + if(heap->a_mod[mdegA]->length>0 && heap->b_mod[mdegB]->length>0){ + + double start_mod = omp_get_wtime(); + update_poly_tables_with_prime(heap, pos, prime); + double t = omp_get_wtime(); + nmod_bpoly_resultant_allocated_feval(heap, mdegA, mdegB, pos); + e_res += (omp_get_wtime() - t); + e_mod += (omp_get_wtime() - start_mod); + pos++; + fmpz_mul_ui(heap->prod_primes[pos], heap->prod_primes[pos - 1], prime); + + nbits_prime += LOG2(prime); + prime = n_nextprime(prime, 0); + count_nprimes++; + } + else{ + prime = n_nextprime(prime, 0); + } + } + + //on verifie si les images modulaires collent au resultant qu'on a calcule + if(check_modular_images(res, heap, size_table, &maxdegree)){ + fprintf(stderr, "\n\nfinal prime = %lu\n\n", prime); + boo = 0; + } + else{//ca colle pas, on continue la reconstruction. + fmpz_poly_fit_length(res, maxdegree+1); + fmpz_one(coeff); + for(ulong j = 0; j <= maxdegree; j++){ + fmpz_set(coeff, res->coeffs + j); + for(int i = 0; i < size_table; i++){ + myfmpz_CRT_ui(coeff, coeff, + heap->prod_primes[i], (heap->res_mod_array[i]->coeffs)[j], heap->primes_array[i], 1, heap->prod_mod); + } + fmpz_poly_set_coeff_fmpz(res, j, coeff); + } + fmpz_set(heap->prod_primes[0], heap->prod_primes[size_table]); + } + } + + fprintf(stderr, "Wall time spent in modular resultant = %f\n", e_res); + count_nprimes--; + fprintf(stderr, "Number of used primes = %lu\n", count_nprimes); + fprintf(stderr, "Elapsed time (modp): %f\n", e_mod); + fprintf(stderr, "Elapsed time (total): %f\n", omp_get_wtime() - e); + + fprintf(stderr, "Final size coeffs: %ld\n", FLINT_ABS(_fmpz_vec_max_bits(res->coeffs, res->length))); + fprintf(stderr, "Degree of the output: %ld\n", res->length-1); + + fmpz_clear(coeff); + free_data_heap(mdegA, mdegB, size_table, heap); + return; +} + + +static void _fmpz_bpoly_sqfree_resultant_probabilistic(fmpz_poly_t res, + fmpz_poly_t *A, slong mdegA, + fmpz_poly_t *B, slong mdegB){ + + slong tdegA, tdegB, sdegA, sdegB; + ulong nbitsA, nbitsB; + get_degrees_and_nbits(A, mdegA, + B, mdegB, + &tdegA, &tdegB, + &sdegA, &sdegB, + &nbitsA, &nbitsB); + int size_table = 4; + data_heap_t *heap = allocate_data_heap(tdegA, tdegB, + mdegA, mdegB, + sdegA, sdegB, + size_table); + + fprintf(stderr, "Total degrees : %ld %ld\n", tdegA, tdegB); + fprintf(stderr, "numpoints = %lu\n", heap->npts); + + //Hadamard-type (Goldstein-Graham) + ulong bound_nbits = nbitsA*(mdegB) + nbitsB*(mdegA); + + fprintf(stderr, "Bound (nbits) = %lu\n", bound_nbits); + + mp_limb_t prime = 1073741827; + //On devrait mettre un peu d'alea + prime = n_nextprime(1152921504606847009, 0); + ulong nbits_prime = LOG2(prime); + + ulong count_nprimes = 1; + + //max degree reached during multi-mod computation + slong maxdegree = -1; + + double e = omp_get_wtime(); + nbits_prime = 0; + + fmpz_t coeff; + fmpz_init(coeff); + + double e_mod = 0; + + //On teste si le resultant est square-free + make_nmod_bpoly(heap->a_mod, A, mdegA, prime); + make_nmod_bpoly(heap->b_mod, B, mdegB, prime); + + update_poly_tables_with_prime(heap, 0, prime); + nmod_bpoly_resultant_allocated_feval(heap, mdegA, mdegB, 0); + + fprintf(stderr, "prime = %lu\n", prime); + fprintf(stderr, "Degree of the resultant is %ld\n", heap->res_mod_array[0]->length - 1); + if(!is_non_square_free(heap->res_mod_array[0], heap->sqf_part)){ + fprintf(stderr, "The resultant is square-free\n"); + + free_data_heap(mdegA, mdegB, size_table, heap); + fprintf(stderr, "free heap done\n"); + _fmpz_bpoly_resultant_probabilistic(res, + A, mdegA, + B, mdegB); + return; + } + fprintf(stderr, "The resultant is not square-free\n"); + prime = n_nextprime(prime, 0); + + while(nbits_prime < bound_nbits || 0 == 0){ + int pos = 0; + + while(pos < size_table){ + make_nmod_bpoly(heap->a_mod, A, mdegA, prime); + make_nmod_bpoly(heap->b_mod, B, mdegB, prime); + + if(heap->a_mod[mdegA]->length>0 && heap->b_mod[mdegB]->length>0){ + + double start_mod = omp_get_wtime(); + update_poly_tables_with_prime(heap, pos, prime); + nmod_bpoly_resultant_allocated_feval(heap, mdegA, mdegB, pos); + + square_free_part_nmod_poly(heap->res_mod_array[pos], heap->sqf_part); + + e_mod += (omp_get_wtime() - start_mod); + pos++; + fmpz_mul_ui(heap->prod_primes[pos], heap->prod_primes[pos - 1], prime); + nbits_prime += LOG2(prime); + prime = n_nextprime(prime, 0); + count_nprimes++; + } + else{ + prime = n_nextprime(prime, 0); + } + } + + //on verifie si les images modulaires collent au resultant qu'on a calcule + if(check_modular_images(res, heap, size_table, &maxdegree)){ + fprintf(stderr, "\n\nfinal prime = %lu\n\n", prime); + break; + } + else{//ca colle pas, on continue la reconstruction. + fmpz_poly_fit_length(res, maxdegree+1); + fmpz_one(coeff); + for(ulong j = 0; j <= maxdegree; j++){ + fmpz_set(coeff, res->coeffs + j); + for(int i = 0; i < size_table; i++){ + myfmpz_CRT_ui(coeff, coeff, + heap->prod_primes[i], (heap->res_mod_array[i]->coeffs)[j], heap->primes_array[i], 1, heap->prod_mod); + } + fmpz_poly_set_coeff_fmpz(res, j, coeff); + // fmpz_print(coeff);fprintf(stdout, "\n"); + } + fmpz_set(heap->prod_primes[0], heap->prod_primes[size_table]); + } + } + + count_nprimes--; + fprintf(stderr, "Number of used primes = %lu\n", count_nprimes); + fprintf(stderr, "Elapsed time (modp): %f\n", e_mod); + fprintf(stderr, "Elapsed time (total): %f\n", omp_get_wtime() - e); + + fprintf(stderr, "Final size coeffs: %ld\n", FLINT_ABS(_fmpz_vec_max_bits(res->coeffs, res->length))); + fprintf(stderr, "Degree of the output: %ld\n", res->length-1); + + fmpz_clear(coeff); + free_data_heap(mdegA, mdegB, size_table, heap); + return; +} + +/* /\* */ +/* Input: A et B sont des pointeurs sur tableaux de fmpz_poly_t de */ +/* tailles respectives degA + 1 et degB + 1 */ + +/* *\/ */ + + +static void fmpz_bpoly_sqfree_resultant_probabilistic(fmpz_poly_t res, + fmpz_poly_t *A, slong degA, + fmpz_poly_t *B, slong degB){ + if(degA < degB){ + _fmpz_bpoly_sqfree_resultant_probabilistic(res, B, degB, A, degA); + } + else{ + _fmpz_bpoly_sqfree_resultant_probabilistic(res, + A, degA, + B, degB); + } +} + + +static void fmpz_bpoly_resultant_probabilistic(fmpz_poly_t res, + fmpz_poly_t *A, slong degA, + fmpz_poly_t *B, slong degB){ + if(degA < degB){ + _fmpz_bpoly_resultant_probabilistic(res, B, degB, A, degA); + } + else{ + _fmpz_bpoly_resultant_probabilistic(res, + A, degA, + B, degB); + } +} + + +int main(int argc, char **argv){ + + bsolve_flags * flags = allocate_initialize_flags(); + + int binary_format = 0; + getoptions(argc, argv, flags); + + FILE *file = fopen(flags->input_file,"r"); + + if(file==NULL){ + fprintf(stderr, "No such file\n"); + return 1; + } + slong degA = 0, degB = 0; + //Array est un tableau de fmpz_poly_t de lgr degA + degB + 1 + fmpz_poly_t *Array = get_input_polynomials(file, °A, °B); + fmpz_poly_t *bA = Array; + fmpz_poly_t *bB = Array + (degA + 1); + fclose(file); + + if(DEBUG >= 2){ + + fprintf(stderr, "\nA := "); + fmpz_bpoly_fprint_pretty(stderr, bA, degA); + fprintf(stderr, "\n"); + fflush(stderr); + fprintf(stderr, "B := "); + fmpz_bpoly_fprint_pretty(stderr, bB, degB); + fprintf(stderr, "\n"); + fflush(stderr); + } + + + + if(0==1){ + flint_rand_t state; + flint_randinit(state); + fmpz_bpoly_random_dense(bA, degA, degA, state); + fmpz_bpoly_random_dense(bB, degB, degB, state); + flint_randclear(state); + } + + fprintf(stderr, "flags->task = %d\n", flags->task); + if(flags->task == 1){ + fmpz_poly_t res; + fmpz_poly_init(res); + fmpz_bpoly_resultant_probabilistic(res, bA, degA, bB, degB); + display_resutant(res, flags, binary_format); + fmpz_poly_clear(res); + } + if(flags->task == 2){ + fmpz_poly_t res; + fmpz_poly_init(res); + fmpz_bpoly_sqfree_resultant_probabilistic(res, bA, degA, bB, degB); + display_resutant(res, flags, binary_format); + fmpz_poly_clear(res); + } + if(DEBUG>10){ + fmpz_poly_t res; + fmpz_poly_init(res); + fmpz_bpoly_resultant_deterministic(res, bA, degA, bB, degB); + fmpz_poly_clear(res); + } + if(flags->task==0){ + bsolve_fmpz_all_params_t *bs_param = malloc(sizeof(bsolve_fmpz_all_params_t)); + if(fmpz_bpoly_param(bs_param, bA, degA, bB, degB)){ + if(flags->output_file != NULL){ + FILE *ofile = fopen(flags->output_file, "w"); + if(flags->binary){ + print_bs_fmpz_all_params_bin(ofile, bs_param); + } + else{ + print_bs_fmpz_all_params_pretty(ofile, bs_param); + } + fclose(ofile); + } + else{ + if(flags->binary){ + print_bs_fmpz_all_params_bin(stdout, bs_param); + } + else{ + print_bs_fmpz_all_params_pretty(stdout, bs_param); + } + } + + free_bsolve_fmpz_all_params(bs_param); + return 0; + } + free(bs_param); + return 0; + } + + for(ulong i = 0; i <= degA + degB + 1; i++){ + fmpz_poly_clear(Array[i]); + } + free(Array); + free_flags(flags); + return 0; +} diff --git a/src/connectcurves/src/resultant/out.txt b/src/connectcurves/src/resultant/out.txt new file mode 100644 index 0000000..ce01362 --- /dev/null +++ b/src/connectcurves/src/resultant/out.txt @@ -0,0 +1 @@ +hello diff --git a/src/connectcurves/src/resultant/ratreconstruct.c b/src/connectcurves/src/resultant/ratreconstruct.c new file mode 100644 index 0000000..bb0fb6f --- /dev/null +++ b/src/connectcurves/src/resultant/ratreconstruct.c @@ -0,0 +1,176 @@ +#define ROT(u,v,t) \ + do { fmpz _t = *u; *u = *v; *v = *t; *t = _t; } while (0); + +void myfmpz_CRT_ui(fmpz_t out, const fmpz_t r1, const fmpz_t m1, + ulong r2, ulong m2, int sign, fmpz_t *m1m2) +{ + mp_limb_t c; + // fmpz_t m1m2; + + c = fmpz_fdiv_ui(m1, m2); + c = n_invmod(c, m2); + + if (c == 0) + { + flint_printf("Exception (fmpz_CRT_ui). m1 not invertible modulo m2.\n"); + flint_abort(); + } + + // fmpz_init(m1m2); + fmpz_mul_ui(m1m2[0], m1, m2); + + _fmpz_CRT_ui_precomp(out, r1, m1, r2, m2, n_preinvert_limb(m2), + m1m2[0], c, sign); + + // fmpz_clear(m1m2); +} + +int +_myfmpq_reconstruct_fmpz_2(fmpz_t n, fmpz_t d, + const fmpz_t a, const fmpz_t m, const fmpz_t N, const fmpz_t D) +{ + fmpz_t q, r, s, t; + int success = 0; + + /* Quickly identify small integers */ + if (fmpz_cmp(a, N) <= 0) + { + fmpz_set(n, a); + fmpz_one(d); + return 1; + } + fmpz_sub(n, a, m); + if(fmpz_cmp_ui(n, 0)>=0){ + if(fmpz_cmp(n, N) <= 0){ + fmpz_one(d); + return 1; + } + } + else{ + fmpz_neg(n, n); + if(fmpz_cmp(n, N) <= 0){ + fmpz_one(d); + fmpz_neg(n, n); + return 1; + } + } + /* if (fmpz_cmpabs(n, N) <= 0) */ + /* { */ + /* fmpz_one(d); */ + /* fprintf(stderr, "ici?\n"); */ + /* return 1; */ + /* } */ + + fmpz_init(q); + fmpz_init(r); + fmpz_init(s); + fmpz_init(t); + + fmpz_set(r, m); fmpz_zero(s); + fmpz_set(n, a); fmpz_one(d); + + while (fmpz_cmpabs(n, N) > 0) + { + fmpz_fdiv_q(q, r, n); + fmpz_mul(t, q, n); fmpz_sub(t, r, t); ROT(r, n, t); + fmpz_mul(t, q, d); fmpz_sub(t, s, t); ROT(s, d, t); + } + + if (fmpz_sgn(d) < 0) + { + fmpz_neg(n, n); + fmpz_neg(d, d); + } + + if (fmpz_cmp(d, D) <= 0) + { + fmpz_gcd(t, n, d); + success = fmpz_is_one(t); + } + + fmpz_clear(q); + fmpz_clear(r); + fmpz_clear(s); + fmpz_clear(t); + return success; +} + +int +myfmpq_reconstruct_fmpz_2(fmpq_t res, const fmpz_t a, const fmpz_t m, + const fmpz_t N, const fmpz_t D) +{ + return _myfmpq_reconstruct_fmpz_2(fmpq_numref(res), + fmpq_denref(res), a, m, N, D); +} + +int +_myfmpq_reconstruct_fmpz(fmpz_t n, fmpz_t d, + const fmpz_t a, const fmpz_t m) +{ + fmpz_t N; + int result; + + fmpz_init(N); + fmpz_fdiv_q_2exp(N, m, 1); + fmpz_sqrt(N, N); + result = _myfmpq_reconstruct_fmpz_2(n, d, a, m, N, N); + fmpz_clear(N); + + return result; +} + +int +myfmpq_reconstruct_fmpz(mpz_rat_t *res, fmpz_t a, const fmpz_t m) +{ + if(fmpz_cmp_ui(a, 0)>=0){ + return _myfmpq_reconstruct_fmpz(res->numer, + res->denom, a, m); + } + else{ + while(fmpz_cmp_ui(a, 0) < 0){ + // fmpz_fprint(stderr, a); fprintf(stderr, "\n"); + fmpz_add(a, a, m); + } + int b = _myfmpq_reconstruct_fmpz(res->numer, + res->denom, a, m); + return b; + } +} + +/* returns 0 if the rational reconstruction failed */ +int rat_recon(fmpz_poly_t poly, fmpz_poly_t poly_num, fmpz_poly_t poly_den, fmpz_t lcm, + data_heap_t *heap, ulong deg, ulong *rec_poly){ + fprintf(stderr, "[%lu, %lu] ", (*rec_poly), deg); + ulong size = heap->size_mod_array; + fmpz_mul_ui(heap->h_prod, heap->prod_primes[size-1], heap->primes_array[size-1]); + int b = myfmpq_reconstruct_fmpz(heap->coef, poly->coeffs+(*rec_poly), heap->h_prod); + fmpz_lcm(lcm, lcm, heap->coef->denom); + fmpz_set(poly_num->coeffs + (*rec_poly), heap->coef->numer); + fmpz_set(poly_den->coeffs + (*rec_poly), heap->coef->denom); + if(b==0){ + (*rec_poly) = 0; + fmpz_one(lcm); + fprintf(stderr, "--> [%lu, %lu]\n", (*rec_poly), deg); + return b; + } + for(ulong i = (*rec_poly) + 1; i <= deg; i++){ + b = myfmpq_reconstruct_fmpz(heap->coef, poly->coeffs+i, heap->h_prod); + if(b == 0){ + (*rec_poly) = i-1; + fprintf(stderr, "--> [%lu, %lu]\n", (*rec_poly), deg); + return b; + } + fmpz_lcm(lcm, lcm, heap->coef->denom); + fmpz_set(poly_num->coeffs + i, heap->coef->numer); + fmpz_set(poly_den->coeffs + i, heap->coef->denom); + } + (*rec_poly) = deg; + for(ulong i = 0; i <= deg; i++){ + fmpz_divexact(heap->coef->numer, lcm, poly_den->coeffs + i); + fmpz_mul(poly_num->coeffs + i, poly_num->coeffs + i, heap->coef->numer); + } + fprintf(stderr, "--> [%lu, %lu]\n", (*rec_poly), deg); + return b; +} + + diff --git a/src/connectcurves/src/usolve/usolve 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z+N-a!fA9VM82`P$ALGB{XuUzV{d1l6A00h(gVKI`z4-*xHt^-B8>cG^?j|CPV* z;)nQO_rK$R6Z8McAcOVmF8#cp&)N3{RjU;H1s%KhIdH8;2ao=3F*k}vo|H#obsKH~aQulKjIeRu!A`y2k4+y8^n z=J88EKbGy+YxR0ZKOXHr@w-0u`v2Y|+E3o`rS9_G|J{1eW!zHwnfxfQTgvqJ%}-wT z)bRO4uPrH5ZjbG-+j}D^6pWtcyi4FZMU?KjzY5b2Ke!1I!!H4~){-- x -> split(x, ": ")[end] * "s") + #elseif v == 2 + # println(stderr(out)) + #end + Ls = usolve_out_to_tuple(fname2) + Is = tuple_to_inter(Ls) + if output == "inter" + return Is + else + ff = open(fname2, "r") + return Ls, Is + end +end + + +#using Nemo +#R, (x,y) = Nemo.polynomial_ring(Nemo.ZZ, [:x,:y]) +#f = x^2+5*x-4 diff --git a/src/connectcurves/tools.jl b/src/connectcurves/tools.jl new file mode 100644 index 0000000..a48c8e2 --- /dev/null +++ b/src/connectcurves/tools.jl @@ -0,0 +1,84 @@ +#using Nemo +using Singular + +function randQQ(size=3) + fac = 10^(size) + return Nemo.QQ((-1)^(trunc(Int,rand()*10))*trunc(Int,rand()*fac),trunc(Int,rand()*fac)) +end + +function _mpoly_to_singular(f) + @assert Nemo.is_univariate(f) "Not univariate polynomial" + R, x = Singular.polynomial_ring(Singular.QQ, [:x]) + x = first(x) + cf = Nemo.coefficients_of_univariate(f) + return sum([ cf[j]*x^(j-1) for j = eachindex(cf) ]) +end + +function nb_roots_interval(f,a,b) + g = _mpoly_to_singular(f) + return Singular.LibRootsur.sturm(g, Singular.QQ(a), Singular.QQ(b)) +end + +""" + nb_roots_interval_partition(f, a, b) + +Compute the number of real roots of f(x) in the intervals: + (-infinity, a), (a,b), (b, +infinity) + +# Input: +* f: polynomial with involving one variable, with coeffients in QQ +* a,b: rational elements of QQ +# Output: +* [ n(-infinity, a), n(a,b), n(b, +infinity) ] + +""" +function nb_roots_interval_partition(f, a, b) + g = _mpoly_to_singular(f) + M = Singular.LibRootsur.maxabs(g) + a1, b1 = Singular.QQ(a), Singular.QQ(b) + M1, M2 = min(-M, a1), max(b1, M) + B = [ M1-1, a1, b1, M2+1 ] + return [ Singular.LibRootsur.sturm(g, B[i], B[i+1]) for i=1:3 ] +end + +function sturm_habicht_seq(f) + g = _mpoly_to_singular(f) + SH = map(Singular.coefficients_of_univariate, Singular.LibRootsur.sturmhaseq(g)) + return [ vcat(SH[k], [n_Q(0) for _=1:(k-length(SH[k]))]) for k in eachindex(SH) ] +end + +function subresultants_seq(f) + SH = sturm_habicht_seq(f) + d(k) = (-1)^((k*(k+1))>>1) + return [ d(length(SH)-1-k)*SH[k] for k=1:length(SH)-2 ] +end + +function subresultants_seq_biv(f, iv) + iu = iv%2+1 + # Modern computer Algebra Th 6.51. + degs = degrees(f) + n, d = degs[iv], degs[iu] + degsmax = [ (2*n-1-2*k)*d for k=0:d-2 ] + Dmax = degsmax[end]>>1+1 + ## + xs = [ randQQ() for _=1:(degsmax[1]+1) ] + @time begin + Srev = [ subresultants_seq(evaluate(f,[iu],[xx])) for xx in xs ] + end + S,t = Nemo.polynomial_ring(Nemo.QQ,"t") + Sr = [ [ S(0) for _=1:i] for i=1:n-2 ] + for i = 1:n-2 + for j = 1:i + ys = [ Nemo.QQ(Srev[l][i][j]) for l=eachindex(Srev) ] + Sr[i][j] = Nemo.interpolate(S, xs, ys) + end + end + return Sr +end + +#R, (x,y) = Nemo.polynomial_ring(Nemo.QQ, [:x,:y]) +#f = x^7+y^2*x^5-2*x*y^3+1+y^6 +#f = (x^2+y^2-1)*(2*x-y) +#Sr = subresultants_seq_biv(f, 1) + + From faae3c581539480c6265e72b6e87c2f270b4b8bf Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 22 Mar 2024 19:56:08 +0100 Subject: [PATCH 002/180] graph --- .../src/algorithms/solvers.jl | 3 +- src/connectcurves/data.jl | 2 +- src/connectcurves/main.ipynb | 137 ++++++++++++------ src/connectcurves/src/usolve/usolve.jl | 8 +- 4 files changed, 99 insertions(+), 51 deletions(-) diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl index 11cd320..00674db 100644 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl @@ -151,6 +151,7 @@ function _core_msolve( rat_param[3], rat_param[4]) if jl_nb_sols == 0 I.real_sols = QQFieldElem[] + I.inter_sols = QQFieldElem[] return rat_param, Vector{QQFieldElem}[] end @@ -419,7 +420,7 @@ function inter_solutions( precision::Int=32 # precision of the solution set ) - isdefined(I, :real_sols) || + isdefined(I, :inter_sols) || _core_msolve(I, initial_hts = initial_hts, nr_thrds = nr_thrds, diff --git a/src/connectcurves/data.jl b/src/connectcurves/data.jl index c1533c4..d7ff222 100644 --- a/src/connectcurves/data.jl +++ b/src/connectcurves/data.jl @@ -1,5 +1,5 @@ #using Nemo -R, (x,y) = Nemo.polynomial_ring(Nemo.QQ, [:x, :y]) +R, (x,y) = polynomial_ring(QQ, [:x, :y]) f = 1594627541097114368612385*x^16 + 24126594979283487048484560*x^15*y - 648897523515553246784074808*x^14*y^2 + 9227671981881181765203810480*x^13*y^3 + 775388988595641728298874736332*x^12*y^4 + 10787151407096126900712389934720*x^11*y^5 + 77139559828286619230682855993096*x^10*y^6 + 452145503210946168432702707056320*x^9*y^7 + 1603450939087454055697523432885078*x^8*y^8 + 472422761323888641034023872620080*x^7*y^9 + 69254293553970771431091788378664*x^6*y^10 + 8171004998268972015374643672912*x^5*y^11 + 486748426688048642456485687660*x^4*y^12 - 12064621488868591078399181568*x^3*y^13 - 1468208821458887902925840024*x^2*y^14 + 12892282240123223587086528*x*y^15 + 1551343473382248651380209*y^16 - 7416582067989458752697004*x^14 - 86407846455606538783280976*x^13*y + 2644747193988832166794696620*x^12*y^2 + 4962811393512179992436546328*x^11*y^3 - 852556155710875435151137729948*x^10*y^4 - 9006223258524272797865687202672*x^9*y^5 - 37408868951040006789841449492372*x^8*y^6 - 96029136974599596104658658159536*x^7*y^7 - 25805546034923632520724584708244*x^6*y^8 - 5242437191813955076157431442064*x^5*y^9 - 409699928605220782678759186860*x^4*y^10 + 39375118017080555511082417752*x^3*y^11 + 4414478650057190403833967932*x^2*y^12 - 62266637085710610417717552*x*y^13 - 7665646840583710272384908*y^14 + 14233446085691566995553618*x^12 + 132571431253302115292123136*x^11*y - 3677320627079906075667837422*x^10*y^2 - 28335523591694036134043888352*x^9*y^3 + 186478273436442358105601202678*x^8*y^4 + 979680543110585521095162296976*x^7*y^5 - 2082167356121156563744172163572*x^6*y^6 - 30539225710419394554664076544*x^5*y^7 + 25429103844006118137220734342*x^4*y^8 - 40056866529454773916181059488*x^3*y^9 - 4741918132209313788162640030*x^2*y^10 + 120063392649421566997191792*x*y^11 + 15453863115268541628254722*y^12 - 14508062550440954802512688*x^10 - 115292786706841839957190896*x^9*y + 2178406370189758736513057100*x^8*y^2 + 17911006599365461837132806264*x^7*y^3 + 18721721306068791970712906740*x^6*y^4 + 140144222573062968441350663256*x^5*y^5 + 15151268277268342933019382004*x^4*y^6 + 14388997206020218965816744888*x^3*y^7 + 2181175955893013097832336108*x^2*y^8 - 116823607901494850142791760*x*y^9 - 16262571151436698863824960*y^10 + 8412196412628079801200763*x^8 + 60038503306269383516796672*x^7*y - 526872554079154536701276538*x^6*y^2 - 2627205980235442180204133952*x^5*y^3 + 1415955761616170935932891503*x^4*y^4 - 1207248891865676270007025776*x^3*y^5 - 411102077811099614734692666*x^2*y^6 + 59338125380312133254699856*x*y^7 + 9471776668272238878375147*y^8 - 2755131867388737857954960*x^6 - 16865677220581290594690288*x^5*y + 37152628773628751552853580*x^4*y^2 - 32454665768852564904473352*x^3*y^3 + 31405824474395795210222812*x^2*y^4 - 14499431708247069028795056*x*y^5 - 2982642484703489520084064*y^6 + 476197729395824935891282*x^4 + 1850003538678786657657456*x^3*y - 861756868723874605906006*x^2*y^2 + 1328290412641467896291664*x*y^3 + 466653249763538900703730*y^4 - 37550891878150349195068*x^2 - 32144769403583975845728*x*y - 33575411625230211328108*y^2 + 864999024811562109121 diff --git a/src/connectcurves/main.ipynb b/src/connectcurves/main.ipynb index e74f544..75b7c11 100644 --- a/src/connectcurves/main.ipynb +++ b/src/connectcurves/main.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 17, + "execution_count": 22, "metadata": {}, "outputs": [ { @@ -11,26 +11,22 @@ "text": [ "Loading libraries and data..\n" ] - }, - { - "data": { - "text/plain": [ - "subresultants_seq_biv (generic function with 1 method)" - ] - }, - "metadata": {}, - "output_type": "display_data" } ], "source": [ "println(\"Loading libraries and data..\")\n", - "using Oscar\n", - "include(\"tools.jl\")" + "using AlgebraicSolving\n", + "#import Nemo:\n", + "# is_univariate,\n", + "# coefficients_of_univariate\n", + "using Nemo\n", + "#using Oscar\n", + "#include(\"tools.jl\")" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 23, "metadata": {}, "outputs": [ { @@ -52,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": 316, + "execution_count": 130, "metadata": {}, "outputs": [ { @@ -79,14 +75,14 @@ "end\n", "\n", "function isolate(f; prec = 32, software=\"usolve\")\n", - " @assert Nemo.is_univariate(f) \"Not univariate polynomial\"\n", + " @assert is_univariate(f) \"Not univariate polynomial\"\n", "\tif software == \"usolve\"\n", "\t\treturn usolve(f, precision = prec, uspath=\"src/usolve/usolve\")\n", " end\n", "end\n", "\n", "function isolate_eval(f, ivar, val; prec=64)\n", - " sols = real_solutions(ideal(R, [f, gens(R)[ivar] - val]), precision=prec)[1]\n", + " sols = real_solutions(AlgebraicSolving.Ideal([f, gens(R)[ivar] - val]), precision=prec)\n", " return [ s[ivar%2+1] for s in sols ]\n", "end\n", "\n", @@ -109,7 +105,7 @@ }, { "cell_type": "code", - "execution_count": 283, + "execution_count": 131, "metadata": {}, "outputs": [ { @@ -130,7 +126,7 @@ }, { "cell_type": "code", - "execution_count": 284, + "execution_count": 132, "metadata": {}, "outputs": [ { @@ -146,13 +142,38 @@ "#RR(x) = Arb(x, prec=120)\n", "RR = ArbField(150)\n", "Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ]\n", - "LBcrit = [ [ [ map(AbstractAlgebra.QQ, pc[1]), map(AbstractAlgebra.QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ];\n", + "LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ];\n", "Pcrit = [ [ [ rat_to_Arb(pc[1]), pc[2] ] for pc in pcrit] for pcrit in Pcrit ];" ] }, { "cell_type": "code", - "execution_count": 317, + "execution_count": 187, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[0.00592297584970014544321252 +/- 4.43e-27]" + ], + "text/latex": [ + "[0.00592297584970014544321252 +/- 4.43e-27]" + ], + "text/plain": [ + "[0.00592297584970014544321252 +/- 4.43e-27]" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Pcrit[1][1][2]" + ] + }, + { + "cell_type": "code", + "execution_count": 191, "metadata": {}, "outputs": [ { @@ -177,7 +198,7 @@ " # Lyi\n", " L[i+2] = Array{Any}(undef,2)\n", " L[i+2][1] = isolate_eval(f, 1, B[1][i], prec=150)\n", - " L[i+2][2] = [ j for (j, l) in pairs(L[i+2][1]) if (l> B[1][1] && l B[2][1] && l Date: Mon, 25 Mar 2024 11:29:05 +0100 Subject: [PATCH 003/180] until plot ! --- .../src/algorithms/solvers.jl | 8 +- src/connectcurves/main.ipynb | 4972 ++++++++++++++++- 2 files changed, 4886 insertions(+), 94 deletions(-) diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl index 00674db..5051541 100644 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl +++ b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl @@ -142,7 +142,9 @@ function _core_msolve( jl_vnames = Base.unsafe_wrap(Array, res_vnames[], jl_rp_nr_vars) - vsymbols = [Symbol(unsafe_string(jl_vnames[i])) for i in 1:jl_rp_nr_vars] + vsymbols = [Symbol(unsafe_string(jl_vnames[i])) for i in 1:jl_rp_nr_vars] + #= get possible variable permutation =# + perm = sortperm(vsymbols[1:nr_vars]) rat_param = _get_rational_parametrization(jl_ld, jl_len, jl_cf, jl_cf_lf, jl_rp_nr_vars) @@ -180,8 +182,8 @@ function _core_msolve( inter_tmp_coeff = Vector{QQFieldElem}(undef, 2) inter_tmp_coeff[1] = QQFieldElem(unsafe_load(jl_sols_num, i)) >> Int64(unsafe_load(jl_sols_den, i)) inter_tmp_coeff[2] = QQFieldElem(unsafe_load(jl_sols_num, i+1)) >> Int64(unsafe_load(jl_sols_den, i+1)) - inter_tmp[j] = inter_tmp_coeff - tmp[j] = sum(inter_tmp_coeff) >> 1 + inter_tmp[perm[j]] = inter_tmp_coeff + tmp[perm[j]] = sum(inter_tmp_coeff) >> 1 i += 2 j += 1 end diff --git a/src/connectcurves/main.ipynb b/src/connectcurves/main.ipynb index 75b7c11..0b11b4c 100644 --- a/src/connectcurves/main.ipynb +++ b/src/connectcurves/main.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 22, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -11,14 +11,24 @@ "text": [ "Loading libraries and data..\n" ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/Documents/gittravail/AlgCurves/AlgebraicSolving.jl-main`\n" + ] } ], "source": [ "println(\"Loading libraries and data..\")\n", - "using AlgebraicSolving\n", + "using Pkg\n", + "using Revise\n", + "Pkg.activate(\"AlgebraicSolving.jl-main\")\n", "#import Nemo:\n", "# is_univariate,\n", "# coefficients_of_univariate\n", + "using AlgebraicSolving\n", "using Nemo\n", "#using Oscar\n", "#include(\"tools.jl\")" @@ -26,7 +36,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -48,7 +58,7 @@ }, { "cell_type": "code", - "execution_count": 130, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -82,7 +92,7 @@ "end\n", "\n", "function isolate_eval(f, ivar, val; prec=64)\n", - " sols = real_solutions(AlgebraicSolving.Ideal([f, gens(R)[ivar] - val]), precision=prec)\n", + " sols = inter_solutions(AlgebraicSolving.Ideal([f, gens(R)[ivar] - val]), precision=prec)\n", " return [ s[ivar%2+1] for s in sols ]\n", "end\n", "\n", @@ -105,7 +115,7 @@ }, { "cell_type": "code", - "execution_count": 131, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -126,7 +136,7 @@ }, { "cell_type": "code", - "execution_count": 132, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -148,7 +158,7 @@ }, { "cell_type": "code", - "execution_count": 187, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -173,7 +183,7 @@ }, { "cell_type": "code", - "execution_count": 191, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -193,12 +203,12 @@ " for i in 1:2\n", " # Lxi\n", " L[i] = Array{Any}(undef,2)\n", - " L[i][1] = isolate_eval(f, 2, B[2][i], prec=150)\n", - " L[i][2] = [ j for (j, l) in pairs(L[i][1]) if (l> B[1][1] && l B[1][1] && l[2] B[2][1] && l B[2][1] && l[2] 1 && sum(npcside[1:2]) != 0\n", + " println(npcside)\n", " @assert false \"\\nRefine singular boxes along x-axis\"\n", " #refine_xboxes(QQ[\"x\"](params[2][1]), LBcrit[2])\n", " #i -= 1\n", @@ -277,20 +292,72 @@ " println(\"\")\n", "end\n", "LnPCside = [ [[length(indI) for (L, indI) in PB] for PB in lpcside] for lpcside in LPCside ] \n", - "println(\"Average time for one point: $(mean(Ltm))s\")\n", + "println(\"Average time for one point: $(sum(Ltm)/length(Ltm))s\")\n", "println(\"Elapsed time to compute critical boxes: $(time()-ts)s\")\n" ] }, { "cell_type": "code", - "execution_count": 190, + "execution_count": 10, "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "true" + "data": { + "text/plain": [ + "16-element Vector{Vector{Int64}}:\n", + " [0, 0, 0, 2]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 2, 0]\n", + " [1, 1, 0, 0]\n", + " [0, 0, 0, 2]\n", + " [1, 1, 0, 0]\n", + " [1, 1, 0, 0]\n", + " [0, 0, 2, 0]\n", + " [1, 1, 0, 0]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 2, 0]\n", + " [0, 0, 2, 0]\n", + " [0, 0, 2, 0]\n", + " [0, 0, 2, 0]" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "LnPCside[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "ename": "MethodError", + "evalue": "MethodError: no method matching isless(::Vector{QQFieldElem}, ::QQFieldElem)\n\nClosest candidates are:\n isless(!Matched::qqbar, ::QQFieldElem)\n @ Nemo ~/.julia/packages/Nemo/VHAIi/src/calcium/qqbar.jl:633\n isless(!Matched::Float64, ::QQFieldElem)\n @ Nemo ~/.julia/packages/Nemo/VHAIi/src/HeckeMiscInteger.jl:28\n isless(!Matched::NegInf, ::Union{QQFieldElem, ZZRingElem})\n @ Nemo ~/.julia/packages/Nemo/VHAIi/src/HeckeMiscInfinity.jl:79\n ...\n", + "output_type": "error", + "traceback": [ + "MethodError: no method matching isless(::Vector{QQFieldElem}, ::QQFieldElem)\n", + "\n", + "Closest candidates are:\n", + " isless(!Matched::qqbar, ::QQFieldElem)\n", + " @ Nemo ~/.julia/packages/Nemo/VHAIi/src/calcium/qqbar.jl:633\n", + " isless(!Matched::Float64, ::QQFieldElem)\n", + " @ Nemo ~/.julia/packages/Nemo/VHAIi/src/HeckeMiscInteger.jl:28\n", + " isless(!Matched::NegInf, ::Union{QQFieldElem, ZZRingElem})\n", + " @ Nemo ~/.julia/packages/Nemo/VHAIi/src/HeckeMiscInfinity.jl:79\n", + " ...\n", + "\n", + "\n", + "Stacktrace:\n", + " [1] <(x::Vector{QQFieldElem}, y::QQFieldElem)\n", + " @ Base ./operators.jl:352\n", + " [2] top-level scope\n", + " @ ~/Documents/gittravail/AlgCurves/main.ipynb:4" ] } ], @@ -303,14 +370,14 @@ }, { "cell_type": "code", - "execution_count": 196, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# Update extreme boxes\n", "for j in eachindex(LBcrit[1])\n", - " # If the curve does not intersect the box only on vertical sides or not at all\n", - " if !(LnPCside[1][j][1:2] == [0, 0]) || sum(LnPCside[1][j])==0\n", + " # If the curve does not intersect the box only on vertical sides\n", + " if !(LnPCside[1][j][1:2] == [0, 0])\n", " PCside, nPCside = LPCside[1][j], LnPCside[1][j]\n", " I = [ l[1] for l in PCside[3:end] ]\n", " nI = [ l[2] for l in PCside[3:end] ]\n", @@ -319,11 +386,11 @@ " # s=1: left; s=2: right\n", " s = argmax([length(I[1]), length(I[2])])\n", " # Ordinate range of the extreme point\n", - " ycrit = Pcrit[1][j][2]\n", + " ycrit = LBcrit[1][j][2]\n", " # If it intersects on the bottom side\n", " if nPCside[1] == 1\n", " # yinf: the intersection with the vertical side just below the extreme point\n", - " yinf = maximum([i for (i, yy) in pairs(I[s]) if yy < ycrit])\n", + " yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[2]])\n", " # We vertically enlarge the box until it intersects on the horizontal side\n", " push!(LPCside[1][j][s + 2][2], yinf)\n", " LPCside[1][j][1][2] = []\n", @@ -334,7 +401,7 @@ " # If it intersects on the top side\n", " if nPCside[2] == 1 \n", " # ymax: the intersection with the vertical side just above the extreme point\n", - " ymax = minimum([i for (i, yy) in pairs(I[s]) if yy > ycrit])\n", + " ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[1]])\n", " # We vertically enlarge the box until it intersects on the horizontal side\n", " push!(LPCside[1][j][s + 2][2], ymax)\n", " LPCside[1][j][2][2] = []\n", @@ -348,34 +415,46 @@ }, { "cell_type": "code", - "execution_count": 205, + "execution_count": 13, "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Graph computation\n", - "I :Vector{QQFieldElem}[[], []]" - ] - }, - { - "ename": "BoundsError", - "evalue": "BoundsError: attempt to access 0-element Vector{QQFieldElem} at index [1]", - "output_type": "error", - "traceback": [ - "BoundsError: attempt to access 0-element Vector{QQFieldElem} at index [1]\n", - "\n", - "Stacktrace:\n", - " [1] getindex(A::Vector{QQFieldElem}, i1::Int64)\n", - " @ Base ./essentials.jl:13\n", - " [2] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/main.ipynb:28" - ] + "data": { + "text/plain": [ + "16-element Vector{Vector{Int64}}:\n", + " [0, 0, 0, 2]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 2, 0]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 2, 0]\n", + " [0, 0, 2, 0]\n", + " [0, 0, 2, 0]\n", + " [0, 0, 0, 2]\n", + " [0, 0, 2, 0]\n", + " [0, 0, 2, 0]\n", + " [0, 0, 2, 0]\n", + " [0, 0, 2, 0]" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "print(\"Graph computation\")\n", + "LnPCside[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [], + "source": [ + "#print(\"Graph computation\")\n", "# Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot\n", "# And even remove this fiber for the graph\n", "Vert = []\n", @@ -386,63 +465,67 @@ "\n", "for ind in 1:length(xcritpermut)\n", " i, j = xcritpermut[ind]\n", + "\n", " if ind > 1\n", " i1, j1 = xcritpermut[ind - 1]\n", " end\n", " if ind < length(xcritpermut)\n", " i2, j2 = xcritpermut[ind + 1]\n", - " I2L, nI2L = LPCside[i2][j2][2]\n", + " I2L, nI2L = LPCside[i2][j2][3]\n", " end\n", "\n", " PCside, nPCside = LPCside[i][j], LnPCside[i][j]\n", " I = [ l[1] for l in PCside[3:end] ]\n", " nI = [ l[2] for l in PCside[3:end] ]\n", - " \n", - " ymincrit = min(nI[1][1] + nI[1][2] + [length(I[1][1])])\n", "\n", + " xcmid = sum(LBcrit[i][j][1])//2\n", + " ycmid = sum(LBcrit[i][j][2])//2\n", + "\n", + " ymincrit = minimum(vcat(nI[1], nI[2], [length(I[1])+1]))\n", " # Construct vertices\n", " ###########################\n", " # On the vertical left side\n", " if ind > 1\n", - " for k in 1:length(I[1][1])\n", - " push!(Corr[i][j][1][1], Corr[i1][j1][3][k])\n", + " for k in 1:length(I[1])\n", + " push!(Corr[i][j][1], Corr[i1][j1][3][k])\n", " end\n", " else\n", - " for k in 1:length(I[1][1])\n", - " push!(Vert, (xcrit[i][j].lower() - exp, I[1][1][k]))\n", - " push!(Corr[i][j][1][1], ite)\n", + " for k in 1:length(I[1])\n", + " push!(Vert, [xcrit[i][j][1], sum(I[1][k])//2])\n", + " push!(Corr[i][j][1], ite)\n", " ite += 1\n", " end\n", " end\n", " ###########################\n", " # On the vertical right side\n", " if ind < length(xcritpermut)\n", - " for k in 1:length(I[1][2])\n", - " push!(Vert, ((xcrit[i][j] + xcrit[i2][j2]).lower() / 2 + exp, (I[1][2][k] + I2L[k]).lower() / 2))\n", + " for k in 1:length(I[2])\n", + " push!(Vert, [(xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4])\n", " push!(Corr[i][j][3], ite)\n", " ite += 1\n", " end\n", " else\n", - " for k in 1:length(I[1][2])\n", - " push!(Vert, (xcrit[i][j].upper() + exp, I[1][2][k]))\n", + " for k in 1:length(I[2])\n", + " push!(Vert, [xcrit[i][j][2], sum(I[2][k])//2])\n", " push!(Corr[i][j][3], ite)\n", " ite += 1\n", " end\n", " end\n", " ###########################\n", " # Below the critical point\n", - " for k in 1:ymincrit\n", - " push!(Vert, (xcrit[i][j], (I[1][1][k] + I[1][2][k]) / 2))\n", + "\n", + " for k in 1:ymincrit-1\n", + " push!(Vert, [xcmid, sum(I[1][k] + I[2][k])// 4])\n", " push!(Corr[i][j][2][1], ite)\n", - " push!(Edg, (Corr[i][j][1][1][k], ite)) # left\n", - " push!(Edg, (ite, Corr[i][j][3][k])) # right\n", + " push!(Edg, [Corr[i][j][1][k], ite]) # left\n", + " push!(Edg, [ite, Corr[i][j][3][k]]) # right\n", " ite += 1\n", " end\n", " ###########################\n", " # The critical point\n", " ##########################\n", " # if it is an isolated point\n", - " if isempty(nI[1][1]) && isempty(nI[1][2])\n", + " if isempty(nI[1]) && isempty(nI[2])\n", " #pass\n", " # We can add the isolated vertex\n", " # push!(Vert, Pcrit[i][j])\n", @@ -455,31 +538,31 @@ " ## works for space curves without nodes ##\n", " ############################################\n", " # If we are dealing with a node\n", - " elseif i == 1\n", + " elseif i == 2\n", " # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2\n", - " push!(Edg, (Corr[i][j][1][1][nI[1][1][1]], Corr[i][j][3][nI[1][2][2]]))\n", - " push!(Edg, (Corr[i][j][1][1][nI[1][1][2]], Corr[i][j][3][nI[1][2][1]]))\n", + " push!(Edg, [Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]]])\n", + " push!(Edg, [Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]]])\n", " else\n", " # We can add the vertex\n", - " push!(Vert, Pcrit[i][j])\n", - " push!(Corr[i][j][2][1], ite)\n", + " push!(Vert, [xcmid, ycmid])\n", + " push!(Corr[i][j][2][2], ite)\n", " # We connect to the vertical left side of the critical box\n", - " for k in nI[1][1]\n", - " push!(Edg, (Corr[i][j][1][1][k], ite))\n", + " for k in nI[1]\n", + " push!(Edg, [Corr[i][j][1][k], ite])\n", " end\n", " # We connect to the vertical right side of the critical box\n", - " for k in nI[1][2]\n", - " push!(Edg, (ite, Corr[i][j][3][k]))\n", + " for k in nI[2]\n", + " push!(Edg, [ite, Corr[i][j][3][k]])\n", " end\n", " ite += 1\n", " end\n", " ###########################\n", " # Above the critical point\n", - " for k in length(I[1][1]) - length(nI[1][1]) - ymincrit:-1:1\n", - " push!(Vert, (xcrit[i][j], (I[1][1][end - k + 1] + I[1][2][end - k + 1]) / 2))\n", + " for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1\n", + " push!(Vert, [xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4])\n", " push!(Corr[i][j][2][3], ite)\n", - " push!(Edg, (Corr[i][j][1][1][end - k + 1], ite)) # left\n", - " push!(Edg, (ite, Corr[i][j][3][end - k + 1])) # right\n", + " push!(Edg, [Corr[i][j][1][end - k + 1], ite]) # left\n", + " push!(Edg, [ite, Corr[i][j][3][end - k + 1]]) # right\n", " ite += 1\n", " end\n", "end" @@ -487,32 +570,4739 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "using Plots;" + ] + }, + { + "cell_type": "code", + "execution_count": 16, "metadata": {}, "outputs": [ { - "ename": "UndefVarError", - "evalue": "UndefVarError: `LnPCside` not defined", + "data": { + "text/html": [ + "311354880742658165020823809451303138468859396825965249675828338269318772975884775//60708402882054033466233184588234965832575213720379360039119137804340758912662765568" + ], + "text/latex": [ + "\\frac{311354880742658165020823809451303138468859396825965249675828338269318772975884775}{60708402882054033466233184588234965832575213720379360039119137804340758912662765568}" + ], + "text/plain": [ + "311354880742658165020823809451303138468859396825965249675828338269318772975884775//60708402882054033466233184588234965832575213720379360039119137804340758912662765568" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Vert[1][2]" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "plot_graph (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "function plot_graph(V, E)\n", + " println(\"Plotting the graph\")\n", + " plot(legend=false)\n", + " for e in E\n", + " xe, ye = map(Float64,[e[1][1], e[2][1]]), map(Float64,[e[1][2], e[2][2]])\n", + " plot!(xe, ye, lc=\"red\", lw=3)\n", + " end\n", + " scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc=\"black\", m=:diamond)\n", + " #plt.show(block=true)\n", + " plot!()\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Plotting the graph\n" + ] + }, + { + "data": { + "image/png": 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"ErrorException", + "evalue": "type Array has no field vertices", "output_type": "error", "traceback": [ - "UndefVarError: `LnPCside` not defined\n", + "type Array has no field vertices\n", "\n", "Stacktrace:\n", - " [1] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/main.ipynb:1" + " [1] getproperty\n", + " @ ./Base.jl:37 [inlined]\n", + " [2] (::var\"#198#199\")(cG::Vector{Int64})\n", + " @ Main ./none:0\n", + " [3] iterate\n", + " @ ./generator.jl:47 [inlined]\n", + " [4] collect(itr::Base.Generator{Vector{Vector{Int64}}, var\"#198#199\"})\n", + " @ Base ./array.jl:834\n", + " [5] top-level scope\n", + " @ ~/Documents/gittravail/AlgCurves/main.ipynb:2" ] } ], - "source": [] + "source": [ + "CG = connected_components(G); \n", + "CVert = [ cG.vertices() for cG in CG ]\n", + "CEdg = [[ e[:2] for e in cG.edges()] for cG in CG]" + ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 93, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "([[1], [2], [3], [4], [5], [6], [7], [8], [9], [10] … [141], [142], [143], [144], [145], [146], [147], [148], [149], [150]], Dict(1071 => 150, 937 => 113, 879 => 100, 830 => 87, 719 => 66, 700 => 63, 731 => 68, 734 => 69, 985 => 126, 510 => 32…))" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "I" + "Graphs.components(connected_components(G)[4])" ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1108-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:\n", + " Edge 1 => 3\n", + " Edge 1 => 9\n", + " Edge 2 => 3\n", + " Edge 2 => 10\n", + " Edge 4 => 8\n", + " Edge 4 => 15\n", + " Edge 5 => 8\n", + " Edge 5 => 13\n", + " Edge 6 => 9\n", + " Edge 6 => 12\n", + " â‹®\n", + " Edge 1097 => 1105\n", + " Edge 1098 => 1106\n", + " Edge 1099 => 1107\n", + " Edge 1100 => 1102\n", + " Edge 1100 => 1107\n", + " Edge 1103 => 1105\n", + " Edge 1103 => 1108\n", + " Edge 1104 => 1106\n", + " Edge 1104 => 1108" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "collect(edges(G))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { From a09b01691ba378d39c2ec9ccd9d3aace659cb141 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 26 Mar 2024 00:01:38 +0100 Subject: [PATCH 004/180] end color --- src/connectcurves/main.ipynb | 11571 +++++++++++++++++++-------------- 1 file changed, 6865 insertions(+), 4706 deletions(-) diff --git a/src/connectcurves/main.ipynb b/src/connectcurves/main.ipynb index 0b11b4c..76b8109 100644 --- a/src/connectcurves/main.ipynb +++ b/src/connectcurves/main.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -36,7 +36,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -58,7 +58,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -115,7 +115,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -136,7 +136,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -158,7 +158,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -183,7 +183,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -216,7 +216,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -237,7 +237,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -248,8 +248,8 @@ "Compute intersections with critical boxes\n", "mult=1 ; 16/16 pts\n", "mult=2 ; 60/60 pts\n", - "Average time for one point: 0.20092660502383583s\n", - "Elapsed time to compute critical boxes: 15.649327993392944s\n" + "Average time for one point: 0.1860845590892591s\n", + "Elapsed time to compute critical boxes: 14.443221092224121s\n" ] } ], @@ -296,82 +296,10 @@ "println(\"Elapsed time to compute critical boxes: $(time()-ts)s\")\n" ] }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "16-element Vector{Vector{Int64}}:\n", - " [0, 0, 0, 2]\n", - " [0, 0, 0, 2]\n", - " [0, 0, 0, 2]\n", - " [0, 0, 0, 2]\n", - " [0, 0, 2, 0]\n", - " [1, 1, 0, 0]\n", - " [0, 0, 0, 2]\n", - " [1, 1, 0, 0]\n", - " [1, 1, 0, 0]\n", - " [0, 0, 2, 0]\n", - " [1, 1, 0, 0]\n", - " [0, 0, 0, 2]\n", - " [0, 0, 2, 0]\n", - " [0, 0, 2, 0]\n", - " [0, 0, 2, 0]\n", - " [0, 0, 2, 0]" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "LnPCside[1]" - ] - }, { "cell_type": "code", "execution_count": 11, "metadata": {}, - "outputs": [ - { - "ename": "MethodError", - "evalue": "MethodError: no method matching isless(::Vector{QQFieldElem}, ::QQFieldElem)\n\nClosest candidates are:\n isless(!Matched::qqbar, ::QQFieldElem)\n @ Nemo ~/.julia/packages/Nemo/VHAIi/src/calcium/qqbar.jl:633\n isless(!Matched::Float64, ::QQFieldElem)\n @ Nemo ~/.julia/packages/Nemo/VHAIi/src/HeckeMiscInteger.jl:28\n isless(!Matched::NegInf, ::Union{QQFieldElem, ZZRingElem})\n @ Nemo ~/.julia/packages/Nemo/VHAIi/src/HeckeMiscInfinity.jl:79\n ...\n", - "output_type": "error", - "traceback": [ - "MethodError: no method matching isless(::Vector{QQFieldElem}, ::QQFieldElem)\n", - "\n", - "Closest candidates are:\n", - " isless(!Matched::qqbar, ::QQFieldElem)\n", - " @ Nemo ~/.julia/packages/Nemo/VHAIi/src/calcium/qqbar.jl:633\n", - " isless(!Matched::Float64, ::QQFieldElem)\n", - " @ Nemo ~/.julia/packages/Nemo/VHAIi/src/HeckeMiscInteger.jl:28\n", - " isless(!Matched::NegInf, ::Union{QQFieldElem, ZZRingElem})\n", - " @ Nemo ~/.julia/packages/Nemo/VHAIi/src/HeckeMiscInfinity.jl:79\n", - " ...\n", - "\n", - "\n", - "Stacktrace:\n", - " [1] <(x::Vector{QQFieldElem}, y::QQFieldElem)\n", - " @ Base ./operators.jl:352\n", - " [2] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/main.ipynb:4" - ] - } - ], - "source": [ - "y1, y2 = [ l[1] for l in LPCside[1][1] ][4]\n", - "yB1, yB2 = LBcrit[1][1][2]\n", - "yRB = Pcrit[1][1][2]\n", - "print(y2\n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - 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"\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n" ] }, @@ -5179,75 +5047,73 @@ }, { "cell_type": "code", - "execution_count": 66, + "execution_count": 114, "metadata": {}, "outputs": [ { - "name": "stderr", - "output_type": "stream", - "text": [ - "WARNING: using Graphs.radius in module Main conflicts with an existing identifier.\n" - ] + "data": { + "text/plain": [ + "connected_components_bis (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "using Graphs" + "function connected_components_bis(edges)\n", + " adj_list = Dict{Int, Vector{Int}}()\n", + " visited = Set{Int}()\n", + " components = Vector{Vector{Tuple{Int, Int}}}()\n", + "\n", + " # Build adjacency list\n", + " for (i, j) in edges\n", + " push!(get!(adj_list, i, []), j)\n", + " push!(get!(adj_list, j, []), i)\n", + " end\n", + "\n", + " # Depth-first search\n", + " function dfs(node, component)\n", + " push!(visited, node)\n", + " for neighbor in adj_list[node]\n", + " if !(neighbor in visited)\n", + " push!(component, (node, neighbor))\n", + " dfs(neighbor, component)\n", + " end\n", + " end\n", + " end\n", + "\n", + " # Find connected components\n", + " for node in keys(adj_list)\n", + " if !(node in visited)\n", + " component = Vector{Tuple{Int, Int}}()\n", + " dfs(node, component)\n", + " push!(components, component)\n", + " end\n", + " end\n", + "\n", + " return components\n", + "end\n" ] }, { "cell_type": "code", - "execution_count": 80, + "execution_count": 145, "metadata": {}, "outputs": [], "source": [ - "G = SimpleGraph()\n", - "add_vertices!(G, length(Vert))\n", - "for e in Edg\n", - " add_edge!(G, e[1],e[2])\n", - "end" + "CEdg = connected_components_bis(Edg);" ] }, { "cell_type": "code", - "execution_count": 94, - "metadata": {}, - "outputs": [ - { - "ename": "ErrorException", - "evalue": "type Array has no field vertices", - "output_type": "error", - "traceback": [ - "type Array has no field vertices\n", - "\n", - "Stacktrace:\n", - " [1] getproperty\n", - " @ ./Base.jl:37 [inlined]\n", - " [2] (::var\"#198#199\")(cG::Vector{Int64})\n", - " @ Main ./none:0\n", - " [3] iterate\n", - " @ ./generator.jl:47 [inlined]\n", - " [4] collect(itr::Base.Generator{Vector{Vector{Int64}}, var\"#198#199\"})\n", - " @ Base ./array.jl:834\n", - " [5] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/main.ipynb:2" - ] - } - ], - "source": [ - "CG = connected_components(G); \n", - "CVert = [ cG.vertices() for cG in CG ]\n", - "CEdg = [[ e[:2] for e in cG.edges()] for cG in CG]" - ] - }, - { - "cell_type": "code", - "execution_count": 93, + "execution_count": 142, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "([[1], [2], [3], [4], [5], [6], [7], [8], [9], [10] … [141], [142], [143], [144], [145], [146], [147], [148], [149], [150]], Dict(1071 => 150, 937 => 113, 879 => 100, 830 => 87, 719 => 66, 700 => 63, 731 => 68, 734 => 69, 985 => 126, 510 => 32…))" + "plot_graph_comp (generic function with 2 methods)" ] }, "metadata": {}, @@ -5255,38 +5121,2331 @@ } ], "source": [ - "Graphs.components(connected_components(G)[4])" + "function plot_graph_comp(V, CE)\n", + " println(\"Plotting the graph\")\n", + " plot(legend=false)\n", + " col = distinguishable_colors(length(CE)+2)\n", + " for j in eachindex(CE)\n", + " for e in CE[j]\n", + " v1, v2 = map(Float64, V[e[1]]), map(Float64, V[e[2]])\n", + " plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=3)\n", + " end\n", + " end\n", + " #plt.show(block=true)\n", + " plot!()\n", + "end" ] }, { "cell_type": "code", - "execution_count": 85, + "execution_count": 143, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Plotting the graph\n" + ] + }, { "data": { - "text/plain": [ - "1108-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:\n", - " Edge 1 => 3\n", - " Edge 1 => 9\n", - " Edge 2 => 3\n", - " Edge 2 => 10\n", - " Edge 4 => 8\n", - " Edge 4 => 15\n", - " Edge 5 => 8\n", - " Edge 5 => 13\n", - " Edge 6 => 9\n", - " Edge 6 => 12\n", - " â‹®\n", - " Edge 1097 => 1105\n", - " Edge 1098 => 1106\n", - " Edge 1099 => 1107\n", - " Edge 1100 => 1102\n", - " Edge 1100 => 1107\n", - " Edge 1103 => 1105\n", - " Edge 1103 => 1108\n", - " Edge 1104 => 1106\n", - " Edge 1104 => 1108" + "image/png": 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a/src/connectcurves/main.ipynb b/src/connectcurves/main.ipynb index 76b8109..014a1f1 100644 --- a/src/connectcurves/main.ipynb +++ b/src/connectcurves/main.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -36,7 +36,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -50,7 +50,6 @@ } ], "source": [ - "\n", "include(\"data.jl\")\n", "include(\"src/usolve/usolve.jl\")\n", "#using Arblib" @@ -58,7 +57,17 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "using BenchmarkTools\n", + "using IntervalArithmetic" + ] + }, + { + "cell_type": "code", + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -115,7 +124,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -156,31 +165,6 @@ "Pcrit = [ [ [ rat_to_Arb(pc[1]), pc[2] ] for pc in pcrit] for pcrit in Pcrit ];" ] }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "[0.00592297584970014544321252 +/- 4.43e-27]" - ], - "text/latex": [ - "[0.00592297584970014544321252 +/- 4.43e-27]" - ], - "text/plain": [ - "[0.00592297584970014544321252 +/- 4.43e-27]" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Pcrit[1][1][2]" - ] - }, { "cell_type": "code", "execution_count": 8, @@ -347,7 +331,7 @@ "metadata": {}, "outputs": [], "source": [ - "#print(\"Graph computation\")\n", + "print(\"Graph computation\")\n", "# Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot\n", "# And even remove this fiber for the graph\n", "Vert = []\n", @@ -5047,7 +5031,7 @@ }, { "cell_type": "code", - "execution_count": 114, + "execution_count": 163, "metadata": {}, "outputs": [ { @@ -5072,6 +5056,7 @@ " push!(get!(adj_list, j, []), i)\n", " end\n", "\n", + " \n", " # Depth-first search\n", " function dfs(node, component)\n", " push!(visited, node)\n", @@ -5082,12 +5067,29 @@ " end\n", " end\n", " end\n", + " \n", + "\n", + " # Breadth-first search\n", + " function bfs(node, component)\n", + " queue = [node]\n", + " push!(visited, node)\n", + " while !isempty(queue)\n", + " current = popfirst!(queue)\n", + " for neighbor in adj_list[current]\n", + " if !(neighbor in visited)\n", + " push!(visited, neighbor)\n", + " push!(component, (current, neighbor))\n", + " push!(queue, neighbor)\n", + " end\n", + " end\n", + " end\n", + " end\n", "\n", " # Find connected components\n", " for node in keys(adj_list)\n", " if !(node in visited)\n", " component = Vector{Tuple{Int, Int}}()\n", - " dfs(node, component)\n", + " bfs(node, component)\n", " push!(components, component)\n", " end\n", " end\n", @@ -5098,9 +5100,17 @@ }, { "cell_type": "code", - "execution_count": 145, + "execution_count": 162, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 486.504 μs (8496 allocations: 535.11 KiB)\n" + ] + } + ], "source": [ "CEdg = connected_components_bis(Edg);" ] diff --git a/src/connectcurves/main.jl b/src/connectcurves/main.jl index 6aed3b6..d7741a3 100644 --- a/src/connectcurves/main.jl +++ b/src/connectcurves/main.jl @@ -1,10 +1,13 @@ println("Loading libraries and data..") -using Oscar +using Pkg +using Revise +Pkg.activate("AlgebraicSolving.jl-main") +using AlgebraicSolving +using Nemo +using Colors +using PyPlot include("data.jl") include("src/usolve/usolve.jl") -#include("tools.jl") - -#using Arblib function order_permut2d(L) # Create a list of tuples with elements and their corresponding indices @@ -19,9 +22,15 @@ function order_permut2d(L) end function isolate(f; prec = 32, software="usolve") + @assert is_univariate(f) "Not univariate polynomial" if software == "usolve" return usolve(f, precision = prec, uspath="src/usolve/usolve") - end + end +end + +function isolate_eval(f, ivar, val; prec=64) + sols = inter_solutions(AlgebraicSolving.Ideal([f, gens(R)[ivar] - val]), precision=prec) + return [ s[ivar%2+1] for s in sols ] end function Arb_to_rat(x) @@ -29,90 +38,265 @@ function Arb_to_rat(x) return map(simplest_rational_inside, [x-2*r, x+2*r]) end +function rat_to_Arb(x) + x1,x2 = x + xm, xd = RR((x1+x2)/2), RR(x2-x1) + return ball(xm,xd) +end + function evaluate_Arb(f, x) cf = coefficients_of_univariate(f) return evalpoly(RR(x), cf) end +# To try/do : isolate with usolve, call msolve with only one variable +function intersect_box(f, B) + L = Array{Any}(undef, 4) + for i in 1:2 + # Lxi + L[i] = Array{Any}(undef,2) + L[i][1] = isolate_eval(f, 2, B[2][i], prec=200) + L[i][2] = [ j for (j, l) in pairs(L[i][1]) if (l[1]> B[1][1] && l[2] B[2][1] && l[2] 2 + @assert false "\nRefine extreme boxes along x-axis" + #refine_xboxes(QQ["x"](params[1][1]), LBcrit[1]) + #i = 0 + #j = 1 + #break + elseif i > 1 && sum(npcside[1:2]) != 0 + println(npcside) + @assert false "\nRefine singular boxes along x-axis" + #refine_xboxes(QQ["x"](params[2][1]), LBcrit[2]) + #i -= 1 + #break + end + LPCside[i][j] = pcside + push!(Ltm, time() - tm) + end + i += 1 + println("") +end +LnPCside = [ [[length(indI) for (L, indI) in PB] for PB in lpcside] for lpcside in LPCside ] +println("Average time for one point: $(sum(Ltm)/length(Ltm))s") +println("Elapsed time to compute critical boxes: $(time()-ts)s") -printstep("Graph computation") +# Update extreme boxes +for j in eachindex(LBcrit[1]) + # If the curve does not intersect the box only on vertical sides + if !(LnPCside[1][j][1:2] == [0, 0]) + PCside, nPCside = LPCside[1][j], LnPCside[1][j] + I = [ l[1] for l in PCside[3:end] ] + nI = [ l[2] for l in PCside[3:end] ] + # Locate the orientation of the extreme point + # s is the index on the side where there are more branches + # s=1: left; s=2: right + s = argmax([length(I[1]), length(I[2])]) + # Ordinate range of the extreme point + ycrit = LBcrit[1][j][2] + # If it intersects on the bottom side + if nPCside[1] == 1 + # yinf: the intersection with the vertical side just below the extreme point + yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[2]]) + # We vertically enlarge the box until it intersects on the horizontal side + push!(LPCside[1][j][s + 2][2], yinf) + LPCside[1][j][1][2] = [] + # We update the intersection numbers + LnPCside[1][j][s + 2] += 1 + LnPCside[1][j][1] = 0 + end + # If it intersects on the top side + if nPCside[2] == 1 + # ymax: the intersection with the vertical side just above the extreme point + ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[1]]) + # We vertically enlarge the box until it intersects on the horizontal side + push!(LPCside[1][j][s + 2][2], ymax) + LPCside[1][j][2][2] = [] + # We update the intersection numbers + LnPCside[1][j][s + 2] += 1 + LnPCside[1][j][2] = 0 + end + end +end + +print("Graph computation") # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot # And even remove this fiber for the graph Vert = [] Edg = [] -Corr = [[[[], [[], [], []], []] for _ in xcrit[i] ] for _ in xcrit ] +Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ] Viso = [] ite = 1 for ind in 1:length(xcritpermut) + global ite + local i i, j = xcritpermut[ind] + if ind > 1 i1, j1 = xcritpermut[ind - 1] end if ind < length(xcritpermut) i2, j2 = xcritpermut[ind + 1] - I2L, nI2L = LPCside[i2][j2][2] + I2L, nI2L = LPCside[i2][j2][3] end PCside, nPCside = LPCside[i][j], LnPCside[i][j] - I, nI = unzip(PCside[2:end]) - ymincrit = min(nI[1][1] + nI[1][2] + [length(I[1][1])]) + I = [ l[1] for l in PCside[3:end] ] + nI = [ l[2] for l in PCside[3:end] ] + xcmid = sum(LBcrit[i][j][1])//2 + ycmid = sum(LBcrit[i][j][2])//2 + + ymincrit = minimum(vcat(nI[1], nI[2], [length(I[1])+1])) # Construct vertices ########################### # On the vertical left side if ind > 1 - for k in 1:length(I[1][1]) - push!(Corr[i][j][1][1], Corr[i1][j1][3][k]) + for k in 1:length(I[1]) + push!(Corr[i][j][1], Corr[i1][j1][3][k]) end else - for k in 1:length(I[1][1]) - push!(Vert, (xcrit[i][j].lower() - exp, I[1][1][k])) - push!(Corr[i][j][1][1], ite) + for k in 1:length(I[1]) + push!(Vert, [xcrit[i][j][1], sum(I[1][k])//2]) + push!(Corr[i][j][1], ite) ite += 1 end end ########################### # On the vertical right side if ind < length(xcritpermut) - for k in 1:length(I[1][2]) - push!(Vert, ((xcrit[i][j] + xcrit[i2][j2]).lower() / 2 + exp, (I[1][2][k] + I2L[k]).lower() / 2)) + for k in 1:length(I[2]) + push!(Vert, [(xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4]) push!(Corr[i][j][3], ite) ite += 1 end else - for k in 1:length(I[1][2]) - push!(Vert, (xcrit[i][j].upper() + exp, I[1][2][k])) + for k in 1:length(I[2]) + push!(Vert, [xcrit[i][j][2], sum(I[2][k])//2]) push!(Corr[i][j][3], ite) ite += 1 end end ########################### # Below the critical point - for k in 1:ymincrit - push!(Vert, (xcrit[i][j], (I[1][1][k] + I[1][2][k]) / 2)) + + for k in 1:ymincrit-1 + push!(Vert, [xcmid, sum(I[1][k] + I[2][k])// 4]) push!(Corr[i][j][2][1], ite) - push!(Edg, (Corr[i][j][1][1][k], ite)) # left - push!(Edg, (ite, Corr[i][j][3][k])) # right + push!(Edg, [Corr[i][j][1][k], ite]) # left + push!(Edg, [ite, Corr[i][j][3][k]]) # right ite += 1 end ########################### # The critical point ########################## # if it is an isolated point - if isempty(nI[1][1]) && isempty(nI[1][2]) + if isempty(nI[1]) && isempty(nI[2]) #pass # We can add the isolated vertex # push!(Vert, Pcrit[i][j]) @@ -125,31 +309,38 @@ for ind in 1:length(xcritpermut) ## works for space curves without nodes ## ############################################ # If we are dealing with a node - elseif i == 1 + elseif i == 2 # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 - push!(Edg, (Corr[i][j][1][1][nI[1][1][1]], Corr[i][j][3][nI[1][2][2]])) - push!(Edg, (Corr[i][j][1][1][nI[1][1][2]], Corr[i][j][3][nI[1][2][1]])) + push!(Edg, [Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]]]) + push!(Edg, [Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]]]) else # We can add the vertex - push!(Vert, Pcrit[i][j]) - push!(Corr[i][j][2][1], ite) + push!(Vert, [xcmid, ycmid]) + push!(Corr[i][j][2][2], ite) # We connect to the vertical left side of the critical box - for k in nI[1][1] - push!(Edg, (Corr[i][j][1][1][k], ite)) + for k in nI[1] + push!(Edg, [Corr[i][j][1][k], ite]) end # We connect to the vertical right side of the critical box - for k in nI[1][2] - push!(Edg, (ite, Corr[i][j][3][k])) + for k in nI[2] + push!(Edg, [ite, Corr[i][j][3][k]]) end ite += 1 end ########################### # Above the critical point - for k in length(I[1][1]) - length(nI[1][1]) - ymincrit:-1:1 - push!(Vert, (xcrit[i][j], (I[1][1][end - k + 1] + I[1][2][end - k + 1]) / 2)) + for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1 + push!(Vert, [xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4]) push!(Corr[i][j][2][3], ite) - push!(Edg, (Corr[i][j][1][1][end - k + 1], ite)) # left - push!(Edg, (ite, Corr[i][j][3][end - k + 1])) # right + push!(Edg, [Corr[i][j][1][end - k + 1], ite]) # left + push!(Edg, [ite, Corr[i][j][3][end - k + 1]]) # right ite += 1 end -end \ No newline at end of file +end + +EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] +plot_graph(Vert, EdgPlot) + +CEdg = connected_components_bis(Edg); + +plot_graph_comp(Vert,CEdg) \ No newline at end of file diff --git a/src/connectcurves/subresultant.ipynb b/src/connectcurves/subresultant.ipynb new file mode 100644 index 0000000..5e0402c --- /dev/null +++ b/src/connectcurves/subresultant.ipynb @@ -0,0 +1,431 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "using Nemo" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "subresultants (generic function with 2 methods)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingElement\n", + " if degree(P) < degree(Q)\n", + " P, Q = Q, P\n", + " end\n", + " S = []\n", + " s = leading_coefficient(Q)^(degree(P)-degree(Q))\n", + " A = Q\n", + " B = pseudorem(P,-Q)\n", + " ring = parent(P)\n", + " while true\n", + " d = degree(A)\n", + " e = degree(B)\n", + " if iszero(B)\n", + " return S\n", + " end\n", + " pushfirst!(S, copy(B))\n", + " delta = d - e\n", + " if delta > 1\n", + " if length(S) > 1\n", + " n = degree(S[2]) - degree(S[1]) - 1\n", + " if n == 0\n", + " C = copy(S[1])\n", + " else\n", + " x = leading_coefficient(S[1])\n", + " y = leading_coefficient(S[2])\n", + " a = 1 << (length(bits(ZZ(n))) - 1)\n", + " c = x\n", + " n = n - a\n", + " while a > 1\n", + " a Ă·= 2\n", + " c = c^2 / y\n", + " if n >= a\n", + " c = c * x / y\n", + " n = n - a\n", + " end\n", + " end\n", + " C = c * S[1] / y\n", + " end\n", + " else\n", + " C = leading_coefficient(B)^(delta-1) * B / s^(delta-1)\n", + " end\n", + " pushfirst!(S, copy(C))\n", + " else\n", + " C = copy(B)\n", + " end\n", + " if e == 0\n", + " return S\n", + " end\n", + " B = pseudorem(A,-B) / (s^delta * leading_coefficient(A))\n", + " A = copy(C)\n", + " s = leading_coefficient(A)\n", + " end\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "f" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-x*y^2 + (x^2 + 6)*y - x^2 - x - 6" + ], + "text/latex": [ + "-x y^{2} + \\left(x^{2} + 6\\right) y - x^{2} - x - 6" + ], + "text/plain": [ + "-x*y^2 + (x^2 + 6)*y - x^2 - x - 6" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#using Nemo\n", + "R, x = polynomial_ring(QQ, \"x\")\n", + "#f = x^8 + x^6 -3*x^4 -3*x^3 +8*x^2 +2*x -5\n", + "#g = 3*x^6 +5*x^4 -4*x^2 -9*x +21\n", + "S, y = polynomial_ring(R, \"y\")\n", + "f = (y^2 + 6)*(x - 1) - y*(x^2 + 1)\n", + "g = (x^2 + 6)*(y - 1) - x*(y^2 + 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2-element Vector{Any}:\n", + " 2*x^6 - 22*x^5 + 102*x^4 - 274*x^3 + 488*x^2 - 552*x + 288\n", + " (-x^2 + 5*x - 6)*y - x^3 + 6*x^2 - 11*x + 6" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "subresultants(f,g)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "11//8" + ], + "text/latex": [ + "\\frac{11}{8}" + ], + "text/plain": [ + "11//8" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "divrem(f,-g)[2]" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "64" + ], + "text/latex": [ + "64" + ], + "text/plain": [ + "64" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "prevpow2(ZZ(100))" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Integers" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "parent(degree(f))" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[a, b])" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "RR, (a,b) = Nemo.polynomial_ring(QQ,[:a,:b])" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "a^2 + a*b^2 + b" + ], + "text/latex": [ + "a^{2} + a b^{2} + b" + ], + "text/plain": [ + "a^2 + a*b^2 + b" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P = a^2+b+a*b^2" + ] + }, + { + "cell_type": "code", + "execution_count": 140, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "view_as_univariate (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "function view_as_univariate(P, x)\n", + " A = parent(P)\n", + " # Find the index of the variable x\n", + " idx = var_index(x)\n", + "\n", + " # If x is not found, return P unchanged\n", + " if idx === nothing\n", + " return P\n", + " end\n", + "\n", + " # Extract variables of the polynomial ring\n", + " vars = gens(A)\n", + " varsbis = filter(y -> y != x, vars)\n", + "\n", + " symbs = symbols(A)\n", + "\n", + " R, () = polynomial_ring(base_ring(A), [symbs[1:idx-1]; symbs[idx+1:end]])\n", + " S, t = polynomial_ring(R, symbs[idx])\n", + "\n", + " print([symbs[1:idx-1]; symbs[idx+1:end]][1])\n", + " \n", + " # Create the new polynomial Q by treating the variable x as the main variable\n", + " Q_coeffs = [ R(coeff(P,[x],[i])) for i in 0:degree(P,idx) ]\n", + " #Q = S(Q_coeffs)\n", + " \n", + " return Q_coeffs\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 141, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "b" + ] + }, + { + "ename": "ErrorException", + "evalue": "Unable to coerce polynomial", + "output_type": "error", + "traceback": [ + "Unable to coerce polynomial\n", + "\n", + "Stacktrace:\n", + " [1] error(s::String)\n", + " @ Base ./error.jl:35\n", + " [2] QQMPolyRing\n", + " @ ~/.julia/packages/Nemo/RGGys/src/flint/fmpq_mpoly.jl:1189 [inlined]\n", + " [3] #62\n", + " @ ./none:0 [inlined]\n", + " [4] iterate\n", + " @ ./generator.jl:47 [inlined]\n", + " [5] collect(itr::Base.Generator{UnitRange{Int64}, var\"#62#64\"{QQMPolyRingElem, QQMPolyRingElem, QQMPolyRing}})\n", + " @ Base ./array.jl:834\n", + " [6] view_as_univariate(P::QQMPolyRingElem, x::QQMPolyRingElem)\n", + " @ Main ~/Documents/gittravail/AlgCurves/subresultant.ipynb:23\n", + " [7] top-level scope\n", + " @ ~/Documents/gittravail/AlgCurves/subresultant.ipynb:1" + ] + } + ], + "source": [ + "view_as_univariate(P,a)" + ] + }, + { + "cell_type": "code", + "execution_count": 144, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(Multivariate polynomial ring in 1 variable over QQ, QQMPolyRingElem[b])" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "test, () = polynomial_ring(QQ,[:b])" + ] + }, + { + "cell_type": "code", + "execution_count": 145, + "metadata": {}, + "outputs": [ + { + "ename": "ErrorException", + "evalue": "Unable to coerce polynomial", + "output_type": "error", + "traceback": [ + "Unable to coerce polynomial\n", + "\n", + "Stacktrace:\n", + " [1] error(s::String)\n", + " @ Base ./error.jl:35\n", + " [2] (::QQMPolyRing)(a::QQMPolyRingElem)\n", + " @ Nemo ~/.julia/packages/Nemo/RGGys/src/flint/fmpq_mpoly.jl:1189\n", + " [3] top-level scope\n", + " @ ~/Documents/gittravail/AlgCurves/subresultant.ipynb:1" + ] + } + ], + "source": [ + "test(b^2+1)" + ] + }, + { + "cell_type": "code", + "execution_count": 146, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1-element Vector{QQMPolyRingElem}:\n", + " b" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gens(test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.10.1", + "language": "julia", + "name": "julia-1.10" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From f43180754ccb1066a6bd001327c5490905653306 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 10 May 2024 12:43:35 +0200 Subject: [PATCH 006/180] finish subresultant code --- src/connectcurves/subresultant.ipynb | 393 +++++++++++++++++++-------- src/connectcurves/subresultants.jl | 121 +++++++++ 2 files changed, 403 insertions(+), 111 deletions(-) create mode 100644 src/connectcurves/subresultants.jl diff --git a/src/connectcurves/subresultant.ipynb b/src/connectcurves/subresultant.ipynb index 5e0402c..70d51cc 100644 --- a/src/connectcurves/subresultant.ipynb +++ b/src/connectcurves/subresultant.ipynb @@ -11,13 +11,13 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "subresultants (generic function with 2 methods)" + "subresultants (generic function with 1 method)" ] }, "metadata": {}, @@ -82,16 +82,7 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "f" - ] - }, - { - "cell_type": "code", - "execution_count": 68, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -122,7 +113,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -143,23 +134,28 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 13, "metadata": {}, "outputs": [ { - "data": { - "text/html": [ - "11//8" - ], - "text/latex": [ - "\\frac{11}{8}" - ], - "text/plain": [ - "11//8" - ] - }, - "metadata": {}, - "output_type": "display_data" + "ename": "ArgumentError", + "evalue": "ArgumentError: not an exact division", + "output_type": "error", + "traceback": [ + "ArgumentError: not an exact division\n", + "\n", + "Stacktrace:\n", + " [1] divexact(x::QQPolyRingElem, y::QQPolyRingElem; check::Bool)\n", + " @ Nemo ~/.julia/packages/Nemo/RGGys/src/flint/fmpq_poly.jl:454\n", + " [2] divexact\n", + " @ ~/.julia/packages/Nemo/RGGys/src/flint/fmpq_poly.jl:449 [inlined]\n", + " [3] inv\n", + " @ ~/.julia/packages/AbstractAlgebra/KwfqS/src/Rings.jl:38 [inlined]\n", + " [4] divrem(f::AbstractAlgebra.Generic.Poly{QQPolyRingElem}, g::AbstractAlgebra.Generic.Poly{QQPolyRingElem})\n", + " @ Nemo ~/.julia/packages/Nemo/RGGys/src/HeckeMiscPoly.jl:450\n", + " [5] top-level scope\n", + " @ ~/Documents/gittravail/AlgCurves/subresultant.ipynb:1" + ] } ], "source": [ @@ -168,7 +164,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -193,7 +189,7 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -212,7 +208,7 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -231,19 +227,107 @@ }, { "cell_type": "code", - "execution_count": 95, + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "a^2 + a*b^2 + a*b + b" + ], + "text/latex": [ + "a^{2} + a b^{2} + a b + b" + ], + "text/plain": [ + "a^2 + a*b^2 + a*b + b" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 196, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "asvar_to_parray (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "function poly_to_array(P::MPolyRingElem)\n", + " # return P as two lists ci and vi of resp. coeffs and exponents\n", + " return [collect(coefficients(P)), collect(exponent_vectors(P))]\n", + "end\n", + "\n", + "function rem_ind(L,i)\n", + " # remove element at index i\n", + " return [ L[1:i-1]; L[i+1:end] ]\n", + "end\n", + "\n", + "function add_ind(L,i,x)\n", + " # add element x at index i\n", + " return [ L[1:i-1]; [x]; L[i:end] ]\n", + "end\n", + "\n", + "function parray_asvar(LP, idx)\n", + " # takes a sparse representation of a poly P \n", + " # and outputs a sparse rpz of P seen as a univariate poly in the i-th variable\n", + " deg = sort(LP[2], by= x->x[idx])[end][idx]\n", + " NLP = [ [[],[]] for _ in 1:deg+1 ]\n", + " for i in eachindex(LP[2])\n", + " di = LP[2][i][idx]+1\n", + " push!(NLP[di][1], LP[1][i])\n", + " push!(NLP[di][2], rem_ind(LP[2][i], idx)) \n", + " end\n", + " return NLP\n", + "end\n", + "\n", + "function array_to_poly(LP, A)\n", + " C = MPolyBuildCtx(A)\n", + " R = base_ring(A)\n", + " for i in eachindex(LP[1])\n", + " push_term!(C, R(LP[1][i]), LP[2][i]);\n", + " end\n", + " return finish(C)\n", + "end\n", + "\n", + "function asvar_to_parray(NLP, idx)\n", + " LP = [[],[]]\n", + " for i in 1:length(NLP)\n", + " for j in eachindex(NLP[i][1])\n", + " push!(LP[1], NLP[i][1][j])\n", + " push!(LP[2], add_ind(NLP[i][2][j], idx, i-1))\n", + " end\n", + " end\n", + " return LP\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 133, "metadata": {}, "outputs": [ { "data": { "text/html": [ - "a^2 + a*b^2 + b" + "a*b + 1" ], "text/latex": [ - "a^{2} + a b^{2} + b" + "a b + 1" ], "text/plain": [ - "a^2 + a*b^2 + b" + "a*b + 1" ] }, "metadata": {}, @@ -251,18 +335,18 @@ } ], "source": [ - "P = a^2+b+a*b^2" + "Q = a*b+1a" ] }, { "cell_type": "code", - "execution_count": 140, + "execution_count": 217, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "view_as_univariate (generic function with 1 method)" + "subresultants (generic function with 3 methods)" ] }, "metadata": {}, @@ -270,85 +354,88 @@ } ], "source": [ - "function view_as_univariate(P, x)\n", - " A = parent(P)\n", - " # Find the index of the variable x\n", - " idx = var_index(x)\n", + "function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx) where T <: RingElement\n", + " LPQ = map(poly_to_array, [P,Q])\n", + " ULPQ = [ parray_asvar(lpq, idx) for lpq in LPQ ]\n", "\n", - " # If x is not found, return P unchanged\n", - " if idx === nothing\n", - " return P\n", - " end\n", + " R, x = polynomial_ring(base_ring(parent(P)), \"x\")\n", + " S, y = polynomial_ring(R, \"y\")\n", "\n", - " # Extract variables of the polynomial ring\n", - " vars = gens(A)\n", - " varsbis = filter(y -> y != x, vars)\n", + " UP, UQ = [ S([ array_to_poly(l, R) for l in lpq ]) for lpq in ULPQ ]\n", "\n", - " symbs = symbols(A)\n", + " sr = subresultants(UP, UQ)\n", "\n", - " R, () = polynomial_ring(base_ring(A), [symbs[1:idx-1]; symbs[idx+1:end]])\n", - " S, t = polynomial_ring(R, symbs[idx])\n", + " # Get it back to initial polynomial ring\n", + " Lsr = [ [collect(coefficients(csr)) for csr in coefficients(sr)] for sr in sr]\n", + " newsr = []\n", + " for lsr in Lsr\n", + " mlsr = [[],[]]\n", + " for i in 1:length(lsr)\n", + " for j in 1:length(lsr[i])\n", + " push!(mlsr[1], lsr[i][j])\n", + " push!(mlsr[2],add_ind([j-1],idx, i-1))\n", + " end\n", + " end\n", + " push!(newsr, array_to_poly(mlsr, parent(P)))\n", + " end\n", "\n", - " print([symbs[1:idx-1]; symbs[idx+1:end]][1])\n", - " \n", - " # Create the new polynomial Q by treating the variable x as the main variable\n", - " Q_coeffs = [ R(coeff(P,[x],[i])) for i in 0:degree(P,idx) ]\n", - " #Q = S(Q_coeffs)\n", - " \n", - " return Q_coeffs\n", + " return newsr\n", "end" ] }, { "cell_type": "code", - "execution_count": 141, + "execution_count": 2, "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "b" - ] - }, + "data": { + "text/plain": [ + "subresultants (generic function with 2 methods)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "include(\"subresultants.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ { - "ename": "ErrorException", - "evalue": "Unable to coerce polynomial", - "output_type": "error", - "traceback": [ - "Unable to coerce polynomial\n", - "\n", - "Stacktrace:\n", - " [1] error(s::String)\n", - " @ Base ./error.jl:35\n", - " [2] QQMPolyRing\n", - " @ ~/.julia/packages/Nemo/RGGys/src/flint/fmpq_mpoly.jl:1189 [inlined]\n", - " [3] #62\n", - " @ ./none:0 [inlined]\n", - " [4] iterate\n", - " @ ./generator.jl:47 [inlined]\n", - " [5] collect(itr::Base.Generator{UnitRange{Int64}, var\"#62#64\"{QQMPolyRingElem, QQMPolyRingElem, QQMPolyRing}})\n", - " @ Base ./array.jl:834\n", - " [6] view_as_univariate(P::QQMPolyRingElem, x::QQMPolyRingElem)\n", - " @ Main ~/Documents/gittravail/AlgCurves/subresultant.ipynb:23\n", - " [7] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/subresultant.ipynb:1" - ] + "data": { + "text/plain": [ + "Any[]" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "view_as_univariate(P,a)" + "R, (x,y) = polynomial_ring(ZZ, [:x,:y])\n", + "f = (y^2 + 6)*(x - 1) - y*(x^2 + 1)\n", + "g = (x^2 + 6)*(y - 1) - x*(y^2 + 1)\n", + "idx = 2\n", + "subresultants(x,x,1)" ] }, { "cell_type": "code", - "execution_count": 144, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(Multivariate polynomial ring in 1 variable over QQ, QQMPolyRingElem[b])" + "2-element Vector{Any}:\n", + " 2*x^6 - 22*x^5 + 102*x^4 - 274*x^3 + 488*x^2 - 552*x + 288\n", + " -x^3 - x^2*y + 6*x^2 + 5*x*y - 11*x - 6*y + 6" ] }, "metadata": {}, @@ -356,45 +443,111 @@ } ], "source": [ - "test, () = polynomial_ring(QQ,[:b])" + "res = subresultants(f,g,idx)" ] }, { "cell_type": "code", - "execution_count": 145, + "execution_count": 213, "metadata": {}, "outputs": [ { - "ename": "ErrorException", - "evalue": "Unable to coerce polynomial", - "output_type": "error", - "traceback": [ - "Unable to coerce polynomial\n", - "\n", - "Stacktrace:\n", - " [1] error(s::String)\n", - " @ Base ./error.jl:35\n", - " [2] (::QQMPolyRing)(a::QQMPolyRingElem)\n", - " @ Nemo ~/.julia/packages/Nemo/RGGys/src/flint/fmpq_mpoly.jl:1189\n", - " [3] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/subresultant.ipynb:1" - ] + "data": { + "text/plain": [ + "1" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "idx" + ] + }, + { + "cell_type": "code", + "execution_count": 204, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2-element Vector{Vector{Any}}:\n", + " [1, 1, 1, 1]\n", + " [[0, 1], [1, 2], [1, 1], [2, 0]]" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "NLP = parray_asvar(LP,1)\n", + "asvar_to_parray(NLP,1)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 128, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "y^2 + (x^2 + x)*y + x" + ], + "text/latex": [ + "y^{2} + \\left(x^{2} + x\\right) y + x" + ], + "text/plain": [ + "y^2 + (x^2 + x)*y + x" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "test(b^2+1)" + "S([ array_to_poly(lp, R) for lp in NLP ])" ] }, { "cell_type": "code", - "execution_count": 146, + "execution_count": 129, "metadata": {}, "outputs": [ { "data": { + "text/html": [ + "a^2 + a*b^2 + a*b + b" + ], + "text/latex": [ + "a^{2} + a b^{2} + a b + b" + ], "text/plain": [ - "1-element Vector{QQMPolyRingElem}:\n", - " b" + "a^2 + a*b^2 + a*b + b" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 106, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4-element Vector{Vector{Int64}}:\n", + " [0, 1]\n", + " [1, 2]\n", + " [1, 1]\n", + " [2, 0]" ] }, "metadata": {}, @@ -402,9 +555,27 @@ } ], "source": [ - "gens(test)" + "idx=1\n", + "sort(LP[2], by= x->x[idx])" ] }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Base.Generator{UnitRange{Int64}, typeof(identity)}(identity, 1:2)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [] + }, { "cell_type": "code", "execution_count": null, diff --git a/src/connectcurves/subresultants.jl b/src/connectcurves/subresultants.jl new file mode 100644 index 0000000..b91b75f --- /dev/null +++ b/src/connectcurves/subresultants.jl @@ -0,0 +1,121 @@ +# Some tools +function poly_to_array(P::MPolyRingElem) + # return P as two lists ci and vi of resp. coeffs and exponents + return [collect(coefficients(P)), collect(exponent_vectors(P))] +end + +function rem_ind(L,i) + # remove element at index i + return [ L[1:i-1]; L[i+1:end] ] +end + +function add_ind(L,i,x) + # add element x at index i + return [ L[1:i-1]; [x]; L[i:end] ] +end + +function parray_asvar(LP, idx) + # takes a sparse representation of a poly P + # and outputs a sparse rpz of P seen as a univariate poly in the i-th variable + deg = sort(LP[2], by= x->x[idx])[end][idx] + NLP = [ [[],[]] for _ in 1:deg+1 ] + for i in eachindex(LP[2]) + di = LP[2][i][idx]+1 + push!(NLP[di][1], LP[1][i]) + push!(NLP[di][2], rem_ind(LP[2][i], idx)) + end + return NLP +end + +function array_to_poly(LP, A) + C = MPolyBuildCtx(A) + R = base_ring(A) + for i in eachindex(LP[1]) + push_term!(C, R(LP[1][i]), LP[2][i]); + end + return finish(C) +end + +# Univariate resultant +function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingElement + if degree(P) < degree(Q) + P, Q = Q, P + end + S = [] + s = leading_coefficient(Q)^(degree(P)-degree(Q)) + A = Q + B = pseudorem(P,-Q) + ring = parent(P) + while true + d = degree(A) + e = degree(B) + if iszero(B) + return S + end + pushfirst!(S, copy(B)) + delta = d - e + if delta > 1 + if length(S) > 1 + n = degree(S[2]) - degree(S[1]) - 1 + if n == 0 + C = copy(S[1]) + else + x = leading_coefficient(S[1]) + y = leading_coefficient(S[2]) + a = 1 << (length(bits(ZZ(n))) - 1) + c = x + n = n - a + while a > 1 + a Ă·= 2 + c = c^2 / y + if n >= a + c = c * x / y + n = n - a + end + end + C = c * S[1] / y + end + else + C = leading_coefficient(B)^(delta-1) * B / s^(delta-1) + end + pushfirst!(S, copy(C)) + else + C = copy(B) + end + if e == 0 + return S + end + B = pseudorem(A,-B) / (s^delta * leading_coefficient(A)) + A = copy(C) + s = leading_coefficient(A) + end +end + +#Bivariate subresultants +function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx) where T <: RingElement + LPQ = map(poly_to_array, [P,Q]) + ULPQ = [ parray_asvar(lpq, idx) for lpq in LPQ ] + + R, x = polynomial_ring(base_ring(parent(P)), "x") + S, y = polynomial_ring(R, "y") + + UP, UQ = [ S([ array_to_poly(l, R) for l in lpq ]) for lpq in ULPQ ] + + sr = subresultants(UP, UQ) + + # Get it back to initial polynomial ring + Lsr = [ [collect(coefficients(csr)) for csr in coefficients(sr)] for sr in sr] + newsr = [] + for lsr in Lsr + mlsr = [[],[]] + for i in 1:length(lsr) + for j in 1:length(lsr[i]) + push!(mlsr[1], lsr[i][j]) + push!(mlsr[2],add_ind([j-1],idx, i-1)) + end + end + push!(newsr, array_to_poly(mlsr, parent(P))) + end + + return newsr +end \ No newline at end of file From 936820576f0c5f3a7df107d616f5b62948851eb5 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 10 May 2024 14:55:35 +0200 Subject: [PATCH 007/180] list argument subres --- src/connectcurves/data.jl | 4 +++- src/connectcurves/subresultants.jl | 32 ++++++++++++++++++++++-------- 2 files changed, 27 insertions(+), 9 deletions(-) diff --git a/src/connectcurves/data.jl b/src/connectcurves/data.jl index d7ff222..b0dc223 100644 --- a/src/connectcurves/data.jl +++ b/src/connectcurves/data.jl @@ -1,10 +1,12 @@ #using Nemo -R, (x,y) = polynomial_ring(QQ, [:x, :y]) +R, (x,y) = Nemo.polynomial_ring(ZZ, [:x, :y]) f = 1594627541097114368612385*x^16 + 24126594979283487048484560*x^15*y - 648897523515553246784074808*x^14*y^2 + 9227671981881181765203810480*x^13*y^3 + 775388988595641728298874736332*x^12*y^4 + 10787151407096126900712389934720*x^11*y^5 + 77139559828286619230682855993096*x^10*y^6 + 452145503210946168432702707056320*x^9*y^7 + 1603450939087454055697523432885078*x^8*y^8 + 472422761323888641034023872620080*x^7*y^9 + 69254293553970771431091788378664*x^6*y^10 + 8171004998268972015374643672912*x^5*y^11 + 486748426688048642456485687660*x^4*y^12 - 12064621488868591078399181568*x^3*y^13 - 1468208821458887902925840024*x^2*y^14 + 12892282240123223587086528*x*y^15 + 1551343473382248651380209*y^16 - 7416582067989458752697004*x^14 - 86407846455606538783280976*x^13*y + 2644747193988832166794696620*x^12*y^2 + 4962811393512179992436546328*x^11*y^3 - 852556155710875435151137729948*x^10*y^4 - 9006223258524272797865687202672*x^9*y^5 - 37408868951040006789841449492372*x^8*y^6 - 96029136974599596104658658159536*x^7*y^7 - 25805546034923632520724584708244*x^6*y^8 - 5242437191813955076157431442064*x^5*y^9 - 409699928605220782678759186860*x^4*y^10 + 39375118017080555511082417752*x^3*y^11 + 4414478650057190403833967932*x^2*y^12 - 62266637085710610417717552*x*y^13 - 7665646840583710272384908*y^14 + 14233446085691566995553618*x^12 + 132571431253302115292123136*x^11*y - 3677320627079906075667837422*x^10*y^2 - 28335523591694036134043888352*x^9*y^3 + 186478273436442358105601202678*x^8*y^4 + 979680543110585521095162296976*x^7*y^5 - 2082167356121156563744172163572*x^6*y^6 - 30539225710419394554664076544*x^5*y^7 + 25429103844006118137220734342*x^4*y^8 - 40056866529454773916181059488*x^3*y^9 - 4741918132209313788162640030*x^2*y^10 + 120063392649421566997191792*x*y^11 + 15453863115268541628254722*y^12 - 14508062550440954802512688*x^10 - 115292786706841839957190896*x^9*y + 2178406370189758736513057100*x^8*y^2 + 17911006599365461837132806264*x^7*y^3 + 18721721306068791970712906740*x^6*y^4 + 140144222573062968441350663256*x^5*y^5 + 15151268277268342933019382004*x^4*y^6 + 14388997206020218965816744888*x^3*y^7 + 2181175955893013097832336108*x^2*y^8 - 116823607901494850142791760*x*y^9 - 16262571151436698863824960*y^10 + 8412196412628079801200763*x^8 + 60038503306269383516796672*x^7*y - 526872554079154536701276538*x^6*y^2 - 2627205980235442180204133952*x^5*y^3 + 1415955761616170935932891503*x^4*y^4 - 1207248891865676270007025776*x^3*y^5 - 411102077811099614734692666*x^2*y^6 + 59338125380312133254699856*x*y^7 + 9471776668272238878375147*y^8 - 2755131867388737857954960*x^6 - 16865677220581290594690288*x^5*y + 37152628773628751552853580*x^4*y^2 - 32454665768852564904473352*x^3*y^3 + 31405824474395795210222812*x^2*y^4 - 14499431708247069028795056*x*y^5 - 2982642484703489520084064*y^6 + 476197729395824935891282*x^4 + 1850003538678786657657456*x^3*y - 861756868723874605906006*x^2*y^2 + 1328290412641467896291664*x*y^3 + 466653249763538900703730*y^4 - 37550891878150349195068*x^2 - 32144769403583975845728*x*y - 33575411625230211328108*y^2 + 864999024811562109121 +#= params = [[122052108945321231460815317670274232129992226114393994453269787251191586772999998478131397177313291168794930288045095160607171215109769903956555756352425696420971136000*x^64 - 959032695327466028896923007278462984351139470332688180556285108098088661529598320753396670253784301046095380112992662697008888935637597834208399524065939904172979990400*x^62 + 3394978440692000014057928614441958536159991996524914295852869400764921537705344371827178578116630227593461086898603789268227871843165040143533225447517362520002264974800*x^60 - 7151371831353663495035969461496662107369926971805594266199814693934146824218470195335493405697799780940541485521905675079385537261608449869138456973383228166236613263400*x^58 + 9969225814413837627444295403089186126663063577024217974344348166293461403972870910362754229719173808528360575889159764318118369001502184631485479443883015454011986682401*x^56 - 9671970836026456572298276720419947917471887665345986456817982798052297567912195266544191601002444674028621075312189430899896487514797955240881296337049837774935220682554*x^54 + 6681253172122667315238370397663913411776674477687428422442566526332877899682627142356726322165129405054337925114753161026023235352332208537631829530720089337124514136431*x^52 - 3301410220211424089271602152949473244107752962675011991847086104224995592785126226533504503253978553482754788676052797285321438414446348241998541528575215579369013124460*x^50 + 1153625866312801287615810700563023657416207647590355069763669808767031346841963349314203748595540207647317590903229427229222903703337667856594101141720943044058246069661*x^48 - 276471592632708955049516345940728535991597233768181885239869998582202243235193161503559987330426394282206550597625187581438180394843195337797005605877049995316127695732*x^46 + 42737111275022991036352608355606704897004210791721525996001628183626684128731822288746507037652796985104971734258839597661990354701818586349532900569181156658317172207*x^44 - 3742456659729901795861910080707269450979334093567063228455494047866720922141384258882510820384796174299426197864998469723296217948916294920720322245806788642212733938*x^42 + 124812901359186404102761973487936940587045208569099655070567763717545194869573966522045794363331888832044983896823256208123220099774770839702377440264548366585875579*x^40 + 2402338897585167721834533757115848973167440112325375263084520900477387202262408067511574486301847230054475590188439623088746403126201859025390930755087726059729702*x^38 - 68509937805104958231250341298198031936556840566332137015619239026451252039955810994277373605204223562430671087252591788826574761461118005709558506131791338007874*x^36 - 624602767543007223732132614350621970157553190644735452951939828727474543281390897520224663781381549515690693601166843655358728226002634853702893282072044534446*x^34 + 13841266243479813050333800913292143354226161213381471885203716731691523929640826181288978526617610615435538667085754539706451681501647162951472291089154824022*x^32 + 120202491171080915413185710414618689298315719480659390922869136636343650585376626433724584508907638709141858027047096646486866527054227623638334411322800692*x^30 - 520591115945881824376922076313706995768341899579304100913919000966844639567084555161071560271316369176537001034660519442033156769127410794732325730833980*x^28 - 3485964685779200797630002115057298589671830992286919107804731817646799770252462542189098663357180222904705862318369496603121342757549021191050978703064*x^26 + 21960953746028294720952888991143449905438039053336576582969186618106616244531983175814359264493400282340064599061237274909143339406981178759294248193*x^24 + 73849240175221567401011603553831401615608762932323920532235266189598220913324575676844395015176244479642509332983260487654003662496573180220444096*x^22 - 376824027305240350061272895486201229386360304928699585073020054777149244212956978325887719740315377634155833720619243461026923211826746813178656*x^20 - 1077064125063587403221749603783288580367506330701672842182847262625730650810368754865855958990017905698599286814095848949968486760592194466304*x^18 + 5690103572241003396861444757775613338734813344268307690846513823537481856958196599518133023344306311618066441904169231969794689720488173824*x^16 - 10193839327115713468262671581488410024134801061440399158183138926040393332773799485810782661251229174430436880799884660484369504300179456*x^14 + 10561325681560734971801564218210350941952186355064260084093107402195122950258107824859961357557778152241183977545309415213720791023616*x^12 - 46534691368958178600787555636054508288151498256013167919729116181621692838186009927608371499220570421327776499385092138476518768640*x^10 + 112909129306236789340828850326424134729652275074889648909431954832582428189211468993530209558892954944558876736171329175238475776*x^8 + 9772474340268998156394334148170923898672647267241149302597227839920236210220248425669412935053351970347661778775772607021056*x^6 + 390776074003361993581463215777520753745410226728214668964145360784605806127348743913715665385142126139767899281950769152*x^4 + 6380957595087055938360705671638193919990757753374547762909246062754723245830257862488492320528552761664667467644928*x^2 + 44165363089227334737474203421916712589754518865024815570613297228753546509038442785333463624505223591573323776, 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20179380142058508207916676906504558798143137134737375383785775280984768957208053471532768862237394630651847100572145659197442068471994105818971953412359553848047639258980711237466127568136491950657667423064913892842509690301919818696920670025070952564708223774178129499149278154432195976091432031412813159091961852467961843055813500728034432029476489683648421062036042239824120325174625410675345948653918225847005348795421961265667452471316456471485600096018962769440789188379652275394790256255475204915671865590680811547632170483878886572397449831265119313007318519552300470951426861482606989674908683994641274427306221406443238710944557095693142842073423208523723185642504384396938089647389854462953877894563956967097056216471624008594727178292891644526937795488049194012031702101543134920519559046496025779124479640348143471514640040575715655497757491200*x^209 - 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328542746994039528990683830538368748662822614424998874074480542339873661879752753767274804609732230837135071701389858106088787304640844540289249173244983027767402952843441813259510188608732052575493403174867799932354095522380896508909425920835484364022101340902163564348162403835548031631987407921247082402262239969681417023790485929579734361804006729180344780831371893836188883701250916777996743011627718434917800892329413735106793038201530013418232039440909130656728244988644719346177264130702958313297128898318084809758369503405059377062313572728941860493065614112585861258013731404233808000392144517324465782245598024216834205894390160959108994819542582314220468088480028960778173749733096605387973938171308004081664*x^26 + 61461325332565258941274939460796441514388230643882949141343422864599323133735085608853308558102105735597277975461583721448581105060010642245391889073832296819187207513866304330611872717887101099558687604009305780065196164873572653836350885305181041350153579697593899735993862233577362989148331609082396441480648309476757861766389129782395766147230027793561817798116072133893146454898934297001557991643202455274082855330573400684877225957381599670805368871754502112220158891338178950226119019155641191334973648165798390035879916194648308898650296712996311946709619162574858373126996241724581793174174450354005060569126710487808116392676743188986857526416263837045810748005915626469637592251073820868944927641456082944*x^24 - 3883324668856423612446092800667094150320259697151367320226422814495152338791133336877301068022001925013980560337485123317351271262815861959196520221284006653302789331259145290378430764735537849290861948858717815219822169071991253088266062471844292497150935376100568270612819903204041346582104295189187828002049752727073188767690513536835380714970240394050367058274878665426268406474621229783847244890466955475123457669618857838103478081719873257631606712223042304829240845135957063817601389057762099330915329545276327296389823137055060479088600984205450773261810290040287943375447007407561801850203550104551299284604828814780938712437668547090666687779610286822980928026444241790367419694027601081171160797806592*x^22 - 751535721689490635602726160758343740928826940673121338778302747609797410744715060289298071059289942912694073469602042157195159040645023416219148198990308955434330383762129537908570623448423649238094884469835715932763858841866906190150786482342054042342731140250272752591444502181163447348729408798021285148443833088516483233817616630213169669417701428496430042096983229714906048164441151780977111536642509516904668701606180313251232063095363820525086568769999715875585216849779150412006845439349103947854279557660478759928486358929520853026401648242002965746475781979082697376557938052223108305426560275321379681542136357969467395024769253074682371712000676608324171335903089428276627629775177410856049704960*x^20 + 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50958306305261076752358194339545694928507225030977648408087258342013939142856432849435688263739731395545536680576652650614664539942150765613702037721485113551947052254944096341028078176408763257208616887571613527085791769294438990279685372266595708796958236334808107441480453944247454277990106070370209310487867543341839776224976660882151885115448375905140909308491612764101097483357455650795629993941539554136858936026910731687399963542017446590052917772745465122169873952141665708438415420812113553459654431408604060411703593440001667256744572894961800318472595793191253120569290991202076163616761133848506841893150781129033795641412956762867858036929543282950355101841180554507314361554629033984*x^16 - 650188828198774002608840858704113147631914846394013323855760348772792047346524954492186625027803588839315220838871634319050726521417767120188044210442093981652413029449454193656650975975894776142163898960873362301886103851593495066917817900263969777651081420250338544006366479876434720118406831137577459317141047860544522886036017588736646561174813636976484737265270943285246353700236811014018410144914516119477281253438253452458138457789066087735553584902114613337945164413501568205341912780924217797465395540143593317947955458044977117734754252914043829969697783422742369290142608093919671920290426399498353838549130305027219258730857042543675733877200926190057366962997563132098243424478560256*x^14 - 40861926570920959266184836493356487870101556498754365516581070114072518091189180068818820457863666698637605119857943187068983288250369863769940564758680953959887006279710923723611093816879531236700799224864997543482099048552660093498402873737977477878914142327203850612590518745668324625073167196655598853675048725291811822907221166746705050428592365581215053703960197023195029173397765610741357245733787930846305599947526603998608467466925663907160552791837303677050517769171384071139547902293479611126942596557163688337306547063596708855958776745722989329824824765024350932915546809460619689781927529121128775001574238746079556057069698886073721044771233933555075979271312038965197032914944*x^12 - 833124753794084640688037276215838669810167821426909298079819213895977644719819165599551266863818992602486166100521070732183379264504317517725873072933252108955469319806377299832404317039593724525658349695282228260134180345130070692615177601547359215253666584822098959395065183293676713007595596733366761959494919803119055875217130615334419699140906087798091373066854021813914501139753617893258163370781495356697852534020858303081733961286021174267574599891197148412999018401884051800916979269763700430554839848279393936903403968359843109042265627807071934454749450827071291058746685172656578386240531842073002002934511734839931947015408559751396076237632250338304856571567081700097785856*x^10 - 7658771618725884748391330938184669372433555954012241782723250710187787203760680649512963498992496408753376086439317515470971187550342509648135600256775055375747285598088997689403432718670035283922985695981614071033648198688170329541911963604718833139088728875684492770415778345349529336462034521272003610851542705422168047136991466169609285399351431104278602837041725333448163552986367470786589957095824606986581538902066418857879307622677635919790783044576891547878441671444126259908645368621950279065035661247809242239807623059271459188039846065519706144020111503573057674327408899865218627504506320806753588729362614715803746221825052026410921736413191705399088362911154772639744*x^8 - 16702567857203944352220222714963108829106565357395107454939865050669758612182200764101986747978197641921273414994875419667808215520877334939365038225290173446236643517881221669480017863871750927015963868760882719540147915762098906279786363273275742496569433501589826885468800735326031467965915990689273474830346752350933191146933485568965520419747935778054524883480013846734781978528383284809136014413009009144603902741385798034222138661411716892287230722920430565914506528132546014332668966111331666655206155742176355391236803719395898910941496600795040770285245449864139988840361464348390670081987574430726296881521856462573617660146588583291996940006882107441263477017018368*x^6 + 179782983655119035426809632822292010043322998080063145867493639194245739413644037741114955417763712148638757392745530307589858555969565820688419743815666086980304051170991581170290846672741818483159449120571441041279952770886645847890021249748579975059644805702156387722032257338446056276886076183359708839626702552458712083173844607335771164274124581313469178768494303465225020165590036620071686936758651254255162188831952375913152201628036706318886051165105008731971580811896481283049053883504571000628631550572045490366900528299775651342918932464482551071356622939013074872993124546958506098401663798133739760583386797810035714293101111354268849000352696905729310720*x^4 - 444197758052136116820947897695110521029794817251021934401181887740289358145846327491337544229683766554798883228243782871248641955973141102950804972276382531416874817011849504001105212340786679083467770811544278317948156695506340338722593025111105815768803766919105647251186565800487492140902716159763626654251136151953823895089730783501228795046526318604927487651461852337447878343654131635973382434640039782873335615115451925767611925478761250949473658982286038364626985823011552713897981212454750093123965724399560721568846778993595360108691913082816059008803044189452248953504408461730575921524060519694814257801237438618852560065556604495781368906796498944*x^2 - 76093196872372578373119402591542924336595309825576292045515391246379464763158228784639574310982195640136389028170516631428420420489719956379967145212728402543856172428301827720835720619511746291529555478771232044026977196487380606051408105650931853037339102824546133136096406879899656252503263781924026226251779704232683941753426157396355555386426406923634579674802667468556932278540083239541771095586953543174979462316844522007563225998088037858674707962626971083428228623682979720860644003550437215307280073434204980445128604856611045119274229393897316722277964178023092238372341675934924661369445149897548641019617913507175210877932947651340271616]] +=# \ No newline at end of file diff --git a/src/connectcurves/subresultants.jl b/src/connectcurves/subresultants.jl index b91b75f..4ecb27a 100644 --- a/src/connectcurves/subresultants.jl +++ b/src/connectcurves/subresultants.jl @@ -92,7 +92,7 @@ function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingEl end #Bivariate subresultants -function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx) where T <: RingElement +function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false) where T <: RingElement LPQ = map(poly_to_array, [P,Q]) ULPQ = [ parray_asvar(lpq, idx) for lpq in LPQ ] @@ -106,15 +106,31 @@ function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx) where T <: # Get it back to initial polynomial ring Lsr = [ [collect(coefficients(csr)) for csr in coefficients(sr)] for sr in sr] newsr = [] - for lsr in Lsr - mlsr = [[],[]] - for i in 1:length(lsr) - for j in 1:length(lsr[i]) - push!(mlsr[1], lsr[i][j]) - push!(mlsr[2],add_ind([j-1],idx, i-1)) + if list + for lsr in Lsr + mlsr = [] + for i in 1:length(lsr) + tmp = [[],[]] + for j in 1:length(lsr[i]) + push!(tmp[1], lsr[i][j]) + push!(tmp[2],add_ind([j-1],idx, 0)) + end + push!(mlsr, tmp) + end + mlsr = [ array_to_poly(tmp, parent(P)) for tmp in mlsr ] + push!(newsr, mlsr) + end + else + for lsr in Lsr + mlsr = [[],[]] + for i in 1:length(lsr) + for j in 1:length(lsr[i]) + push!(mlsr[1], lsr[i][j]) + push!(mlsr[2],add_ind([j-1],idx, i-1)) + end end + push!(newsr, array_to_poly(mlsr, parent(P))) end - push!(newsr, array_to_poly(mlsr, parent(P))) end return newsr From 2f7dbcb8970f2a4f367c08866c5825e915ac9167 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sat, 11 May 2024 13:29:30 +0200 Subject: [PATCH 008/180] manage when no singular points --- src/connectcurves/data.jl | 6 +- src/connectcurves/main.ipynb | 13607 +++++++++++++------------ src/connectcurves/subresultant.ipynb | 133 +- 3 files changed, 6933 insertions(+), 6813 deletions(-) diff --git a/src/connectcurves/data.jl b/src/connectcurves/data.jl index b0dc223..1d5f9f6 100644 --- a/src/connectcurves/data.jl +++ b/src/connectcurves/data.jl @@ -1,8 +1,10 @@ #using Nemo -R, (x,y) = Nemo.polynomial_ring(ZZ, [:x, :y]) +R, (x,y) = Nemo.polynomial_ring(QQ, [:x, :y]) -f = 1594627541097114368612385*x^16 + 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76093196872372578373119402591542924336595309825576292045515391246379464763158228784639574310982195640136389028170516631428420420489719956379967145212728402543856172428301827720835720619511746291529555478771232044026977196487380606051408105650931853037339102824546133136096406879899656252503263781924026226251779704232683941753426157396355555386426406923634579674802667468556932278540083239541771095586953543174979462316844522007563225998088037858674707962626971083428228623682979720860644003550437215307280073434204980445128604856611045119274229393897316722277964178023092238372341675934924661369445149897548641019617913507175210877932947651340271616], diff --git a/src/connectcurves/main.ipynb b/src/connectcurves/main.ipynb index 014a1f1..f33ea28 100644 --- a/src/connectcurves/main.ipynb +++ b/src/connectcurves/main.ipynb @@ -31,7 +31,9 @@ "using AlgebraicSolving\n", "using Nemo\n", "#using Oscar\n", - "#include(\"tools.jl\")" + "#include(\"tools.jl\")\n", + "using BenchmarkTools\n", + "using IntervalArithmetic" ] }, { @@ -42,7 +44,7 @@ { "data": { "text/plain": [ - "usolve (generic function with 1 method)" + "subresultants (generic function with 2 methods)" ] }, "metadata": {}, @@ -52,23 +54,49 @@ "source": [ "include(\"data.jl\")\n", "include(\"src/usolve/usolve.jl\")\n", + "include(\"subresultants.jl\")\n", "#using Arblib" ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ - "using BenchmarkTools\n", - "using IntervalArithmetic" + "# Generic change of variables\n", + "changemat = [1 0; 0 1]\n", + "#changemat = rand(-100:100, 2, 2)\n", + "invchangemat = inv(changemat)\n", + "f = evaluate(f, collect(changemat*[x; y]));\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "sr = subresultants(f, derivative(f,y),2, list=true);" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, + "outputs": [], + "source": [ + "# Take the deg>0 sqfree factors of the resultant and order by multiplicity\n", + "# TODO : group by multiplicity\n", + "sqr = collect(factor_squarefree(sr[1][1]))\n", + "# Construct the parametrization of the critical points\n", + "params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in sqr ];" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, "outputs": [ { "data": { @@ -106,7 +134,7 @@ "end\n", "\n", "function Arb_to_rat(x)\n", - "\tr = radius(x)\n", + "\tr = Nemo.radius(x)\n", "\treturn map(simplest_rational_inside, [x-2*r, x+2*r])\n", "end\n", "\n", @@ -124,7 +152,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -145,7 +173,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -167,7 +195,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -187,11 +215,11 @@ " for i in 1:2\n", " # Lxi\n", " L[i] = Array{Any}(undef,2)\n", - " L[i][1] = isolate_eval(f, 2, B[2][i], prec=200)\n", + " L[i][1] = isolate_eval(f, 2, B[2][i], prec=250)\n", " L[i][2] = [ j for (j, l) in pairs(L[i][1]) if (l[1]> B[1][1] && l[2] B[2][1] && l[2]\n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - 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"\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n" ] }, @@ -5031,7 +5069,7 @@ }, { "cell_type": "code", - "execution_count": 163, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -5100,30 +5138,30 @@ }, { "cell_type": "code", - "execution_count": 162, + "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - " 486.504 μs (8496 allocations: 535.11 KiB)\n" + "4\n" ] } ], "source": [ - "CEdg = connected_components_bis(Edg);" + "CEdg = connected_components_bis(Edg); println(length(CEdg))" ] }, { "cell_type": "code", - "execution_count": 142, + "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "plot_graph_comp (generic function with 2 methods)" + "plot_graph_comp (generic function with 1 method)" ] }, "metadata": {}, @@ -5148,7 +5186,7 @@ }, { "cell_type": "code", - "execution_count": 143, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -5160,2301 +5198,2301 @@ }, { "data": { - "image/png": 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51246814607830925572984225226927208888746033464081384603866031195443529191439021140897280298062855897503193246357037311780775441464489112978006817142048824509713247956658846746278539691125611314341646742325102917308336459065414489198379976374538930953456397434430117124050851851343288090952477455570649035650018719318244093563470494064088968056437812900520421053660937437727790678315123679788663803233611714075267371255146090776212525594699019167819726697656828374222199820926970057900798816516228491114828902358815744166274298637063883442186506606423447557890220916621074167465413937001474494324091664792037492326841007612372700562188533110188999967472871104181990775393990521428835945463051583804557991010309800975131716950219063296694299183291114536482249142670765135461613568//57963*x^34 + 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6085494245839220017114202103880105526019222639457209375671642547418239631344681053416241354622171002668140903050478658346541164615280671941049060634511487549557643060983812206565954942051201927195728461035129336358905929759885327445574699724124332653389020913280684364165283288893650727924471193981011224973411721126594468694035634056140889574542279880705680823291348831308569668186918488259486864128109781961412565900987225900000773664352255111709441462616655441616604960673526403269246602604625220920424407352905278033328004253799944403265370399440851465628240741310932927480203257951306580859444489421704678440298985912592300422503740039274400779483821492812800859782775747880517507217517371991291794362406803619709902756336505507785166799835890064575577039160588894208//19321*x^30 + 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5775821363344371681989566197347043739947006017660941430159784843540329247374523300994168608276358405881811618955449232350926791065209387727920326687880881581877819189311180447336570076206511548336686649987368706668088044592550890944505040371240809875763563090576215638448459444642040907478641161849530258042703373216116940503071222869370912656047438331067186074653675064670090809981521948780442872226980110590604513790371144231869240543276706128246025136602030522625658211826834169016103406251703931427213595108552683387669021283310235594635888388647183022600904380380762616114080771974347068617753248189043944123629591452882161701340113303485559365971297303280429129066298698262332122178452021566949369588469939157995764914215281875053502654342197240115933216768//139*x^26 + 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221806683711643020442442331121909447003001255050809395507107878193257907876231563575120249547763049845368719491757504733027330708106830998240183260118385884047195337887952055435204637200653766698991105272691981892619922621114663644424127744668125274232386772688341338205940743486213981281987680523608919307368035909676951956527703382329579830929363782859249017547125928906517362680938968014092784259794958870822011550969551759094400847547802276319120636261255361287884524271153482303146234701684918483406622712788591639626633671928193084737366588427096078406816312959176154036440209207366510363811069360215110702197693586275458577234889571013931596020645986228572924666350586045360784383935845998428389368549349885275422885195111927489618462447531091558400//139*x^22 + 22205592939016105490341087528745100198670333229251916963012843242990809025273700087683801993751299789218513846720460695941355633630734953536189303388658981265645741677259686522214287015935272674712409849592257853537011388684958472820814803750820524967319004768733341510288089703695278044046286312093915203324256446299682668476303162392297446150816964411176012042318710587054052189711203288164551410230385561113024960049362921213914782295347339367000093872143962071293979704909519443142734296704475968683808228804737104315697406353451233330408645625492462028074648362396524540315577542245751405684526577228544368937730371493592458632115726533734099991197772758961032880582070947372062518480883714404743240640146439116594639287114921184606000498931138560//139*x^20 - 874339530119398844814335868955537063815421225095997541978485472193755089099867858752406506632644271047821586052534969749322465951917899740769870603669122941173054334910216748161296368361117079915446558829202344506686855063223595631699569094595840191842081880757858460550520388445091953446093291183608070145165511150118473666271724233707434419506219146352826910161351072766194696701424137766289621794725655790210721416910073468309281566006191347110365273215281988982794763918903219944872107101169095977353270867313801063613920244421962031702342422125226739501290044974428337639588514458814445835230679972024108226436291269873954371956459515170822716511545809533793799555560343491633610270951688853130330357891733009725906028402658396197917909057536//139*x^18 - 40667757725115605213403049434747344352777249587807518725953006424754157065816009484233583928382956291103711368905365197865702485744209482727205612301601747061857181312089870943914663545170173167805726812387422263044218841207222764649813922209059288407964204390142211391494547270509193452396570554329821802998952465336593440676763896208864768733133567752616038624753946407280169306819215539517080656784613517949952685700178556052690563772748219017753101902452910870271190149967654823799591982220066000656581215524518457821685575295462427075130814388261762235154996564535328725802672274719442665787700997924689194007948084490219641517206061228481658445634822475372659255131847409546679222343011313263637692654591541474448940845953910812516024320//139*x^16 + 11570456799178144708175940842137396357362024410404214111590502507318246057804737265027643941472334133676410357388475847717275136203155872781429041782100146476281610028767666905385412722995107472357461568134009475805073495349455249521522472732204728596397598176485445680354115155954540069041176842596619121480641692955885021719134229192445133110781388277419800753564690516088593347596485855708248428836515650557272123082428533528399584584147890286061351213083570603643866460156381419200751278178647272679293615954657764069184349760738123197948860884168918467923497764335787171397127790713413865570575290414221574470154963616192297230069986726005490399521037773424110573201551131466545717734860748577465914797637201637698633081343549898752*x^14 + 2006342536427479195548837319031070280201235500881533863362741762514399417752443232386455298298616175758463256146061896921603743268689615729908772970077486409746322025743206524421631884516110324915556354236206372624650371183264883434079006109661046732365367507417716213089517106527029131921476247013419790420516375905326668745492891592624649420204825646254749711295343691854692434437601920798136517914553162000577785900006257285661941489861742743562062055286583965463119788431787244773029416533128753716610089803872063920113927192141798717603406021464551390925285415506622806660362079922129192968705320871220920776554321349336157200507352955808919674947986164133855877442285285730722807414310483536970194874667130151292146914613526528*x^12 + 44333681532412951449799018151096558148105883408232032292846468078220408542990784641139100920697882583778029775478629777223485855782427250300856279464308935232638993771404044257370380909476699218885568837894563218427211282016379854885062656154815736308962491114588142645545465641145875120846991190940673493467768097858306557882523729461063910231538167208042421700247834953275498701442627606740128726330176494416112101939238382830251483778167768369927947823282851520566543571662741273625927245563630274700308746111109955148670056317012807328495520655826697557117231317596856615955902967749442415556476192501308178266814071910069661927143094769549050158982553732175998216265609481408470481791888578698634736275724100618579003572224*x^10 + 375791315234274446594631571238015053451854015012670254749418565759281413894586944427935389058304320865975871477402738393182497517441555303660403305391953065171471818063314354083472733293668699850521450138357095397804273398323065699998900913806774929115264558366068853254082704847950077461945675988777667703792556448075147694366459752532710610723958784058207770942266374253383349433610965455280891994318941868988092290791082575142394726846267562444440136637901026945989082770890655992401742422970947923018961678024378507274952348722609772472488671278176786769542616933469256151444487630605424294126826418080891220271514189177114783441105777438200456527331120692463101607095950593739878443976580247371830380211627532339904512*x^8 - 4060326754525257358025880734256754928235003918124782886601789574258708520402752717289580434757874533360933387438212164960448054267885323414054591983496092133486799183041456543536036226154490851952862424462578295972357616443779897277488093855097050664775920886796665973235299271350266650300450370699303050165941682557526770511969449147571939190817278411638634685499183215342313297161424033509172844226168680710088471274763441221754323248611748288197705034976412981375479822540703993422759743251078469285819801535483250874029189603117104523015976623121244162857500968085001130894197052552494355192547233605612871209159257412556791269702687662080130538699811589384779891212555522088283179029853110057953482128031219712*x^6 + 11594651820604831013660298778208240155030931109647446553469820232084470205428085562121262185585796179462574509626745766195913628659752695695306992831435878610136195150717344787178246624869470290586232004437501762055144352044599887530569955166908865955536125463866094320319044512178834640526440885248257898109916502234382375328105887760099505067571140110000387199127258573156646731738701154751816749282327820082724573990325338364243151998053529190209613661786419663060322332390562897272450793101247373330454308366361606020493886918891300281526651132435630815684506927851358132915550056532964910281423226866966550883060066159305285896802493171242558483841282355436208867207207656978864181026706910535168819200*x^4 - 3421550289861650154660988298259339325212725798049675866312785292849447184320819454252726155751467324924175345425985937210349456254644936933602681820549950380097838080845793113682204294156330451262517952530315299135500329762332117442529897469133931475519031274492079273026005346504194016717256337083657325536957498356352453991844720129731992208762649201774267218583562137383263260093102814369200389835976922628681345008532460056925619653541898713767165706917290097304591957492496246179140228901181292656743816027460981610653651060039129610659171654391641024772229762785206447933352956481203919411017250826956911477231382456284555359727621440350684109703143515235347164541125912668463745147651227648*x^2 + 267017168801975889620773483071915352384790774018395154483129522466123573213216806857406062144348207741552112997489490500551614557189405351549584015058076558214965844062237303764342265893456168434648273979153889830711350223834757345503808780236377461975451558729308817837793624372506111602330833968286172371822671258113712949577319795174692318671487007468328714173385931195458704191836619049185406052425671051211954647005109947426141489403584734823670298186042654510935370911211835510411203709329607425944607296636258085392098702763644088044929764331607704216173010822963227750596640099273852767761268602118379282151640365543510396757218741165544218534247055286610626827734439859840876544" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "res = (subresultants(f,fy,2)[1])\n", + "#D = collect(factor_squarefree(res))" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -82,7 +154,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -113,19 +185,20 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 6, "metadata": {}, "outputs": [ { - "data": { - "text/plain": [ - "2-element Vector{Any}:\n", - " 2*x^6 - 22*x^5 + 102*x^4 - 274*x^3 + 488*x^2 - 552*x + 288\n", - " (-x^2 + 5*x - 6)*y - x^3 + 6*x^2 - 11*x + 6" - ] - }, - "metadata": {}, - "output_type": "display_data" + "ename": "UndefVarError", + "evalue": "UndefVarError: `g` not defined", + "output_type": "error", + "traceback": [ + "UndefVarError: `g` not defined\n", + "\n", + "Stacktrace:\n", + " [1] top-level scope\n", + " @ ~/Documents/gittravail/AlgCurves/subresultant.ipynb:1" + ] } ], "source": [ @@ -404,13 +477,14 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "Any[]" + "Multivariate polynomial ring in 2 variables x, y\n", + " over integer ring" ] }, "metadata": {}, @@ -427,7 +501,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -448,21 +522,34 @@ }, { "cell_type": "code", - "execution_count": 213, + "execution_count": 24, "metadata": {}, "outputs": [ { - "data": { - "text/plain": [ - "1" - ] - }, - "metadata": {}, - "output_type": "display_data" + "ename": "MethodError", + "evalue": "MethodError: no method matching keys(::Fac{ZZMPolyRingElem})\n\nClosest candidates are:\n keys(!Matched::Pkg.Registry.RegistryInstance)\n @ Pkg /opt/julia-1.10.1/share/julia/stdlib/v1.10/Pkg/src/Registry/registry_instance.jl:447\n keys(!Matched::Cmd)\n @ Base process.jl:678\n keys(!Matched::Core.SimpleVector)\n @ Base essentials.jl:781\n ...\n", + "output_type": "error", + "traceback": [ + "MethodError: no method matching keys(::Fac{ZZMPolyRingElem})\n", + "\n", + "Closest candidates are:\n", + " keys(!Matched::Pkg.Registry.RegistryInstance)\n", + " @ Pkg /opt/julia-1.10.1/share/julia/stdlib/v1.10/Pkg/src/Registry/registry_instance.jl:447\n", + " keys(!Matched::Cmd)\n", + " @ Base process.jl:678\n", + " keys(!Matched::Core.SimpleVector)\n", + " @ Base essentials.jl:781\n", + " ...\n", + "\n", + "\n", + "Stacktrace:\n", + " [1] top-level scope\n", + " @ ~/Documents/gittravail/AlgCurves/subresultant.ipynb:2" + ] } ], "source": [ - "idx" + "sq = collect(factor_squarefree(res[1]))\n" ] }, { From cf899f34b5cf3705c07f009626edef7298e2a024 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 01:07:03 +0200 Subject: [PATCH 009/180] refine xboxes --- src/connectcurves/main.ipynb | 7112 ++-------------------------------- src/connectcurves/tools.jl | 2 - 2 files changed, 297 insertions(+), 6817 deletions(-) diff --git a/src/connectcurves/main.ipynb b/src/connectcurves/main.ipynb index f33ea28..95ff19e 100644 --- a/src/connectcurves/main.ipynb +++ b/src/connectcurves/main.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 231, "metadata": {}, "outputs": [ { @@ -38,7 +38,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 232, "metadata": {}, "outputs": [ { @@ -60,7 +60,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 233, "metadata": {}, "outputs": [], "source": [ @@ -73,7 +73,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 234, "metadata": {}, "outputs": [], "source": [ @@ -82,7 +82,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 235, "metadata": {}, "outputs": [], "source": [ @@ -95,7 +95,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 236, "metadata": {}, "outputs": [ { @@ -152,7 +152,16 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 274, + "metadata": {}, + "outputs": [], + "source": [ + "precx = 150;" + ] + }, + { + "cell_type": "code", + "execution_count": 275, "metadata": {}, "outputs": [ { @@ -165,15 +174,15 @@ ], "source": [ "println(\"Isolating critical values..\")\n", - "xcrit = [ isolate(first(p), prec=150) for p in params ]\n", + "xcrit = [ isolate(first(p), prec=precx) for p in params ]\n", "xcrit_usolve = getindex.(xcrit, 1)\n", "xcrit = getindex.(xcrit, 2)\n", - "xcritorder, xcritpermut = order_permut2d(xcrit);" + "_, xcritpermut = order_permut2d(xcrit);" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 276, "metadata": {}, "outputs": [ { @@ -189,19 +198,20 @@ "#RR(x) = Arb(x, prec=120)\n", "RR = ArbField(150)\n", "Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ]\n", - "LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ];\n", - "Pcrit = [ [ [ rat_to_Arb(pc[1]), pc[2] ] for pc in pcrit] for pcrit in Pcrit ];" + "LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ]\n", + "#Pcrit = [ [ [ rat_to_Arb(pc[1]), pc[2] ] for pc in pcrit] for pcrit in Pcrit ];\n", + "print(\"\")" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 282, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "intersect_box (generic function with 1 method)" + "intersect_box (generic function with 2 methods)" ] }, "metadata": {}, @@ -209,18 +219,54 @@ } ], "source": [ + "function in_inter(I, J)\n", + " return J[1] < I[1] && I[2] < J[2]\n", + "end\n", + "\n", + "function overlap_inter(I,J)\n", + " return max(I[1], J[1]) <= min(I[2], J[2])\n", + "end\n", + "\n", "# To try/do : isolate with usolve, call msolve with only one variable\n", - "function intersect_box(f, B)\n", + "function intersect_box(f, B; prec=100)\n", " L = Array{Any}(undef, 4)\n", " for i in 1:2\n", " # Lxi\n", " L[i] = Array{Any}(undef,2)\n", - " L[i][1] = isolate_eval(f, 2, B[2][i], prec=250)\n", - " L[i][2] = [ j for (j, l) in pairs(L[i][1]) if (l[1]> B[1][1] && l[2] B[2][1] && l[2] 2\n", - " @assert false \"\\nRefine extreme boxes along x-axis\"\n", - " #refine_xboxes(QQ[\"x\"](params[1][1]), LBcrit[1])\n", - " #i = 0\n", - " #j = 1\n", - " #break\n", - " elseif i > 1 && sum(npcside[1:2]) != 0\n", - " println(npcside)\n", - " @assert false \"\\nRefine singular boxes along x-axis\"\n", - " #refine_xboxes(QQ[\"x\"](params[2][1]), LBcrit[2])\n", - " #i -= 1\n", - " #break\n", + " while true\n", + " flag = false\n", + " for j in eachindex(LBcrit[i])\n", + " print(\"mult=$i ; $(j)/$(length(LBcrit[i]))$(repeat(\" \", ndig-ndigi+1))pts\",\"\\r\")\n", + " tm = time()\n", + " pcside = intersect_box(f, LBcrit[i][j], prec=precx)\n", + " npcside = [length(n) for (I, n) in pcside]\n", + " if i == 1 && sum(npcside) > 2\n", + " precx *= 2\n", + " println(\"\\nRefine extreme boxes along x-axis\")\n", + " refine_xboxes(params[1][1], LBcrit[1], precx)\n", + " #break\n", + " elseif i > 1 && sum(npcside[1:2]) != 0\n", + " precx *= 2\n", + " println(\"\\nRefine singular boxes along x-axis\")\n", + " refine_xboxes(params[2][1], LBcrit[2], precx)\n", + " #refine_xboxes(QQ[\"x\"](params[2][1]), LBcrit[2])\n", + " #i -= 1\n", + " #break\n", + " end\n", + " LPCside[i][j] = pcside\n", + " push!(Ltm, time() - tm)\n", " end\n", - " LPCside[i][j] = pcside\n", - " push!(Ltm, time() - tm)\n", + " flag || break\n", " end\n", " i += 1\n", " println(\"\")\n", @@ -310,9 +388,24 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 281, "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "UndefRefError", + "evalue": "UndefRefError: access to undefined reference", + "output_type": "error", + "traceback": [ + "UndefRefError: access to undefined reference\n", + "\n", + "Stacktrace:\n", + " [1] getindex(A::Vector{Any}, i1::Int64)\n", + " @ Base ./essentials.jl:13\n", + " [2] top-level scope\n", + " @ ~/Documents/gittravail/AlgCurves/main.ipynb:5" + ] + } + ], "source": [ "# Update extreme boxes\n", "for j in eachindex(LBcrit[1])\n", @@ -355,7 +448,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 244, "metadata": {}, "outputs": [ { @@ -364,6 +457,20 @@ "text": [ "Graph computation" ] + }, + { + "ename": "UndefRefError", + "evalue": "UndefRefError: access to undefined reference", + "output_type": "error", + "traceback": [ + "UndefRefError: access to undefined reference\n", + "\n", + "Stacktrace:\n", + " [1] getindex(A::Vector{Any}, i1::Int64)\n", + " @ Base ./essentials.jl:13\n", + " [2] top-level scope\n", + " @ ~/Documents/gittravail/AlgCurves/main.ipynb:18" + ] } ], "source": [ @@ -485,7 +592,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 245, "metadata": {}, "outputs": [], "source": [ @@ -494,7 +601,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 246, "metadata": {}, "outputs": [ { @@ -524,7 +631,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 247, "metadata": {}, "outputs": [ { @@ -536,4526 +643,94 @@ }, { "data": { - "image/png": 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", + "image/png": 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"code", - "execution_count": 19, + "execution_count": 250, "metadata": {}, "outputs": [ { @@ -5186,7 +861,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 251, "metadata": {}, "outputs": [ { @@ -5198,2302 +873,102 @@ }, { "data": { - "image/png": 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"execution_count": 252, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/src/connectcurves/tools.jl b/src/connectcurves/tools.jl index a48c8e2..7bfc2ef 100644 --- a/src/connectcurves/tools.jl +++ b/src/connectcurves/tools.jl @@ -80,5 +80,3 @@ end #f = x^7+y^2*x^5-2*x*y^3+1+y^6 #f = (x^2+y^2-1)*(2*x-y) #Sr = subresultants_seq_biv(f, 1) - - From 60c5c10e606dc9a8f89ada99dae3820793373dcb Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 10:53:43 +0200 Subject: [PATCH 010/180] move into .jl --- src/connectcurves/main.ipynb | 8747 +++++++++++++++++++++++++++++++++- src/connectcurves/main.jl | 173 +- 2 files changed, 8641 insertions(+), 279 deletions(-) diff --git a/src/connectcurves/main.ipynb b/src/connectcurves/main.ipynb index 95ff19e..31f37a9 100644 --- a/src/connectcurves/main.ipynb +++ b/src/connectcurves/main.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 231, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -38,7 +38,7 @@ }, { "cell_type": "code", - "execution_count": 232, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -60,7 +60,7 @@ }, { "cell_type": "code", - "execution_count": 233, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -73,7 +73,7 @@ }, { "cell_type": "code", - "execution_count": 234, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -82,7 +82,7 @@ }, { "cell_type": "code", - "execution_count": 235, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -95,7 +95,7 @@ }, { "cell_type": "code", - "execution_count": 236, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -152,16 +152,16 @@ }, { "cell_type": "code", - "execution_count": 274, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ - "precx = 150;" + "precx = 50;" ] }, { "cell_type": "code", - "execution_count": 275, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -182,7 +182,7 @@ }, { "cell_type": "code", - "execution_count": 276, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -191,27 +191,37 @@ "text": [ "Computing isolating critical boxes using Arb..\n" ] + }, + { + "data": { + "text/plain": [ + "2-element Vector{Vector{Vector{Vector{QQFieldElem}}}}:\n", + " [[[-274010517572908139//288230376151711744, -1096042070291632555//1152921504606846976], [148491350383//25070396056151, 78153733013//13195011257214]], [[-267143983447885//281474976710656, -4274303735166159//4503599627370496], [-365779936255//99916048642522, -197192020319//53864757306904]], [[-455352681580283//562949953421312, -910705363160565//1125899906842624], [601274288//69794093211, 146284163//16980221359]], [[-113766868472479127//144115188075855872, -56883434236239563//72057594037927936], [4084042//52425681, 1847855//23720387]], [[-112609494040521015//144115188075855872, -56304747020260507//72057594037927936], [-232131047//10956212642, -56447159//2664215257]], [[-111136732147721837//288230376151711744, -27784183036930459//72057594037927936], [-72314963326117841//817860633297220798, -107420850167329337//1214897726643074057]], [[-69149191445559//1125899906842624, -138298382891117//2251799813685248], [27060885441366443//32540491451087654, 20184346394132054//24271509988362021]], [[-892193306636371//18014398509481984, -1784386613272741//36028797018963968], [-30967489235236664//67802651081482593, -26118116459118551//57185053774657721]], [[1784386613272741//36028797018963968, 892193306636371//18014398509481984], [36121390461987567//79087006876004932, 15902784603368251//34818804569490693]], [[138298382891117//2251799813685248, 69149191445559//1125899906842624], [-8386567780117769//10084779348789146, -11100458990737279//13348211393135144]], [[27784183036930459//72057594037927936, 111136732147721837//288230376151711744], [33857503183397213//382918247093062622, 57970637393837277//655630591939248884]], [[56304747020260507//72057594037927936, 112609494040521015//144115188075855872], [260721215//12305622659, 208703880//9850487981]], [[56883434236239563//72057594037927936, 113766868472479127//144115188075855872], [-1556482//19980115, -4389017//56340558]], [[910705363160565//1125899906842624, 455352681580283//562949953421312], [-402076683//46671840209, -559494719//64944447731]], [[4274303735166159//4503599627370496, 267143983447885//281474976710656], [438712785936//119838306355657, 394174453087//107672263906857]], [[1096042070291632555//1152921504606846976, 274010517572908139//288230376151711744], [-53415403341//9018338871617, -168239527753//28404560819122]]]\n", + " [[[-61678188462433291//18014398509481984, -123356376924866581//36028797018963968], [550693503279189118561//3417683961495272680909, 319695290759235983869//1984075463551412914679]], [[-1158819215143832931//1152921504606846976, -4635276860575331723//4611686018427387904], [-1168146669335//2762202054704291, -815591818271//1928550117350119]], [[-8428531151509891205//9223372036854775808, -2107132787877472801//2305843009213693952], [-363088907743//138639422386908, -317978308755//121414695181387]], [[-14527782462265069//18014398509481984, -3631945615566267//4503599627370496], [188729606//282063524559, 177718959//265607696741]], [[-113314000037319275//144115188075855872, -226628000074638549//288230376151711744], [144444682//4986302841, 307072892//10600310185]], [[-14095297027035463//18014398509481984, -7047648513517731//9007199254740992], [-180563571//9149305936, -351346351//17803011078]], [[-12826797309815463//18014398509481984, -6413398654907731//9007199254740992], [627411350419//17075213885172, 590460050963//16069571667949]], [[-198890733629894925//288230376151711744, -49722683407473731//72057594037927936], [-713351100652//17061031056187, -502435630281//12016621105826]], [[-46484052523520541//72057594037927936, -11621013130880135//18014398509481984], [10460313859130//237474950921567, 3041559958453//69050920611545]], [[-597881105146324101//2305843009213693952, -149470276286581025//576460752303423488], [-401193109938604817//7494865495701836063, -342183256103003299//6392476380678051520]] … [[149470276286581025//576460752303423488, 597881105146324101//2305843009213693952], [291335742995464770//5442571554071590247, 414601584818903642//7745355130844661241]], [[11621013130880135//18014398509481984, 46484052523520541//72057594037927936], [-11208752097561//254466346813966, -9751261426405//221377710061512]], [[49722683407473731//72057594037927936, 198890733629894925//288230376151711744], [801163984581//19161228754735, 557173813871//13325779876780]], [[6413398654907731//9007199254740992, 12826797309815463//18014398509481984], [-382920231168//10421304689159, -480263544722//13070536167225]], [[7047648513517731//9007199254740992, 14095297027035463//18014398509481984], [312381169//15828612981, 227974424//11551653189]], [[226628000074638549//288230376151711744, 113314000037319275//144115188075855872], [-227805871//7863972879, -318723511//11002495394]], [[3631945615566267//4503599627370496, 14527782462265069//18014398509481984], [-53716103//80280744812, -65474121//97853546818]], [[2107132787877472801//2305843009213693952, 8428531151509891205//9223372036854775808], [356501362501//136124078492280, 186266425034//71122716850019]], [[4635276860575331723//4611686018427387904, 1158819215143832931//1152921504606846976], [934166602017//2208932298712475, 695998211675//1645758825348213]], [[123356376924866581//36028797018963968, 61678188462433291//18014398509481984], [-434343255691151054367//2695597405671055878238, -153306279919032148208//951441066502193646015]]]" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ "println(\"Computing isolating critical boxes using Arb..\")\n", "#RR(x) = Arb(x, prec=120)\n", - "RR = ArbField(150)\n", + "RR = ArbField(max(precx,150))\n", "Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ]\n", "LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ]\n", - "#Pcrit = [ [ [ rat_to_Arb(pc[1]), pc[2] ] for pc in pcrit] for pcrit in Pcrit ];\n", - "print(\"\")" + "#Pcrit = [ [ [ rat_to_Arb(pc[1]), pc[2] ] for pc in pcrit] for pcrit in Pcrit ];" ] }, { "cell_type": "code", - "execution_count": 282, + "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "intersect_box (generic function with 2 methods)" + "intersect_box (generic function with 1 method)" ] }, "metadata": {}, @@ -242,7 +252,7 @@ " push!(L[i][2], j)\n", " elseif overlap_inter(l, B[1])\n", " prec *= 2\n", - " println(\"Increase precision to \", prec)\n", + " #println(\"Increase precision to \", prec)\n", " flag = true\n", " break\n", " end\n", @@ -260,7 +270,7 @@ " push!(L[i+2][2], j)\n", " elseif overlap_inter(l, B[2])\n", " prec *= 2\n", - " println(\"Increase precision to \", prec)\n", + " #println(\"Increase precision to \", prec)\n", " flag = true\n", " break\n", " end\n", @@ -274,13 +284,13 @@ }, { "cell_type": "code", - "execution_count": 283, + "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "refine_xboxes (generic function with 2 methods)" + "refine_xboxes (generic function with 1 method)" ] }, "metadata": {}, @@ -299,7 +309,7 @@ }, { "cell_type": "code", - "execution_count": 284, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -308,33 +318,12 @@ "text": [ "\n", "Compute intersections with critical boxes\n", - "Increase precision to 300\n", - "Increase precision to 300\n", - "mult=1 ; 8/16 pts\r" - ] - }, - { - "ename": "InterruptException", - "evalue": "InterruptException:", - "output_type": "error", - "traceback": [ - "InterruptException:\n", - "\n", - "Stacktrace:\n", - " [1] _core_msolve(I::AlgebraicSolving.Ideal{QQMPolyRingElem}; initial_hts::Int64, nr_thrds::Int64, max_nr_pairs::Int64, la_option::Int64, info_level::Int64, precision::Int64)\n", - " @ AlgebraicSolving ~/Documents/gittravail/AlgCurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl:103\n", - " [2] _core_msolve\n", - " @ ~/Documents/gittravail/AlgCurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl:55 [inlined]\n", - " [3] #inter_solutions#35\n", - " @ ~/Documents/gittravail/AlgCurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl:425 [inlined]\n", - " [4] isolate_eval(f::QQMPolyRingElem, ivar::Int64, val::QQFieldElem; prec::Int64)\n", - " @ Main ~/Documents/gittravail/AlgCurves/main.ipynb:21\n", - " [5] isolate_eval\n", - " @ ~/Documents/gittravail/AlgCurves/main.ipynb:20 [inlined]\n", - " [6] intersect_box(f::QQMPolyRingElem, B::Vector{Vector{QQFieldElem}}; prec::Int64)\n", - " @ Main ~/Documents/gittravail/AlgCurves/main.ipynb:35\n", - " [7] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/main.ipynb:20" + "mult=1 ; 16/16 pts\n", + "mult=2 ; 3/60 pts\n", + "Refine singular boxes along x-axis\n", + "mult=2 ; 60/60 pts\n", + "Average time for one point: 0.12342744912856664s\n", + "Elapsed time to compute critical boxes: 10.098644018173218s\n" ] } ], @@ -364,14 +353,14 @@ " precx *= 2\n", " println(\"\\nRefine extreme boxes along x-axis\")\n", " refine_xboxes(params[1][1], LBcrit[1], precx)\n", - " #break\n", + " flag = true\n", + " break\n", " elseif i > 1 && sum(npcside[1:2]) != 0\n", " precx *= 2\n", " println(\"\\nRefine singular boxes along x-axis\")\n", " refine_xboxes(params[2][1], LBcrit[2], precx)\n", - " #refine_xboxes(QQ[\"x\"](params[2][1]), LBcrit[2])\n", - " #i -= 1\n", - " #break\n", + " flag = true\n", + " break\n", " end\n", " LPCside[i][j] = pcside\n", " push!(Ltm, time() - tm)\n", @@ -388,24 +377,9 @@ }, { "cell_type": "code", - "execution_count": 281, + "execution_count": 15, "metadata": {}, - "outputs": [ - { - "ename": "UndefRefError", - "evalue": "UndefRefError: access to undefined reference", - "output_type": "error", - "traceback": [ - "UndefRefError: access to undefined reference\n", - "\n", - "Stacktrace:\n", - " [1] getindex(A::Vector{Any}, i1::Int64)\n", - " @ Base ./essentials.jl:13\n", - " [2] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/main.ipynb:5" - ] - } - ], + "outputs": [], "source": [ "# Update extreme boxes\n", "for j in eachindex(LBcrit[1])\n", @@ -448,7 +422,7 @@ }, { "cell_type": "code", - "execution_count": 244, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -459,17 +433,17 @@ ] }, { - "ename": "UndefRefError", - "evalue": "UndefRefError: access to undefined reference", + "ename": "BoundsError", + "evalue": "BoundsError: attempt to access 8-element Vector{Vector{QQFieldElem}} at index [9]", "output_type": "error", "traceback": [ - "UndefRefError: access to undefined reference\n", + "BoundsError: attempt to access 8-element Vector{Vector{QQFieldElem}} at index [9]\n", "\n", "Stacktrace:\n", - " [1] getindex(A::Vector{Any}, i1::Int64)\n", + " [1] getindex(A::Vector{Vector{QQFieldElem}}, i1::Int64)\n", " @ Base ./essentials.jl:13\n", " [2] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/main.ipynb:18" + " @ ~/Documents/gittravail/AlgCurves/main.ipynb:64" ] } ], @@ -592,7 +566,7 @@ }, { "cell_type": "code", - "execution_count": 245, + "execution_count": 17, "metadata": {}, "outputs": [], "source": [ @@ -601,7 +575,7 @@ }, { "cell_type": "code", - "execution_count": 246, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -631,7 +605,7 @@ }, { "cell_type": "code", - "execution_count": 247, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -643,7 +617,7 @@ }, { "data": { - "image/png": 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QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEC0awjhe++9FxER0bNnz48++qjhRzMyMsaOHRseHt63b9+//OUvtbW12vjbb78d/7sxY8Y0zaoBAGgini7OW7du3T//+c/NmzfbbLaHHnqoW7duDz74YN0JP//8c0JCwt///veLFy8mJydbrdZ3331XUZSffvqpZ8+eiYmJiqIYDIYm/wQAALgRroYwJSVl9uzZvXv3VhRl5syZKSkp9UI4bdo05/aMGTOWL1/uvBgeHj5ixIimWC0AAE3M1YdGf/rpp6ioKG07KioqOzv7CpMzMjL69OnjvPjxxx/HxMQkJSUdO3bsuhcKAMDN4OoR4YULF/z9/bXtu+66q6SkpLGZ69at27p165EjR7SL48aNmz59uo+Pz6ZNmwYPHnzkyJEuXbpc9ooXL17s2rWrTqfTLo4aNWrp0qWN3YvZbDYYDJ6erq4fTevSpUvOrxSaH/vfjex2u8Visdvt7l6IUNXV1VarVa/Xuzjf29v7qqVwNSQBAQGVlZXadmVlpclkuuy0bdu2zZgxY+vWrSEhIdrI6NGjtY2BAwcePHhw7dq1c+fOvex1/fz8fvjhh4CAAO2ij4+Pt7d3Y+vR6/WE0I1UVfX19XX3KuRi/7uRFkIfHx93L0QoDw8Po9Hoeghduk0X53Xr1i03N1fbzsnJ6datW8M533777aRJk7766qvo6OjL3kirVq3MZnNjd6HT6Vq1ahXwuytUEACApuJqCCdNmvTxxx9XVlaWl5enpKRMnDhRG3/hhRfy8/MVRUlLSxs7duyyZcsiIiLKysoqKioURbHb7du2bbNYLKqqbt68ecuWLQkJCTfpMwEA4Dq4+tDis88++8MPP4SGhiqKMnHixKeeekob37Rp05NPPtm9e/dt27YFBATMnj1bG2/fvn16erqqqq+88kp2drbBYGjXrl1KSkpMTMzN+DQAALg+OlVVXZ9ts9l0Ot21PjirqqrFYjEajVeeZjKZ8vLyWrdu7cptcrKMe1VWVvr5+bl7FXKx/92I5wjdq7q6usmfI7y2kFxfeHQ63VUrCACAW/BeowAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0a4thFar9coTHA6H3W6/jisCAOAWroawuLh4+PDhJpOpTZs2K1eubDhBVdUXX3yxVatWAQEBU6ZMsdls2vjPP/8cGRlpMpk6deq0c+fOJls4AABNwdUQzpkzp3PnzmVlZdu3b585c+apU6fqTVizZk1qaurJkycLCwsPHz68dOlSbXzSpElPPvlkRUXFokWLnnzySbPZ3JTLBwDgxrgUwqqqqvXr17/yyit6vT4qKio+Pn7VqlX15qxYsWLatGmBgYG+vr6zZs1asWKFoig//fRTTk7OCy+8oNPpRo8e3bZt26+//rrJPwcAAK6bSyH87bff7HZ7WFiYdrFnz575+fn15uTn5/fs2bPehPz8/C5duvj4+DjH8/LyGrsXVVXLy8vLfldTU3OtnwwAANfK05VJ5eXlLVu21Ol02kU/P7/S0tKGc3x9fZ0TysvLHQ6HdkXnHD8/v7KyssbupbKyMioqynkvo0aNcj6+2pDZbDYYDJ6eLq0fTe7SpUvOrxSaH/vfjex2u8ViuexZgWgG1dXVVqtVr9e7ON/b2/uqpXApJIGBgZWVlQ6Hw8PDQ1GUsrKytm3bNpxTUVGhbZeXl7dp08bDwyMwMPDixYvOOWVlZXfffXdj9+Lv75+Xl9e6dWtXlqTX6wmhG6mq6vy7B82P/e9GWgidD3ShmXl4eBiNRtdD6NJtujKpQ4cOLVq0OHr0qHYxKysrIiKi3pyePXsePny43oSIiIiTJ086A5mVlXWFEAIA0PxcCqGPj8/TTz/9+uuvFxcXb9iwYf/+/UlJSYqi5OTkPPDAA9qcadOmLVmyJCsrKy8vb8GCBdOmTVMUpXv37kOGDJk3b9758+c//PBDh8PhnA8AwK3A1YcW33333dmzZw8YMCA4OHj9+vVBQUGKojgcjtraWm1CQkLCvHnzxo8fb7PZkpOTJ0yYoI1/9tlnM2bMiIqK6t69+9dff82DmQCAW4pOVVV3r+F/TCaT688Rrl+/vmvXrvfcc8/NXhUu65133pk1a1bdM6HQbMxm88KFC1977TV3L0SoY8eO5eTkPPHEE+5eiFD//ve/IyMje/Xq1YS3ebu+1+iWLVsOHjzo7lXItXTp0uLiYnevQqiSkpIlS5a4exVyHTp0aPPmze5ehVypqamZmZlNe5u3awgBAGgShBAAIBohBACIdgudLOPj4xMcHKy9Zv+qzp8/bzQa/fz8bvaqcFmnT58ODg7mHGC3sNvthYWFHTp0cPdChKqqqjKbzW3atHH3QoQ6d+5cixYtXD9Tb8KECfPnz7/ynFvoF1l+fr7zxRhXpb3FjovVRJOrra01Go3uXoVc7H830v7rqsFgcPdChLrWX/4hISFXnXMLHRECAND8OKICAIhGCAEAohFCAIBohBAAINotdNZoXVar9dNPPz1+/Hjfvn2ffvrpy/7rqW+//Xbz5s1BQUHPPvus81TmixcvLlu27MyZM3FxcY888kjzrvrOUVVVtWzZsoKCgiFDhowZM6beRx0OR0ZGRlpaWkVFRVRU1BNPPKF9gU6dOrV9+3bntFGjRnGK//U5cuTIF198YTAYJk2a1L1793ofPXv27MaNG50Xhw0bFhYWpm3v2bMnNTU1MDAwOTm54T8NhYvS09M3btxoMpmSk5ODg4PrfXTnzp0nT550XvT19dX+x8C6deuc/7E8ODiY3z/XwW635+TkZGVl2Wy2yZMnX3aO1Wpdvnx5bm5u7969J02a5KxDbm7uqlWrHA7HU089da3vRHqLHhFOmjRp1apVYWFhixcvnjlzZsMJq1evnjBhQufOnU+cODFo0CCz2awoisPhuP/++zMyMrp16zZ79uwPP/yw2Rd+J1BVNT4+Pi0trXv37nPnzn3//ffrTcjKypoyZUp1dXX79u3feeedxx57TBs/evToW2+9dfJ31dXVzb72O0FmZuaQIUP8/f0dDseAAQN+/fXXehN++eWX1157zbmfq6qqtPH169ePHTu2Y8eOJ0+ejImJcY7jmmzcuPGxxx7r0KHDb7/9NnDgwLr/Wlxz9uxZ585fvHjxZ599po3Pnz9/z5492viZM2eafeF3gu3btyckJCxevPj5559vbM4zzzzz2WefhYWFpaSkPPfcc9rgiRMnYmJiPDw8WrRoERsbe+zYsWu7Y/XWk5+f7+3tfeHCBVVVCwoKjEZjUVFRvTl9+vT5/PPPte177713+fLlqqpu3bq1U6dOVqtVVdVdu3aFhIRYLJZmXfodYceOHaGhodqu27t3b1BQUG1tbd0JtbW1drtd2y4oKFAUpaCgQFXVTZs2DR48uPkXfIcZP378q6++qm0nJye/+OKL9SZkZGREREQ0vGJ0dPSKFSu07cGDB6ekpNzUdd6pBg4cuGzZMm176NChH3/8cWMzHQ5H165d16xZo13s27fv7t27m2GFdzDtF8vBgwf9/f0vO+HkyZNGo/HcuXOqqhYWFhqNxsLCQlVVZ8yYMX36dG3OnDlzJk+efE33eyseEe7duzcqKkr7f0yhoaHdu3ffv39/3QllZWXHjh2Lj4/XLmqHL4qipKWlDRs2THu7kz/84Q9lZWUnTpxo9uXf9tLS0uLi4rTXC8fGxl66dCk3N7fuBC8vL+erWWtra3U6nfNdHs6dO/f+++9/8sknhYWFzbzsO0Z6enrD7+16KisrP/jgg5SUFOfxYlVVVWZm5ogRI658RVxZTU3NoUOHrrr/NTt37qyoqKj7EOjGjRs/+OCDb7755qYv9A511ZfJ7927t1+/foGBgYqihISEhIeHf/fdd4qipKenjxw5UptzHd/8t2IIi4uL6759Udu2bev9Vi0qKtLr9SaTqd6EulfUJhQVFTXXqu8cdXejh4dHmzZtGquaw+H485//PH369ICAAEVRWrZsGRUVVV5evm3btrvvvlv7BsU1cTgcZ8+ede7/oKCght/DRqMxJiamtLQ0PT29b9++W7duVRRFm+a8YsOfGriiuLhYVVXtH48rV9uNn376aVJSkvMtfiIjI/V6fVFR0ZQpU8aPH98cy5WnsToUFRVd+afmym7Fk2U8PT3tdrvzotVq9fLyqjvBYDA4HA6Hw6H9+WC1WrXvxateEa5wcTeqqjpr1qyysrIvv/xSGxk+fPjw4cO17Xnz5s2bN2/37t3NsOA7iU6n8/T0tNls2kWbzdZw50dHR69bt07bXrhw4csvvzxq1CjtCN75hXP+UOCaaI8nOff/FXZjaWnpV199deDAAeeI88nCl156KSws7LvvvouNjb3J6xWnsd9OV/2pubJb8Yiwffv2dZ9qPnPmTLt27epO0N47zvmX2pkzZ7SRulc0m82lpaX1rghX1N2NtbW158+fv+xunDNnTmZm5rZt23x9fRt+NDY2tu6ZdXCRTqcLCQlx7v+G3/z1OPez9ob1da/oylssop7g4GC9Xu/Kbvz888/79OkTGRnZ8ENt27bt1q0b3/83Q2N1qDt+1Z+ahm7FEMbHx+fm5mpP7/3444/nz58fOnSooiinTp3KyspSFMXX13fYsGFr165VFKWmpiY1NVV7mD4xMXHnzp3l5eWKonz11Vc9evRoeOo5rioxMfHbb7/VTgRPTU3t1KlTeHi4oii5ubnHjx/X5rz22mu7d+/esmWLv7+/84raubua1NTUPn36NO/C7xCJiYnOA761a9cmJiZq27t27dLOYKypqXFOTk1N7d27t6Io3t7eI0eO1K5osVg2btzI6fvXwdPTc9SoUdrvFqvV6tyNZrN5165dVqvVOXP58uXJycnOixaLxXmkkpeXl5ube61n8OMKMjMzT58+rSjKiBEj8vPztbMWjhw5UlxcHBcXpyhKYmKi9lVT/u9Pjatu4ASfm+itt97q0KFDcnJySEjIokWLtMH58+fff//92nZGRobJZEpKSurfv39CQoLNZtPGk5KSevbsOXny5MDAwE2bNrln9be/yZMnR0RETJ48uU2bNv/5z3+cg1OnTlVVNSMjQ1GUsLCw6N8dPnxYVdVx48YNHTo0KSkpOjq6Y8eO2dnZ7vwcblunTp0KDQ0dM2bMyJEj77777tLSUlVVHQ6HoigHDhxQVfW5556LjY1NSkqKjY0NDg7WBlVVPXjwoMlkeuqppwYMGDB8+HDt9Glcqx9++MFkMk2YMCEmJmbo0KHa6dN5eXmKopSUlGhzMjMzfXx8ysrKnNfKysrq0KHD448//vjjj/v7+8+dO9c9q7/NFRYWRkdHR0RE6PX66Ojo0aNHa+MDBgxYuHChtv3222+HhoYmJye3a9fOOVhSUhIWFvbAAw888sgjnTt3PnPmzDXd76373ycOHz6cm5vbp08f7Q9eRVEKCwsrKyu1o8PcatkAAAFQSURBVBNFUYqKitLT0wMDA+Pi4pyvqVRVdd++fadPn46Nje3UqZN7ln5H2LdvX0FBQUxMTJcuXbSRX3/9VafTde7cubKyst7puOHh4b6+vhUVFQcPHrxw4UJwcPCgQYO8vb3dsfA7wcWLF3fu3GkwGEaMGOHj46MNHjp0qFevXi1btqyqqjp06JB2Tk1MTEzdh6bPnj27Z88ek8kUFxfHf4u8biUlJXv27AkICHCehV5bW3vkyJGoqCjtYklJSWlpaUREhPMqqqr+/PPPubm5Hh4ekZGR3bp1c9vqb2cWi6XuSwCNRqP2+z87O9tkMjnfIyIrKysnJ6d37951H3aqrq7euXOnw+EYMWLEZZ+vuYJbN4QAADSDW/E5QgAAmg0hBACIRggBAKIRQgCAaIQQACAaIQQAiEYIAQCiEUIAgGiEEAAgGiEEAIhGCAEAov0/bgAuSm3s1AIAAAAASUVORK5CYII=", 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"\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" ] }, "metadata": {}, @@ -744,7 +4250,7 @@ }, { "cell_type": "code", - "execution_count": 248, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -813,14 +4319,14 @@ }, { "cell_type": "code", - "execution_count": 249, + "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "0\n" + "8\n" ] } ], @@ -830,7 +4336,7 @@ }, { "cell_type": "code", - "execution_count": 250, + "execution_count": 22, "metadata": {}, "outputs": [ { @@ -861,127 +4367,4910 @@ }, { "cell_type": "code", - "execution_count": 251, + "execution_count": 23, "metadata": {}, "outputs": [ { - "name": "stdout", + "name": "stderr", "output_type": "stream", "text": [ - "Plotting the graph\n" + "┌ Warning: backend `PyPlot` is not installed.\n", + "└ @ Plots /home/remi/.julia/packages/Plots/ju9dp/src/backends.jl:43\n" ] }, { "data": { - "image/png": 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+ "output_type": "stream", + "text": [ + "Plotting the graph\n" + ] } ], "source": [ - "plot_graph_comp(Vert,CEdg)" + "pyplot()\n", + "display(plot_graph_comp(Vert,CEdg))" ] }, { "cell_type": "code", - "execution_count": 252, + "execution_count": 24, "metadata": {}, "outputs": [], "source": [] diff --git a/src/connectcurves/main.jl b/src/connectcurves/main.jl index d7741a3..627c480 100644 --- a/src/connectcurves/main.jl +++ b/src/connectcurves/main.jl @@ -1,13 +1,14 @@ -println("Loading libraries and data..") +println("\nLoading libraries and data..") using Pkg using Revise Pkg.activate("AlgebraicSolving.jl-main") using AlgebraicSolving using Nemo -using Colors -using PyPlot +#using Plots, Colors +#pythonplot() include("data.jl") include("src/usolve/usolve.jl") +include("subresultants.jl") function order_permut2d(L) # Create a list of tuples with elements and their corresponding indices @@ -49,22 +50,67 @@ function evaluate_Arb(f, x) return evalpoly(RR(x), cf) end +function in_inter(I, J) + return J[1] < I[1] && I[2] < J[2] +end + +function overlap_inter(I,J) + return max(I[1], J[1]) <= min(I[2], J[2]) +end + # To try/do : isolate with usolve, call msolve with only one variable -function intersect_box(f, B) +function intersect_box(f, B; prec=100) L = Array{Any}(undef, 4) for i in 1:2 # Lxi L[i] = Array{Any}(undef,2) - L[i][1] = isolate_eval(f, 2, B[2][i], prec=200) - L[i][2] = [ j for (j, l) in pairs(L[i][1]) if (l[1]> B[1][1] && l[2] B[2][1] && l[2]0 sqfree factors of the resultant and order by multiplicity +# TODO : group by multiplicity +sqr = collect(factor_squarefree(sr[1][1])) +# Construct the parametrization of the critical points +params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in sqr ]; +end + +############### +precx = 150; +############### +println("\nIsolating critical values at precision ", precx,"..") +@time begin +xcrit = [ isolate(first(p), prec=precx) for p in params ] xcrit_usolve = getindex.(xcrit, 1) xcrit = getindex.(xcrit, 2) -xcritorder, xcritpermut = order_permut2d(xcrit); +_, xcritpermut = order_permut2d(xcrit); +end -println("Computing isolating critical boxes using Arb..") +println("\nComputing isolating critical boxes using Arb with precision ",max(precx,150),"..") +@time begin #RR(x) = Arb(x, prec=120) -RR = ArbField(150) +RR = ArbField(max(precx,150)) Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ] -LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ]; -Pcrit = [ [ [ rat_to_Arb(pc[1]), pc[2] ] for pc in pcrit] for pcrit in Pcrit ]; +LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ] +end # Could be improved by handling nodes as extreme boxes: -# when npcside = [2,2,0,0] just take nearest elow and above +# when npcside = [2,2,0,0] just take nearest below and above # intersections b with the curves on the vertical sides # and change into npcside = [0,0,2,2] -println("\nCompute intersections with critical boxes") -ts = time() -LPCside = Array{Any}(undef,2) -ndig = maximum([Int(floor(log10(length(LBcrit[i])))) for i in 1:2]) -Ltm = [] -i = 1 -while i <= length(LBcrit) - global i +## TODO : Refine only the intervals that need to be refined +println("\nCompute intersections with critical boxes..") +@time begin +LPCside = Array{Any}(undef,length(LBcrit)) +ndig = maximum([Int(floor(log10(length(LB)))) for LB in LBcrit]) +for i in eachindex(LBcrit) ndigi = Int(floor(log10(length(LBcrit[i])))) LPCside[i] = Array{Any}(undef, length(LBcrit[i])) - for j in eachindex(LBcrit[i]) - print("mult=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") - tm = time() - pcside = intersect_box(f, LBcrit[i][j]) - npcside = [length(n) for (I, n) in pcside] - if i == 1 && sum(npcside) > 2 - @assert false "\nRefine extreme boxes along x-axis" - #refine_xboxes(QQ["x"](params[1][1]), LBcrit[1]) - #i = 0 - #j = 1 - #break - elseif i > 1 && sum(npcside[1:2]) != 0 - println(npcside) - @assert false "\nRefine singular boxes along x-axis" - #refine_xboxes(QQ["x"](params[2][1]), LBcrit[2]) - #i -= 1 - #break + precxtmp = precx + while true + flag = false + for j in eachindex(LBcrit[i]) + print("mult=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") + pcside = intersect_box(f, LBcrit[i][j], prec=precx) + npcside = [length(n) for (I, n) in pcside] + if i == 1 && sum(npcside) > 2 + precxtmp *= 2 + println("\nRefine extreme boxes along x-axis to precision ", precxtmp) + refine_xboxes(params[1][1], LBcrit[1], precxtmp) + flag = true + break + elseif i > 1 && sum(npcside[1:2]) != 0 + precxtmp *= 2 + println("\nRefine singular boxes along x-axis to precision ", precxtmp) + refine_xboxes(params[2][1], LBcrit[2], precxtmp) + flag = true + break + end + LPCside[i][j] = pcside end - LPCside[i][j] = pcside - push!(Ltm, time() - tm) + flag || break end - i += 1 println("") end LnPCside = [ [[length(indI) for (L, indI) in PB] for PB in lpcside] for lpcside in LPCside ] -println("Average time for one point: $(sum(Ltm)/length(Ltm))s") -println("Elapsed time to compute critical boxes: $(time()-ts)s") # Update extreme boxes for j in eachindex(LBcrit[1]) @@ -222,8 +289,10 @@ for j in eachindex(LBcrit[1]) end end end +end -print("Graph computation") +#print("\nGraph computation :") +#@time begin # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot # And even remove this fiber for the graph Vert = [] @@ -337,10 +406,14 @@ for ind in 1:length(xcritpermut) ite += 1 end end +#end -EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] -plot_graph(Vert, EdgPlot) +#EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] +#plot_graph(Vert, EdgPlot) +#gui() CEdg = connected_components_bis(Edg); -plot_graph_comp(Vert,CEdg) \ No newline at end of file +println("\n## The curve has ", length(CEdg), " connected components ##") + +#plot_graph_comp(Vert,CEdg) \ No newline at end of file From 5c942a8638ea2a1de1622a37e723f75f6601b61b Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 13:08:36 +0200 Subject: [PATCH 011/180] fix bug graph and square free decomposition --- src/connectcurves/main.ipynb | 17720 ++++++++++++++++++++------------- src/connectcurves/main.jl | 66 +- 2 files changed, 11116 insertions(+), 6670 deletions(-) diff --git a/src/connectcurves/main.ipynb b/src/connectcurves/main.ipynb index 31f37a9..87ef610 100644 --- a/src/connectcurves/main.ipynb +++ b/src/connectcurves/main.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 53, "metadata": {}, "outputs": [ { @@ -38,7 +38,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 54, "metadata": {}, "outputs": [ { @@ -60,7 +60,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 55, "metadata": {}, "outputs": [], "source": [ @@ -73,7 +73,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 56, "metadata": {}, "outputs": [], "source": [ @@ -82,20 +82,51 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 111, "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "MethodError", + "evalue": "MethodError: no method matching *(::Vector{Int64}, ::QQMPolyRingElem)\n\nClosest candidates are:\n *(::Any, ::Any, !Matched::Any, !Matched::Any...)\n @ Base operators.jl:587\n *(!Matched::QQMPolyRingElem, ::QQMPolyRingElem)\n @ Nemo ~/.julia/packages/Nemo/VHAIi/src/flint/fmpq_mpoly.jl:335\n *(!Matched::ZZRingElem, ::QQMPolyRingElem)\n @ Nemo ~/.julia/packages/Nemo/VHAIi/src/flint/fmpq_mpoly.jl:381\n ...\n", + "output_type": "error", + "traceback": [ + "MethodError: no method matching *(::Vector{Int64}, ::QQMPolyRingElem)\n", + "\n", + "Closest candidates are:\n", + " *(::Any, ::Any, !Matched::Any, !Matched::Any...)\n", + " @ Base operators.jl:587\n", + " *(!Matched::QQMPolyRingElem, ::QQMPolyRingElem)\n", + " @ Nemo ~/.julia/packages/Nemo/VHAIi/src/flint/fmpq_mpoly.jl:335\n", + " *(!Matched::ZZRingElem, ::QQMPolyRingElem)\n", + " @ Nemo ~/.julia/packages/Nemo/VHAIi/src/flint/fmpq_mpoly.jl:381\n", + " ...\n", + "\n", + "\n", + "Stacktrace:\n", + " [1] top-level scope\n", + " @ ~/Documents/gittravail/AlgCurves/main.ipynb:10" + ] + } + ], "source": [ - "# Take the deg>0 sqfree factors of the resultant and order by multiplicity\n", - "# TODO : group by multiplicity\n", + "# Take sqfree factors of the resultant\n", "sqr = collect(factor_squarefree(sr[1][1]))\n", + "# Keep only deg>0 factors \n", + "filter(t->t[2]>0, sqr)\n", + "# Order by multiplicity\n", + "sqr = sort(sqr, by=t->t[2])\n", + "# Group by multiplicity\n", + "group_sqr = [ [R(1),i] for i in 1:sqr[end][2] ]\n", + "for r in sqr\n", + " group_sqr[r[2]] *= r[1]\n", + "end\n", "# Construct the parametrization of the critical points\n", - "params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in sqr ];" + "params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in group_sqr ];" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 58, "metadata": {}, "outputs": [ { @@ -152,16 +183,16 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 59, "metadata": {}, "outputs": [], "source": [ - "precx = 50;" + "precx = 150;" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 60, "metadata": {}, "outputs": [ { @@ -182,7 +213,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 61, "metadata": {}, "outputs": [ { @@ -196,8 +227,8 @@ "data": { "text/plain": [ "2-element Vector{Vector{Vector{Vector{QQFieldElem}}}}:\n", - " [[[-274010517572908139//288230376151711744, -1096042070291632555//1152921504606846976], [148491350383//25070396056151, 78153733013//13195011257214]], [[-267143983447885//281474976710656, -4274303735166159//4503599627370496], [-365779936255//99916048642522, -197192020319//53864757306904]], [[-455352681580283//562949953421312, 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"metadata": {}, "outputs": [ { @@ -284,7 +315,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 63, "metadata": {}, "outputs": [ { @@ -309,7 +340,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 64, "metadata": {}, "outputs": [ { @@ -319,11 +350,9 @@ "\n", "Compute intersections with critical boxes\n", "mult=1 ; 16/16 pts\n", - "mult=2 ; 3/60 pts\n", - "Refine singular boxes along x-axis\n", "mult=2 ; 60/60 pts\n", - "Average time for one point: 0.12342744912856664s\n", - "Elapsed time to compute critical boxes: 10.098644018173218s\n" + "Average time for one point: 0.17550745135859439s\n", + "Elapsed time to compute critical boxes: 13.488043069839478s\n" ] } ], @@ -377,7 +406,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 65, "metadata": {}, "outputs": [], "source": [ @@ -422,7 +451,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 66, "metadata": {}, "outputs": [ { @@ -431,20 +460,6 @@ "text": [ "Graph computation" ] - }, - { - "ename": "BoundsError", - "evalue": "BoundsError: attempt to access 8-element Vector{Vector{QQFieldElem}} at index [9]", - "output_type": "error", - "traceback": [ - "BoundsError: attempt to access 8-element Vector{Vector{QQFieldElem}} at index [9]\n", - "\n", - "Stacktrace:\n", - " [1] getindex(A::Vector{Vector{QQFieldElem}}, i1::Int64)\n", - " @ Base ./essentials.jl:13\n", - " [2] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/main.ipynb:64" - ] } ], "source": [ @@ -566,7 +581,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 67, "metadata": {}, "outputs": [], "source": [ @@ -575,7 +590,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 68, "metadata": {}, "outputs": [ { @@ -605,7 +620,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 69, "metadata": {}, "outputs": [ { @@ -617,3770 +632,7 @@ }, { "data": { - "image/png": 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"metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg]\n", - "plot_graph(Vert, EdgPlot)" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "connected_components_bis (generic function with 1 method)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "function connected_components_bis(edges)\n", - " adj_list = Dict{Int, Vector{Int}}()\n", - " visited = Set{Int}()\n", - " components = Vector{Vector{Tuple{Int, Int}}}()\n", - "\n", - " # Build adjacency list\n", - " for (i, j) in edges\n", - " push!(get!(adj_list, i, []), j)\n", - " push!(get!(adj_list, j, []), i)\n", - " end\n", - "\n", - " \n", - " # Depth-first search\n", - " function dfs(node, component)\n", - " push!(visited, node)\n", - " for neighbor in adj_list[node]\n", - " if !(neighbor in visited)\n", - " push!(component, (node, neighbor))\n", - " dfs(neighbor, component)\n", - " end\n", - " end\n", - " end\n", - " \n", - "\n", - " # Breadth-first search\n", - " function bfs(node, component)\n", - " queue = [node]\n", - " push!(visited, node)\n", - " while !isempty(queue)\n", - " current = popfirst!(queue)\n", - " for neighbor in adj_list[current]\n", - " if !(neighbor in visited)\n", - " push!(visited, neighbor)\n", - " push!(component, (current, neighbor))\n", - " push!(queue, neighbor)\n", - " end\n", - " end\n", - " end\n", - " end\n", - "\n", - " # Find connected components\n", - " for node in keys(adj_list)\n", - " if !(node in visited)\n", - " component = Vector{Tuple{Int, Int}}()\n", - " bfs(node, component)\n", - " push!(components, component)\n", - " end\n", - " end\n", - "\n", - " return components\n", - "end\n" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "8\n" - ] - } - ], - "source": [ - "CEdg = connected_components_bis(Edg); println(length(CEdg))" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "plot_graph_comp (generic function with 1 method)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "function plot_graph_comp(V, CE)\n", - " println(\"Plotting the graph\")\n", - " plot(legend=false)\n", - " col = distinguishable_colors(length(CE)+2)\n", - " for j in eachindex(CE)\n", - " for e in CE[j]\n", - " v1, v2 = map(Float64, V[e[1]]), map(Float64, V[e[2]])\n", - " plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=3)\n", - " end\n", - " end\n", - " #plt.show(block=true)\n", - " plot!()\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "┌ Warning: backend `PyPlot` is not installed.\n", - "â”” @ Plots /home/remi/.julia/packages/Plots/ju9dp/src/backends.jl:43\n" - ] - }, - { - "data": { - "image/png": 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", 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[ + { + "data": { + "text/plain": [ + "connected_components (generic function with 2 methods)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "function connected_components(vert, edges)\n", + " adj_list = Dict{Int, Vector{Int}}()\n", + " visited = Set{Int}()\n", + " components = Vector{Vector{Int}}()\n", + "\n", + " # Build adjacency list\n", + " for (i, j) in edges\n", + " push!(get!(adj_list, i, []), j)\n", + " push!(get!(adj_list, j, []), i)\n", + " end\n", + "\n", + " # Depth-first search\n", + " function dfs(node, component)\n", + " push!(visited, node)\n", + " push!(component, node)\n", + " for neighbor in adj_list[node]\n", + " if !(neighbor in visited)\n", + " dfs(neighbor, component)\n", + " end\n", + " end\n", + " end\n", + "\n", + " # Find connected components\n", + " for node in keys(adj_list)\n", + " if !(node in visited)\n", + " component = Vector{Int}()\n", + " dfs(node, component)\n", + " push!(components, component)\n", + " end\n", + " end\n", + "\n", + " # Group edges by connected component\n", + " grouped_edges = [Tuple{Int, Int}[] for _ in components]\n", + " for (idx, component) in enumerate(components)\n", + " for node in component\n", + " for neighbor in adj_list[node]\n", + " if neighbor > node && neighbor in component\n", + " push!(grouped_edges[idx], (node, neighbor))\n", + " end\n", + " end\n", + " end\n", + " end\n", + "\n", + " grouped_vert = [ [ vert[cv] for cv in c ] for c in components ]\n", + " return grouped_vert, grouped_edges\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": 108, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4\n" + ] + } + ], + "source": [ + "CVert, CEdg = connected_components(Vert, Edg); println(length(CVert))" + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "plot_graph_comp (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "function plot_graph_comp(V, CE)\n", + " println(\"Plotting the graph\")\n", + " plot(legend=false)\n", + " col = distinguishable_colors(length(CE)+2)\n", + " for j in eachindex(CE)\n", + " for e in CE[j]\n", + " v1, v2 = map(Float64, V[e[1]]), map(Float64, V[e[2]])\n", + " plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=3)\n", + " end\n", + " end\n", + " #plt.show(block=true)\n", + " plot!()\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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"code", - "execution_count": 24, + "execution_count": 74, "metadata": {}, "outputs": [], "source": [] diff --git a/src/connectcurves/main.jl b/src/connectcurves/main.jl index 627c480..e5685c0 100644 --- a/src/connectcurves/main.jl +++ b/src/connectcurves/main.jl @@ -138,10 +138,10 @@ function plot_graph_comp(V, CE) end ## Graph functions -function connected_components_bis(edges) +function connected_components(vert, edges) adj_list = Dict{Int, Vector{Int}}() visited = Set{Int}() - components = Vector{Vector{Tuple{Int, Int}}}() + components = Vector{Vector{Int}}() # Build adjacency list for (i, j) in edges @@ -149,18 +149,13 @@ function connected_components_bis(edges) push!(get!(adj_list, j, []), i) end - # Breadth-first search - function bfs(node, component) - queue = [node] + # Depth-first search + function dfs(node, component) push!(visited, node) - while !isempty(queue) - current = popfirst!(queue) - for neighbor in adj_list[current] - if !(neighbor in visited) - push!(visited, neighbor) - push!(component, (current, neighbor)) - push!(queue, neighbor) - end + push!(component, node) + for neighbor in adj_list[node] + if !(neighbor in visited) + dfs(neighbor, component) end end end @@ -168,34 +163,56 @@ function connected_components_bis(edges) # Find connected components for node in keys(adj_list) if !(node in visited) - component = Vector{Tuple{Int, Int}}() - bfs(node, component) + component = Vector{Int}() + dfs(node, component) push!(components, component) end end - return components + # Group edges by connected component + grouped_edges = [Tuple{Int, Int}[] for _ in components] + for (idx, component) in enumerate(components) + for node in component + for neighbor in adj_list[node] + if neighbor > node && neighbor in component + push!(grouped_edges[idx], (node, neighbor)) + end + end + end + end + + grouped_vert = [ [ vert[cv] for cv in c ] for c in components ] + return grouped_vert, grouped_edges end # Generic change of variables changemat = [1 0; 0 1] -#changemat = rand(-100:100, 2, 2) +changemat = rand(-100:100, 2, 2) invchangemat = inv(changemat) f = evaluate(f, collect(changemat*[x; y])); println("\nCompute parametrization of critical pts...") @time begin sr = subresultants(f, derivative(f,y),2, list=true); -# Take the deg>0 sqfree factors of the resultant and order by multiplicity -# TODO : group by multiplicity +# Take sqfree factors of the resultant sqr = collect(factor_squarefree(sr[1][1])) +# Keep only deg>0 factors +filter(t->t[2]>0, sqr) +# Order by multiplicity +sqr = sort(sqr, by=t->t[2]) +# Group by multiplicity +group_sqr = [ [R(1),i] for i in 1:sqr[end][2] ] +for r in sqr + group_sqr[r[2]][1] *= r[1] +end # Construct the parametrization of the critical points -params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in sqr ]; +params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in group_sqr ]; end ############### -precx = 150; +precx = 200; ############### +# TODO : check that no overlap between different isolations println("\nIsolating critical values at precision ", precx,"..") @time begin xcrit = [ isolate(first(p), prec=precx) for p in params ] @@ -229,9 +246,10 @@ for i in eachindex(LBcrit) flag = false for j in eachindex(LBcrit[i]) print("mult=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") - pcside = intersect_box(f, LBcrit[i][j], prec=precx) + pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp) npcside = [length(n) for (I, n) in pcside] if i == 1 && sum(npcside) > 2 + print((i,j)," ",npcside) precxtmp *= 2 println("\nRefine extreme boxes along x-axis to precision ", precxtmp) refine_xboxes(params[1][1], LBcrit[1], precxtmp) @@ -412,8 +430,8 @@ end #plot_graph(Vert, EdgPlot) #gui() -CEdg = connected_components_bis(Edg); +CVert, CEdg = connected_components(Vert, Edg); -println("\n## The curve has ", length(CEdg), " connected components ##") +println("\n## Lifted curve has ", length(CVert), " connected components ##") #plot_graph_comp(Vert,CEdg) \ No newline at end of file From 965413142481f55dbc5d797e50d9786f59641fc6 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 13:13:49 +0200 Subject: [PATCH 012/180] changemat --- src/connectcurves/main.jl | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/src/connectcurves/main.jl b/src/connectcurves/main.jl index e5685c0..4ca4e8b 100644 --- a/src/connectcurves/main.jl +++ b/src/connectcurves/main.jl @@ -187,8 +187,7 @@ end # Generic change of variables changemat = [1 0; 0 1] -changemat = rand(-100:100, 2, 2) -invchangemat = inv(changemat) +changemat = rand(-500:500, 2, 2) f = evaluate(f, collect(changemat*[x; y])); println("\nCompute parametrization of critical pts...") From a48140883ff34f875ec5fadb5a19ba7788ad5439 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 15:10:14 +0200 Subject: [PATCH 013/180] cleaning files --- .../.github/workflows/CI.yml | 85 - .../.github/workflows/CleanupDocPreview.yml | 29 - .../.github/workflows/TagBot.yml | 15 - .../AlgebraicSolving.jl-main/.gitignore | 3 - .../AlgebraicSolving.jl-main/LICENSE.md | 636 - .../AlgebraicSolving.jl-main/Manifest.toml | 675 - .../AlgebraicSolving.jl-main/Project.toml | 33 - .../AlgebraicSolving.jl-main/README.md | 22 - .../docs/Project.toml | 11 - .../AlgebraicSolving.jl-main/docs/make.jl | 36 - .../docs/src/groebner-bases.md | 65 - .../docs/src/index.md | 23 - .../docs/src/katsura.md | 34 - .../docs/src/normal-forms.md | 44 - .../docs/src/solvers.md | 57 - .../docs/src/types.md | 53 - .../src/AlgebraicSolving.jl | 21 - .../src/algorithms/groebner-bases.jl | 184 - .../src/algorithms/normal-forms.jl | 174 - .../src/algorithms/solvers.jl | 435 - .../src/examples/cyclic.jl | 23 - .../src/examples/katsura.jl | 90 - .../AlgebraicSolving.jl-main/src/exports.jl | 4 - .../AlgebraicSolving.jl-main/src/imports.jl | 61 - .../src/interfaces/nemo.jl | 118 - .../src/siggb/hashtable.jl | 472 - .../src/siggb/linear_algebra.jl | 156 - .../src/siggb/monomials.jl | 127 - .../src/siggb/siggb.jl | 256 - .../src/siggb/symbolic_pp.jl | 368 - .../src/siggb/typedefs.jl | 109 - .../src/siggb/update.jl | 350 - .../AlgebraicSolving.jl-main/src/types.jl | 51 - .../test/algorithms/groebner-bases.jl | 70 - .../test/algorithms/normal-forms.jl | 18 - .../test/algorithms/solvers.jl | 53 - .../test/examples/katsura.jl | 28 - .../test/interfaces/nemo.jl | 16 - .../AlgebraicSolving.jl-main/test/runtests.jl | 10 - src/connectcurves/data.jl | 14 - src/connectcurves/main.ipynb | 13722 ---------------- src/connectcurves/subresultant.ipynb | 689 - 42 files changed, 19440 deletions(-) delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CI.yml delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CleanupDocPreview.yml delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/TagBot.yml delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/.gitignore delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/LICENSE.md delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/Manifest.toml delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/Project.toml delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/README.md delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/Project.toml delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/make.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/src/groebner-bases.md delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/src/index.md delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/src/katsura.md delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/src/normal-forms.md delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/src/solvers.md delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/docs/src/types.md delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/AlgebraicSolving.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/groebner-bases.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/normal-forms.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/examples/cyclic.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/examples/katsura.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/exports.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/imports.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/interfaces/nemo.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/hashtable.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/linear_algebra.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/monomials.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/siggb.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/symbolic_pp.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/typedefs.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/siggb/update.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/src/types.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/groebner-bases.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/normal-forms.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/solvers.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/examples/katsura.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/interfaces/nemo.jl delete mode 100644 src/connectcurves/AlgebraicSolving.jl-main/test/runtests.jl delete mode 100644 src/connectcurves/data.jl delete mode 100644 src/connectcurves/main.ipynb delete mode 100644 src/connectcurves/subresultant.ipynb diff --git a/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CI.yml b/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CI.yml deleted file mode 100644 index 730421f..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CI.yml +++ /dev/null @@ -1,85 +0,0 @@ -name: Run tests - -on: - push: - branches: - - main - pull_request: - workflow_dispatch: - -concurrency: - # group by workflow and ref; the last slightly strange component ensures that for pull - # requests, we limit to 1 concurrent job, but for the main branch we don't - group: ${{ github.workflow }}-${{ github.ref }}-${{ github.ref != 'refs/heads/main' || github.run_number }} - # Cancel intermediate builds, but only if it is a pull request build. - cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }} - -jobs: - test: - runs-on: ${{ matrix.os }} - timeout-minutes: 120 - continue-on-error: ${{ matrix.julia-version == 'nightly' }} - strategy: - fail-fast: false - matrix: - julia-version: - - '1.6' - - '1.9' - - '~1.10.0-0' - - 'nightly' - julia-arch: - - x64 - os: - - ubuntu-latest - include: - # Add a few macOS jobs (not too many, the number we can run in parallel is limited) - - julia-version: '1.6' - julia-arch: x64 - os: macOS-latest - - julia-version: 'nightly' - julia-arch: x64 - os: macOS-latest - - steps: - - uses: actions/checkout@v2 - with: - # For Codecov, we must also fetch the parent of the HEAD commit to - # be able to properly deal with PRs / merges - fetch-depth: 2 - - name: "Set up Julia" - uses: julia-actions/setup-julia@v1 - with: - version: ${{ matrix.julia-version }} - arch: ${{ matrix.julia-arch }} - - name: "Build package" - uses: julia-actions/julia-buildpkg@latest - - name: "Run tests" - uses: julia-actions/julia-runtest@latest - - name: "Run doctests" - if: ${{ matrix.julia-version == '1.6' }} - run: | - julia --project=docs --color=yes --code-coverage -e ' - using Pkg - Pkg.develop(PackageSpec(path=pwd())) - Pkg.instantiate() - using Documenter: doctest - using AlgebraicSolving - doctest(AlgebraicSolving)' - - name: "Process code coverage" - uses: julia-actions/julia-processcoverage@v1 - with: - directories: src - - name: "Upload coverage data to Codecov" - continue-on-error: true - uses: codecov/codecov-action@v2 - docs: - name: Documentation - runs-on: ubuntu-latest - steps: - - uses: actions/checkout@v2 - - uses: julia-actions/cache@v1 - - uses: julia-actions/julia-buildpkg@latest - - uses: julia-actions/julia-docdeploy@latest - env: - GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} - DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} diff --git a/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CleanupDocPreview.yml b/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CleanupDocPreview.yml deleted file mode 100644 index 18be754..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/CleanupDocPreview.yml +++ /dev/null @@ -1,29 +0,0 @@ -name: Cleanup Doc Preview - -on: - pull_request: - types: [closed] - -jobs: - cleanup-doc-preview: - runs-on: ubuntu-latest - steps: - - name: Checkout gh-pages branch - uses: actions/checkout@v2 - with: - ref: gh-pages - - name: Delete preview - run: | - if [ -d "previews/PR$PRNUM" ]; then - git config user.name "Documenter.jl" - git config user.email "documenter@juliadocs.github.io" - git rm -rf "previews/PR$PRNUM" - git commit -m "delete preview for $PRNUM" - git push origin gh-pages:gh-pages - fi - env: - PRNUM: ${{ github.event.number }} - -# adapted from here: -# https://juliadocs.github.io/Documenter.jl/stable/man/hosting/#gh-pages-Branch -# without history cleanup diff --git a/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/TagBot.yml b/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/TagBot.yml deleted file mode 100644 index f49313b..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/.github/workflows/TagBot.yml +++ /dev/null @@ -1,15 +0,0 @@ -name: TagBot -on: - issue_comment: - types: - - created - workflow_dispatch: -jobs: - TagBot: - if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot' - runs-on: ubuntu-latest - steps: - - uses: JuliaRegistries/TagBot@v1 - with: - token: ${{ secrets.GITHUB_TOKEN }} - ssh: ${{ secrets.DOCUMENTER_KEY }} diff --git a/src/connectcurves/AlgebraicSolving.jl-main/.gitignore b/src/connectcurves/AlgebraicSolving.jl-main/.gitignore deleted file mode 100644 index 014cf71..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/.gitignore +++ /dev/null @@ -1,3 +0,0 @@ -*~ -docs/build/* -docs/make-dep.jl diff --git a/src/connectcurves/AlgebraicSolving.jl-main/LICENSE.md b/src/connectcurves/AlgebraicSolving.jl-main/LICENSE.md deleted file mode 100644 index 18d88dc..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/LICENSE.md +++ /dev/null @@ -1,636 +0,0 @@ -The AlgebraicSolving.jl package is licensed under the GNU Public License, Version 3.0+: - 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-[[deps.msolve_jll]] -deps = ["Artifacts", "CompilerSupportLibraries_jll", "FLINT_jll", "GMP_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl", "MPFR_jll"] -git-tree-sha1 = "6d02a110f583341deea0d249b1a741352631aed6" -uuid = "6d01cc9a-e8f6-580e-8c54-544227e08205" -version = "0.6.3+0" - -[[deps.nghttp2_jll]] -deps = ["Artifacts", "Libdl"] -uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" -version = "1.52.0+1" - -[[deps.p7zip_jll]] -deps = ["Artifacts", "Libdl"] -uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" -version = "17.4.0+2" diff --git a/src/connectcurves/AlgebraicSolving.jl-main/Project.toml b/src/connectcurves/AlgebraicSolving.jl-main/Project.toml deleted file mode 100644 index 631e6dc..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/Project.toml +++ /dev/null @@ -1,33 +0,0 @@ -name = "AlgebraicSolving" -uuid = "66b61cbe-0446-4d5d-9090-1ff510639f9d" -authors = ["ederc ", "Mohab Safey El Din "] -version = "0.4.6" - -[deps] -BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" -ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" -LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" -Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" -LoopVectorization = "bdcacae8-1622-11e9-2a5c-532679323890" -Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" -Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" -Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" -Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" -Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" -Singular = "bcd08a7b-43d2-5ff7-b6d4-c458787f915c" -StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" -Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" -msolve_jll = "6d01cc9a-e8f6-580e-8c54-544227e08205" - -[compat] -LinearAlgebra = "1.6" -Logging = "1.6" -LoopVectorization = "0.12" -Markdown = "1.6" -Nemo = "0.35.1, 0.36, 0.37, 0.38, 0.39" -Printf = "1.6" -Random = "1.6" -StaticArrays = "1" -Test = "1.6" -julia = "1.6" -msolve_jll = "0.6.3" diff --git a/src/connectcurves/AlgebraicSolving.jl-main/README.md b/src/connectcurves/AlgebraicSolving.jl-main/README.md deleted file mode 100644 index 5063df7..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/README.md +++ /dev/null @@ -1,22 +0,0 @@ -# AlgebraicSolving.jl - -A julia package for algebraically solving multivariate polynomial systems. - -## Installation -AlgebraicSolving requires Julia 1.6 or newer. In principle it can be installed and used -like any other Julia package: - -```julia -julia> using Pkg -julia> Pkg.add("AlgebraicSolving") -julia> using AlgebraicSolving -``` - -## Documentation and Examples - -You can find a detailed documentation including various examples at -https://algebraic-solving.github.io/ . - -# Funding - -The development of `AlgebraicSolving` is supported by the [Forschungsinitiative Rheinland-Pfalz](https://rptu.de/forschung/forschungsinitiative-rlp). diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/Project.toml b/src/connectcurves/AlgebraicSolving.jl-main/docs/Project.toml deleted file mode 100644 index ee69314..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/docs/Project.toml +++ /dev/null @@ -1,11 +0,0 @@ -[deps] -AlgebraicSolving= "66b61cbe-0446-4d5d-9090-1ff510639f9d" -LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" -Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" -msolve_jll = "6d01cc9a-e8f6-580e-8c54-544227e08205" -Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" -Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" - -[compat] -Documenter = "0.26" -msolve_jll = "0.6.1" diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/make.jl b/src/connectcurves/AlgebraicSolving.jl-main/docs/make.jl deleted file mode 100644 index ab996ee..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/docs/make.jl +++ /dev/null @@ -1,36 +0,0 @@ -using AlgebraicSolving -using Documenter - -push!(LOAD_PATH, "../src") - -DocMeta.setdocmeta!(AlgebraicSolving, :DocTestSetup, :(using AlgebraicSolving); recursive=true) - -# Build documentation. -# ==================== - -makedocs( - # options - modules = [AlgebraicSolving], - doctest = true, - clean = true, - checkdocs = :none, - sitename = "AlgebraicSolving.jl", - format = Documenter.HTML(), - pages = [ - "index.md", - "types.md", - "Algorithms" => ["groebner-bases.md", - "normal-forms.md", - "solvers.md"], - "Examples" => "katsura.md" - ] -) - -# Deploy built documentation from Travis. -# ======================================= - -deploydocs( - # options - repo = "github.com/algebraic-solving/AlgebraicSolving.jl.git", - target = "build", -) diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/groebner-bases.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/groebner-bases.md deleted file mode 100644 index 58792c0..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/groebner-bases.md +++ /dev/null @@ -1,65 +0,0 @@ -```@meta -CurrentModule = AlgebraicSolving -DocTestSetup = quote - using AlgebraicSolving -end -``` - -```@setup algebraicsolving -using AlgebraicSolving -``` - -```@contents -Pages = ["groebner-bases.md"] -``` - -# Gröbner bases - -## Introduction - -AlgebraicSolving allows to compute Gröbner bases for input generators over finite -fields of characteristic smaller $2^{31}$ w.r.t. the degree reverse -lexicographical monomial order. - -At the moment different variants of Faugère's F4 Algorithm are implemented as -well as a signature based algorithm to compute Gröbner bases. - -## Functionality - -```@docs - groebner_basis( - I::Ideal{T} where T <: MPolyRingElem; - initial_hts::Int=17, - nr_thrds::Int=1, - max_nr_pairs::Int=0, - la_option::Int=2, - eliminate::Int=0, - complete_reduction::Bool=true, - info_level::Int=0 - ) -``` - -The engine supports the elimination of one block of variables considering the -product monomial ordering of two blocks, both ordered w.r.t. the degree -reverse lexicographical order. One can either directly add the number of -variables of the first block via the `eliminate` parameter in the -`groebner_basis` call. We have also implemented an alias for this call: - -```@docs - eliminate( - I::Ideal{T} where T <: MPolyRingElem, - eliminate::Int; - initial_hts::Int=17, - nr_thrds::Int=1, - max_nr_pairs::Int=0, - la_option::Int=2, - complete_reduction::Bool=true, - info_level::Int=0 - ) -``` - -To compute signature Gröbner bases use - -```@docs - sig_groebner_basis(sys::Vector{T}; info_level::Int = 0, degbound::Int = 0) where {T <: MPolyRingElem} -``` diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/index.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/index.md deleted file mode 100644 index 4ae0cec..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/index.md +++ /dev/null @@ -1,23 +0,0 @@ -# Getting Started - -AlgebraicSolving is a computer algebra package for the Julia programming -language, maintained by Christian Eder and Mohab Safey El Din. - -- (Source code) - -The features of AlgebraicSolving include algorithms for computing -Gröbner bases over finite fields and for computing real solutions. -The main workhorse of AlgebraicSolving is the [msolve -library](https://msolve.lip6.fr/) . - -## Installation - -To use Nemo we require Julia 1.6 or higher. Please see - for instructions on -how to obtain julia for your system. - -At the Julia prompt simply type - -``` -julia> using Pkg; Pkg.add("AlgebraicSolving") -``` diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/katsura.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/katsura.md deleted file mode 100644 index fa72c56..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/katsura.md +++ /dev/null @@ -1,34 +0,0 @@ -```@meta -CurrentModule = AlgebraicSolving -DocTestSetup = quote - using AlgebraicSolving -end -``` - -```@setup algebraicsolving -using AlgebraicSolving -``` - -```@contents -Pages = ["katsura.md"] -``` - -# Examples - -Here we include some well-known example multivariate polynomial systems. - -## Katsura-n - -These systems appeared in a problem of magnetism in physics. -For a given $n$ `katsura(n)` has $2^n$ solutions and is defined in a -polynomial ring with $n+1$ variables. For a given polynomial ring `R` -with $n$ variables `katsura(R)` defines the corresponding system with -$2^{n-1}$ solutions. - -### Functionality - -```@docs - katsura(n::Int) - katsura(R::MPolyRing) -``` - diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/normal-forms.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/normal-forms.md deleted file mode 100644 index bf04482..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/normal-forms.md +++ /dev/null @@ -1,44 +0,0 @@ -```@meta -CurrentModule = AlgebraicSolving -DocTestSetup = quote - using AlgebraicSolving -end -``` - -```@setup algebraicsolving -using AlgebraicSolving -``` - -```@contents -Pages = ["normal-forms.md"] -``` - -# Normal forms - -## Introduction - -AlgebraicSolving allows to compute normal forms of a polynomial resp. a finite -array of polynomials w.r.t. some given ideal over a finite field of -characteristic smaller $2^{31}$ w.r.t. the degree reverse lexicographical -monomial order. - -**Note:** It therefore might first compute a Gröbner bases for the ideal. -## Functionality - -```@docs - normal_form( - f::T, - I::Ideal{T}; - nr_thrds::Int=1, - info_level::Int=0 - ) where T <: MPolyRingElem -``` - -```@docs - normal_form( - F::Vector{T}, - I::Ideal{T}; - nr_thrds::Int=1, - info_level::Int=0 - ) where T <: MPolyRingElem -``` diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/solvers.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/solvers.md deleted file mode 100644 index 0017986..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/solvers.md +++ /dev/null @@ -1,57 +0,0 @@ -```@meta -CurrentModule = AlgebraicSolving -DocTestSetup = quote - using AlgebraicSolving -end -``` - -```@setup algebraicsolving -using AlgebraicSolving -``` - -```@contents -Pages = ["solvers.md"] -``` - -# Algebraic Systems Solving - -## Introduction - -AlgebraicSolving allows to solve systems for input generators over finite -fields of characteristic smaller $2^{31}$ and over the rationals. - -The underlying engine is provided by msolve. - -## Functionality - -```@docs - rational_parametrization( - I::Ideal{T} where T <: MPolyRingElem; - initial_hts::Int=17, - nr_thrds::Int=1, - max_nr_pairs::Int=0, - la_option::Int=2, - info_level::Int=0, - precision::Int=32 - ) - - real_solutions( - I::Ideal{T} where T <: MPolyRingElem; - initial_hts::Int=17, - nr_thrds::Int=1, - max_nr_pairs::Int=0, - la_option::Int=2, - info_level::Int=0, - precision::Int=32 - ) - rational_solutions( - I::Ideal{T} where T <: MPolyRingElem; - initial_hts::Int=17, - nr_thrds::Int=1, - max_nr_pairs::Int=0, - la_option::Int=2, - info_level::Int=0, - precision::Int=32 - ) -``` - diff --git a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/types.md b/src/connectcurves/AlgebraicSolving.jl-main/docs/src/types.md deleted file mode 100644 index 80fcd90..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/docs/src/types.md +++ /dev/null @@ -1,53 +0,0 @@ -```@meta -CurrentModule = AlgebraicSolving -DocTestSetup = quote - using AlgebraicSolving -end -``` - -```@setup algebraicsolving -using AlgebraicSolving -``` - -```@contents -Pages = ["types.md"] -``` - -# Data Types - -## Introduction - -AlgebraicSolving handles ideals in multivariate polynomial rings over a prime -field of characteristic $0$ or $p$ where $p$ is a prime number $<2^{31}$. - -## Polynomial Rings - -We use [Nemo](https://www.nemocas.org/index.html)'s multivariate polynomial -ring structures: - -```@repl -using AlgebraicSolving -R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"], ordering=:degrevlex) -``` -The above example defines a multivariate polynomial ring in three variables `x`, -`y`, and `z` over the rationals using the dgree reverse lexicographical ordering -for printing polynomials in the following. One can also define polynomial rings -over finite fields: - -```@repl -using AlgebraicSolving -R, (x,y,z) = polynomial_ring(GF(101), ["x", "y", "z"], ordering=:degrevlex) -``` - -## Ideals - -Ideals can be constructed by giving an array of generators. Ideals cache varies -data structures connected to ideals in order to make computational algebra more -effective: - -```@repl -using AlgebraicSolving -R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"], ordering=:degrevlex) -I = Ideal([x+y+1, y*z^2-13*y^2]) -``` - diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/AlgebraicSolving.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/AlgebraicSolving.jl deleted file mode 100644 index 54ddc46..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/AlgebraicSolving.jl +++ /dev/null @@ -1,21 +0,0 @@ -module AlgebraicSolving - -greet() = print("AlgebraicSolving -- a package for algebraic solving based on msolve") - -#= io =# -include("imports.jl") -include("exports.jl") -#= types =# -include("types.jl") -#= functionality =# -include("interfaces/nemo.jl" ) -include("algorithms/groebner-bases.jl") -include("algorithms/normal-forms.jl") -include("algorithms/solvers.jl") -#= siggb =# -include("siggb/siggb.jl") -#= examples =# -include("examples/katsura.jl") -include("examples/cyclic.jl") - -end # module AlgebraicSolving diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/groebner-bases.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/groebner-bases.jl deleted file mode 100644 index 3d2f495..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/groebner-bases.jl +++ /dev/null @@ -1,184 +0,0 @@ -import msolve_jll: libneogb - -export groebner_basis, eliminate - -@doc Markdown.doc""" - eliminate(I::Ideal{T} where T <: MPolyRingElem, eliminate::Int, ) - -Compute a Groebner basis of the ideal `I` w.r.t. to the product monomial ordering defined by two blocks -w.r.t. the degree reverse lexicographical monomial ordering using Faugère's F4 algorithm. Hereby the first block includes -the first `eliminate` variables. - -At the moment the underlying algorithm is based on variants of Faugère's F4 Algorithm. - -**Note**: At the moment only ground fields of characteristic `p`, `p` prime, `p < 2^{31}` are supported. - -# Arguments -- `I::Ideal{T} where T <: MPolyRingElem`: input generators. -- `initial_hts::Int=17`: initial hash table size `log_2`. -- `nr_thrds::Int=1`: number of threads for parallel linear algebra. -- `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`. -- `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`). -- `complete_reduction::Bool=true`: compute a reduced Gröbner basis for `I` -- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). - -# Examples -```jldoctest -julia> using AlgebraicSolving - -julia> R, (x,y,z) = polynomial_ring(GF(101),["x","y","z"], ordering=:degrevlex) -(Multivariate polynomial ring in 3 variables over GF(101), FqMPolyRingElem[x, y, z]) - -julia> I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y]) -FqMPolyRingElem[x + 2*y + 2*z + 100, x^2 + 2*y^2 + 2*z^2 + 100*x, 2*x*y + 2*y*z + 100*y] - -julia> eliminate(I, 2) -1-element Vector{FqMPolyRingElem}: - z^4 + 38*z^3 + 95*z^2 + 95*z -``` -""" -function eliminate( - I::Ideal{T} where T <: MPolyRingElem, - eliminate::Int; - initial_hts::Int=17, - nr_thrds::Int=1, - max_nr_pairs::Int=0, - la_option::Int=2, - complete_reduction::Bool=true, - info_level::Int=0 - ) - if eliminate <= 0 - error("Number of variables to be eliminated is <= 0.") - else - return groebner_basis(I, initial_hts=initial_hts, nr_thrds=nr_thrds, - max_nr_pairs=max_nr_pairs, la_option=la_option, - eliminate=eliminate, - complete_reduction=complete_reduction, - info_level=info_level) - end -end - -@doc Markdown.doc""" - groebner_basis(I::Ideal{T} where T <: MPolyRingElem, ) - -Compute a Groebner basis of the ideal `I` w.r.t. to the degree reverse lexicographical monomial ordering using Faugère's F4 algorithm. -At the moment the underlying algorithm is based on variants of Faugère's F4 Algorithm. - -**Note**: At the moment only ground fields of characteristic `p`, `p` prime, `p < 2^{31}` are supported. - -# Arguments -- `I::Ideal{T} where T <: MPolyRingElem`: input generators. -- `initial_hts::Int=17`: initial hash table size `log_2`. -- `nr_thrds::Int=1`: number of threads for parallel linear algebra. -- `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`. -- `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`). -- `eliminate::Int=0`: size of first block of variables to be eliminated. -- `complete_reduction::Bool=true`: compute a reduced Gröbner basis for `I` -- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). - -# Examples -```jldoctest -julia> using AlgebraicSolving - -julia> R, (x,y,z) = polynomial_ring(GF(101),["x","y","z"], ordering=:degrevlex) -(Multivariate polynomial ring in 3 variables over GF(101), FqMPolyRingElem[x, y, z]) - -julia> I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y]) -FqMPolyRingElem[x + 2*y + 2*z + 100, x^2 + 2*y^2 + 2*z^2 + 100*x, 2*x*y + 2*y*z + 100*y] - -julia> groebner_basis(I) -4-element Vector{FqMPolyRingElem}: - x + 2*y + 2*z + 100 - y*z + 82*z^2 + 10*y + 40*z - y^2 + 60*z^2 + 20*y + 81*z - z^3 + 28*z^2 + 64*y + 13*z - -julia> groebner_basis(I, eliminate=2) -1-element Vector{FqMPolyRingElem}: - z^4 + 38*z^3 + 95*z^2 + 95*z -``` -""" -function groebner_basis( - I::Ideal{T} where T <: MPolyRingElem; - initial_hts::Int=17, - nr_thrds::Int=1, - max_nr_pairs::Int=0, - la_option::Int=2, - eliminate::Int=0, - complete_reduction::Bool=true, - info_level::Int=0 - ) - - return get!(I.gb, eliminate) do - _core_groebner_basis(I, initial_hts = initial_hts, nr_thrds = nr_thrds, - max_nr_pairs = max_nr_pairs, la_option = la_option, - eliminate = eliminate, - complete_reduction = complete_reduction, - info_level = info_level) - end -end - -function _core_groebner_basis( - I::Ideal{T} where T <: MPolyRingElem; - initial_hts::Int=17, - nr_thrds::Int=1, - max_nr_pairs::Int=0, - la_option::Int=2, - eliminate::Int=0, - complete_reduction::Bool=true, - info_level::Int=0 - ) - - F = I.gens - R = first(F).parent - if F == [R(0)] - return F - end - nr_vars = nvars(R) - nr_gens = length(F) - field_char = Int(characteristic(R)) - - mon_order = 0 - elim_block_size = eliminate - reduce_gb = Int(complete_reduction) - - # convert ideal to flattened arrays of ints - if !(is_probable_prime(field_char)) - error("At the moment we only supports finite fields.") - end - - lens, cfs, exps = _convert_to_msolve(F) - - gb_ld = Ref(Cint(0)) - gb_len = Ref(Ptr{Cint}(0)) - gb_exp = Ref(Ptr{Cint}(0)) - gb_cf = Ref(Ptr{Cvoid}(0)) - - nr_terms = ccall((:export_f4, libneogb), Int, - (Ptr{Nothing}, Ptr{Cint}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cvoid}}, - Ptr{Cint}, Ptr{Cint}, Ptr{Cvoid}, Cint, Cint, Cint, Cint, Cint, Cint, - Cint, Cint, Cint, Cint, Cint, Cint, Cint), - cglobal(:jl_malloc), gb_ld, gb_len, gb_exp, gb_cf, lens, exps, cfs, - field_char, mon_order, elim_block_size, nr_vars, nr_gens, initial_hts, - nr_thrds, max_nr_pairs, 0, la_option, reduce_gb, 0, info_level) - - # convert to julia array, also give memory management to julia - jl_ld = gb_ld[] - jl_len = Base.unsafe_wrap(Array, gb_len[], jl_ld) - jl_exp = Base.unsafe_wrap(Array, gb_exp[], nr_terms*nr_vars) - ptr = reinterpret(Ptr{Int32}, gb_cf[]) - jl_cf = Base.unsafe_wrap(Array, ptr, nr_terms) - - basis = _convert_finite_field_array_to_abstract_algebra( - jl_ld, jl_len, jl_cf, jl_exp, R, eliminate) - - - ccall((:free_f4_julia_result_data, libneogb), Nothing , - (Ptr{Nothing}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}}, - Ptr{Ptr{Cvoid}}, Int, Int), - cglobal(:jl_free), gb_len, gb_exp, gb_cf, jl_ld, field_char) - - I.gb[eliminate] = basis - - return basis -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/normal-forms.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/normal-forms.jl deleted file mode 100644 index 36a7913..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/normal-forms.jl +++ /dev/null @@ -1,174 +0,0 @@ -import msolve_jll: libneogb - -export normal_form - -@doc Markdown.doc""" - normal_form( - f::T, - I::Ideal{T}; - nr_thrds::Int=1, - info_level::Int=0 - ) where T <: MPolyRingElem - -Compute the normal forms of the elements of `F` w.r.t. a degree reverse -lexicographical Gröbner basis of `I`. - -**Note:** If `I` has not already cached a degree reverse lexicographical -Gröbner basis, then this one is first computed. - -# Arguments -- `F::Vector{T} where T <: MPolyRingElem`: elements to be reduced. -- `I::Ideal{T} where T <: MPolyRingElem`: ideal data to reduce with. -- `nr_thrds::Int=1`: number of threads for parallel linear algebra. -- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). - -# Examples -```jldoctest -julia> using AlgebraicSolving - -julia> R, (x,y) = polynomial_ring(GF(101),["x","y"]) -(Multivariate polynomial ring in 2 variables over GF(101), FqMPolyRingElem[x, y]) - -julia> I = Ideal([y*x^3+12-y, x+y]) -FqMPolyRingElem[x^3*y + 100*y + 12, x + y] - -julia> f = 2*x^2+7*x*y -2*x^2 + 7*x*y - -julia> normal_form(f, I) -96*y^2 -``` -""" -function normal_form( - f::T, - I::Ideal{T}; - nr_thrds::Int=1, - info_level::Int=0 - ) where T <: MPolyRingElem - nf = _core_normal_form([f], I; nr_thrds, info_level) - return nf[1] -end - -@doc Markdown.doc""" - normal_form( - F::Vector{T}, - I::Ideal{T}; - nr_thrds::Int=1, - info_level::Int=0 - ) where T <: MPolyRingElem - -Compute the normal forms of the elements of `F` w.r.t. a degree reverse -lexicographical Gröbner basis of `I`. - -**Note:** If `I` has not already cached a degree reverse lexicographical -Gröbner basis, then this one is first computed. - -# Arguments -- `F::Vector{T} where T <: MPolyRingElem`: elements to be reduced. -- `I::Ideal{T} where T <: MPolyRingElem`: ideal data to reduce with. -- `nr_thrds::Int=1`: number of threads for parallel linear algebra. -- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). - -# Examples -```jldoctest -julia> using AlgebraicSolving - -julia> R, (x,y) = polynomial_ring(GF(101),["x","y"]) -(Multivariate polynomial ring in 2 variables over GF(101), FqMPolyRingElem[x, y]) - -julia> I = Ideal([y*x^3+12-y, x+y]) -FqMPolyRingElem[x^3*y + 100*y + 12, x + y] - -julia> F = [2*x^2+7*x*y, x+y] -2-element Vector{FqMPolyRingElem}: - 2*x^2 + 7*x*y - x + y - -julia> normal_form(F,I) -2-element Vector{FqMPolyRingElem}: - 96*y^2 - 0 -``` -""" -function normal_form( - F::Vector{T}, - I::Ideal{T}; - nr_thrds::Int=1, - info_level::Int=0 - ) where T <: MPolyRingElem - return _core_normal_form(F, I; nr_thrds, info_level) -end - -function _core_normal_form( - F::Vector{T}, - I::Ideal{T}; - nr_thrds::Int=1, - info_level::Int=0 - ) where T <: MPolyRingElem - - - if (length(F) == 0 || length(I.gens) == 0) - error("Input data not valid.") - end - - R = first(F).parent - nr_vars = nvars(R) - field_char = Int(characteristic(R)) - - if !(is_probable_prime(field_char)) - error("At the moment we only supports finite fields.") - end - - #= first get a degree reverse lexicographical Gröbner basis for I =# - if !haskey(I.gb, 0) - if field_char > 2^17 - groebner_basis(I, eliminate = 0, la_option = 44, info_level = info_level) - else - groebner_basis(I, eliminate = 0, la_option = 2, info_level = info_level) - end - end - G = I.gb[0] - - if G == [R(0)] - return F - end - - tbr_nr_gens = length(F) - bs_nr_gens = length(G) - is_gb = 1 - - # convert ideal to flattened arrays of ints - tbr_lens, tbr_cfs, tbr_exps = _convert_to_msolve(F) - bs_lens, bs_cfs, bs_exps = _convert_to_msolve(G) - - nf_ld = Ref(Cint(0)) - nf_len = Ref(Ptr{Cint}(0)) - nf_exp = Ref(Ptr{Cint}(0)) - nf_cf = Ref(Ptr{Cvoid}(0)) - - nr_terms = ccall((:export_nf, libneogb), Int, - (Ptr{Nothing}, Ptr{Cint}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cvoid}}, - Cint, Ptr{Cint}, Ptr{Cint}, Ptr{Cvoid}, Cint, Ptr{Cint}, Ptr{Cint}, Ptr{Cvoid}, - Cint, Cint, Cint, Cint, Cint, Cint, Cint), - cglobal(:jl_malloc), nf_ld, nf_len, nf_exp, nf_cf, tbr_nr_gens, tbr_lens, tbr_exps, - tbr_cfs, bs_nr_gens, bs_lens, bs_exps, bs_cfs, field_char, 0, 0, nr_vars, is_gb, - nr_thrds, info_level) - - # convert to julia array, also give memory management to julia - jl_ld = nf_ld[] - jl_len = Base.unsafe_wrap(Array, nf_len[], jl_ld) - jl_exp = Base.unsafe_wrap(Array, nf_exp[], nr_terms*nr_vars) - ptr = reinterpret(Ptr{Int32}, nf_cf[]) - jl_cf = Base.unsafe_wrap(Array, ptr, nr_terms) - - basis = _convert_finite_field_array_to_abstract_algebra( - jl_ld, jl_len, jl_cf, jl_exp, R, 0) - - ccall((:free_f4_julia_result_data, libneogb), Nothing , - (Ptr{Nothing}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cint}}, - Ptr{Ptr{Cvoid}}, Int, Int), - cglobal(:jl_free), nf_len, nf_exp, nf_cf, jl_ld, field_char) - - return basis -end - diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl deleted file mode 100644 index 5051541..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/algorithms/solvers.jl +++ /dev/null @@ -1,435 +0,0 @@ -import msolve_jll: libmsolve - -export inter_solutions, real_solutions, rational_solutions, rational_parametrization - -@doc Markdown.doc""" - _get_rational_parametrization(nr::Int32, lens::Vector{Int32}, cfs::Ptr{BigInt}) - -Construct the rational parametrization of the solution set computed via msolve. - -**Note**: This is an internal function and should only be used inside `msolve()`. -""" -function _get_rational_parametrization( - nr::Int32, - lens::Vector{Int32}, - cfs::Ptr{BigInt}, - cfs_lf::Ptr{BigInt}, - nr_vars::Int32 - ) - if cfs_lf != Ptr{BigInt}(0) - lf = [ZZRingElem(unsafe_load(cfs_lf, i)) for i in 1:nr_vars] - else - lf = ZZRingElem[] - end - C, x = polynomial_ring(QQ,"x") - ctr = 0 - - elim = C([unsafe_load(cfs, i) for i in 1:lens[1]]) - ctr += lens[1] - - denom = C([unsafe_load(cfs, i+ctr) for i in 1:lens[2]]) - ctr += lens[2] - - size = nr-2 - p = Vector{PolyRingElem}(undef, size) - k = 1 - for i in 3:nr - p[k] = C([unsafe_load(cfs, j+ctr) for j in 1:lens[i]-1]) - # multiply parametrization polynomial directly with - # corresponding coefficients - p[k] *= (-1) * ZZRingElem(unsafe_load(cfs, lens[i]+ctr)) - ctr += lens[i] - k += 1 - end - - return lf, elim, denom, p -end - -@doc Markdown.doc""" - _core_msolve(I::Ideal{T} where T <: MPolyRingElem, ) - -Compute a rational parametrization and the real solutions of the ideal `I` via msolve. - -**Note**: This is an internal function. -""" -function _core_msolve( - I::Ideal{T} where T <: MPolyRingElem; # input generators - initial_hts::Int=17, # hash table size, default 2^17 - nr_thrds::Int=1, # number of threads - max_nr_pairs::Int=0, # number of pairs maximally chosen - # in symbolic preprocessing - la_option::Int=2, # linear algebra option - info_level::Int=0, # info level for print outs - precision::Int=32 # precision of the solution set - ) - - F = I.gens - R = first(F).parent - nr_vars = nvars(R) - nr_gens = length(F) - field_char = Int(characteristic(R)) - - variable_names = map(string, R.S) - - #= add new variables and linear forms, =# - genericity_handling = 2 - - reset_ht = 0 - print_gb = 0 - get_param = 1 - - mon_order = 0 - elim_block_size = 0 - use_signatures = 0 - - if field_char != 0 - error("At the moment we only support the rationals as ground field.") - end - # convert Singular ideal to flattened arrays of ints - lens, cfs, exps = _convert_to_msolve(F) - - res_ld = Ref(Cint(0)) - res_nr_vars = Ref(Cint(0)) - res_dim = Ref(Cint(0)) - res_dquot = Ref(Cint(0)) - nb_sols = Ref(Cint(0)) - res_len = Ref(Ptr{Cint}(0)) - res_vnames = Ref(Ptr{Ptr{Cchar}}(0)) - res_cf_lf = Ref(Ptr{Cvoid}(0)) - res_cf = Ref(Ptr{Cvoid}(0)) - sols_num = Ref(Ptr{Cvoid}(0)) - sols_den = Ref(Ptr{Cint}(0)) - - ccall((:msolve_julia, libmsolve), Cvoid, - (Ptr{Nothing}, Ptr{Cint}, Ptr{Cint}, Ptr{Cint}, Ptr{Cint}, Ptr{Ptr{Cint}}, - Ptr{Ptr{Ptr{Cchar}}}, Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cint}, Ptr{Cvoid}, Ptr{Ptr{Cint}}, Ptr{Cint}, - Ptr{Cint}, Ptr{Cvoid}, Ptr{Ptr{Cchar}}, Ptr{Cchar}, Cint, Cint, - Cint, Cint, Cint, Cint, Cint, Cint, Cint, Cint, Cint, Cint, Cint, - Cint, Cint, Cint), - cglobal(:jl_malloc), res_ld, res_nr_vars, res_dim, res_dquot, res_len, res_vnames, - res_cf_lf, res_cf, - nb_sols, sols_num, sols_den, lens, exps, cfs, variable_names, - "/dev/null", field_char, mon_order, elim_block_size, nr_vars, - nr_gens, initial_hts, nr_thrds, max_nr_pairs, reset_ht, la_option, - use_signatures, print_gb, get_param, genericity_handling, precision, - info_level) - # convert to julia array, also give memory management to julia - jl_ld = res_ld[] - jl_rp_nr_vars = res_nr_vars[] - jl_dim = res_dim[] - jl_dquot = res_dquot[] - jl_nb_sols = nb_sols[] - - # set dimension - I.dim = jl_dim - if jl_dim > 0 - error("Dimension of ideal is greater than zero, no solutions provided.") - end - - # get rational parametrization - jl_len = Base.unsafe_wrap(Array, res_len[], jl_ld) - nterms = 0 - - if jl_dquot == 0 - C,x = polynomial_ring(QQ,"x") - I.rat_param = RationalParametrization(Symbol[], ZZRingElem[], C(-1), C(-1), PolyRingElem[]) - I.real_sols = QQFieldElem[] - return I.rat_param, I.real_sols - end - [nterms += jl_len[i] for i=1:jl_ld] - jl_cf = reinterpret(Ptr{BigInt}, res_cf[]) - jl_cf_lf = reinterpret(Ptr{BigInt}, res_cf_lf[]) - - jl_vnames = Base.unsafe_wrap(Array, res_vnames[], jl_rp_nr_vars) - - vsymbols = [Symbol(unsafe_string(jl_vnames[i])) for i in 1:jl_rp_nr_vars] - #= get possible variable permutation =# - perm = sortperm(vsymbols[1:nr_vars]) - - rat_param = _get_rational_parametrization(jl_ld, jl_len, - jl_cf, jl_cf_lf, jl_rp_nr_vars) - - I.rat_param = RationalParametrization(vsymbols, rat_param[1],rat_param[2], - rat_param[3], rat_param[4]) - if jl_nb_sols == 0 - I.real_sols = QQFieldElem[] - I.inter_sols = QQFieldElem[] - return rat_param, Vector{QQFieldElem}[] - end - - # get solutions - jl_sols_num = reinterpret(Ptr{BigInt}, sols_num[]) - jl_sols_den = reinterpret(Ptr{Int32}, sols_den[]) - # elseif is_prime(field_char) - # jl_cf = reinterpret(Ptr{Int32}, res_cf[]) - # jl_sols_num = reinterpret(Ptr{Int32}, sols_num[]) - # end - - #= solutions are returned as intervals, i.e. a minimum and a maximum entry for - = the numerator and denominator; thus we sum up and divide by 2 =# - - inter_solutions = Vector{Vector{Vector{QQFieldElem}}}(undef, jl_nb_sols) - solutions = Vector{Vector{QQFieldElem}}(undef, jl_nb_sols) - - len = 2*jl_nb_sols*nr_vars - i = 1 - k = 1 - while i <= len - j = 1 - inter_tmp = Vector{Vector{QQFieldElem}}(undef, nr_vars) - tmp = Vector{QQFieldElem}(undef, nr_vars) - while j <= nr_vars - inter_tmp_coeff = Vector{QQFieldElem}(undef, 2) - inter_tmp_coeff[1] = QQFieldElem(unsafe_load(jl_sols_num, i)) >> Int64(unsafe_load(jl_sols_den, i)) - inter_tmp_coeff[2] = QQFieldElem(unsafe_load(jl_sols_num, i+1)) >> Int64(unsafe_load(jl_sols_den, i+1)) - inter_tmp[perm[j]] = inter_tmp_coeff - tmp[perm[j]] = sum(inter_tmp_coeff) >> 1 - i += 2 - j += 1 - end - inter_solutions[k] = inter_tmp - solutions[k] = tmp - k += 1 - end - I.inter_sols = inter_solutions - I.real_sols = solutions - - ccall((:free_msolve_julia_result_data, libmsolve), Nothing , - (Ptr{Nothing}, Ptr{Ptr{Cint}}, Ptr{Ptr{Cvoid}}, - Ptr{Ptr{Cvoid}}, Ptr{Ptr{Cint}}, Cint, Cint, Cint), - cglobal(:jl_free), res_len, res_cf, sols_num, sols_den, - jl_ld, jl_nb_sols, field_char) - - return rat_param, solutions -end - -@doc Markdown.doc""" - rational_parametrization(I::Ideal{T} where T <: MPolyRingElem, ) - -Given an ideal `I` with a finite solution set over the complex numbers, return -the rational parametrization of the ideal with a given precision (default 32 bits). - -**Note**: At the moment only QQ is supported as ground field. If the dimension of the ideal -is greater then zero an empty array is returned. - -# Arguments -- `I::Ideal{T} where T <: MPolyRingElem`: input generators. -- `initial_hts::Int=17`: initial hash table size `log_2`. -- `nr_thrds::Int=1`: number of threads for parallel linear algebra. -- `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`. -- `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`). -- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). -- `precision::Int=32`: bit precision for the computed solutions. - -# Examples -```jldoctest -julia> using AlgebraicSolving - -julia> R,(x1,x2,x3) = polynomial_ring(QQ, ["x1","x2","x3"]) -(Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x1, x2, x3]) - -julia> I = Ideal([x1+2*x2+2*x3-1, x1^2+2*x2^2+2*x3^2-x1, 2*x1*x2+2*x2*x3-x2]) -QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2] - -julia> rational_parametrization(I) -AlgebraicSolving.RationalParametrization([:x1, :x2, :x3], ZZRingElem[], 84*x^4 - 40*x^3 + x^2 + x, 336*x^3 - 120*x^2 + 2*x + 1, AbstractAlgebra.PolyRingElem[184*x^3 - 80*x^2 + 4*x + 1, 36*x^3 - 18*x^2 + 2*x]) -``` -""" -function rational_parametrization( - I::Ideal{T} where T <: MPolyRingElem; # input generators - initial_hts::Int=17, # hash table size, default 2^17 - nr_thrds::Int=1, # number of threads - max_nr_pairs::Int=0, # number of pairs maximally chosen - # in symbolic preprocessing - la_option::Int=2, # linear algebra option - info_level::Int=0, # info level for print outs - precision::Int=32 # precision of the solution set - ) - - isdefined(I, :rat_param) || - _core_msolve(I, - initial_hts = initial_hts, - nr_thrds = nr_thrds, - max_nr_pairs = max_nr_pairs, - la_option = la_option, - info_level = info_level, - precision = precision) - - return I.rat_param -end - - -@doc Markdown.doc""" - rational_solutions(I::Ideal{T} where T <: MPolyRingElem, ) - -Given an ideal `I` with a finite solution set over the complex numbers, return -the rational roots of the ideal. - -# Arguments -- `I::Ideal{T} where T <: MPolyRingElem`: input generators. -- `initial_hts::Int=17`: initial hash table size `log_2`. -- `nr_thrds::Int=1`: number of threads for parallel linear algebra. -- `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`. -- `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`). -- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). -- `precision::Int=32`: bit precision for the computed solutions. - -# Examples -```jldoctest -julia> using AlgebraicSolving - -julia> R,(x1,x2,x3) = polynomial_ring(QQ, ["x1","x2","x3"]) -(Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x1, x2, x3]) - -julia> I = Ideal([x1+2*x2+2*x3-1, x1^2+2*x2^2+2*x3^2-x1, 2*x1*x2+2*x2*x3-x2]) -QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2] - -julia> rat_sols = rational_solutions(I) -2-element Vector{Vector{QQFieldElem}}: - [1, 0, 0] - [1//3, 0, 1//3] - -julia> map(r->map(p->evaluate(p, r), I.gens), rat_sols) -2-element Vector{Vector{QQFieldElem}}: - [0, 0, 0] - [0, 0, 0] -``` -""" -function rational_solutions( - I::Ideal{T} where T <: MPolyRingElem; # input generators - initial_hts::Int=17, # hash table size, default 2^17 - nr_thrds::Int=1, # number of threads - max_nr_pairs::Int=0, # number of pairs maximally chosen - # in symbolic preprocessing - la_option::Int=2, # linear algebra option - info_level::Int=0, # info level for print outs - precision::Int=32 # precision of the solution set - ) - isdefined(I, :rat_param) || - _core_msolve(I, - initial_hts = initial_hts, - nr_thrds = nr_thrds, - max_nr_pairs = max_nr_pairs, - la_option = la_option, - info_level = info_level, - precision = precision) - param_t = I.rat_param - - nvars = length(param_t.vars) - lpol = filter(l->degree(l) == 1, keys(factor(param_t.elim).fac)) - nb = length(lpol) - - rat_elim = [-coeff(l, 0)// coeff(l, 1) for l in lpol] - rat_den = map(l->evaluate(param_t.denom, l), rat_elim) - rat_num = map(r->map(l->evaluate(l, r), param_t.param), rat_elim) - - rat_sols = Vector{Vector{QQFieldElem}}(undef, nb) - - if length(param_t.vars) == parent(I).nvars - - for i in 1:nb - rat_sols[i] = Vector{QQFieldElem}(undef, nvars) - for j in 1:(nvars-1) - rat_sols[i][j] = rat_num[i][j] // rat_den[i] - end - rat_sols[i][nvars] = rat_elim[i] - end - - else - - for i in 1:nb - rat_sols[i] = Vector{QQFieldElem}(undef, nvars - 1) - for j in 1:(nvars-1) - rat_sols[i][j] = rat_num[i][j] // rat_den[i] - end - end - - end - - I.rat_sols = rat_sols - - return I.rat_sols -end - - -@doc Markdown.doc""" - real_solutions(I::Ideal{T} where T <: MPolyRingElem, ) - -Given an ideal `I` with a finite solution set over the complex numbers, return -the real roots of the ideal with a given precision (default 32 bits). - -**Note**: At the moment only QQ is supported as ground field. If the dimension of the ideal -is greater than zero an empty array is returned. - -# Arguments -- `I::Ideal{T} where T <: MPolyRingElem`: input generators. -- `initial_hts::Int=17`: initial hash table size `log_2`. -- `nr_thrds::Int=1`: number of threads for parallel linear algebra. -- `max_nr_pairs::Int=0`: maximal number of pairs per matrix, only bounded by minimal degree if `0`. -- `la_option::Int=2`: linear algebra option: exact sparse-dense (`1`), exact sparse (`2`, default), probabilistic sparse-dense (`42`), probabilistic sparse(`44`). -- `info_level::Int=0`: info level printout: off (`0`, default), summary (`1`), detailed (`2`). -- `precision::Int=32`: bit precision for the computed solutions. - -# Examples -```jldoctest -julia> using AlgebraicSolving - -julia> R,(x1,x2,x3) = polynomial_ring(QQ, ["x1","x2","x3"]) -(Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x1, x2, x3]) - -julia> I = Ideal([x1+2*x2+2*x3-1, x1^2+2*x2^2+2*x3^2-x1, 2*x1*x2+2*x2*x3-x2]) -QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2] - -julia> real_solutions(I) -4-element Vector{Vector{QQFieldElem}}: - [5416829397//8589934592, 2708414699//8589934592, -2844258330290649520990905062759917788583//21778071482940061661655974875633165533184] - [1, 0, 0] - [1945971683//8589934592, 972985841//8589934592, 744426424910260862653434112767010536665//2722258935367507707706996859454145691648] - [2863311531//8589934592, 0, 3629678580490010276942662479272194255531//10889035741470030830827987437816582766592] -``` -""" -function real_solutions( - I::Ideal{T} where T <: MPolyRingElem; # input generators - initial_hts::Int=17, # hash table size, default 2^17 - nr_thrds::Int=1, # number of threads - max_nr_pairs::Int=0, # number of pairs maximally chosen - # in symbolic preprocessing - la_option::Int=2, # linear algebra option - info_level::Int=0, # info level for print outs - precision::Int=32 # precision of the solution set - ) - - isdefined(I, :real_sols) || - _core_msolve(I, - initial_hts = initial_hts, - nr_thrds = nr_thrds, - max_nr_pairs = max_nr_pairs, - la_option = la_option, - info_level = info_level, - precision = precision) - - return I.real_sols -end - -function inter_solutions( - I::Ideal{T} where T <: MPolyRingElem; # input generators - initial_hts::Int=17, # hash table size, default 2^17 - nr_thrds::Int=1, # number of threads - max_nr_pairs::Int=0, # number of pairs maximally chosen - # in symbolic preprocessing - la_option::Int=2, # linear algebra option - info_level::Int=0, # info level for print outs - precision::Int=32 # precision of the solution set - ) - - isdefined(I, :inter_sols) || - _core_msolve(I, - initial_hts = initial_hts, - nr_thrds = nr_thrds, - max_nr_pairs = max_nr_pairs, - la_option = la_option, - info_level = info_level, - precision = precision) - - return I.inter_sols -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/examples/cyclic.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/examples/cyclic.jl deleted file mode 100644 index 10c539c..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/examples/cyclic.jl +++ /dev/null @@ -1,23 +0,0 @@ -@doc Markdown.doc""" - cyclic(R::MPolyRing) - -Return the Cyclic ideal in the variables of `R`. - -# Example -```jldoctest -julia> using AlgebraicSolving - -julia> R, vars = polynomial_ring(QQ, ["x$i" for i in 1:4]) -(Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x1, x2, x3, x4]) - -julia> cyclic(R) -QQMPolyRingElem[x1 + x2 + x3 + x4, x1*x2 + x1*x4 + x2*x3 + x3*x4, x1*x2*x3 + x1*x2*x4 + x1*x3*x4 + x2*x3*x4, x1*x2*x3*x4 - 1] -``` -""" -function cyclic(R::MPolyRing) - vars = gens(R) - n = length(vars) - pols = [sum(prod(vars[j%n+1] for j in k:k+i) for k in 1:n) for i in 0:n-2] - push!(pols, prod(vars[i] for i in 1:n)-1) - return Ideal(pols) -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/examples/katsura.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/examples/katsura.jl deleted file mode 100644 index 07b6d0a..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/examples/katsura.jl +++ /dev/null @@ -1,90 +0,0 @@ -export katsura - -function _get_katsura_exponent(n::Int, m::Int, l::Int) - e = zeros(Int, n + 1) - if abs(l) == abs(m - l) - e[abs(l) + 1] = 2 - else - e[abs(l) + 1] = 1 - e[abs(m - l) + 1] = 1 - end - - return e -end - -@doc Markdown.doc""" - katsura(n::Int) - -Given a natural number `n` returns the Katsura ideal generated by -$u_m - \sum_{l=n}^n u_{l-m} u_l$, $1 - \sum_{l = -n}^n u_l$ -where $u_{-i} = u_i$, and $u_i = 0$ for $i > n$ and $m \in \{-n, \ldots, n\}$. -Also note that indices have been shifted to start from 1. - -# Example -```jldoctest -julia> using AlgebraicSolving - -julia> katsura(2) -QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 + 2*x2^2 + 2*x3^2 - x1, 2*x1*x2 + 2*x2*x3 - x2] -``` -""" -function katsura(log_solutions::Int, characteristic::Int=0) - if characteristic == 0 - R, _ = polynomial_ring(QQ, log_solutions + 1, ordering=:degrevlex) - elseif is_probable_prime(characteristic) - R, _ = polynomial_ring(GF(characteristic), log_solutions + 1, ordering=:degrevlex) - else - error("We only support finite fields or QQ as ground fields.") - end - - return katsura(R) -end - -@doc Markdown.doc""" - katsura(R::MPolyRing) - -Returns the Katsura ideal in the given polynomial ring `R`. - -# Example -```jldoctest -julia> using AlgebraicSolving - -julia> R, _ = QQ["x", "y", "z"] -(Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z]) - -julia> katsura(R) -QQMPolyRingElem[x + 2*y + 2*z - 1, x^2 - x + 2*y^2 + 2*z^2, 2*x*y + 2*y*z - y] -``` -""" -function katsura(R::MPolyRing) - CR = base_ring(R) - polys = elem_type(R)[] - n = nvars(R) - 1 - coeffs_vec = 2 * fill(CR(1), n + 1) - coeffs_vec[1] = CR(1) - mono_exps = Matrix(1I, n+1, n+1) - #= mono_exps = Matrix{Int}(identity_matrix(ZZ, n + 1)) =# - linear_poly = R(coeffs_vec, [mono_exps[:, i] for i in 1:n+1]) - linear_poly -= R(1) - push!(polys, linear_poly) - - for m in 0:n - 1 - polynomial = MPolyBuildCtx(R) - for l in -n:n - if abs(l) > n || abs(m - l) > n - continue - end - e = _get_katsura_exponent(n, m, l) - push_term!(polynomial, CR(1), e) - end - - e = zeros(Int, n + 1) - e[abs(m) + 1] = 1 - push_term!(polynomial, CR(-1), e) - poly = finish(polynomial) - push!(polys, poly) - end - - return Ideal(polys) -end - diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/exports.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/exports.jl deleted file mode 100644 index 9346798..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/exports.jl +++ /dev/null @@ -1,4 +0,0 @@ -export polynomial_ring, MPolyRing, GFElem, MPolyRingElem, finite_field, GF, fpMPolyRingElem, - characteristic, degree, ZZ, QQ, vars, nvars, ngens, ZZRingElem, QQFieldElem, QQMPolyRingElem, - base_ring, coefficient_ring, evaluate, prime_field, sig_groebner_basis, cyclic, leading_coefficient, - FqMPolyRingElem, derivative diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/imports.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/imports.jl deleted file mode 100644 index ccf335a..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/imports.jl +++ /dev/null @@ -1,61 +0,0 @@ -using Markdown -using Test -using msolve_jll -using Nemo -using LinearAlgebra -using StaticArrays -using LoopVectorization - -import Random: MersenneTwister -import Logging: ConsoleLogger, with_logger, Warn, Info -import Printf: @sprintf - -import Nemo: - bell, - binomial, - degree, - denominator, - divexact, - divides, - divisor_sigma, - euler_phi, - evaluate, - factorial, - fibonacci, - fits, - fpMPolyRingElem, - fqPolyRepFieldElem, - fraction_field, - GF, - height, - is_prime, - is_probable_prime, - is_square, - is_unit, - isqrtrem, - jacobi_symbol, - leading_coefficient, - matrix_space, - moebius_mu, - MPolyRing, - MPolyRingElem, - number_of_partitions, - numerator, - polynomial_ring, - PolyRing, - PolyRingElem, - prime_field, - primorial, - QQ, - QQField, - QQFieldElem, - QQMatrix, - QQMPolyRingElem, - rising_factorial, - root, - unit, - vars, - ZZ, - ZZMatrix, - ZZRing, - ZZRingElem diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/interfaces/nemo.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/interfaces/nemo.jl deleted file mode 100644 index 1078047..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/interfaces/nemo.jl +++ /dev/null @@ -1,118 +0,0 @@ - -@doc Markdown.doc""" - _convert_to_msolve( - F::Vector{T}) where T <: MPolyRingElem - -Convert a vector of polynomials to input data for msolve. - -**Note**: This is an internal function. -""" -function _convert_to_msolve( - F::Vector{T}) where T <: MPolyRingElem - - R = parent(first(F)) - - nr_vars = nvars(R) - nr_gens = length(F) - lens = Int32[length(F[i]) for i in 1:nr_gens] - nr_terms = sum(lens) - field_char = characteristic(R) - - if field_char > 2^31 || degree(base_ring(R)) != 1 - error("At the moment we only support prime fields up to prime characteristic < 2^31.") - end - # get coefficients - if field_char == 0 - cfs = BigInt[] - else - cfs = Int32[] - end - if field_char == 0 - for i in 1:nr_gens - for cf in coefficients(F[i]) - push!(cfs, BigInt(numerator(cf))) - push!(cfs, BigInt(denominator(cf))) - end - end - else - for i in 1:nr_gens - for cf in coefficients(F[i]) - push!(cfs, Int32(lift(Nemo.ZZ, cf))) - end - end - end - - # get exponent vectors - exps = Int32[] - for i in 1:nr_gens - for ev in exponent_vectors(F[i]) - append!(exps, convert(Vector{Int32}, ev)) - end - end - - return lens, cfs, exps -end - -@doc Markdown.doc""" - _convert_finite_field_gb_to_abstract_algebra( - bld::Int32, - blen::Vector{Int32}, - bcf::Vector{Int32}, - bexp::Vector{Int32}, - R::MPolyRing, - eliminate::Int=0 - ) - -Converts a finite Gröbner basis computed internally via msolve -to a vector of polynomials. - -**Note**: This is an internal function. -""" -function _convert_finite_field_array_to_abstract_algebra( - bld::Int32, - blen::Vector{Int32}, - bcf::Vector{Int32}, - bexp::Vector{Int32}, - R::MPolyRing, - eliminate::Int=0 - ) - - if characteristic(R) == 0 - error("At the moment we only support finite fields.") - end - - nr_gens = bld - nr_vars = nvars(R) - CR = coefficient_ring(R) - - basis = (typeof(R(0)))[] - #= basis = Vector{MPolyRingElem}(undef, bld) =# - - len = 0 - - if eliminate > 0 - z = zeros(Int, eliminate) - end - for i in 1:nr_gens - #= check if element is part of the eliminated basis =# - if eliminate > 0 - cmp = convert(Vector{Int}, bexp[(len)*nr_vars+1:(len+1)*nr_vars]) - if cmp[1:eliminate] > z - continue - end - end - g = MPolyBuildCtx(R) - if bcf[len+1] == 0 - g.poly = R(0) - else - for j in 1:blen[i] - push_term!(g, CR(bcf[len+j]), - convert(Vector{Int}, bexp[(len+j-1)*nr_vars+1:(len+j)*nr_vars])) - end - end - len += blen[i] - push!(basis, g.poly) - end - - return basis -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/hashtable.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/hashtable.jl deleted file mode 100644 index 3f9d955..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/hashtable.jl +++ /dev/null @@ -1,472 +0,0 @@ -# TAKEN AND ADJUSTED FROM GROEBNER.JL BY ALEXANDER DEMIN -# MIT License - -# Copyright (c) 2022 Alexander Demin - -# Permission is hereby granted, free of charge, to any person obtaining a copy -# of this software and associated documentation files (the "Software"), to deal -# in the Software without restriction, including without limitation the rights -# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -# copies of the Software, and to permit persons to whom the Software is -# furnished to do so, subject to the following conditions: - -# The above copyright notice and this permission notice shall be included in all -# copies or substantial portions of the Software. - -# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -# SOFTWARE. - -mutable struct Hashvalue - hash::MonHash - divmask::DivMask -end - -function copy_hashvalue(x::Hashvalue) - Hashvalue(x.hash, x.divmask) -end - -# Hashtable designed to store monomials -mutable struct MonomialHashtable{N} - exponents::Vector{Monomial{N}} - - # for buffering exponent vectors during certain operations - buffer::MVector{N, Exp} - - # maps exponent hash to its position in exponents array - hashtable::Vector{MonIdx} - - # stores hashes, division masks, - # and other valuable info - # for each hashtable enrty - hashdata::Vector{Hashvalue} - - #= Monom divisibility =# - # divisor map to check divisibility faster - divmap::Vector{UInt32} - # bits per div variable - ndivbits::Int - - size::Int - # elements added - load::Int -end - -#------------------------------------------------------------------------------ - -# Returns the next look-up position in the table -function nexthashindex(h::MonHash, j::MonHash, mod::MonHash) - (h + j) & mod + MonHash(1) -end - -#------------------------------------------------------------------------------ - -# initialize and set fields for basis hashtable -function initialize_basis_hash_table(::Val{N}) where N - - # for now at most 32 variables - if N > 32 - error("At most 32 variables currently supported.") - end - - # not necessary to create `initial_size` exponents - exponents = Vector{Monomial{N}}(undef, init_ht_size) - hashdata = Vector{Hashvalue}(undef, init_ht_size) - hashtable = zeros(MonIdx, init_ht_size) - - # exponents[1:load] cover all stored exponents - load = 0 - size = init_ht_size - - # initialize fast divisibility params - int32bits = 32 - ndivbits = div(int32bits, N) - # division mask stores at least 1 bit - # per each of first ndivvars variables - ndivbits == 0 && (ndivbits += 1) - divmap = Vector{DivMask}(undef, N * ndivbits) - - # first stored exponent used as buffer lately - buffer = MVector{N}(zeros(Exp, N)) - - MonomialHashtable{N}(exponents, buffer, hashtable, - hashdata, divmap, ndivbits, - size, load) -end - -# initialize hashtable for `symbolic_preprocessing` -# These are of the same purpose and structure as basis hashtable, -# but are more local oriented -function initialize_secondary_hash_table(basis_ht::MonomialHashtable{N}) where {N} - # 2^6 seems to be the best out of 2^5, 2^6, 2^7 - initial_size = 2^6 - - exponents = Vector{Monomial{N}}(undef, initial_size) - hashdata = Vector{Hashvalue}(undef, initial_size) - hashtable = zeros(MonIdx, initial_size) - - # preserve division info - divmap = basis_ht.divmap - ndivbits = basis_ht.ndivbits - - load = 0 - size = initial_size - - buffer = MVector{N}(zeros(Exp, N)) - - MonomialHashtable(exponents, buffer, hashtable, - hashdata, divmap, ndivbits, - size, load) -end - -function select_tablesize(nvars, syssize) - nvars = ring.nvars - tablesize = 2^10 - if nvars > 4 - tablesize = 2^14 - end - if nvars > 7 - tablesize = 2^16 - end - - if syssize < 3 - tablesize = div(tablesize, 2) - end - if syssize < 2 - tablesize = div(tablesize, 2) - end - - return tablesize -end - -#------------------------------------------------------------------------------ - -ht_resize_threshold() = 0.4 -ht_needs_resize(size, load, added) = (load + added)/size > ht_resize_threshold() - -function check_enlarge_hashtable!(ht::MonomialHashtable, added::Integer) - newsize = ht.size - while ht_needs_resize(newsize, ht.load, added) - newsize *= 2 - end - if newsize != ht.size - ht.size = newsize - @assert ispow2(ht.size) - - resize!(ht.hashdata, ht.size) - resize!(ht.exponents, ht.size) - ht.hashtable = zeros(Int, ht.size) - - mod = MonHash(ht.size - 1) - - for i in 1:ht.load - # hash for this elem is already computed - he = ht.hashdata[i].hash - hidx = he - @inbounds for j in MonHash(1):MonHash(ht.size) - hidx = nexthashindex(he, j, mod) - !iszero(ht.hashtable[hidx]) && continue - ht.hashtable[hidx] = i - break - end - end - end - nothing -end - -#------------------------------------------------------------------------------ - -# if hash collision happened -function ishashcollision(ht::MonomialHashtable{N}, vidx, exps, he) where N - # if not free and not same hash - @inbounds if ht.hashdata[vidx].hash != he - return true - end - # if not free and not same monomial - # TODO: is this shitty? - @inbounds for i in 1:N - if ht.exponents[vidx].exps[i] != exps[i] - return true - end - end - return false -end - -function insert_in_hash_table!(ht::MonomialHashtable{N}, e::Monomial{N}) where {N} - # generate hash - he = Base.hash(e) - - # find new elem position in the table - hidx = he - # power of twoooo - @assert ispow2(ht.size) - mod = MonHash(ht.size - 1) - i = MonHash(1) - hsize = MonHash(ht.size) - - @inbounds while i < hsize - hidx = nexthashindex(he, i, mod) - - vidx = ht.hashtable[hidx] - - # if free - iszero(vidx) && break - - # if not free and not same hash - if ishashcollision(ht, vidx, e.exps, he) - i += MonHash(1) - continue - end - - # already present in hashtable - return vidx - end - - # add its position to hashtable, and insert exponent to that position - vidx = MonIdx(ht.load + 1) - @inbounds ht.hashtable[hidx] = vidx - @inbounds ht.exponents[vidx] = e - divm = divmask(e, ht.divmap, ht.ndivbits) - @inbounds ht.hashdata[vidx] = Hashvalue(he, divm) - - ht.load += 1 - - return vidx -end - -function find_in_hash_table(ht::MonomialHashtable{N}, e::Monomial{N}) where {N} - # generate hash - he = Base.hash(e) - - # find new elem position in the table - hidx = he - # power of twoooo - @assert ispow2(ht.size) - mod = MonHash(ht.size - 1) - i = MonHash(1) - hsize = MonHash(ht.size) - - @inbounds while i < hsize - hidx = nexthashindex(he, i, mod) - - vidx = ht.hashtable[hidx] - - # if free - iszero(vidx) && break - - # if not free and not same hash - if ishashcollision(ht, vidx, e.exps, he) - i += MonHash(1) - continue - end - - # already present in hashtable - return vidx - end - - return zero(MonIdx) -end - -#------------------------------------------------------------------------------ - -#= - Having `ht` filled with monomials from input polys, - computes ht.divmap and divmask for each of already stored monomials -=# -function fill_divmask!(ht::MonomialHashtable{N}) where N - - min_exp = Vector{UInt64}(undef, N) - max_exp = Vector{UInt64}(undef, N) - - e = first(ht.exponents).exps - - @inbounds for i in 1:N - min_exp[i] = e[i] - max_exp[i] = e[i] - end - - @inbounds for i in 1:ht.load - e = ht.exponents[i].exps - for j in 1:N - if e[j] > max_exp[j] - max_exp[j] = e[j] - continue - end - if e[j] < min_exp[j] - min_exp[j] = e[j] - end - end - end - - ctr = 1 - steps = UInt32(0) - @inbounds for i in 1:N - steps = div(max_exp[i] - min_exp[i], UInt32(ht.ndivbits)) - (iszero(steps)) && (steps += UInt32(1)) - for j in 1:ht.ndivbits - ht.divmap[ctr] = steps - steps += UInt32(1) - ctr += 1 - end - end - @inbounds for vidx in 1:ht.load - m = ht.exponents[vidx] - divm = divmask(m, ht.divmap, ht.ndivbits) - hsh = Base.hash(m) - ht.hashdata[vidx] = Hashvalue(hsh, divm) - end - - nothing -end - -#------------------------------------------------------------------------------ - -# add monomials from `poly` multiplied by exponent vector `etmp` -# with hash `htmp` to hashtable `symbol_ht`, -# and substitute hashes in row -function insert_multiplied_poly_in_hash_table!(row::Vector{MonIdx}, - htmp::MonHash, - etmp::Monomial{N}, - poly::Vector{MonIdx}, - ht::MonomialHashtable{N}, - symbol_ht::MonomialHashtable{N}) where N - - # length of poly to add - len = length(poly) - - mod = MonHash(symbol_ht.size - 1) - - bexps = ht.exponents - bdata = ht.hashdata - - sexps = symbol_ht.exponents - sdata = symbol_ht.hashdata - - l = 1 # hardcoding 1 does not seem nice =( - @label Letsgo - @inbounds while l <= len - # we iterate over all monoms of the given poly, - # multiplying them by htmp/etmp, - # and inserting into symbolic hashtable - - # hash is linear, so that - # hash(e1 + e2) = hash(e1) + hash(e2) - h = htmp + bdata[poly[l]].hash - - e = bexps[poly[l]] - - lastidx = symbol_ht.load + 1 - mul!(symbol_ht.buffer, etmp, e) - - # insert into hashtable - k = h - - i = MonHash(1) - ssize = MonHash(symbol_ht.size) - @inbounds while i <= ssize - k = nexthashindex(h, i, mod) - vidx = symbol_ht.hashtable[k] - - # if index is free - iszero(vidx) && break - - if ishashcollision(symbol_ht, vidx, symbol_ht.buffer, h) - i += MonHash(1) - continue - end - - # hit - row[l] = vidx - l += 1 - - @goto Letsgo - end - # miss - - # add multiplied exponent to hash table - sexps[lastidx] = Monomial(etmp.deg + e.deg, - SVector(copy(symbol_ht.buffer))) - symbol_ht.hashtable[k] = lastidx - - divm = divmask(sexps[lastidx], symbol_ht.divmap, symbol_ht.ndivbits) - sdata[lastidx] = Hashvalue(h, divm) - - row[l] = lastidx - l += 1 - symbol_ht.load += 1 - end - - row -end - -function multiplied_poly_to_matrix_row!( - symbolic_ht::MonomialHashtable{N}, basis_ht::MonomialHashtable{N}, - htmp::MonHash, etmp::Monomial{N}, poly::Vector{MonIdx}) where {N} - - row = similar(poly) - check_enlarge_hashtable!(symbolic_ht, length(poly)) - - insert_multiplied_poly_in_hash_table!(row, htmp, etmp, poly, basis_ht, symbolic_ht) -end - -#------------------------------------------------------------------------------ -function insert_in_basis_hash_table_pivots!( - row::Vector{MonIdx}, - ht::MonomialHashtable{N}, - symbol_ht::MonomialHashtable{N}) where {N} - - check_enlarge_hashtable!(ht, length(row)) - - sdata = symbol_ht.hashdata - sexps = symbol_ht.exponents - - mod = MonHash(ht.size - 1) - bdata = ht.hashdata - bexps = ht.exponents - bhash = ht.hashtable - - l = 1 - @label Letsgo - @inbounds while l <= length(row) - hidx = row[l] - - # symbolic hash - h = sdata[hidx].hash - - lastidx = ht.load + 1 - bexps[lastidx] = sexps[hidx] - e = bexps[lastidx] - - k = h - i = MonHash(1) - @inbounds while i <= ht.size - k = nexthashindex(h, i, mod) - hm = bhash[k] - - iszero(hm) && break - - if ishashcollision(ht, hm, e.exps, h) - i += MonHash(1) - continue - end - - row[l] = hm - l += 1 - @goto Letsgo - end - - bhash[k] = pos = lastidx - row[l] = pos - l += 1 - - bdata[pos] = Hashvalue(h, sdata[hidx].divmask) - - ht.load += 1 - end - - nothing -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/linear_algebra.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/linear_algebra.jl deleted file mode 100644 index 1178901..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/linear_algebra.jl +++ /dev/null @@ -1,156 +0,0 @@ -function echelonize!(matrix::MacaulayMatrix, - char::Val{Char}, - shift::Val{Shift}) where {Char, Shift} - - arit_ops = 0 - - col2hash = matrix.col2hash - buffer = zeros(Cbuf, matrix.ncols) - hash2col = Vector{MonIdx}(undef, matrix.ncols) - rev_sigorder = Vector{Int}(undef, matrix.nrows) - pivots = matrix.pivots - - @inbounds for i in 1:matrix.nrows - rev_sigorder[matrix.sig_order[i]] = i - row_ind = matrix.sig_order[i] - end - - @inbounds for i in 1:matrix.ncols - hash2col[col2hash[i]] = MonIdx(i) - end - - @inbounds for i in 1:matrix.nrows - row_ind = matrix.sig_order[i] - - row_cols = matrix.rows[row_ind] - l_col_idx = hash2col[first(row_cols)] - pivots[l_col_idx] == row_ind && continue - - # check if the row can be reduced - does_red = false - for (j, m_idx) in enumerate(row_cols) - colidx = hash2col[m_idx] - pividx = pivots[colidx] - does_red = !iszero(pividx) && rev_sigorder[pividx] < i - does_red && break - end - if !does_red - pivots[l_col_idx] = row_ind - continue - end - - # buffer the row - row_coeffs = matrix.coeffs[row_ind] - @inbounds for (k, j) in enumerate(row_cols) - col_idx = hash2col[j] - buffer[col_idx] = row_coeffs[k] - end - - # do the reduction - @inbounds for j in 1:matrix.ncols - a = buffer[j] % Char - iszero(a) && continue - pividx = pivots[j] - if iszero(pividx) || rev_sigorder[pividx] >= i - continue - end - - # subtract m*rows[pivots[j]] from buffer - pivmons = matrix.rows[pividx] - pivcoeffs = matrix.coeffs[pividx] - - arit_ops_new = critical_loop!(buffer, j, a, hash2col, pivmons, - pivcoeffs, shift) - arit_ops += arit_ops_new - end - - new_row_length = 0 - @inbounds for j in 1:matrix.ncols - iszero(buffer[j]) && continue - buffer[j] = buffer[j] % Char - iszero(buffer[j]) && continue - new_row_length += 1 - end - - # write out matrix row again - j = 1 - inver = one(Coeff) - new_row = Vector{MonIdx}(undef, new_row_length) - new_coeffs = Vector{Coeff}(undef, new_row_length) - @inbounds for k in 1:matrix.ncols - iszero(buffer[k]) && continue - if isone(j) - pivots[k] = row_ind - inver = inv(Coeff(buffer[k]), char) - end - new_row[j] = col2hash[k] - new_coeffs[j] = isone(j) ? one(Coeff) : mul(inver, buffer[k], char) - buffer[k] = zero(Cbuf) - j += 1 - end - - # check if row lead reduced, TODO: dont know if this is reliable - s = matrix.sigs[row_ind] - m = monomial(s) - @inbounds if isempty(new_row) || (matrix.rows[row_ind][1] != new_row[1] && any(!iszero, m.exps)) - matrix.toadd[matrix.toadd_length+1] = row_ind - matrix.toadd_length += 1 - end - - matrix.rows[row_ind] = new_row - matrix.coeffs[row_ind] = new_coeffs - end - if !iszero(arit_ops) - @info "$(arit_ops) submul's" - end -end - -# subtract mult -# TODO: for module tracking we won't be able to assume that mult = buffer[bufind] -@inline function critical_loop!(buffer::Vector{Cbuf}, - bufind::Int, - mult::Cbuf, - hash2col::Vector{MonIdx}, - pivmons::Vector{MonIdx}, - pivcoeffs::Vector{Coeff}, - shift::Val{Shift}) where Shift - - @inbounds buffer[bufind] = zero(Cbuf) - l = length(pivmons) - @turbo warn_check_args=false for k in 2:l - c = pivcoeffs[k] - m_idx = pivmons[k] - colidx = hash2col[m_idx] - buffer[colidx] = submul(buffer[colidx], mult, c, shift) - end - return l-1 -end - -# helper functions -# field arithmetic -function maxshift(::Val{Char}) where Char - bufchar = Cbuf(Char) - return bufchar << leading_zeros(bufchar) -end - -# compute a representation of a - b*c mod char (char ~ Shift) -@inline function submul(a::Cbuf, b::Cbuf, c::Coeff, ::Val{Shift}) where Shift - r0 = a - b*Cbuf(c) - r1 = r0 + Shift - r0 > a ? r1 : r0 -end - -@inline function inv(a::Coeff, ::Val{Char}) where Char - return invmod(Cbuf(a), Cbuf(Char)) % Coeff -end - -@inline function mul(a, b, ::Val{Char}) where Char - return Coeff((Cbuf(a) * Cbuf(b)) % Char) -end - -# for debug helping - -function is_triangular(matrix::MacaulayMatrix) - lms = [first(row) for row in matrix.rows[1:matrix.nrows] if !isempty(row)] - return length(lms) == length(unique(lms)) -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/monomials.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/monomials.jl deleted file mode 100644 index d2aab7d..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/monomials.jl +++ /dev/null @@ -1,127 +0,0 @@ -#-- Monomial arithmetic --# - -function mul(a::Monomial, b::Monomial) - return Monomial(a.deg + b.deg, a.exps + b.exps) -end - -function mul!(buf::MVector{N, Exp}, a::Monomial{N}, b::Monomial{N}) where N - @inbounds for i in 1:N - buf[i] = a.exps[i] + b.exps[i] - end -end - -function divide(a::Monomial, b::Monomial) - return Monomial(a.deg - b.deg, a.exps - b.exps) -end - -# lcm(a, b) / a -function lcm_div(a::Monomial{N}, b::Monomial{N}) where N - e1 = a.exps - e2 = b.exps - @inbounds exps = SVector{N, Exp}([e1[i] >= e2[i] ? zero(Exp) : e2[i] - e1[i] for i in 1:N]) - return Monomial(sum(exps), exps) -end - -# false if the monomial corresponding to a does not divide -# the monomial corresponding to b -@inline function divch(a::DivMask, b::DivMask) - return iszero(a & (~b)) -end - -@inline function divch(a::Monomial{N}, b::Monomial{N}) where N - if a.deg <= b.deg - @inbounds for i in 1:N - a.exps[i] > b.exps[i] && return false - end - return true - end - return false -end - -@inline function divch(a::Monomial, b::Monomial, - am::DivMask, bm::DivMask) - - return divch(am, bm) && divch(a, b) -end - -# TODO: unroll this loop -@inline function divch!(buf::MVector{N, Exp}, - a::Monomial{N}, - b::Monomial{N}) where N - - @inbounds for i in 1:N - buf[i] = a.exps[i] - b.exps[i] - if buf[i] < 0 - return false - end - end - return true -end - -#-- Monomial Orders --# - -# DRL comparison -@generated function lt_drl(a::Monomial{N}, b::Monomial{N}) where N - quote - a.deg < b.deg && return true - a.deg > b.deg && return false - - ae = a.exps - be = b.exps - $([:(ae[$i] < be[$i] && return false ; ae[$i] > be[$i] && return true) for i in N:-1:1]...) - - return false - end -end - -function lt_pot(a::Sig, b::Sig) - if index(a) == index(b) - return lt_drl(a[2], b[2]) - else - return index(a) < index(b) - end -end - -#---------------------# - -#-- Masking and hashing --# - -# from groebner.jl -# TODO: make this generated? -function divmask(e::Monomial{N}, - divmap, - ndivbits) where N - - ctr = one(DivMask) - res = zero(DivMask) - o = one(DivMask) - for i in N:-1:1 - for j in 1:ndivbits - @inbounds if e.exps[i] >= divmap[ctr] - res |= o << (ctr - 1) - end - ctr += o - end - end - - res -end - -@generated function makehash(::Val{N}, m) where {N} - rng = MersenneTwister(18121987) - hash = :( $(UInt64(0)) ) - for i in 1:N - hash = :($hash + $(rand(rng, MonHash))*(m[$i])) - end - return :($hash % MonHash) -end - -Base.hash(a::Monomial{N}) where N = makehash(Val(N), a.exps) - -#-------------------------# - -# for readibility -index(a::Sig) = a[1] -monomial(a::Sig) = a[2] -index(a::MaskSig) = a[1] -mask(a::MaskSig) = a[2] diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/siggb.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/siggb.jl deleted file mode 100644 index b598352..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/siggb.jl +++ /dev/null @@ -1,256 +0,0 @@ -# sizes for initialization -const init_ht_size = 2^17 -const init_basis_size = 10000 -const init_syz_size = 1000 -const init_pair_size = 10000 -# default sorting alg -const def_sort_alg = Base.Sort.DEFAULT_UNSTABLE -include("typedefs.jl") -include("monomials.jl") -include("hashtable.jl") -include("update.jl") -include("symbolic_pp.jl") -include("linear_algebra.jl") - -@doc Markdown.doc""" - sig_groebner_basis(sys::Vector{T}; info_level::Int = 0, degbound::Int = 0) where {T <: MPolyRingElem} - -Compute a Signature Gröbner basis of the sequence `sys` w.r.t. to the -degree reverse lexicographical monomial ordering and the degree -position-over-term ordering induced by `sys`. The output is a vector -of `Tuple{Tuple{Int64, T}, T}` where the first element indicates the -signature and the second the underlying polynomial. - -**Note**: At the moment only ground fields of characteristic `p`, `p` prime, `p < 2^{31}` are supported. -**Note**: The input generators must be homogeneous. -**Note**: The algorithms behaviour may depend heavily on how the elements in `sys` are sorted. - -# Arguments -- `sys::Vector{T} where T <: MpolyElem`: input generators. -- `info_level::Int=0`: info level printout: off (`0`, default), computational details (`1`) -- `degbound::Int=0`: degree bound for Gröbner basis computation, compute a full Gröbner basis if `0` (default) or only up to degree `d`. - -# Example -```jldoctest -julia> using AlgebraicSolving - -julia> R, vars = polynomial_ring(GF(17), ["x$i" for i in 1:4]) -(Multivariate polynomial ring in 4 variables over GF(17), FqMPolyRingElem[x1, x2, x3, x4]) - -julia> F = AlgebraicSolving.cyclic(R) -FqMPolyRingElem[x1 + x2 + x3 + x4, x1*x2 + x1*x4 + x2*x3 + x3*x4, x1*x2*x3 + x1*x2*x4 + x1*x3*x4 + x2*x3*x4, x1*x2*x3*x4 + 16] - -julia> Fhom = AlgebraicSolving._homogenize(F.gens) -4-element Vector{FqMPolyRingElem}: - x1 + x2 + x3 + x4 - x1*x2 + x2*x3 + x1*x4 + x3*x4 - x1*x2*x3 + x1*x2*x4 + x1*x3*x4 + x2*x3*x4 - x1*x2*x3*x4 + 16*x5^4 - -julia> sig_groebner_basis(Fhom) -7-element Vector{Tuple{Tuple{Int64, FqMPolyRingElem}, FqMPolyRingElem}}: - ((1, 1), x1 + x2 + x3 + x4) - ((2, 1), x2^2 + 2*x2*x4 + x4^2) - ((3, 1), x2*x3^2 + x3^2*x4 + 16*x2*x4^2 + 16*x4^3) - ((4, 1), x2*x3*x4^2 + x3^2*x4^2 + 16*x2*x4^3 + x3*x4^3 + 16*x4^4 + 16*x5^4) - ((4, x3), x3^3*x4^2 + x3^2*x4^3 + 16*x3*x5^4 + 16*x4*x5^4) - ((4, x2), x2*x4^4 + x4^5 + 16*x2*x5^4 + 16*x4*x5^4) - ((4, x2*x3), x3^2*x4^4 + x2*x3*x5^4 + 16*x2*x4*x5^4 + x3*x4*x5^4 + 15*x4^2*x5^4) -``` -""" -function sig_groebner_basis(sys::Vector{T}; info_level::Int=0, degbound::Int=0) where {T <: MPolyRingElem} - R = parent(first(sys)) - Rchar = characteristic(R) - - # check if input is ok - if Rchar > 2^31 || iszero(Rchar) - error("At the moment we only support finite fields up to prime characteristic < 2^31.") - end - sysl = length(sys) - degs = Vector{Exp}(undef, sysl) - @inbounds for (i, f) in enumerate(sys) - deg = total_degree(f) - if deg > typemax(Exp) - error("input degrees too large.") - end - degs[i] = Exp(deg) - for m in exponent_vectors(f) - if sum(m) != deg - error("input system must be homogeneous.") - end - end - end - - # constants for fast arithmetic - char = Val(Coeff(Rchar.d)) - shift = Val(maxshift(char)) - - # convert to and initialize our data structures - nv = nvars(R) - basis_ht = initialize_basis_hash_table(Val(nv)) - - # initialize basis - sigs = Vector{Sig{nv}}(undef, init_basis_size) - sigmasks = Vector{MaskSig}(undef, init_basis_size) - sigratios = Vector{Monomial{nv}}(undef, init_basis_size) - rewrite_nodes = Vector{Vector{Int}}(undef, init_basis_size+1) - lm_masks = Vector{DivMask}(undef, init_basis_size) - monomials = Vector{Vector{MonIdx}}(undef, init_basis_size) - coeffs = Vector{Vector{Coeff}}(undef, init_basis_size) - is_red = Vector{Bool}(undef, init_basis_size) - syz_sigs = Vector{Monomial{nv}}(undef, init_syz_size) - syz_masks = Vector{MaskSig}(undef, init_syz_size) - basis = Basis(sigs, sigmasks, sigratios, rewrite_nodes, - lm_masks, monomials, coeffs, is_red, - syz_sigs, syz_masks, degs, sysl, - init_basis_size, sysl + 1, 0, init_syz_size) - - # root node - basis.rewrite_nodes[1] = vcat([length(sys)-1, -1], - collect(2:length(sys)+1)) - - # initialize pairset - pairset = Pairset{nv}(Vector{SPair{nv}}(undef, init_pair_size), - sysl, - init_pair_size) - - one_mon = monomial(SVector{nv}(zeros(Exp, nv))) - zero_sig = (zero(SigIndex), one_mon) - # store initial pols in basis and pairset - @inbounds for i in 1:sysl - f = sys[i] - lf = length(f) - - # gather up monomials and coeffs - exps = collect(exponent_vectors(f)) - cfs = collect(coefficients(f)) - mons = Vector{MonIdx}(undef, lf) - coeffs = Vector{Coeff}(undef, lf) - inver = one(Coeff) - @inbounds for j in 1:lf - m = monomial(SVector{nv}((Exp).(exps[j]))) - eidx = insert_in_hash_table!(basis_ht, m) - if isone(j) - inver = inv(Coeff(lift(ZZ, cfs[1])), char) - end - cf = isone(j) ? one(Coeff) : mul(inver, Coeff(lift(ZZ, cfs[j])), char) - mons[j] = eidx - coeffs[j] = cf - end - s = sortperm(mons, by = eidx -> basis_ht.exponents[eidx], - lt = lt_drl, rev = true) - @inbounds mons = mons[s] - @inbounds coeffs = coeffs[s] - - # signatures - sig = (SigIndex(i), one_mon) - lm_exps = SVector{nv}((Exp).(exps[1])) - sigr = monomial(lm_exps) - - # store stuff in basis - basis.sigs[i] = sig - basis.sigratios[i] = sigr - basis.rewrite_nodes[i+1] = [-1, 1] - basis.monomials[i] = mons - basis.coefficients[i] = coeffs - basis.is_red[i] = false - - # add unitvector as pair - pairset.elems[i] = SPair{nv}(sig, zero_sig, zero(DivMask), - zero(DivMask), i, 0, degs[i]) - end - - # compute divmasks - fill_divmask!(basis_ht) - dm_one_mon = divmask(one_mon, basis_ht.divmap, basis_ht.ndivbits) - @inbounds for i in 1:sysl - basis.sigmasks[i] = (SigIndex(i), dm_one_mon) - pairset.elems[i].top_sig_mask = basis.sigmasks[i][2] - basis.lm_masks[i] = basis_ht.hashdata[basis.monomials[i][1]].divmask - end - - logger = ConsoleLogger(stdout, info_level == 0 ? Warn : Info) - with_logger(logger) do - siggb!(basis, pairset, basis_ht, char, shift, degbound = degbound) - end - - # output - eltp = typeof(first(sys)) - outp = Tuple{Tuple{Int, eltp}, eltp}[] - @inbounds for i in basis.basis_offset:basis.basis_load - exps = [basis_ht.exponents[m].exps for m in basis.monomials[i]] - ctx = MPolyBuildCtx(R) - for (e, c) in zip(exps, basis.coefficients[i]) - push_term!(ctx, coefficient_ring(R)(c), Vector{Int}(e)) - end - pol = finish(ctx) - - s = basis.sigs[i] - ctx = MPolyBuildCtx(R) - push_term!(ctx, one(coefficient_ring(R)), Vector{Int}(monomial(s).exps)) - sig = (Int(index(s)), finish(ctx)) - - push!(outp, (sig, pol)) - end - return outp -end - -function siggb!(basis::Basis{N}, - pairset::Pairset, - basis_ht::MonomialHashtable, - char::Val{Char}, - shift::Val{Shift}; - degbound = 0) where {N, Char, Shift} - - while !iszero(pairset.load) - if !iszero(degbound) && first(pairset.elems).deg > degbound - break - end - matrix = initialize_matrix(Val(N)) - symbol_ht = initialize_secondary_hash_table(basis_ht) - - select_normal!(pairset, basis, matrix, basis_ht, symbol_ht) - symbolic_pp!(basis, matrix, basis_ht, symbol_ht) - finalize_matrix!(matrix, symbol_ht) - echelonize!(matrix, char, shift) - - update_basis!(basis, matrix, pairset, symbol_ht, basis_ht) - end -end - - -# miscallaneous helper functions -function sort_pairset_by_degree!(pairset::Pairset, from::Int, sz::Int) - ordr = Base.Sort.ord(isless, p -> p.deg, false, Base.Sort.Forward) - sort!(pairset.elems, from, from+sz, def_sort_alg, ordr) -end - -# homogenize w.r.t. the last variable -function _homogenize(F::Vector{P}) where {P <: MPolyRingElem} - R = parent(first(F)) - S, vars = polynomial_ring(base_ring(R), ["x$i" for i in 1:nvars(R)+1], - ordering = :degrevlex) - res = typeof(first(F))[] - for f in F - ctx = MPolyBuildCtx(S) - d = total_degree(f) - for (e, c) in zip(exponent_vectors(f), coefficients(f)) - enew = push!(e, d - sum(e)) - push_term!(ctx, c, e) - end - push!(res, finish(ctx)) - end - return res -end - -# test against msolve -function _is_gb(gb::Vector{Tuple{Tuple{Int, P}, P}}) where {P <: MPolyRingElem} - gb_pols = [p[2] for p in gb] - gb_msolve = groebner_basis(Ideal(gb_pols), complete_reduction = true) - - lms_gb = (Nemo.leading_monomial).(gb_pols) - lms_msolve = (Nemo.leading_monomial).(gb_msolve) - res1 = all(u -> any(v -> divides(u, v)[1], lms_gb), lms_msolve) - res2 = all(u -> any(v -> divides(u, v)[1], lms_msolve), lms_gb) - return res1 && res2 -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/symbolic_pp.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/symbolic_pp.jl deleted file mode 100644 index d3380da..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/symbolic_pp.jl +++ /dev/null @@ -1,368 +0,0 @@ -function select_normal!(pairset::Pairset{N}, - basis::Basis{N}, - matrix::MacaulayMatrix, - ht::MonomialHashtable, - symbol_ht::MonomialHashtable) where N - - # sort pairset - sort_pairset_by_degree!(pairset, 1, pairset.load-1) - - # number of selected pairs - npairs = 0 - deg = zero(Exp) - for i in 1:pairset.load - if iszero(deg) - deg = pairset.elems[i].deg - npairs += 1 - continue - end - if pairset.elems[i].deg == deg - npairs += 1 - else - break - end - end - - @info "selected $(npairs) pairs, degree $(deg)" - added_to_matrix = 0 - - # allocate matrix - reinitialize_matrix!(matrix, npairs) - skip = falses(npairs) - - @inbounds for i in 1:npairs - if skip[i] - continue - end - - pair = pairset.elems[i] - # for each unique pair signature - curr_top_sig = pair.top_sig - rewr_ind = find_canonical_rewriter(basis, pair.top_sig, - pair.top_sig_mask) - - pair_with_rewr_ind = 0 - for j in i:npairs - pair2 = pairset.elems[j] - if pair2.top_sig == curr_top_sig - skip[j] = true - if pair2.top_index == rewr_ind - pair_with_rewr_ind = j - end - end - end - - if !iszero(pair_with_rewr_ind) - - # take pair with non-rewr top signature - pair = pairset.elems[pair_with_rewr_ind] - - # add if pair is a unit vector - add_cond = iszero(pair.bot_index) - - # check if we have a pivot already - if !add_cond - mult = divide(monomial(curr_top_sig), - monomial(basis.sigs[rewr_ind])) - lm = mul(mult, leading_monomial(basis, ht, rewr_ind)) - l_idx = find_in_hash_table(symbol_ht, lm) - if !iszero(l_idx) - if !iszero(matrix.pivots[l_idx]) - add_cond = matrix.sigs[matrix.pivots[l_idx]] != curr_top_sig - end - end - end - - # check if there is a non-rewriteable reducer - if !add_cond - mult = divide(monomial(curr_top_sig), - monomial(basis.sigs[rewr_ind])) - lm = mul(mult, leading_monomial(basis, ht, rewr_ind)) - red_sig_mon = similar(symbol_ht.buffer) - @inbounds for j in 1:N - red_sig_mon[j] = zero(Exp) - end - reducer_sig = (zero(SigIndex), monomial(red_sig_mon)) - reducer_ind = zero(SigIndex) - - @inbounds for j in 1:npairs - pair2 = pairset.elems[j] - pair2.bot_sig == curr_top_sig && continue - if iszero(reducer_ind) || lt_pot(pair2.bot_sig, reducer_sig) - !lt_pot(pair2.bot_sig, curr_top_sig) && continue - new_red = false - if !iszero(pair2.bot_index) - rewriteable_basis(basis, pair2.bot_index, - pair2.bot_sig, - pair2.bot_sig_mask) && continue - ind = pair2.bot_index - mult = divide(monomial(pair2.bot_sig), - monomial(basis.sigs[ind])) - lm2 = mul(mult, leading_monomial(basis, ht, ind)) - new_red = lm2 == lm - end - if new_red - reducer_sig = pair2.bot_sig - reducer_ind = pair2.bot_index - end - end - end - - add_cond = !iszero(reducer_ind) - if add_cond - mult = divide(monomial(reducer_sig), - monomial(basis.sigs[reducer_ind])) - lead_idx = write_to_matrix_row!(matrix, basis, - reducer_ind, - symbol_ht, ht, mult, - reducer_sig) - # set pivot - resize_pivots!(matrix, symbol_ht) - matrix.pivots[lead_idx] = matrix.nrows - end - end - - # add row to matrix if any of the add conds is true - if add_cond - mult = divide(monomial(curr_top_sig), - monomial(basis.sigs[rewr_ind])) - l_idx = write_to_matrix_row!(matrix, basis, rewr_ind, - symbol_ht, ht, mult, - curr_top_sig) - added_to_matrix += 1 - if iszero(pair.bot_index) - matrix.toadd[matrix.toadd_length+1] = matrix.nrows - matrix.toadd_length += 1 - end - end - end - end - - if !iszero(added_to_matrix) - @info "$(added_to_matrix) non-rewriteable critical signatures added to matrix" - end - - # remove selected pairs from pairset - @inbounds for i in 1:(pairset.load-npairs) - pairset.elems[i] = pairset.elems[i+npairs] - end - pairset.load -= npairs - resize_pivots!(matrix, symbol_ht) -end - -function symbolic_pp!(basis::Basis{N}, - matrix::MacaulayMatrix, - ht::MonomialHashtable, - symbol_ht::MonomialHashtable) where N - - i = one(MonIdx) - mult = similar(ht.buffer) - mult2 = similar(ht.buffer) - red_sig_mon = similar(ht.buffer) - - # iterate over monomials in symbolic ht - @inbounds while i <= symbol_ht.load - found_reducer = false - # skip if reducer already exists - if !iszero(matrix.pivots[i]) - # exp = symbol_ht.exponents[i] - # println("mon: $(exp.exps)") - # println("reducer exists") - i += one(MonIdx) - continue - end - - red_ind = 0 - @inbounds for j in 1:N - red_sig_mon[j] = zero(Exp) - end - mul_red_sig = (zero(SigIndex), monomial(red_sig_mon)) - - # realloc matrix if necessary - if matrix.size == matrix.nrows - matrix.size *= 2 - resize!(matrix.rows, matrix.size) - resize!(matrix.sigs, matrix.size) - resize!(matrix.parent_inds, matrix.size) - resize!(matrix.coeffs, matrix.size) - resize!(matrix.toadd, matrix.size) - end - - exp = symbol_ht.exponents[i] - divm = symbol_ht.hashdata[i].divmask - - j = basis.basis_offset - @label target - # find element in basis which divmask divides divmask of monomial - @inbounds while j <= basis.basis_load && !divch(basis.lm_masks[j], divm) - j += 1 - end - - if j <= basis.basis_load - @inbounds red_exp = leading_monomial(basis, ht, j) - - # actual divisibility check - if !(divch!(mult2, exp, red_exp)) - j += 1 - @goto target - end - # found_reducer = true - - # check if new reducer sig is smaller than possible previous - if !iszero(red_ind) && lt_pot(mul_red_sig, mul_cand_sig) - j += 1 - @goto target - end - - # check if reducer is rewriteable - cand_sig = basis.sigs[j] - mul_cand_sig = (index(cand_sig), - mul(monomial(mult2), monomial(cand_sig))) - cand_sig_mask = divmask(monomial(mul_cand_sig), ht.divmap, - ht.ndivbits) - if rewriteable(basis, ht, j, mul_cand_sig, cand_sig_mask) - j += 1 - @goto target - end - - # set reducer - red_ind = j - mul_red_sig = mul_cand_sig - j += 1 - @inbounds for k in 1:N - mult[k] = mult2[k] - end - @goto target - end - - # write to matrix - if !iszero(red_ind) - mm = monomial(SVector(mult)) - @inbounds lead_idx = write_to_matrix_row!(matrix, basis, - red_ind, symbol_ht, - ht, mm, - mul_red_sig) - resize_pivots!(matrix, symbol_ht) - matrix.pivots[lead_idx] = matrix.nrows - end - i += one(MonIdx) - end -end - -function finalize_matrix!(matrix::MacaulayMatrix, - symbol_ht::MonomialHashtable) - - # store indices into hashtable in a sorted way - ncols = symbol_ht.load - matrix.ncols = ncols - - col2hash = Vector{ColIdx}(undef, ncols) - @inbounds for i in 1:ncols - col2hash[i] = i - end - exps = symbol_ht.exponents - function cmp(h1, h2) - @inbounds e1 = exps[h1] - @inbounds e2 = exps[h2] - return !lt_drl(e1, e2) - end - sort!(col2hash, lt = cmp) - matrix.col2hash = col2hash - nc = matrix.ncols - @inbounds matrix.pivots[1:nc] = matrix.pivots[1:nc][col2hash] - - if !iszero(matrix.nrows) - @info "matrix of size $((matrix.nrows, matrix.ncols)), density $(@sprintf "%.2f" 100*sum((length).(matrix.rows[1:matrix.nrows]))/(matrix.nrows * matrix.ncols))%" - end - matrix.sig_order = Vector{Int}(undef, matrix.nrows) - # sort signatures - sortperm!(matrix.sig_order, matrix.sigs[1:matrix.nrows], - lt = (sig1, sig2) -> lt_pot(sig1, sig2)) -end - -# TODO: later to optimize: mem allocations for matrix -# helper functions -function initialize_matrix(::Val{N}) where {N} - rows = Vector{Vector{MonIdx}}(undef, 0) - pivots = Vector{Int}(undef, 0) - pivot_size = 0 - sigs = Vector{Sig{N}}(undef, 0) - parent_inds = Vector{Int}(undef, 0) - sig_order = Vector{Int}(undef, 0) - col2hash = Vector{ColIdx}(undef, 0) - coeffs = Vector{Vector{Coeff}}(undef, 0) - toadd = Vector{Int}(undef, 0) - - size = 0 - nrows = 0 - ncols = 0 - toadd_length = 0 - - return MacaulayMatrix(rows, pivots, pivot_size, - sigs, parent_inds, sig_order, - col2hash, coeffs, size, nrows, - ncols, toadd, toadd_length) -end - -# Refresh and initialize matrix for `npairs` elements -function reinitialize_matrix!(matrix::MacaulayMatrix, npairs::Int) - matrix.size = 2 * npairs - matrix.pivot_size = 2 * npairs - resize!(matrix.rows, matrix.size) - resize!(matrix.pivots, matrix.pivot_size) - for i in 1:matrix.pivot_size - matrix.pivots[i] = 0 - end - resize!(matrix.sigs, matrix.size) - resize!(matrix.parent_inds, matrix.size) - resize!(matrix.coeffs, matrix.size) - resize!(matrix.toadd, matrix.size) - for i in 1:npairs - matrix.toadd[i] = 0 - end - return matrix -end - -# resize pivots array if needed -@inline function resize_pivots!(matrix::MacaulayMatrix, - symbol_ht::MonomialHashtable) - if matrix.pivot_size < symbol_ht.load - pv_size = matrix.pivot_size - new_pv_size = 2 * (symbol_ht.load) - resize!(matrix.pivots, new_pv_size) - @inbounds for j in pv_size+1:new_pv_size - matrix.pivots[j] = 0 - end - matrix.pivot_size = new_pv_size - end -end - -# helper function to write row to matrix -function write_to_matrix_row!(matrix::MacaulayMatrix, - basis::Basis, - basis_idx::Int, - symbol_ht::MonomialHashtable, - ht::MonomialHashtable, - mult::Monomial, - sig::Sig, - row_ind=matrix.nrows+1) - - hsh = Base.hash(mult) - poly = basis.monomials[basis_idx] - row = similar(basis.monomials[basis_idx]) - check_enlarge_hashtable!(symbol_ht, length(basis.monomials[basis_idx])) - - s = basis.sigs[basis_idx] - lm = mul(mult, leading_monomial(basis, ht, basis_idx)) - - @inbounds matrix.rows[row_ind] = - insert_multiplied_poly_in_hash_table!(row, hsh, mult, poly, - ht, symbol_ht) - @inbounds matrix.coeffs[row_ind] = basis.coefficients[basis_idx] - @inbounds matrix.sigs[row_ind] = sig - @inbounds matrix.parent_inds[row_ind] = basis_idx - if row_ind == matrix.nrows + 1 - matrix.nrows += 1 - end - return first(matrix.rows[row_ind]) -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/typedefs.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/typedefs.jl deleted file mode 100644 index c8b064e..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/typedefs.jl +++ /dev/null @@ -1,109 +0,0 @@ -# type for signature indices -const SigIndex = UInt16 -# type for exponents in monomials -# ints because sigratios may require negative exponents -const Exp = Int16 -# types for hashvalue, ht index and divisor mask of a monomial -const MonIdx = Int32 -const MonHash = UInt32 -const DivMask = UInt32 -# stuff for matrix -const ColIdx = UInt32 -const Coeff = UInt32 -# 64 bit buffer -const Cbuf = UInt64 - -struct Monomial{N} - deg::Exp - exps::SVector{N, Exp} -end -function monomial(exps::SV) where {N, SV <: StaticArray{Tuple{N}}} - return Monomial{N}(sum(exps), exps) -end -const Sig{N} = Tuple{SigIndex, Monomial{N}} -const MaskSig = Tuple{SigIndex, DivMask} - -mutable struct Basis{N} - sigs::Vector{Sig{N}} - sigmasks::Vector{MaskSig} - - sigratios::Vector{Monomial{N}} - - # tree structure: - # - length of data for i is rewrite_nodes[i][1] - # - parent of i is rewrite_nodes[i][2] - # - children of i are rewrite_nodes[i][3:end] - # careful: indices are shifted by + 1 compared to basis indices - rewrite_nodes::Vector{Vector{Int}} - - lm_masks::Vector{DivMask} - - monomials::Vector{Vector{MonIdx}} - coefficients::Vector{Vector{Coeff}} - - is_red::Vector{Bool} - - syz_sigs::Vector{Monomial{N}} - syz_masks::Vector{MaskSig} - - # degrees of input elements - degs::Vector{Exp} - - basis_load::Int - basis_size::Int - # for storing the initial polynomials from 1 to offset-1 - basis_offset::Int - syz_load::Int - syz_size::Int -end - -# TODO: should these be stored in a more vectorized way? -mutable struct SPair{N} - top_sig::Sig{N} - bot_sig::Sig{N} - top_sig_mask::DivMask - bot_sig_mask::DivMask - # top index = 0 -> pair is redundant - top_index::Int - bot_index::Int - deg::Exp -end - -mutable struct Pairset{N} - elems::Vector{SPair{N}} - load::Int - size::Int -end - -mutable struct MacaulayMatrix{N} - - # stored as vectors of corresponding exponents (already hashed and sorted) - rows::Vector{Vector{MonIdx}} - - # pivot row index for colidx is pivots[colidx] - pivots::Vector{Int} - pivot_size::Int - - sigs::Vector{Sig{N}} - parent_inds::Vector{Int} - # sig(row[i]) < sig(row[j]) <=> sig_order[i] < sig_order[j] - sig_order::Vector{Int} - - # maps column index to corresponding hash index - col2hash::Vector{ColIdx} - - # row coefficients - coeffs::Vector{Vector{Coeff}} - - #= sizes info =# - # total number of allocated rows - size::Int - # number of filled rows, nrows <= size - nrows::Int - # number of columns - ncols::Int - - # for each i in toadd rows[i] should be added to basis/syzygies - toadd::Vector{Int} - toadd_length::Int -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/update.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/update.jl deleted file mode 100644 index bdb3428..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/siggb/update.jl +++ /dev/null @@ -1,350 +0,0 @@ -# updating the pairset and basis - -# add new reduced rows to basis/syzygies -# TODO: make a new symbol ht everytime? -function update_basis!(basis::Basis, - matrix::MacaulayMatrix, - pairset::Pairset{N}, - symbol_ht::MonomialHashtable, - basis_ht::MonomialHashtable) where N - - new_basis_c = 0 - new_syz_c = 0 - - # TODO: this can be done more optimally - toadd = matrix.toadd[1:matrix.toadd_length] - # sort!(toadd, by = i -> matrix.sigs[i], lt = lt_pot) - - @inbounds for i in toadd - # determine if row is zero - row = matrix.rows[i] - new_sig = matrix.sigs[i] - new_idx = index(new_sig) - new_sig_mon = monomial(new_sig) - new_sig_mask = (new_idx, divmask(new_sig_mon, basis_ht.divmap, - basis_ht.ndivbits)) - if isempty(row) - new_syz_c += 1 - - # make sure we have enough space - if basis.syz_load == basis.syz_size - basis.syz_size *= 2 - resize!(basis.syz_sigs, basis.syz_size) - resize!(basis.syz_masks, basis.syz_size) - end - - # add new syz sig - l = basis.syz_load + 1 - basis.syz_sigs[l] = monomial(new_sig) - basis.syz_masks[l] = new_sig_mask - basis.syz_load += 1 - - # kill pairs with known syz signature - @inbounds for j in 1:pairset.load - p = pairset.elems[j] - cond = index(p.top_sig) == new_idx - if cond && divch(new_sig_mon, monomial(p.top_sig), - new_sig_mask[2], p.top_sig_mask) - pairset.elems[j].top_index = 0 - end - cond = index(p.bot_sig) == new_idx - if cond && divch(new_sig_mon, monomial(p.bot_sig), - new_sig_mask[2], p.bot_sig_mask) - pairset.elems[j].top_index = 0 - end - end - - # remove pairs that became rewriteable in previous loop - remove_red_pairs!(pairset) - else - new_basis_c += 1 - - # make sure we have enough space - if basis.basis_load == basis.basis_size - basis.basis_size *= 2 - resize!(basis.sigs, basis.basis_size) - resize!(basis.sigmasks, basis.basis_size) - resize!(basis.sigratios, basis.basis_size) - resize!(basis.rewrite_nodes, basis.basis_size) - resize!(basis.lm_masks, basis.basis_size) - resize!(basis.monomials, basis.basis_size) - resize!(basis.coefficients, basis.basis_size) - resize!(basis.is_red, basis.basis_size) - end - - # add to basis hashtable - insert_in_basis_hash_table_pivots!(row, basis_ht, symbol_ht) - lm = basis_ht.exponents[first(row)] - s = new_sig - - # add everything to basis - l = basis.basis_load + 1 - basis.sigs[l] = new_sig - basis.sigmasks[l] = new_sig_mask - new_sig_ratio = divide(lm, new_sig_mon) - basis.sigratios[l] = new_sig_ratio - - parent_ind = matrix.parent_inds[i] - tree_data = basis.rewrite_nodes[parent_ind+1] - insind = 3 - @inbounds for j in insind:insind+tree_data[1] - child_ind = tree_data[j] - rat = basis.sigratios[child_ind-1] - if lt_drl(new_sig_ratio, rat) - break - end - insind += 1 - end - insert!(tree_data, insind, l+1) - tree_data[1] += 1 - basis.rewrite_nodes[l+1] = [-1, parent_ind+1] - - basis.lm_masks[l] = divmask(lm, basis_ht.divmap, - basis_ht.ndivbits) - basis.monomials[l] = row - basis.coefficients[l] = matrix.coeffs[i] - basis.basis_load = l - - # build new pairs - update_pairset!(pairset, basis, basis_ht, l) - end - end - if new_basis_c != 0 || new_syz_c != 0 - @info "$(new_basis_c) new, $(new_syz_c) zero" - end -end - - -# construct all pairs with basis element at new_basis_idx -# and perform corresponding rewrite checks -# assumes DPOT -function update_pairset!(pairset::Pairset{N}, - basis::Basis, - basis_ht::MonomialHashtable, - new_basis_idx::Int) where N - - - new_sig_mon = monomial(basis.sigs[new_basis_idx]) - new_sig_idx = index(basis.sigs[new_basis_idx]) - - # check existing pairs for rewriteability against element - # at new_basis_idx - @inbounds bmask = basis.sigmasks[new_basis_idx] - @inbounds parent_ind = basis.rewrite_nodes[new_basis_idx+1][2] - @inbounds for i in 1:pairset.load - p = pairset.elems[i] - if p.top_index == parent_ind-1 - if divch(new_sig_mon, monomial(p.top_sig), - mask(bmask), p.top_sig_mask) - pairset.elems[i].top_index = 0 - continue - end - end - if p.bot_index == parent_ind-1 - if divch(new_sig_mon, monomial(p.bot_sig), - mask(bmask), p.bot_sig_mask) - pairset.elems[i].top_index = 0 - end - end - end - - # kill pairs that became rewriteable in the previous round - remove_red_pairs!(pairset) - - # resize pairset if needed - num_new_pairs = new_basis_idx - 1 - if pairset.load + num_new_pairs >= pairset.size - resize!(pairset.elems, max(2 * pairset.size, - pairset.load - num_new_pairs)) - pairset.size *= 2 - end - - new_sig_ratio = basis.sigratios[new_basis_idx] - new_lm = leading_monomial(basis, basis_ht, new_basis_idx) - # pair construction loop - @inbounds for i in basis.basis_offset:(new_basis_idx - 1) - basis_lm = leading_monomial(basis, basis_ht, i) - basis_sig_idx = index(basis.sigs[i]) - - mult_new_elem = lcm_div(new_lm, basis_lm) - new_pair_sig_mon = mul(mult_new_elem, new_sig_mon) - - mult_basis_elem = lcm_div(basis_lm, new_lm) - basis_pair_sig_mon = mul(mult_basis_elem, monomial(basis.sigs[i])) - - new_pair_sig = (new_sig_idx, new_pair_sig_mon) - basis_pair_sig = (basis_sig_idx, basis_pair_sig_mon) - - # check if S-pair is singular - new_pair_sig == basis_pair_sig && continue - - new_pair_sig_mask = divmask(new_pair_sig_mon, - basis_ht.divmap, - basis_ht.ndivbits) - basis_pair_sig_mask = divmask(basis_pair_sig_mon, - basis_ht.divmap, - basis_ht.ndivbits) - - # check both pair sigs against non-trivial syzygies - rewriteable_syz(basis, new_pair_sig, - new_pair_sig_mask) && continue - rewriteable_syz(basis, basis_pair_sig, - basis_pair_sig_mask) && continue - - # check both pair signatures against koszul syzygies - rewriteable_koszul(basis, basis_ht, new_pair_sig, - new_pair_sig_mask) && continue - rewriteable_koszul(basis, basis_ht, basis_pair_sig, - basis_pair_sig_mask) && continue - - top_sig, top_sig_mask, top_index, - bot_sig, bot_sig_mask, bot_index = begin - if lt_pot(basis_pair_sig, new_pair_sig) - new_pair_sig, new_pair_sig_mask, new_basis_idx, - basis_pair_sig, basis_pair_sig_mask, i - else - basis_pair_sig, basis_pair_sig_mask, i, - new_pair_sig, new_pair_sig_mask, new_basis_idx - end - end - - pair_deg = new_pair_sig_mon.deg + basis.degs[new_sig_idx] - new_pair = SPair(top_sig, bot_sig, - top_sig_mask, bot_sig_mask, - top_index, bot_index, - pair_deg) - pairset.elems[pairset.load + 1] = new_pair - pairset.load += 1 - end -end - -@inline function rewriteable_syz(basis::Basis, - sig::Sig, - sigmask::DivMask) - - ind = index(sig) - - @inbounds for i in 1:basis.syz_load - if index(basis.syz_masks[i]) == ind - is_rewr = divch(basis.syz_sigs[i], monomial(sig), - basis.syz_masks[i][2], sigmask) - is_rewr && return true - end - end - return false -end - -@inline function rewriteable_basis(basis::Basis, - idx::Int, - sig::Sig, - sigmask::DivMask) - - k = find_canonical_rewriter(basis, sig, sigmask) - return k != idx -end - -# @inline function rewriteable_basis(basis::Basis, -# idx::Int, -# sig::Sig, -# sigmask::DivMask) - -# ind = index(sig) - -# @inbounds for i in basis.basis_load:-1:basis.basis_offset -# i == idx && continue -# i_sig_idx = index(basis.sigmasks[i]) -# i_sig_idx != ind && continue -# i_sig_mask = mask(basis.sigmasks[i]) -# if divch(monomial(basis.sigs[i]), monomial(sig), -# i_sig_mask, sigmask) -# is_rewr = comp_sigratio(basis, i, idx) -# is_rewr && return true -# end -# end -# return false -# end - -function find_canonical_rewriter(basis::Basis, - sig::Sig, - sigmask::DivMask) - - node_ind = 1 - while true - @inbounds node = basis.rewrite_nodes[node_ind] - @inbounds node[1] == -1 && break - found_div = false - @inbounds for i in 3:3+node[1] - ch = node[i] - basis_sig = basis.sigs[ch - 1] - basis_sigmask = basis.sigmasks[ch - 1] - index(basis_sig) != index(sig) && continue - if divch(monomial(basis_sig), monomial(sig), - mask(basis_sigmask), sigmask) - node_ind = ch - found_div = true - break - end - end - !found_div && break - end - return node_ind - 1 -end - -@inline function rewriteable_koszul(basis::Basis, - basis_ht::MonomialHashtable, - sig::Sig, - sigmask::DivMask) - - @inbounds for i in basis.basis_offset:basis.basis_load - if index(basis.sigs[i]) < index(sig) - if divch(basis.lm_masks[i], sigmask) - if divch(leading_monomial(basis, basis_ht, i), monomial(sig)) - return true - end - end - end - end - return false -end - -function rewriteable(basis::Basis, - basis_ht::MonomialHashtable, - idx::Int, - sig::Sig, - sigmask::DivMask) - - rewriteable_syz(basis, sig, sigmask) && return true - rewriteable_basis(basis, idx, sig, sigmask) && return true - rewriteable_koszul(basis, basis_ht, sig, sigmask) && return true - return false -end - -# helper functions for readability -function leading_monomial(basis::Basis, - basis_ht::MonomialHashtable, - i) - - return basis_ht.exponents[first(basis.monomials[i])] -end - -@inline function comp_sigratio(basis::Basis, ind1::Int, ind2::Int) - - rat1 = basis.sigratios[ind1] - rat2 = basis.sigratios[ind2] - if rat1 == rat2 - return lt_drl(monomial(basis.sigs[ind1]), monomial(basis.sigs[ind2])) - end - return lt_drl(rat1, rat2) -end - -# remove pairs that are rewriteable -function remove_red_pairs!(pairset::Pairset) - iszero(pairset.load) && return - j = 0 - @inbounds for i in 1:pairset.load - iszero(pairset.elems[i].top_index) && continue - j += 1 - pairset.elems[j] = pairset.elems[i] - end - pairset.load = j -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/src/types.jl b/src/connectcurves/AlgebraicSolving.jl-main/src/types.jl deleted file mode 100644 index d193d6d..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/src/types.jl +++ /dev/null @@ -1,51 +0,0 @@ -export Ideal - -mutable struct RationalParametrization - vars::Vector{Symbol} - lf_cfs::Vector{ZZRingElem} - elim::QQPolyRingElem - denom::QQPolyRingElem - param::Vector{PolyRingElem} - - function RationalParametrization( - vars::Vector{Symbol}, - lf_cfs::Vector{ZZRingElem}, - elim::QQPolyRingElem, - denom::QQPolyRingElem, - param::Vector{PolyRingElem} - ) - rp = new() - rp.vars = vars - rp.lf_cfs = lf_cfs - rp.elim = elim - rp.denom = denom - rp.param = param - - return rp - end -end - -mutable struct Ideal{T <: MPolyRingElem} - gens::Vector{T} - dim::Int - gb::Dict{Int, Vector{T}} - inter_sols::Vector{Vector{Vector{QQFieldElem}}} - real_sols::Vector{Vector{QQFieldElem}} - rat_sols::Vector{Vector{QQFieldElem}} - rat_param::RationalParametrization - - function Ideal(F::Vector{T}) where {T <: MPolyRingElem} - I = new{T}() - I.gens = F - I.dim = -1 - I.gb = Dict() - - return I - end -end - -Base.parent(I::Ideal) = Nemo.parent(I.gens[1]) - -Base.show(io::IO, I::Ideal) = print(io, I.gens) - -Base.getindex(I::Ideal, idx::Int) = I.gens[idx] diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/groebner-bases.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/groebner-bases.jl deleted file mode 100644 index f26122f..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/groebner-bases.jl +++ /dev/null @@ -1,70 +0,0 @@ -@testset "Algorithms -> Gröbner bases" begin - R, (x,y,z) = polynomial_ring(QQ,["x","y","z"], ordering=:degrevlex) - F = [x^2+1-3, x*y-z, x*z^2-3*y^2] - #= not a finite field =# - @test_throws ErrorException groebner_basis(Ideal(F)) - R, (x,y,z) = polynomial_ring(GF(101),["x","y","z"], ordering=:degrevlex) - I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y]) - G = groebner_basis(I) - H = MPolyRingElem[ - x + 2*y + 2*z + 100 - y*z + 82*z^2 + 10*y + 40*z - y^2 + 60*z^2 + 20*y + 81*z - z^3 + 28*z^2 + 64*y + 13*z - ] - @test G == H - @test I.gb[0] == H - - G = groebner_basis(I, eliminate=2) - H = MPolyRingElem[ - z^4 + 38*z^3 + 95*z^2 + 95*z - ] - @test G == H - - @test_throws ErrorException eliminate(I,0) - L = eliminate(I,2) - @test L == H - @test I.gb[2] == H - - I = Ideal([R(0)]) - G = groebner_basis(I) - @test G == [R(0)] -end - -@testset "Algorithms -> Sig Gröbner bases" begin - R, (x,y,z) = polynomial_ring(QQ,["x","y","z"], ordering=:degrevlex) - F = [x^2+1-3, x*y-z, x*z^2-3*y^2] - #= not a finite field =# - @test_throws ErrorException sig_groebner_basis(F) - R, (x,y,z) = polynomial_ring(GF(17),["x","y","z"], ordering=:degrevlex) - F = [x^2+1-3, x*y-z, x*z^2-3*y^2] - #= not homogeneous =# - @test_throws ErrorException sig_groebner_basis(F) - - #= GB test 1 =# - Fhom = AlgebraicSolving._homogenize(F) - sgb = sig_groebner_basis(Fhom) - @test AlgebraicSolving._is_gb(sgb) - - #= GB test 2 =# - R, (x,y,z,w) = polynomial_ring(GF(65521),["x","y","z","w"], ordering=:degrevlex) - F = cyclic(R).gens - Fhom = AlgebraicSolving._homogenize(F) - sgb = sig_groebner_basis(Fhom) - @test AlgebraicSolving._is_gb(sgb) - - #= GB test 3 =# - F = katsura(R).gens - Fhom = AlgebraicSolving._homogenize(F) - sgb = sig_groebner_basis(Fhom) - @test AlgebraicSolving._is_gb(sgb) - - #= GB test 4 (pivot setting bug) =# - R, (x1, x2, x3, x4) = polynomial_ring(GF(65521), ["x1", "x2", "x3", "x4"], ordering=:degrevlex) - F = [11523*x1^4 + 30378*x1^3*x2 + 30154*x1^2*x2^2 + 10157*x1*x2^3 - 28136*x2^4 - 4771*x1^3*x3 - 21056*x1^2*x2*x3 + 15696*x1*x2^2*x3 - 16144*x2^3*x3 - 1553*x1^2*x3^2 - 30379*x1*x2*x3^2 - 12735*x2^2*x3^2 + 18058*x1*x3^3 + 24670*x2*x3^3 - 16379*x3^4 + 24196*x1^3*x4 - 19411*x1^2*x2*x4 + 17610*x1*x2^2*x4 - 5715*x2^3*x4 - 21186*x1^2*x3*x4 - 22865*x1*x2*x3*x4 - 1939*x2^2*x3*x4 - 5685*x1*x3^2*x4 + 8508*x2*x3^2*x4 + 21819*x3^3*x4 - 24868*x1^2*x4^2 - 18233*x1*x2*x4^2 - 14116*x2^2*x4^2 + 28291*x1*x3*x4^2 - 9068*x2*x3*x4^2 - 15138*x3^2*x4^2 + 8921*x1*x4^3 - 18808*x2*x4^3 - 3005*x3*x4^3 + 7368*x4^4, - 31703*x1^4 + 23616*x1^3*x2 + 20696*x1^2*x2^2 - 7125*x1*x2^3 + 15334*x2^4 + 26619*x1^3*x3 + 2173*x1^2*x2*x3 - 31312*x1*x2^2*x3 - 31386*x2^3*x3 - 25244*x1^2*x3^2 - 28729*x1*x2*x3^2 + 27244*x2^2*x3^2 - 24892*x1*x3^3 + 2046*x2*x3^3 + 2516*x3^4 - 18588*x1^3*x4 + 9980*x1^2*x2*x4 - 10104*x1*x2^2*x4 + 21688*x2^3*x4 - 1315*x1^2*x3*x4 - 17824*x1*x2*x3*x4 + 14919*x2^2*x3*x4 - 568*x1*x3^2*x4 - 22509*x2*x3^2*x4 + 18494*x3^3*x4 + 25947*x1^2*x4^2 - 28652*x1*x2*x4^2 - 25547*x2^2*x4^2 + 1637*x1*x3*x4^2 - 20130*x2*x3*x4^2 + 19739*x3^2*x4^2 + 3742*x1*x4^3 + 25425*x2*x4^3 + 6342*x3*x4^3 - 3004*x4^4, - 2857*x1^4 + 8898*x1^3*x2 + 16959*x1^2*x2^2 - 28026*x1*x2^3 - 25631*x2^4 + 11030*x1^3*x3 + 29101*x1^2*x2*x3 + 30359*x1*x2^2*x3 + 27330*x2^3*x3 + 19126*x1^2*x3^2 - 26603*x1*x2*x3^2 + 2510*x2^2*x3^2 + 7575*x1*x3^3 - 25033*x2*x3^3 - 21024*x3^4 + 30501*x1^3*x4 + 23834*x1^2*x2*x4 - 1858*x1*x2^2*x4 - 10862*x2^3*x4 + 30320*x1^2*x3*x4 + 19705*x1*x2*x3*x4 + 28359*x2^2*x3*x4 + 17590*x1*x3^2*x4 + 11929*x2*x3^2*x4 + 22830*x3^3*x4 + 13501*x1^2*x4^2 - 24860*x1*x2*x4^2 + 12598*x2^2*x4^2 - 9409*x1*x3*x4^2 - 2827*x2*x3*x4^2 - 8608*x3^2*x4^2 + 30938*x1*x4^3 - 12892*x2*x4^3 + 9165*x3*x4^3 - 5202*x4^4, - -23687*x1^4 + 32692*x1^3*x2 + 20539*x1^2*x2^2 - 27327*x1*x2^3 + 3928*x2^4 - 13018*x1^3*x3 - 13583*x1^2*x2*x3 - 30594*x1*x2^2*x3 - 12584*x2^3*x3 - 9819*x1^2*x3^2 + 14542*x1*x2*x3^2 + 30297*x2^2*x3^2 + 15188*x1*x3^3 + 28438*x2*x3^3 + 13512*x3^4 + 13327*x1^3*x4 + 14335*x1^2*x2*x4 - 15128*x1*x2^2*x4 - 21922*x2^3*x4 - 22104*x1^2*x3*x4 - 23535*x1*x2*x3*x4 - 4393*x2^2*x3*x4 - 20398*x1*x3^2*x4 + 14310*x2*x3^2*x4 - 4426*x3^3*x4 - 23087*x1^2*x4^2 - 21281*x1*x2*x4^2 + 13831*x2^2*x4^2 - 23378*x1*x3*x4^2 + 18852*x2*x3*x4^2 - 11968*x3^2*x4^2 - 31181*x1*x4^3 + 20091*x2*x4^3 - 14043*x3*x4^3 - 10677*x4^4] - sgb = sig_groebner_basis(F) - @test AlgebraicSolving._is_gb(sgb) -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/normal-forms.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/normal-forms.jl deleted file mode 100644 index 6ad4ce7..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/normal-forms.jl +++ /dev/null @@ -1,18 +0,0 @@ -@testset "Algorithms -> Normal forms" begin - R, (x,y) = polynomial_ring(GF(101),["x","y"]) - I = Ideal([y*x+17-y, x+13*y]) - f = x^4+y - @test normal_form(f, I) == 100*y+77 - F = [x+13*y, x*y-4] - @test normal_form(F, I) == [0, y + 80] - R, (x,y) = polynomial_ring(GF(536870923),["x","y"]) - I = Ideal([y*x+17-y, x+13*y]) - F = [x+13*y, x*y-4] - @test normal_form(F, I) == [0, y + 536870902] - R, (x,y) = polynomial_ring(GF(65521),["x","y"]) - I = Ideal([y*x+17-y, x+13*y]) - F = [x+13*y, x*y+16] - @test normal_form(F, I) == [0, y + 65520] - I = Ideal([R(0)]) - @test normal_form(F, I) == F -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/solvers.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/solvers.jl deleted file mode 100644 index ed113e4..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/test/algorithms/solvers.jl +++ /dev/null @@ -1,53 +0,0 @@ -@testset "Algorithms -> Solvers" begin - R, (x1,x2,x3,x4) = polynomial_ring(QQ,["x1","x2","x3","x4"], ordering=:degrevlex) - I = Ideal([x1 + 2*x2 + 2*x3 + 2*x4 - 1, - x1^2 + 2*x2^2 + 2*x3^2 + 2*x4^2 - x1, - 2*x1*x2 + 2*x2*x3 + 2*x3*x4 - x2, - x2^2 + 2*x1*x3 + 2*x2*x4 - x3]) - sols = Vector{QQFieldElem}[ - [4862548775//8589934592, 1281562925//8589934592, 2195068207//8589934592, -32714273694608759819673593948262790419337//174224571863520493293247799005065324265472], - [3779635503//8589934592, 2638476131//8589934592, 908473689//8589934592, -92633843493479102248442236077889080803361//696898287454081973172991196020261297061888], - [1, 0, 0, 0], - [6410479475//8589934592, 2005530653//8589934592, -1585770177//8589934592, 55658687714722201275489356321691134094555601//713623846352979940529142984724747568191373312], - [1611414365//8589934592, 673053615//8589934592, 632173751//8589934592, 708759148891639684402860468800417934359477//2787593149816327892691964784081045188247552], - [2863311531//8589934592, 0, 0, 14518714321960041107770649917088777022123//43556142965880123323311949751266331066368] - ] - rat_sols = Vector{QQFieldElem}[[49, 0, 0, 0], [49//3, 0, 0, 1//3]] - - @test sols == real_solutions(I) - @test rat_sols == rational_solutions(I) - @test I.real_sols == real_solutions(I) - - C, x = polynomial_ring(QQ, "x") - elim = 128304*x^8 - 93312*x^7 + 15552*x^6 + 3144*x^5 - 1120*x^4 + 36*x^3 + 15*x^2 - x - denom = 1026432*x^7 - 653184*x^6 + 93312*x^5 + 15720*x^4 - 4480*x^3 + 108*x^2 + 30*x - 1 - p1 = -3872448*x^7 + 2607552*x^6 - 408528*x^5 - 63088*x^4 + 20224*x^3 - 540*x^2 - 172*x + 7 - p2 = -303264*x^7 + 314928*x^6 - 113544*x^5 + 9840*x^4 + 3000*x^3 - 564*x^2 + 12*x - p3 = -699840*x^7 + 449712*x^6 - 74808*x^5 - 1956*x^4 + 1308*x^3 - 174*x^2 + 18*x - p1 *= -7 - p2 *= -7 - p3 *= -7 - - param = rational_parametrization(I) - - @test param.vars == [:x1, :x2, :x3, :x4] - @test param.lf_cfs == ZZRingElem[] - @test param.elim == elim - @test param.denom == denom - @test param.param[1] == p1 - @test param.param[2] == p2 - @test param.param[3] == p3 - @test I.rat_param.elim == elim - @test I.rat_param.denom == denom - @test I.rat_param.param[1] == p1 - @test I.rat_param.param[2] == p2 - @test I.rat_param.param[3] == p3 - - I = Ideal([x1^2-x2, x1*x3-x4, x2*x4-12, x4^3-x3^2]) - real_solutions(I) - @test I.rat_param.vars == Symbol[] - - I = Ideal([x1^2-x2, x1*x3, x2-12]) - @test_throws ErrorException real_solutions(I) - @test_throws ErrorException rational_solutions(I) -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/examples/katsura.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/examples/katsura.jl deleted file mode 100644 index 7e5127f..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/test/examples/katsura.jl +++ /dev/null @@ -1,28 +0,0 @@ -@testset "Examples -> Katsura" begin - I = katsura(3) - R, x = first(I.gens).parent, vars(first(I.gens)) - G = [x[1] + 2*x[2] + 2*x[3] + 2*x[4] - 1, - x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 - x[1], - 2*x[1]*x[2] + 2*x[2]*x[3] + 2*x[3]*x[4] - x[2], - x[2]^2 + 2*x[1]*x[3] + 2*x[2]*x[4] - x[3]] - - @test I.gens == G - - I = katsura(4, 101) - R, x = first(I.gens).parent, vars(first(I.gens)) - G = [x[1] + 2*x[2] + 2*x[3] + 2*x[4] + 2*x[5] + 100, - x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 + 2*x[5]^2 + 100*x[1], - 2*x[1]*x[2] + 2*x[2]*x[3] + 2*x[3]*x[4] + 2*x[4]*x[5] + 100*x[2], - x[2]^2 + 2*x[1]*x[3] + 2*x[2]*x[4] + 2*x[3]*x[5] + 100*x[3], - 2*x[2]*x[3] + 2*x[1]*x[4] + 2*x[2]*x[5] + 100*x[4]] - - @test I.gens == G - - R, (x,y,z) = polynomial_ring(QQ, ["x","y","z"]) - I = katsura(R) - G = [x + 2*y + 2*z - 1, - x^2 - x + 2*y^2 + 2*z^2, - 2*x*y + 2*y*z - y] - - @test I.gens == G -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/interfaces/nemo.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/interfaces/nemo.jl deleted file mode 100644 index d3ffdcc..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/test/interfaces/nemo.jl +++ /dev/null @@ -1,16 +0,0 @@ -@testset "Interfaces -> Nemo" begin - R, (x,y,z) = polynomial_ring(QQ,["x","y","z"], ordering=:degrevlex) - F = [x^2+1-3, x*y-z, x*z^2-3*y^2] - cmp = (Int32[2, 2, 2], BigInt[1, 1, -2, 1, 1, 1, -1, 1, 1, 1, -3, 1], Int32[2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0]) - @test AlgebraicSolving._convert_to_msolve(F) == cmp - for _GF in [GF, AlgebraicSolving.Nemo.Native.GF] - R, (x,y,z) = polynomial_ring(_GF(2147483659),["x","y","z"], ordering=:degrevlex) - F = [x^2+1-3, x*y-z, x*z^2-3*y^2] - # prime is bigger than 2^31, should throw an error - @test_throws ErrorException AlgebraicSolving._convert_to_msolve(F) - R, (x,y,z) = polynomial_ring(_GF(101),["x","y","z"], ordering=:degrevlex) - F = [x^2+1-3, x*y-z, x*z^2-3*y^2] - res = AlgebraicSolving._convert_to_msolve(F) - @test AlgebraicSolving._convert_finite_field_array_to_abstract_algebra(Int32(3), res..., R) == F - end -end diff --git a/src/connectcurves/AlgebraicSolving.jl-main/test/runtests.jl b/src/connectcurves/AlgebraicSolving.jl-main/test/runtests.jl deleted file mode 100644 index 11a1d92..0000000 --- a/src/connectcurves/AlgebraicSolving.jl-main/test/runtests.jl +++ /dev/null @@ -1,10 +0,0 @@ -using AlgebraicSolving -using Test - -@testset verbose = true "AlgebraicSolving Tests" begin -include("interfaces/nemo.jl") -include("algorithms/groebner-bases.jl") -include("algorithms/normal-forms.jl") -include("algorithms/solvers.jl") -include("examples/katsura.jl") -end diff --git a/src/connectcurves/data.jl b/src/connectcurves/data.jl deleted file mode 100644 index 1d5f9f6..0000000 --- a/src/connectcurves/data.jl +++ /dev/null @@ -1,14 +0,0 @@ -#using Nemo -R, (x,y) = Nemo.polynomial_ring(QQ, [:x, :y]) - -# If you replace y^2 by 2*y^2 you get two very small connected components on the sides -# that maple misses even with grid [1000,1000] - -f = 1594627541097114368612385*x^16 + 24126594979283487048484560*x^15*y - 648897523515553246784074808*x^14*y^2 + 9227671981881181765203810480*x^13*y^3 + 775388988595641728298874736332*x^12*y^4 + 10787151407096126900712389934720*x^11*y^5 + 77139559828286619230682855993096*x^10*y^6 + 452145503210946168432702707056320*x^9*y^7 + 1603450939087454055697523432885078*x^8*y^8 + 472422761323888641034023872620080*x^7*y^9 + 69254293553970771431091788378664*x^6*y^10 + 8171004998268972015374643672912*x^5*y^11 + 486748426688048642456485687660*x^4*y^12 - 12064621488868591078399181568*x^3*y^13 - 1468208821458887902925840024*x^2*y^14 + 12892282240123223587086528*x*y^15 + 1551343473382248651380209*y^16 - 7416582067989458752697004*x^14 - 86407846455606538783280976*x^13*y + 2644747193988832166794696620*x^12*y^2 + 4962811393512179992436546328*x^11*y^3 - 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76093196872372578373119402591542924336595309825576292045515391246379464763158228784639574310982195640136389028170516631428420420489719956379967145212728402543856172428301827720835720619511746291529555478771232044026977196487380606051408105650931853037339102824546133136096406879899656252503263781924026226251779704232683941753426157396355555386426406923634579674802667468556932278540083239541771095586953543174979462316844522007563225998088037858674707962626971083428228623682979720860644003550437215307280073434204980445128604856611045119274229393897316722277964178023092238372341675934924661369445149897548641019617913507175210877932947651340271616]] -=# \ No newline at end of file diff --git a/src/connectcurves/main.ipynb b/src/connectcurves/main.ipynb deleted file mode 100644 index 87ef610..0000000 --- a/src/connectcurves/main.ipynb +++ /dev/null @@ -1,13722 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 53, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Loading libraries and data..\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/Documents/gittravail/AlgCurves/AlgebraicSolving.jl-main`\n" - ] - } - ], - "source": [ - "println(\"Loading libraries and data..\")\n", - "using Pkg\n", - "using Revise\n", - "Pkg.activate(\"AlgebraicSolving.jl-main\")\n", - "#import Nemo:\n", - "# is_univariate,\n", - "# coefficients_of_univariate\n", - "using AlgebraicSolving\n", - "using Nemo\n", - "#using Oscar\n", - "#include(\"tools.jl\")\n", - "using BenchmarkTools\n", - "using IntervalArithmetic" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "subresultants (generic function with 2 methods)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "include(\"data.jl\")\n", - "include(\"src/usolve/usolve.jl\")\n", - "include(\"subresultants.jl\")\n", - "#using Arblib" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "metadata": {}, - "outputs": [], - "source": [ - "# Generic change of variables\n", - "changemat = [1 0; 0 1]\n", - "#changemat = rand(-100:100, 2, 2)\n", - "invchangemat = inv(changemat)\n", - "f = evaluate(f, collect(changemat*[x; y]));\n" - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "metadata": {}, - "outputs": [], - "source": [ - "sr = subresultants(f, derivative(f,y),2, list=true);" - ] - }, - { - "cell_type": "code", - "execution_count": 111, - "metadata": {}, - "outputs": [ - { - "ename": "MethodError", - "evalue": "MethodError: no method matching *(::Vector{Int64}, ::QQMPolyRingElem)\n\nClosest candidates are:\n *(::Any, ::Any, !Matched::Any, !Matched::Any...)\n @ Base operators.jl:587\n *(!Matched::QQMPolyRingElem, ::QQMPolyRingElem)\n @ Nemo ~/.julia/packages/Nemo/VHAIi/src/flint/fmpq_mpoly.jl:335\n *(!Matched::ZZRingElem, ::QQMPolyRingElem)\n @ Nemo ~/.julia/packages/Nemo/VHAIi/src/flint/fmpq_mpoly.jl:381\n ...\n", - "output_type": "error", - "traceback": [ - "MethodError: no method matching *(::Vector{Int64}, ::QQMPolyRingElem)\n", - "\n", - "Closest candidates are:\n", - " *(::Any, ::Any, !Matched::Any, !Matched::Any...)\n", - " @ Base operators.jl:587\n", - " *(!Matched::QQMPolyRingElem, ::QQMPolyRingElem)\n", - " @ Nemo ~/.julia/packages/Nemo/VHAIi/src/flint/fmpq_mpoly.jl:335\n", - " *(!Matched::ZZRingElem, ::QQMPolyRingElem)\n", - " @ Nemo ~/.julia/packages/Nemo/VHAIi/src/flint/fmpq_mpoly.jl:381\n", - " ...\n", - "\n", - "\n", - "Stacktrace:\n", - " [1] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/main.ipynb:10" - ] - } - ], - "source": [ - "# Take sqfree factors of the resultant\n", - "sqr = collect(factor_squarefree(sr[1][1]))\n", - "# Keep only deg>0 factors \n", - "filter(t->t[2]>0, sqr)\n", - "# Order by multiplicity\n", - "sqr = sort(sqr, by=t->t[2])\n", - "# Group by multiplicity\n", - "group_sqr = [ [R(1),i] for i in 1:sqr[end][2] ]\n", - "for r in sqr\n", - " group_sqr[r[2]] *= r[1]\n", - "end\n", - "# Construct the parametrization of the critical points\n", - "params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in group_sqr ];" - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "evaluate_Arb (generic function with 1 method)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "function order_permut2d(L)\n", - " # Create a list of tuples with elements and their corresponding indices\n", - " LL = [(L[i][j], (i, j)) for i in eachindex(L) for j in eachindex(L[i])]\n", - " # Sort the enumerated list based on the values\n", - " sorted_LL = sort(LL, by = x -> x[1])\n", - " # Extract the sorted values and their corresponding indices\n", - " sorted_L = [pair[1] for pair in sorted_LL]\n", - " sorted_ind = [pair[2] for pair in sorted_LL]\n", - " \n", - " return sorted_L, sorted_ind\n", - "end\n", - "\n", - "function isolate(f; prec = 32, software=\"usolve\")\n", - " @assert is_univariate(f) \"Not univariate polynomial\"\n", - "\tif software == \"usolve\"\n", - "\t\treturn usolve(f, precision = prec, uspath=\"src/usolve/usolve\")\n", - " end\n", - "end\n", - "\n", - "function isolate_eval(f, ivar, val; prec=64)\n", - " sols = inter_solutions(AlgebraicSolving.Ideal([f, gens(R)[ivar] - val]), precision=prec)\n", - " return [ s[ivar%2+1] for s in sols ]\n", - "end\n", - "\n", - "function Arb_to_rat(x)\n", - "\tr = Nemo.radius(x)\n", - "\treturn map(simplest_rational_inside, [x-2*r, x+2*r])\n", - "end\n", - "\n", - "function rat_to_Arb(x)\n", - " x1,x2 = x\n", - " xm, xd = RR((x1+x2)/2), RR(x2-x1)\n", - " return ball(xm,xd)\n", - "end\n", - "\n", - "function evaluate_Arb(f, x)\n", - "\tcf = coefficients_of_univariate(f)\n", - "\treturn evalpoly(RR(x), cf) \n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "metadata": {}, - "outputs": [], - "source": [ - "precx = 150;" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Isolating critical values..\n" - ] - } - ], - "source": [ - "println(\"Isolating critical values..\")\n", - "xcrit = [ isolate(first(p), prec=precx) for p in params ]\n", - "xcrit_usolve = getindex.(xcrit, 1)\n", - "xcrit = getindex.(xcrit, 2)\n", - "_, xcritpermut = order_permut2d(xcrit);" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Computing isolating critical boxes using Arb..\n" - ] - }, - { - "data": { - "text/plain": [ - "2-element Vector{Vector{Vector{Vector{QQFieldElem}}}}:\n", - " [[[-24442554936443688467075675834396964293039975518886202698945133//25711008708143844408671393477458601640355247900524685364822016, 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boxes using Arb..\")\n", - "#RR(x) = Arb(x, prec=120)\n", - "RR = ArbField(max(precx,150))\n", - "Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ]\n", - "LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ]\n", - "#Pcrit = [ [ [ rat_to_Arb(pc[1]), pc[2] ] for pc in pcrit] for pcrit in Pcrit ];" - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "intersect_box (generic function with 1 method)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "function in_inter(I, J)\n", - " return J[1] < I[1] && I[2] < J[2]\n", - "end\n", - "\n", - "function overlap_inter(I,J)\n", - " return max(I[1], J[1]) <= min(I[2], J[2])\n", - "end\n", - "\n", - "# To try/do : isolate with usolve, call msolve with only one variable\n", - "function intersect_box(f, B; prec=100)\n", - " L = Array{Any}(undef, 4)\n", - " for i in 1:2\n", - " # Lxi\n", - " L[i] = Array{Any}(undef,2)\n", - " while true\n", - " flag = false\n", - " L[i][1] = isolate_eval(f, 2, B[2][i], prec=prec)\n", - " L[i][2] = []\n", - " for (j, l) in pairs(L[i][1])\n", - " if in_inter(l, B[1])\n", - " push!(L[i][2], j)\n", - " elseif overlap_inter(l, B[1])\n", - " prec *= 2\n", - " #println(\"Increase precision to \", prec)\n", - " flag = true\n", - " break\n", - " end\n", - " end\n", - " flag || break\n", - " end\n", - " # Lyi\n", - " L[i+2] = Array{Any}(undef,2)\n", - " while true\n", - " flag = false\n", - " L[i+2][1] = isolate_eval(f, 1, B[1][i], prec=prec)\n", - " L[i+2][2] = []\n", - " for (j, l) in pairs(L[i+2][1])\n", - " if in_inter(l, B[2])\n", - " push!(L[i+2][2], j)\n", - " elseif overlap_inter(l, B[2])\n", - " prec *= 2\n", - " #println(\"Increase precision to \", prec)\n", - " flag = true\n", - " break\n", - " end\n", - " end\n", - " flag || break\n", - " end\n", - " end\n", - " return L\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "refine_xboxes (generic function with 1 method)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "function refine_xboxes(f, LB, prec)\n", - " # Implementation of refine_xboxes function goes here\n", - " xnew = isolate(f, prec=prec)[2]\n", - " for i in eachindex(LB)\n", - "\t\t LB[i] = [ xnew[i], LB[i][2] ]\n", - " end\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Compute intersections with critical boxes\n", - "mult=1 ; 16/16 pts\n", - "mult=2 ; 60/60 pts\n", - "Average time for one point: 0.17550745135859439s\n", - "Elapsed time to compute critical boxes: 13.488043069839478s\n" - ] - } - ], - "source": [ - "# Could be improved by handling nodes as extreme boxes:\n", - "# when npcside = [2,2,0,0] just take nearest below and above\n", - "# intersections b with the curves on the vertical sides\n", - "# and change into npcside = [0,0,2,2]\n", - "## TODO : Refine only the intervals that need to be refined\n", - "println(\"\\nCompute intersections with critical boxes\")\n", - "ts = time()\n", - "LPCside = Array{Any}(undef,length(LBcrit))\n", - "ndig = maximum([Int(floor(log10(length(LB)))) for LB in LBcrit])\n", - "Ltm = []\n", - "i = 1\n", - "while i <= length(LBcrit)\n", - " ndigi = Int(floor(log10(length(LBcrit[i]))))\n", - " LPCside[i] = Array{Any}(undef, length(LBcrit[i]))\n", - " while true\n", - " flag = false\n", - " for j in eachindex(LBcrit[i])\n", - " print(\"mult=$i ; $(j)/$(length(LBcrit[i]))$(repeat(\" \", ndig-ndigi+1))pts\",\"\\r\")\n", - " tm = time()\n", - " pcside = intersect_box(f, LBcrit[i][j], prec=precx)\n", - " npcside = [length(n) for (I, n) in pcside]\n", - " if i == 1 && sum(npcside) > 2\n", - " precx *= 2\n", - " println(\"\\nRefine extreme boxes along x-axis\")\n", - " refine_xboxes(params[1][1], LBcrit[1], precx)\n", - " flag = true\n", - " break\n", - " elseif i > 1 && sum(npcside[1:2]) != 0\n", - " precx *= 2\n", - " println(\"\\nRefine singular boxes along x-axis\")\n", - " refine_xboxes(params[2][1], LBcrit[2], precx)\n", - " flag = true\n", - " break\n", - " end\n", - " LPCside[i][j] = pcside\n", - " push!(Ltm, time() - tm)\n", - " end\n", - " flag || break\n", - " end\n", - " i += 1\n", - " println(\"\")\n", - "end\n", - "LnPCside = [ [[length(indI) for (L, indI) in PB] for PB in lpcside] for lpcside in LPCside ] \n", - "println(\"Average time for one point: $(sum(Ltm)/length(Ltm))s\")\n", - "println(\"Elapsed time to compute critical boxes: $(time()-ts)s\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "metadata": {}, - "outputs": [], - "source": [ - "# Update extreme boxes\n", - "for j in eachindex(LBcrit[1])\n", - " # If the curve does not intersect the box only on vertical sides\n", - " if !(LnPCside[1][j][1:2] == [0, 0])\n", - " PCside, nPCside = LPCside[1][j], LnPCside[1][j]\n", - " I = [ l[1] for l in PCside[3:end] ]\n", - " nI = [ l[2] for l in PCside[3:end] ]\n", - " # Locate the orientation of the extreme point\n", - " # s is the index on the side where there are more branches\n", - " # s=1: left; s=2: right\n", - " s = argmax([length(I[1]), length(I[2])])\n", - " # Ordinate range of the extreme point\n", - " ycrit = LBcrit[1][j][2]\n", - " # If it intersects on the bottom side\n", - " if nPCside[1] == 1\n", - " # yinf: the intersection with the vertical side just below the extreme point\n", - " yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[2]])\n", - " # We vertically enlarge the box until it intersects on the horizontal side\n", - " push!(LPCside[1][j][s + 2][2], yinf)\n", - " LPCside[1][j][1][2] = []\n", - " # We update the intersection numbers\n", - " LnPCside[1][j][s + 2] += 1\n", - " LnPCside[1][j][1] = 0\n", - " end\n", - " # If it intersects on the top side\n", - " if nPCside[2] == 1 \n", - " # ymax: the intersection with the vertical side just above the extreme point\n", - " ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[1]])\n", - " # We vertically enlarge the box until it intersects on the horizontal side\n", - " push!(LPCside[1][j][s + 2][2], ymax)\n", - " LPCside[1][j][2][2] = []\n", - " # We update the intersection numbers\n", - " LnPCside[1][j][s + 2] += 1\n", - " LnPCside[1][j][2] = 0\n", - " end\n", - " end\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Graph computation" - ] - } - ], - "source": [ - "print(\"Graph computation\")\n", - "# Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot\n", - "# And even remove this fiber for the graph\n", - "Vert = []\n", - "Edg = []\n", - "Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ]\n", - "Viso = []\n", - "ite = 1\n", - "\n", - "for ind in 1:length(xcritpermut)\n", - " i, j = xcritpermut[ind]\n", - "\n", - " if ind > 1\n", - " i1, j1 = xcritpermut[ind - 1]\n", - " end\n", - " if ind < length(xcritpermut)\n", - " i2, j2 = xcritpermut[ind + 1]\n", - " I2L, nI2L = LPCside[i2][j2][3]\n", - " end\n", - "\n", - " PCside, nPCside = LPCside[i][j], LnPCside[i][j]\n", - " I = [ l[1] for l in PCside[3:end] ]\n", - " nI = [ l[2] for l in PCside[3:end] ]\n", - "\n", - " xcmid = sum(LBcrit[i][j][1])//2\n", - " ycmid = sum(LBcrit[i][j][2])//2\n", - "\n", - " ymincrit = minimum(vcat(nI[1], nI[2], [length(I[1])+1]))\n", - " # Construct vertices\n", - " ###########################\n", - " # On the vertical left side\n", - " if ind > 1\n", - " for k in 1:length(I[1])\n", - " push!(Corr[i][j][1], Corr[i1][j1][3][k])\n", - " end\n", - " else\n", - " for k in 1:length(I[1])\n", - " push!(Vert, [xcrit[i][j][1], sum(I[1][k])//2])\n", - " push!(Corr[i][j][1], ite)\n", - " ite += 1\n", - " end\n", - " end\n", - " ###########################\n", - " # On the vertical right side\n", - " if ind < length(xcritpermut)\n", - " for k in 1:length(I[2])\n", - " push!(Vert, [(xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4])\n", - " push!(Corr[i][j][3], ite)\n", - " ite += 1\n", - " end\n", - " else\n", - " for k in 1:length(I[2])\n", - " push!(Vert, [xcrit[i][j][2], sum(I[2][k])//2])\n", - " push!(Corr[i][j][3], ite)\n", - " ite += 1\n", - " end\n", - " end\n", - " ###########################\n", - " # Below the critical point\n", - " #println()\n", - " #println(map(length,I))\n", - " #println(vcat(nI[1], nI[2], [length(I[1])+1]))\n", - " for k in 1:ymincrit-1\n", - " push!(Vert, [xcmid, sum(I[1][k] + I[2][k])// 4])\n", - " push!(Corr[i][j][2][1], ite)\n", - " push!(Edg, [Corr[i][j][1][k], ite]) # left\n", - " push!(Edg, [ite, Corr[i][j][3][k]]) # right\n", - " ite += 1\n", - " end\n", - " ###########################\n", - " # The critical point\n", - " ##########################\n", - " # if it is an isolated point\n", - " if isempty(nI[1]) && isempty(nI[2])\n", - " #pass\n", - " # We can add the isolated vertex\n", - " # push!(Vert, Pcrit[i][j])\n", - " # push!(Corr[i][j][2][1], ite)\n", - " # We will subsequently add the vertex in the graph\n", - " # push!(Viso, ite)\n", - " # ite += 1\n", - " ############################################\n", - " ## TO BE REPLACED BY APPSING IDENTIFICATOR ##\n", - " ## works for space curves without nodes ##\n", - " ############################################\n", - " # If we are dealing with a node\n", - " elseif i == 2\n", - " # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2\n", - " push!(Edg, [Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]]])\n", - " push!(Edg, [Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]]])\n", - " else\n", - " # We can add the vertex\n", - " push!(Vert, [xcmid, ycmid])\n", - " push!(Corr[i][j][2][2], ite)\n", - " # We connect to the vertical left side of the critical box\n", - " for k in nI[1]\n", - " push!(Edg, [Corr[i][j][1][k], ite])\n", - " end\n", - " # We connect to the vertical right side of the critical box\n", - " for k in nI[2]\n", - " push!(Edg, [ite, Corr[i][j][3][k]])\n", - " end\n", - " ite += 1\n", - " end\n", - " ###########################\n", - " # Above the critical point\n", - " for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1\n", - " push!(Vert, [xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4])\n", - " push!(Corr[i][j][2][3], ite)\n", - " push!(Edg, [Corr[i][j][1][end - k + 1], ite]) # left\n", - " push!(Edg, [ite, Corr[i][j][3][end - k + 1]]) # right\n", - " ite += 1\n", - " end\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "metadata": {}, - "outputs": [], - "source": [ - "using Plots,Colors" - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "plot_graph (generic function with 1 method)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "\n", - "function plot_graph(V, E)\n", - " println(\"Plotting the graph\")\n", - " plot(legend=false)\n", - " for e in E\n", - " xe, ye = map(Float64,[e[1][1], e[2][1]]), map(Float64,[e[1][2], e[2][2]])\n", - " plot!(xe, ye, lc=\"red\", lw=3)\n", - " end\n", - " scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc=\"black\", m=:diamond)\n", - " #plt.show(block=true)\n", - " plot!()\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Plotting the graph\n" - ] - }, - { - "data": { - "image/png": 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push!(get!(adj_list, i, []), j)\n", - " push!(get!(adj_list, j, []), i)\n", - " end\n", - "\n", - " # Depth-first search\n", - " function dfs(node, component)\n", - " push!(visited, node)\n", - " push!(component, node)\n", - " for neighbor in adj_list[node]\n", - " if !(neighbor in visited)\n", - " dfs(neighbor, component)\n", - " end\n", - " end\n", - " end\n", - "\n", - " # Find connected components\n", - " for node in keys(adj_list)\n", - " if !(node in visited)\n", - " component = Vector{Int}()\n", - " dfs(node, component)\n", - " push!(components, component)\n", - " end\n", - " end\n", - "\n", - " # Group edges by connected component\n", - " grouped_edges = [Tuple{Int, Int}[] for _ in components]\n", - " for (idx, component) in enumerate(components)\n", - " for node in component\n", - " for neighbor in adj_list[node]\n", - " if neighbor > node && neighbor in component\n", - " push!(grouped_edges[idx], (node, neighbor))\n", - " end\n", - " end\n", - " end\n", - " end\n", - "\n", - " grouped_vert = [ [ vert[cv] for cv in c ] for c in components ]\n", - " return grouped_vert, grouped_edges\n", - "end\n" - ] - }, - { - "cell_type": "code", - "execution_count": 108, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "4\n" - ] - } - ], - "source": [ - "CVert, CEdg = connected_components(Vert, Edg); println(length(CVert))" - ] - }, - { - "cell_type": "code", - "execution_count": 98, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "plot_graph_comp (generic function with 1 method)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "function plot_graph_comp(V, CE)\n", - " println(\"Plotting the graph\")\n", - " plot(legend=false)\n", - " col = distinguishable_colors(length(CE)+2)\n", - " for j in eachindex(CE)\n", - " for e in CE[j]\n", - " v1, v2 = map(Float64, V[e[1]]), map(Float64, V[e[2]])\n", - " plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=3)\n", - " end\n", - " end\n", - " #plt.show(block=true)\n", - " plot!()\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 99, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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(generic function with 1 method)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingElement\n", - " if degree(P) < degree(Q)\n", - " P, Q = Q, P\n", - " end\n", - " S = []\n", - " s = leading_coefficient(Q)^(degree(P)-degree(Q))\n", - " A = Q\n", - " B = pseudorem(P,-Q)\n", - " ring = parent(P)\n", - " while true\n", - " d = degree(A)\n", - " e = degree(B)\n", - " if iszero(B)\n", - " return S\n", - " end\n", - " pushfirst!(S, copy(B))\n", - " delta = d - e\n", - " if delta > 1\n", - " if length(S) > 1\n", - " n = degree(S[2]) - degree(S[1]) - 1\n", - " if n == 0\n", - " C = copy(S[1])\n", - " else\n", - " x = leading_coefficient(S[1])\n", - " y = leading_coefficient(S[2])\n", - " a = 1 << (length(bits(ZZ(n))) - 1)\n", - " c = x\n", - " n = n - a\n", - " while a > 1\n", - " a ÷= 2\n", - " c = c^2 / y\n", - " if n >= a\n", - " c = c * x / y\n", - " n = n - a\n", - " end\n", - " end\n", - " C = c * S[1] / y\n", - " end\n", - " else\n", - " C = leading_coefficient(B)^(delta-1) * B / s^(delta-1)\n", - " end\n", - " pushfirst!(S, copy(C))\n", - " else\n", - " C = copy(B)\n", - " end\n", - " if e == 0\n", - " return S\n", - " end\n", - " B = pseudorem(A,-B) / (s^delta * leading_coefficient(A))\n", - " A = copy(C)\n", - " s = leading_coefficient(A)\n", - " end\n", - "end\n" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "-x*y^2 + (x^2 + 6)*y - x^2 - x - 6" - ], - "text/latex": [ - "-x y^{2} + \\left(x^{2} + 6\\right) y - x^{2} - x - 6" - ], - "text/plain": [ - "-x*y^2 + (x^2 + 6)*y - x^2 - x - 6" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#using Nemo\n", - "R, x = polynomial_ring(QQ, \"x\")\n", - "#f = x^8 + x^6 -3*x^4 -3*x^3 +8*x^2 +2*x -5\n", - "#g = 3*x^6 +5*x^4 -4*x^2 -9*x +21\n", - "S, y = polynomial_ring(R, \"y\")\n", - "f = (y^2 + 6)*(x - 1) - y*(x^2 + 1)\n", - "g = (x^2 + 6)*(y - 1) - x*(y^2 + 1)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "ename": "UndefVarError", - "evalue": "UndefVarError: `g` not defined", - "output_type": "error", - "traceback": [ - "UndefVarError: `g` not defined\n", - "\n", - "Stacktrace:\n", - " [1] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/subresultant.ipynb:1" - ] - } - ], - "source": [ - "subresultants(f,g)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "ename": "ArgumentError", - "evalue": "ArgumentError: not an exact division", - "output_type": "error", - "traceback": [ - "ArgumentError: not an exact division\n", - "\n", - "Stacktrace:\n", - " [1] divexact(x::QQPolyRingElem, y::QQPolyRingElem; check::Bool)\n", - " @ Nemo ~/.julia/packages/Nemo/RGGys/src/flint/fmpq_poly.jl:454\n", - " [2] divexact\n", - " @ ~/.julia/packages/Nemo/RGGys/src/flint/fmpq_poly.jl:449 [inlined]\n", - " [3] inv\n", - " @ ~/.julia/packages/AbstractAlgebra/KwfqS/src/Rings.jl:38 [inlined]\n", - " [4] divrem(f::AbstractAlgebra.Generic.Poly{QQPolyRingElem}, g::AbstractAlgebra.Generic.Poly{QQPolyRingElem})\n", - " @ Nemo ~/.julia/packages/Nemo/RGGys/src/HeckeMiscPoly.jl:450\n", - " [5] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/subresultant.ipynb:1" - ] - } - ], - "source": [ - "divrem(f,-g)[2]" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "64" - ], - "text/latex": [ - "64" - ], - "text/plain": [ - "64" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "prevpow2(ZZ(100))" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Integers" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "parent(degree(f))" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[a, b])" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "RR, (a,b) = Nemo.polynomial_ring(QQ,[:a,:b])" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "a^2 + a*b^2 + a*b + b" - ], - "text/latex": [ - "a^{2} + a b^{2} + a b + b" - ], - "text/plain": [ - "a^2 + a*b^2 + a*b + b" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 196, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "asvar_to_parray (generic function with 1 method)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "function poly_to_array(P::MPolyRingElem)\n", - " # return P as two lists ci and vi of resp. coeffs and exponents\n", - " return [collect(coefficients(P)), collect(exponent_vectors(P))]\n", - "end\n", - "\n", - "function rem_ind(L,i)\n", - " # remove element at index i\n", - " return [ L[1:i-1]; L[i+1:end] ]\n", - "end\n", - "\n", - "function add_ind(L,i,x)\n", - " # add element x at index i\n", - " return [ L[1:i-1]; [x]; L[i:end] ]\n", - "end\n", - "\n", - "function parray_asvar(LP, idx)\n", - " # takes a sparse representation of a poly P \n", - " # and outputs a sparse rpz of P seen as a univariate poly in the i-th variable\n", - " deg = sort(LP[2], by= x->x[idx])[end][idx]\n", - " NLP = [ [[],[]] for _ in 1:deg+1 ]\n", - " for i in eachindex(LP[2])\n", - " di = LP[2][i][idx]+1\n", - " push!(NLP[di][1], LP[1][i])\n", - " push!(NLP[di][2], rem_ind(LP[2][i], idx)) \n", - " end\n", - " return NLP\n", - "end\n", - "\n", - "function array_to_poly(LP, A)\n", - " C = MPolyBuildCtx(A)\n", - " R = base_ring(A)\n", - " for i in eachindex(LP[1])\n", - " push_term!(C, R(LP[1][i]), LP[2][i]);\n", - " end\n", - " return finish(C)\n", - "end\n", - "\n", - "function asvar_to_parray(NLP, idx)\n", - " LP = [[],[]]\n", - " for i in 1:length(NLP)\n", - " for j in eachindex(NLP[i][1])\n", - " push!(LP[1], NLP[i][1][j])\n", - " push!(LP[2], add_ind(NLP[i][2][j], idx, i-1))\n", - " end\n", - " end\n", - " return LP\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 133, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "a*b + 1" - ], - "text/latex": [ - "a b + 1" - ], - "text/plain": [ - "a*b + 1" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Q = a*b+1a" - ] - }, - { - "cell_type": "code", - "execution_count": 217, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "subresultants (generic function with 3 methods)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx) where T <: RingElement\n", - " LPQ = map(poly_to_array, [P,Q])\n", - " ULPQ = [ parray_asvar(lpq, idx) for lpq in LPQ ]\n", - "\n", - " R, x = polynomial_ring(base_ring(parent(P)), \"x\")\n", - " S, y = polynomial_ring(R, \"y\")\n", - "\n", - " UP, UQ = [ S([ array_to_poly(l, R) for l in lpq ]) for lpq in ULPQ ]\n", - "\n", - " sr = subresultants(UP, UQ)\n", - "\n", - " # Get it back to initial polynomial ring\n", - " Lsr = [ [collect(coefficients(csr)) for csr in coefficients(sr)] for sr in sr]\n", - " newsr = []\n", - " for lsr in Lsr\n", - " mlsr = [[],[]]\n", - " for i in 1:length(lsr)\n", - " for j in 1:length(lsr[i])\n", - " push!(mlsr[1], lsr[i][j])\n", - " push!(mlsr[2],add_ind([j-1],idx, i-1))\n", - " end\n", - " end\n", - " push!(newsr, array_to_poly(mlsr, parent(P)))\n", - " end\n", - "\n", - " return newsr\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "subresultants (generic function with 2 methods)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "include(\"subresultants.jl\")" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Multivariate polynomial ring in 2 variables x, y\n", - " over integer ring" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "R, (x,y) = polynomial_ring(ZZ, [:x,:y])\n", - "f = (y^2 + 6)*(x - 1) - y*(x^2 + 1)\n", - "g = (x^2 + 6)*(y - 1) - x*(y^2 + 1)\n", - "idx = 2\n", - "subresultants(x,x,1)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "2-element Vector{Any}:\n", - " 2*x^6 - 22*x^5 + 102*x^4 - 274*x^3 + 488*x^2 - 552*x + 288\n", - " -x^3 - x^2*y + 6*x^2 + 5*x*y - 11*x - 6*y + 6" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "res = subresultants(f,g,idx)" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "ename": "MethodError", - "evalue": "MethodError: no method matching keys(::Fac{ZZMPolyRingElem})\n\nClosest candidates are:\n keys(!Matched::Pkg.Registry.RegistryInstance)\n @ Pkg /opt/julia-1.10.1/share/julia/stdlib/v1.10/Pkg/src/Registry/registry_instance.jl:447\n keys(!Matched::Cmd)\n @ Base process.jl:678\n keys(!Matched::Core.SimpleVector)\n @ Base essentials.jl:781\n ...\n", - "output_type": "error", - "traceback": [ - "MethodError: no method matching keys(::Fac{ZZMPolyRingElem})\n", - "\n", - "Closest candidates are:\n", - " keys(!Matched::Pkg.Registry.RegistryInstance)\n", - " @ Pkg /opt/julia-1.10.1/share/julia/stdlib/v1.10/Pkg/src/Registry/registry_instance.jl:447\n", - " keys(!Matched::Cmd)\n", - " @ Base process.jl:678\n", - " keys(!Matched::Core.SimpleVector)\n", - " @ Base essentials.jl:781\n", - " ...\n", - "\n", - "\n", - "Stacktrace:\n", - " [1] top-level scope\n", - " @ ~/Documents/gittravail/AlgCurves/subresultant.ipynb:2" - ] - } - ], - "source": [ - "sq = collect(factor_squarefree(res[1]))\n" - ] - }, - { - "cell_type": "code", - "execution_count": 204, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "2-element Vector{Vector{Any}}:\n", - " [1, 1, 1, 1]\n", - " [[0, 1], [1, 2], [1, 1], [2, 0]]" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "NLP = parray_asvar(LP,1)\n", - "asvar_to_parray(NLP,1)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 128, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "y^2 + (x^2 + x)*y + x" - ], - "text/latex": [ - "y^{2} + \\left(x^{2} + x\\right) y + x" - ], - "text/plain": [ - "y^2 + (x^2 + x)*y + x" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "S([ array_to_poly(lp, R) for lp in NLP ])" - ] - }, - { - "cell_type": "code", - "execution_count": 129, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "a^2 + a*b^2 + a*b + b" - ], - "text/latex": [ - "a^{2} + a b^{2} + a b + b" - ], - "text/plain": [ - "a^2 + a*b^2 + a*b + b" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 106, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "4-element Vector{Vector{Int64}}:\n", - " [0, 1]\n", - " [1, 2]\n", - " [1, 1]\n", - " [2, 0]" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "idx=1\n", - "sort(LP[2], by= x->x[idx])" - ] - }, - { - "cell_type": "code", - "execution_count": 82, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Base.Generator{UnitRange{Int64}, typeof(identity)}(identity, 1:2)" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Julia 1.10.1", - "language": "julia", - "name": "julia-1.10" - }, - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia", - "version": "1.10.1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From 224f3ece0d8fc59653b627732aff9992204272b0 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 15:13:00 +0200 Subject: [PATCH 014/180] remove tools.jl --- src/connectcurves/subresultants.jl | 8 +-- src/connectcurves/tools.jl | 82 ------------------------------ 2 files changed, 4 insertions(+), 86 deletions(-) delete mode 100644 src/connectcurves/tools.jl diff --git a/src/connectcurves/subresultants.jl b/src/connectcurves/subresultants.jl index 4ecb27a..05e60b4 100644 --- a/src/connectcurves/subresultants.jl +++ b/src/connectcurves/subresultants.jl @@ -15,8 +15,8 @@ function add_ind(L,i,x) end function parray_asvar(LP, idx) - # takes a sparse representation of a poly P - # and outputs a sparse rpz of P seen as a univariate poly in the i-th variable + # takes the above representation of a poly P + # and outputs a representation of P seen as a univariate poly in the i-th variable deg = sort(LP[2], by= x->x[idx])[end][idx] NLP = [ [[],[]] for _ in 1:deg+1 ] for i in eachindex(LP[2]) @@ -66,7 +66,7 @@ function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingEl c = x n = n - a while a > 1 - a ÷= 2 + a /= 2 c = c^2 / y if n >= a c = c * x / y @@ -134,4 +134,4 @@ function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false end return newsr -end \ No newline at end of file +end diff --git a/src/connectcurves/tools.jl b/src/connectcurves/tools.jl deleted file mode 100644 index 7bfc2ef..0000000 --- a/src/connectcurves/tools.jl +++ /dev/null @@ -1,82 +0,0 @@ -#using Nemo -using Singular - -function randQQ(size=3) - fac = 10^(size) - return Nemo.QQ((-1)^(trunc(Int,rand()*10))*trunc(Int,rand()*fac),trunc(Int,rand()*fac)) -end - -function _mpoly_to_singular(f) - @assert Nemo.is_univariate(f) "Not univariate polynomial" - R, x = Singular.polynomial_ring(Singular.QQ, [:x]) - x = first(x) - cf = Nemo.coefficients_of_univariate(f) - return sum([ cf[j]*x^(j-1) for j = eachindex(cf) ]) -end - -function nb_roots_interval(f,a,b) - g = _mpoly_to_singular(f) - return Singular.LibRootsur.sturm(g, Singular.QQ(a), Singular.QQ(b)) -end - -""" - nb_roots_interval_partition(f, a, b) - -Compute the number of real roots of f(x) in the intervals: - (-infinity, a), (a,b), (b, +infinity) - -# Input: -* f: polynomial with involving one variable, with coeffients in QQ -* a,b: rational elements of QQ -# Output: -* [ n(-infinity, a), n(a,b), n(b, +infinity) ] - -""" -function nb_roots_interval_partition(f, a, b) - g = _mpoly_to_singular(f) - M = Singular.LibRootsur.maxabs(g) - a1, b1 = Singular.QQ(a), Singular.QQ(b) - M1, M2 = min(-M, a1), max(b1, M) - B = [ M1-1, a1, b1, M2+1 ] - return [ Singular.LibRootsur.sturm(g, B[i], B[i+1]) for i=1:3 ] -end - -function sturm_habicht_seq(f) - g = _mpoly_to_singular(f) - SH = map(Singular.coefficients_of_univariate, Singular.LibRootsur.sturmhaseq(g)) - return [ vcat(SH[k], [n_Q(0) for _=1:(k-length(SH[k]))]) for k in eachindex(SH) ] -end - -function subresultants_seq(f) - SH = sturm_habicht_seq(f) - d(k) = (-1)^((k*(k+1))>>1) - return [ d(length(SH)-1-k)*SH[k] for k=1:length(SH)-2 ] -end - -function subresultants_seq_biv(f, iv) - iu = iv%2+1 - # Modern computer Algebra Th 6.51. - degs = degrees(f) - n, d = degs[iv], degs[iu] - degsmax = [ (2*n-1-2*k)*d for k=0:d-2 ] - Dmax = degsmax[end]>>1+1 - ## - xs = [ randQQ() for _=1:(degsmax[1]+1) ] - @time begin - Srev = [ subresultants_seq(evaluate(f,[iu],[xx])) for xx in xs ] - end - S,t = Nemo.polynomial_ring(Nemo.QQ,"t") - Sr = [ [ S(0) for _=1:i] for i=1:n-2 ] - for i = 1:n-2 - for j = 1:i - ys = [ Nemo.QQ(Srev[l][i][j]) for l=eachindex(Srev) ] - Sr[i][j] = Nemo.interpolate(S, xs, ys) - end - end - return Sr -end - -#R, (x,y) = Nemo.polynomial_ring(Nemo.QQ, [:x,:y]) -#f = x^7+y^2*x^5-2*x*y^3+1+y^6 -#f = (x^2+y^2-1)*(2*x-y) -#Sr = subresultants_seq_biv(f, 1) From f243af04d5d3dc587ea91d508fed1a1dc1755456 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 15:26:24 +0200 Subject: [PATCH 015/180] split files --- src/connectcurves/boxes.jl | 59 ++++ src/connectcurves/graph.jl | 48 +++ src/connectcurves/isolate.jl | 17 + src/connectcurves/main.jl | 613 +++++++++++++---------------------- src/connectcurves/plots.jl | 26 ++ src/connectcurves/tools,jl | 27 ++ 6 files changed, 398 insertions(+), 392 deletions(-) create mode 100644 src/connectcurves/boxes.jl create mode 100644 src/connectcurves/graph.jl create mode 100644 src/connectcurves/isolate.jl create mode 100644 src/connectcurves/plots.jl create mode 100644 src/connectcurves/tools,jl diff --git a/src/connectcurves/boxes.jl b/src/connectcurves/boxes.jl new file mode 100644 index 0000000..648f5d1 --- /dev/null +++ b/src/connectcurves/boxes.jl @@ -0,0 +1,59 @@ +function in_inter(I, J) + return J[1] < I[1] && I[2] < J[2] +end + +function overlap_inter(I,J) + return max(I[1], J[1]) <= min(I[2], J[2]) +end + +# To try/do : isolate with usolve, call msolve with only one variable +function intersect_box(f, B; prec=100) + L = Array{Any}(undef, 4) + for i in 1:2 + # Lxi + L[i] = Array{Any}(undef,2) + while true + flag = false + L[i][1] = isolate_eval(f, 2, B[2][i], prec=prec) + L[i][2] = [] + for (j, l) in pairs(L[i][1]) + if in_inter(l, B[1]) + push!(L[i][2], j) + elseif overlap_inter(l, B[1]) + prec *= 2 + #println("Increase precision to ", prec) + flag = true + break + end + end + flag || break + end + # Lyi + L[i+2] = Array{Any}(undef,2) + while true + flag = false + L[i+2][1] = isolate_eval(f, 1, B[1][i], prec=prec) + L[i+2][2] = [] + for (j, l) in pairs(L[i+2][1]) + if in_inter(l, B[2]) + push!(L[i+2][2], j) + elseif overlap_inter(l, B[2]) + prec *= 2 + #println("Increase precision to ", prec) + flag = true + break + end + end + flag || break + end + end + return L +end + +function refine_xboxes(f, LB, prec) + # Implementation of refine_xboxes function goes here + xnew = isolate(f, prec=prec)[2] + for i in eachindex(LB) + LB[i] = [ xnew[i], LB[i][2] ] + end +end diff --git a/src/connectcurves/graph.jl b/src/connectcurves/graph.jl new file mode 100644 index 0000000..f20cea3 --- /dev/null +++ b/src/connectcurves/graph.jl @@ -0,0 +1,48 @@ + +## Graph functions +function connected_components(vert, edges) + adj_list = Dict{Int, Vector{Int}}() + visited = Set{Int}() + components = Vector{Vector{Int}}() + + # Build adjacency list + for (i, j) in edges + push!(get!(adj_list, i, []), j) + push!(get!(adj_list, j, []), i) + end + + # Depth-first search + function dfs(node, component) + push!(visited, node) + push!(component, node) + for neighbor in adj_list[node] + if !(neighbor in visited) + dfs(neighbor, component) + end + end + end + + # Find connected components + for node in keys(adj_list) + if !(node in visited) + component = Vector{Int}() + dfs(node, component) + push!(components, component) + end + end + + # Group edges by connected component + grouped_edges = [Tuple{Int, Int}[] for _ in components] + for (idx, component) in enumerate(components) + for node in component + for neighbor in adj_list[node] + if neighbor > node && neighbor in component + push!(grouped_edges[idx], (node, neighbor)) + end + end + end + end + + grouped_vert = [ [ vert[cv] for cv in c ] for c in components ] + return grouped_vert, grouped_edges +end \ No newline at end of file diff --git a/src/connectcurves/isolate.jl b/src/connectcurves/isolate.jl new file mode 100644 index 0000000..02517e6 --- /dev/null +++ b/src/connectcurves/isolate.jl @@ -0,0 +1,17 @@ +include("src/usolve/usolve.jl") + +function isolate(f; prec = 32, software="usolve") + # Univariate isolation using usolve + @assert is_univariate(f) "Not univariate polynomial" + if software == "usolve" + return usolve(f, precision = prec, uspath="src/usolve/usolve") + end +end + +function isolate_eval(f, ivar, val; prec=64) + # univariate isolation of roots of a bivariate polynomial f + # whose ivar-th variable is evaluated at val + # uses msolve + sols = inter_solutions(Ideal([f, gens(R)[ivar] - val]), precision=prec) + return [ s[ivar%2+1] for s in sols ] +end \ No newline at end of file diff --git a/src/connectcurves/main.jl b/src/connectcurves/main.jl index 4ca4e8b..15162d2 100644 --- a/src/connectcurves/main.jl +++ b/src/connectcurves/main.jl @@ -1,436 +1,265 @@ println("\nLoading libraries and data..") -using Pkg -using Revise -Pkg.activate("AlgebraicSolving.jl-main") -using AlgebraicSolving using Nemo #using Plots, Colors #pythonplot() -include("data.jl") -include("src/usolve/usolve.jl") +include("tools.jl") include("subresultants.jl") - -function order_permut2d(L) - # Create a list of tuples with elements and their corresponding indices - LL = [(L[i][j], (i, j)) for i in eachindex(L) for j in eachindex(L[i])] - # Sort the enumerated list based on the values - sorted_LL = sort(LL, by = x -> x[1]) - # Extract the sorted values and their corresponding indices - sorted_L = [pair[1] for pair in sorted_LL] - sorted_ind = [pair[2] for pair in sorted_LL] - - return sorted_L, sorted_ind -end - -function isolate(f; prec = 32, software="usolve") - @assert is_univariate(f) "Not univariate polynomial" - if software == "usolve" - return usolve(f, precision = prec, uspath="src/usolve/usolve") +include("isolate.jl") +include("boxes.jl") +include("graph.jl") +include("plots.jl") + +function compute_graph(f; generic=false, precx = 100) + R = parent(f) + # Generic change of variables + changemat = [1 0; 0 1] + if !generic + changemat = rand(-500:500, 2, 2) + end + f = evaluate(f, collect(changemat*[x; y])); + + println("\nCompute parametrization of critical pts...") + @time begin + sr = subresultants(f, derivative(f,y),2, list=true); + # Take sqfree factors of the resultant + sqr = collect(factor_squarefree(sr[1][1])) + # Keep only deg>0 factors + filter(t->t[2]>0, sqr) + # Order by multiplicity + sqr = sort(sqr, by=t->t[2]) + # Group by multiplicity + group_sqr = [ [R(1),i] for i in 1:sqr[end][2] ] + for r in sqr + group_sqr[r[2]][1] *= r[1] + end + # Construct the parametrization of the critical points + params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in group_sqr ]; end -end - -function isolate_eval(f, ivar, val; prec=64) - sols = inter_solutions(AlgebraicSolving.Ideal([f, gens(R)[ivar] - val]), precision=prec) - return [ s[ivar%2+1] for s in sols ] -end - -function Arb_to_rat(x) - r = radius(x) - return map(simplest_rational_inside, [x-2*r, x+2*r]) -end - -function rat_to_Arb(x) - x1,x2 = x - xm, xd = RR((x1+x2)/2), RR(x2-x1) - return ball(xm,xd) -end - -function evaluate_Arb(f, x) - cf = coefficients_of_univariate(f) - return evalpoly(RR(x), cf) -end -function in_inter(I, J) - return J[1] < I[1] && I[2] < J[2] -end + ############### + precx = 200; + ############### + # TODO : check that no overlap between different isolations + println("\nIsolating critical values at precision ", precx,"..") + @time begin + xcrit = [ isolate(first(p), prec=precx) for p in params ] + xcrit_usolve = getindex.(xcrit, 1) + xcrit = getindex.(xcrit, 2) + _, xcritpermut = order_permut2d(xcrit); + end -function overlap_inter(I,J) - return max(I[1], J[1]) <= min(I[2], J[2]) -end + println("\nComputing isolating critical boxes using Arb with precision ",max(precx,150),"..") + @time begin + #RR(x) = Arb(x, prec=120) + RR = ArbField(max(precx,150)) + Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ] + LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ] + end -# To try/do : isolate with usolve, call msolve with only one variable -function intersect_box(f, B; prec=100) - L = Array{Any}(undef, 4) - for i in 1:2 - # Lxi - L[i] = Array{Any}(undef,2) + # Could be improved by handling nodes as extreme boxes: + # when npcside = [2,2,0,0] just take nearest below and above + # intersections b with the curves on the vertical sides + # and change into npcside = [0,0,2,2] + ## TODO : Refine only the intervals that need to be refined + println("\nCompute intersections with critical boxes..") + @time begin + LPCside = Array{Any}(undef,length(LBcrit)) + ndig = maximum([Int(floor(log10(length(LB)))) for LB in LBcrit]) + for i in eachindex(LBcrit) + ndigi = Int(floor(log10(length(LBcrit[i])))) + LPCside[i] = Array{Any}(undef, length(LBcrit[i])) + precxtmp = precx while true flag = false - L[i][1] = isolate_eval(f, 2, B[2][i], prec=prec) - L[i][2] = [] - for (j, l) in pairs(L[i][1]) - if in_inter(l, B[1]) - push!(L[i][2], j) - elseif overlap_inter(l, B[1]) - prec *= 2 - #println("Increase precision to ", prec) + for j in eachindex(LBcrit[i]) + print("mult=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") + pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp) + npcside = [length(n) for (I, n) in pcside] + if i == 1 && sum(npcside) > 2 + print((i,j)," ",npcside) + precxtmp *= 2 + println("\nRefine extreme boxes along x-axis to precision ", precxtmp) + refine_xboxes(params[1][1], LBcrit[1], precxtmp) flag = true break - end - end - flag || break - end - # Lyi - L[i+2] = Array{Any}(undef,2) - while true - flag = false - L[i+2][1] = isolate_eval(f, 1, B[1][i], prec=prec) - L[i+2][2] = [] - for (j, l) in pairs(L[i+2][1]) - if in_inter(l, B[2]) - push!(L[i+2][2], j) - elseif overlap_inter(l, B[2]) - prec *= 2 - #println("Increase precision to ", prec) + elseif i > 1 && sum(npcside[1:2]) != 0 + precxtmp *= 2 + println("\nRefine singular boxes along x-axis to precision ", precxtmp) + refine_xboxes(params[2][1], LBcrit[2], precxtmp) flag = true break end + LPCside[i][j] = pcside end flag || break end + println("") end - return L -end - -function refine_xboxes(f, LB, prec) - # Implementation of refine_xboxes function goes here - xnew = isolate(f, prec=prec)[2] - for i in eachindex(LB) - LB[i] = [ xnew[i], LB[i][2] ] - end -end - -## Plot functions -function plot_graph(V, E) - println("Plotting the graph") - plot(legend=false) - for e in E - xe, ye = map(Float64,[e[1][1], e[2][1]]), map(Float64,[e[1][2], e[2][2]]) - plot!(xe, ye, lc="red", lw=3) - end - scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) - #plt.show(block=true) - plot!() -end - -function plot_graph_comp(V, CE) - println("Plotting the graph") - plot(legend=false) - col = distinguishable_colors(length(CE)+2) - for j in eachindex(CE) - for e in CE[j] - v1, v2 = map(Float64, V[e[1]]), map(Float64, V[e[2]]) - plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=3) - end - end - #plt.show(block=true) - plot!() -end - -## Graph functions -function connected_components(vert, edges) - adj_list = Dict{Int, Vector{Int}}() - visited = Set{Int}() - components = Vector{Vector{Int}}() - - # Build adjacency list - for (i, j) in edges - push!(get!(adj_list, i, []), j) - push!(get!(adj_list, j, []), i) - end - - # Depth-first search - function dfs(node, component) - push!(visited, node) - push!(component, node) - for neighbor in adj_list[node] - if !(neighbor in visited) - dfs(neighbor, component) + LnPCside = [ [[length(indI) for (L, indI) in PB] for PB in lpcside] for lpcside in LPCside ] + + # Update extreme boxes + for j in eachindex(LBcrit[1]) + # If the curve does not intersect the box only on vertical sides + if !(LnPCside[1][j][1:2] == [0, 0]) + PCside, nPCside = LPCside[1][j], LnPCside[1][j] + I = [ l[1] for l in PCside[3:end] ] + nI = [ l[2] for l in PCside[3:end] ] + # Locate the orientation of the extreme point + # s is the index on the side where there are more branches + # s=1: left; s=2: right + s = argmax([length(I[1]), length(I[2])]) + # Ordinate range of the extreme point + ycrit = LBcrit[1][j][2] + # If it intersects on the bottom side + if nPCside[1] == 1 + # yinf: the intersection with the vertical side just below the extreme point + yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[2]]) + # We vertically enlarge the box until it intersects on the horizontal side + push!(LPCside[1][j][s + 2][2], yinf) + LPCside[1][j][1][2] = [] + # We update the intersection numbers + LnPCside[1][j][s + 2] += 1 + LnPCside[1][j][1] = 0 + end + # If it intersects on the top side + if nPCside[2] == 1 + # ymax: the intersection with the vertical side just above the extreme point + ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[1]]) + # We vertically enlarge the box until it intersects on the horizontal side + push!(LPCside[1][j][s + 2][2], ymax) + LPCside[1][j][2][2] = [] + # We update the intersection numbers + LnPCside[1][j][s + 2] += 1 + LnPCside[1][j][2] = 0 end end end - - # Find connected components - for node in keys(adj_list) - if !(node in visited) - component = Vector{Int}() - dfs(node, component) - push!(components, component) - end end - # Group edges by connected component - grouped_edges = [Tuple{Int, Int}[] for _ in components] - for (idx, component) in enumerate(components) - for node in component - for neighbor in adj_list[node] - if neighbor > node && neighbor in component - push!(grouped_edges[idx], (node, neighbor)) - end - end + #print("\nGraph computation :") + #@time begin + # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot + # And even remove this fiber for the graph + Vert = [] + Edg = [] + Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ] + Viso = [] + ite = 1 + + for ind in 1:length(xcritpermut) + global ite + local i + i, j = xcritpermut[ind] + + if ind > 1 + i1, j1 = xcritpermut[ind - 1] end - end - - grouped_vert = [ [ vert[cv] for cv in c ] for c in components ] - return grouped_vert, grouped_edges -end - -# Generic change of variables -changemat = [1 0; 0 1] -changemat = rand(-500:500, 2, 2) -f = evaluate(f, collect(changemat*[x; y])); - -println("\nCompute parametrization of critical pts...") -@time begin -sr = subresultants(f, derivative(f,y),2, list=true); -# Take sqfree factors of the resultant -sqr = collect(factor_squarefree(sr[1][1])) -# Keep only deg>0 factors -filter(t->t[2]>0, sqr) -# Order by multiplicity -sqr = sort(sqr, by=t->t[2]) -# Group by multiplicity -group_sqr = [ [R(1),i] for i in 1:sqr[end][2] ] -for r in sqr - group_sqr[r[2]][1] *= r[1] -end -# Construct the parametrization of the critical points -params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in group_sqr ]; -end - -############### -precx = 200; -############### -# TODO : check that no overlap between different isolations -println("\nIsolating critical values at precision ", precx,"..") -@time begin -xcrit = [ isolate(first(p), prec=precx) for p in params ] -xcrit_usolve = getindex.(xcrit, 1) -xcrit = getindex.(xcrit, 2) -_, xcritpermut = order_permut2d(xcrit); -end - -println("\nComputing isolating critical boxes using Arb with precision ",max(precx,150),"..") -@time begin -#RR(x) = Arb(x, prec=120) -RR = ArbField(max(precx,150)) -Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ] -LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ] -end - -# Could be improved by handling nodes as extreme boxes: -# when npcside = [2,2,0,0] just take nearest below and above -# intersections b with the curves on the vertical sides -# and change into npcside = [0,0,2,2] -## TODO : Refine only the intervals that need to be refined -println("\nCompute intersections with critical boxes..") -@time begin -LPCside = Array{Any}(undef,length(LBcrit)) -ndig = maximum([Int(floor(log10(length(LB)))) for LB in LBcrit]) -for i in eachindex(LBcrit) - ndigi = Int(floor(log10(length(LBcrit[i])))) - LPCside[i] = Array{Any}(undef, length(LBcrit[i])) - precxtmp = precx - while true - flag = false - for j in eachindex(LBcrit[i]) - print("mult=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") - pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp) - npcside = [length(n) for (I, n) in pcside] - if i == 1 && sum(npcside) > 2 - print((i,j)," ",npcside) - precxtmp *= 2 - println("\nRefine extreme boxes along x-axis to precision ", precxtmp) - refine_xboxes(params[1][1], LBcrit[1], precxtmp) - flag = true - break - elseif i > 1 && sum(npcside[1:2]) != 0 - precxtmp *= 2 - println("\nRefine singular boxes along x-axis to precision ", precxtmp) - refine_xboxes(params[2][1], LBcrit[2], precxtmp) - flag = true - break - end - LPCside[i][j] = pcside + if ind < length(xcritpermut) + i2, j2 = xcritpermut[ind + 1] + I2L, nI2L = LPCside[i2][j2][3] end - flag || break - end - println("") -end -LnPCside = [ [[length(indI) for (L, indI) in PB] for PB in lpcside] for lpcside in LPCside ] -# Update extreme boxes -for j in eachindex(LBcrit[1]) - # If the curve does not intersect the box only on vertical sides - if !(LnPCside[1][j][1:2] == [0, 0]) - PCside, nPCside = LPCside[1][j], LnPCside[1][j] + PCside, nPCside = LPCside[i][j], LnPCside[i][j] I = [ l[1] for l in PCside[3:end] ] nI = [ l[2] for l in PCside[3:end] ] - # Locate the orientation of the extreme point - # s is the index on the side where there are more branches - # s=1: left; s=2: right - s = argmax([length(I[1]), length(I[2])]) - # Ordinate range of the extreme point - ycrit = LBcrit[1][j][2] - # If it intersects on the bottom side - if nPCside[1] == 1 - # yinf: the intersection with the vertical side just below the extreme point - yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[2]]) - # We vertically enlarge the box until it intersects on the horizontal side - push!(LPCside[1][j][s + 2][2], yinf) - LPCside[1][j][1][2] = [] - # We update the intersection numbers - LnPCside[1][j][s + 2] += 1 - LnPCside[1][j][1] = 0 - end - # If it intersects on the top side - if nPCside[2] == 1 - # ymax: the intersection with the vertical side just above the extreme point - ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[1]]) - # We vertically enlarge the box until it intersects on the horizontal side - push!(LPCside[1][j][s + 2][2], ymax) - LPCside[1][j][2][2] = [] - # We update the intersection numbers - LnPCside[1][j][s + 2] += 1 - LnPCside[1][j][2] = 0 - end - end -end -end - -#print("\nGraph computation :") -#@time begin -# Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot -# And even remove this fiber for the graph -Vert = [] -Edg = [] -Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ] -Viso = [] -ite = 1 - -for ind in 1:length(xcritpermut) - global ite - local i - i, j = xcritpermut[ind] - - if ind > 1 - i1, j1 = xcritpermut[ind - 1] - end - if ind < length(xcritpermut) - i2, j2 = xcritpermut[ind + 1] - I2L, nI2L = LPCside[i2][j2][3] - end - - PCside, nPCside = LPCside[i][j], LnPCside[i][j] - I = [ l[1] for l in PCside[3:end] ] - nI = [ l[2] for l in PCside[3:end] ] - xcmid = sum(LBcrit[i][j][1])//2 - ycmid = sum(LBcrit[i][j][2])//2 + xcmid = sum(LBcrit[i][j][1])//2 + ycmid = sum(LBcrit[i][j][2])//2 - ymincrit = minimum(vcat(nI[1], nI[2], [length(I[1])+1])) - # Construct vertices - ########################### - # On the vertical left side - if ind > 1 - for k in 1:length(I[1]) - push!(Corr[i][j][1], Corr[i1][j1][3][k]) + ymincrit = minimum(vcat(nI[1], nI[2], [length(I[1])+1])) + # Construct vertices + ########################### + # On the vertical left side + if ind > 1 + for k in 1:length(I[1]) + push!(Corr[i][j][1], Corr[i1][j1][3][k]) + end + else + for k in 1:length(I[1]) + push!(Vert, [xcrit[i][j][1], sum(I[1][k])//2]) + push!(Corr[i][j][1], ite) + ite += 1 + end end - else - for k in 1:length(I[1]) - push!(Vert, [xcrit[i][j][1], sum(I[1][k])//2]) - push!(Corr[i][j][1], ite) - ite += 1 + ########################### + # On the vertical right side + if ind < length(xcritpermut) + for k in 1:length(I[2]) + push!(Vert, [(xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4]) + push!(Corr[i][j][3], ite) + ite += 1 + end + else + for k in 1:length(I[2]) + push!(Vert, [xcrit[i][j][2], sum(I[2][k])//2]) + push!(Corr[i][j][3], ite) + ite += 1 + end end - end - ########################### - # On the vertical right side - if ind < length(xcritpermut) - for k in 1:length(I[2]) - push!(Vert, [(xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4]) - push!(Corr[i][j][3], ite) + ########################### + # Below the critical point + + for k in 1:ymincrit-1 + push!(Vert, [xcmid, sum(I[1][k] + I[2][k])// 4]) + push!(Corr[i][j][2][1], ite) + push!(Edg, [Corr[i][j][1][k], ite]) # left + push!(Edg, [ite, Corr[i][j][3][k]]) # right ite += 1 end - else - for k in 1:length(I[2]) - push!(Vert, [xcrit[i][j][2], sum(I[2][k])//2]) - push!(Corr[i][j][3], ite) + ########################### + # The critical point + ########################## + # if it is an isolated point + if isempty(nI[1]) && isempty(nI[2]) + #pass + # We can add the isolated vertex + # push!(Vert, Pcrit[i][j]) + # push!(Corr[i][j][2][1], ite) + # We will subsequently add the vertex in the graph + # push!(Viso, ite) + # ite += 1 + ############################################ + ## TO BE REPLACED BY APPSING IDENTIFICATOR ## + ## works for space curves without nodes ## + ############################################ + # If we are dealing with a node + elseif i == 2 + # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 + push!(Edg, [Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]]]) + push!(Edg, [Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]]]) + else + # We can add the vertex + push!(Vert, [xcmid, ycmid]) + push!(Corr[i][j][2][2], ite) + # We connect to the vertical left side of the critical box + for k in nI[1] + push!(Edg, [Corr[i][j][1][k], ite]) + end + # We connect to the vertical right side of the critical box + for k in nI[2] + push!(Edg, [ite, Corr[i][j][3][k]]) + end ite += 1 end - end - ########################### - # Below the critical point - - for k in 1:ymincrit-1 - push!(Vert, [xcmid, sum(I[1][k] + I[2][k])// 4]) - push!(Corr[i][j][2][1], ite) - push!(Edg, [Corr[i][j][1][k], ite]) # left - push!(Edg, [ite, Corr[i][j][3][k]]) # right - ite += 1 - end - ########################### - # The critical point - ########################## - # if it is an isolated point - if isempty(nI[1]) && isempty(nI[2]) - #pass - # We can add the isolated vertex - # push!(Vert, Pcrit[i][j]) - # push!(Corr[i][j][2][1], ite) - # We will subsequently add the vertex in the graph - # push!(Viso, ite) - # ite += 1 - ############################################ - ## TO BE REPLACED BY APPSING IDENTIFICATOR ## - ## works for space curves without nodes ## - ############################################ - # If we are dealing with a node - elseif i == 2 - # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 - push!(Edg, [Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]]]) - push!(Edg, [Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]]]) - else - # We can add the vertex - push!(Vert, [xcmid, ycmid]) - push!(Corr[i][j][2][2], ite) - # We connect to the vertical left side of the critical box - for k in nI[1] - push!(Edg, [Corr[i][j][1][k], ite]) - end - # We connect to the vertical right side of the critical box - for k in nI[2] - push!(Edg, [ite, Corr[i][j][3][k]]) + ########################### + # Above the critical point + for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1 + push!(Vert, [xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4]) + push!(Corr[i][j][2][3], ite) + push!(Edg, [Corr[i][j][1][end - k + 1], ite]) # left + push!(Edg, [ite, Corr[i][j][3][end - k + 1]]) # right + ite += 1 end - ite += 1 - end - ########################### - # Above the critical point - for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1 - push!(Vert, [xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4]) - push!(Corr[i][j][2][3], ite) - push!(Edg, [Corr[i][j][1][end - k + 1], ite]) # left - push!(Edg, [ite, Corr[i][j][3][end - k + 1]]) # right - ite += 1 end -end -#end + #end -#EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] -#plot_graph(Vert, EdgPlot) -#gui() + #EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] + #plot_graph(Vert, EdgPlot) + #gui() -CVert, CEdg = connected_components(Vert, Edg); + CVert, CEdg = connected_components(Vert, Edg); -println("\n## Lifted curve has ", length(CVert), " connected components ##") + println("\n## Lifted curve has ", length(CVert), " connected components ##") -#plot_graph_comp(Vert,CEdg) \ No newline at end of file + #plot_graph_comp(Vert,CEdg) +end \ No newline at end of file diff --git a/src/connectcurves/plots.jl b/src/connectcurves/plots.jl new file mode 100644 index 0000000..b959033 --- /dev/null +++ b/src/connectcurves/plots.jl @@ -0,0 +1,26 @@ +## Plot functions +function plot_graph(V, E) + println("Plotting the graph") + plot(legend=false) + for e in E + xe, ye = map(Float64,[e[1][1], e[2][1]]), map(Float64,[e[1][2], e[2][2]]) + plot!(xe, ye, lc="red", lw=3) + end + scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) + #plt.show(block=true) + plot!() +end + +function plot_graph_comp(V, CE) + println("Plotting the graph") + plot(legend=false) + col = distinguishable_colors(length(CE)+2) + for j in eachindex(CE) + for e in CE[j] + v1, v2 = map(Float64, V[e[1]]), map(Float64, V[e[2]]) + plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=3) + end + end + #plt.show(block=true) + plot!() +end \ No newline at end of file diff --git a/src/connectcurves/tools,jl b/src/connectcurves/tools,jl new file mode 100644 index 0000000..2fbaa11 --- /dev/null +++ b/src/connectcurves/tools,jl @@ -0,0 +1,27 @@ +function order_permut2d(L) + # Create a list of tuples with elements and their corresponding indices + LL = [(L[i][j], (i, j)) for i in eachindex(L) for j in eachindex(L[i])] + # Sort the enumerated list based on the values + sorted_LL = sort(LL, by = x -> x[1]) + # Extract the sorted values and their corresponding indices + sorted_L = [pair[1] for pair in sorted_LL] + sorted_ind = [pair[2] for pair in sorted_LL] + + return sorted_L, sorted_ind +end + +function Arb_to_rat(x) + r = radius(x) + return map(simplest_rational_inside, [x-2*r, x+2*r]) +end + +function rat_to_Arb(x) + x1,x2 = x + xm, xd = RR((x1+x2)/2), RR(x2-x1) + return ball(xm,xd) +end + +function evaluate_Arb(f, x) + cf = coefficients_of_univariate(f) + return evalpoly(RR(x), cf) +end \ No newline at end of file From 5f0817f9fd1cf91dcac9f62965c804c88a5988aa Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 15:29:37 +0200 Subject: [PATCH 016/180] rename main.jl --- .../{main.jl => connectcurves.jl} | 0 src/connectcurves/tools.jl | 82 +++++++++++++++++++ 2 files changed, 82 insertions(+) rename src/connectcurves/{main.jl => connectcurves.jl} (100%) create mode 100644 src/connectcurves/tools.jl diff --git a/src/connectcurves/main.jl b/src/connectcurves/connectcurves.jl similarity index 100% rename from src/connectcurves/main.jl rename to src/connectcurves/connectcurves.jl diff --git a/src/connectcurves/tools.jl b/src/connectcurves/tools.jl new file mode 100644 index 0000000..7bfc2ef --- /dev/null +++ b/src/connectcurves/tools.jl @@ -0,0 +1,82 @@ +#using Nemo +using Singular + +function randQQ(size=3) + fac = 10^(size) + return Nemo.QQ((-1)^(trunc(Int,rand()*10))*trunc(Int,rand()*fac),trunc(Int,rand()*fac)) +end + +function _mpoly_to_singular(f) + @assert Nemo.is_univariate(f) "Not univariate polynomial" + R, x = Singular.polynomial_ring(Singular.QQ, [:x]) + x = first(x) + cf = Nemo.coefficients_of_univariate(f) + return sum([ cf[j]*x^(j-1) for j = eachindex(cf) ]) +end + +function nb_roots_interval(f,a,b) + g = _mpoly_to_singular(f) + return Singular.LibRootsur.sturm(g, Singular.QQ(a), Singular.QQ(b)) +end + +""" + nb_roots_interval_partition(f, a, b) + +Compute the number of real roots of f(x) in the intervals: + (-infinity, a), (a,b), (b, +infinity) + +# Input: +* f: polynomial with involving one variable, with coeffients in QQ +* a,b: rational elements of QQ +# Output: +* [ n(-infinity, a), n(a,b), n(b, +infinity) ] + +""" +function nb_roots_interval_partition(f, a, b) + g = _mpoly_to_singular(f) + M = Singular.LibRootsur.maxabs(g) + a1, b1 = Singular.QQ(a), Singular.QQ(b) + M1, M2 = min(-M, a1), max(b1, M) + B = [ M1-1, a1, b1, M2+1 ] + return [ Singular.LibRootsur.sturm(g, B[i], B[i+1]) for i=1:3 ] +end + +function sturm_habicht_seq(f) + g = _mpoly_to_singular(f) + SH = map(Singular.coefficients_of_univariate, Singular.LibRootsur.sturmhaseq(g)) + return [ vcat(SH[k], [n_Q(0) for _=1:(k-length(SH[k]))]) for k in eachindex(SH) ] +end + +function subresultants_seq(f) + SH = sturm_habicht_seq(f) + d(k) = (-1)^((k*(k+1))>>1) + return [ d(length(SH)-1-k)*SH[k] for k=1:length(SH)-2 ] +end + +function subresultants_seq_biv(f, iv) + iu = iv%2+1 + # Modern computer Algebra Th 6.51. + degs = degrees(f) + n, d = degs[iv], degs[iu] + degsmax = [ (2*n-1-2*k)*d for k=0:d-2 ] + Dmax = degsmax[end]>>1+1 + ## + xs = [ randQQ() for _=1:(degsmax[1]+1) ] + @time begin + Srev = [ subresultants_seq(evaluate(f,[iu],[xx])) for xx in xs ] + end + S,t = Nemo.polynomial_ring(Nemo.QQ,"t") + Sr = [ [ S(0) for _=1:i] for i=1:n-2 ] + for i = 1:n-2 + for j = 1:i + ys = [ Nemo.QQ(Srev[l][i][j]) for l=eachindex(Srev) ] + Sr[i][j] = Nemo.interpolate(S, xs, ys) + end + end + return Sr +end + +#R, (x,y) = Nemo.polynomial_ring(Nemo.QQ, [:x,:y]) +#f = x^7+y^2*x^5-2*x*y^3+1+y^6 +#f = (x^2+y^2-1)*(2*x-y) +#Sr = subresultants_seq_biv(f, 1) From f28229333602e653567016651ccdf54ff62bb72a Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 16:07:36 +0200 Subject: [PATCH 017/180] start 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"LLVMOpenMP_jll", "Libdl", "MPFR_jll"] +git-tree-sha1 = "00d6ebe337ec3935bf6a356f6c6060933c8b73e8" +uuid = "6d01cc9a-e8f6-580e-8c54-544227e08205" +version = "0.600.501+0" + +[[deps.nghttp2_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" +version = "1.52.0+1" + +[[deps.p7zip_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" +version = "17.4.0+2" diff --git a/src/AlgebraicSolving.jl b/src/AlgebraicSolving.jl index 8c65390..385be73 100644 --- a/src/AlgebraicSolving.jl +++ b/src/AlgebraicSolving.jl @@ -18,4 +18,6 @@ include("siggb/siggb.jl") include("examples/katsura.jl") include("examples/cyclic.jl") +include("connectcurves/connectcurves.jl") + end # module AlgebraicSolving diff --git a/src/connectcurves/connectcurves.jl b/src/connectcurves/connectcurves.jl index 15162d2..ef86f09 100644 --- a/src/connectcurves/connectcurves.jl +++ b/src/connectcurves/connectcurves.jl @@ -1,7 +1,10 @@ -println("\nLoading libraries and data..") -using Nemo +#println("\nLoading libraries and data..") +#using Nemo #using Plots, Colors #pythonplot() + +export compute_graph + include("tools.jl") include("subresultants.jl") include("isolate.jl") @@ -11,6 +14,7 @@ include("plots.jl") function compute_graph(f; generic=false, precx = 100) R = parent(f) + x, y = gens(R) # Generic change of variables changemat = [1 0; 0 1] if !generic @@ -20,7 +24,7 @@ function compute_graph(f; generic=false, precx = 100) println("\nCompute parametrization of critical pts...") @time begin - sr = subresultants(f, derivative(f,y),2, list=true); + sr = subresultants(f, derivative(f,y), 2, list=true); # Take sqfree factors of the resultant sqr = collect(factor_squarefree(sr[1][1])) # Keep only deg>0 factors @@ -36,9 +40,6 @@ function compute_graph(f; generic=false, precx = 100) params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in group_sqr ]; end - ############### - precx = 200; - ############### # TODO : check that no overlap between different isolations println("\nIsolating critical values at precision ", precx,"..") @time begin @@ -50,7 +51,6 @@ function compute_graph(f; generic=false, precx = 100) println("\nComputing isolating critical boxes using Arb with precision ",max(precx,150),"..") @time begin - #RR(x) = Arb(x, prec=120) RR = ArbField(max(precx,150)) Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ] LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ] diff --git a/src/connectcurves/isolate.jl b/src/connectcurves/isolate.jl index 02517e6..84314f0 100644 --- a/src/connectcurves/isolate.jl +++ b/src/connectcurves/isolate.jl @@ -1,10 +1,13 @@ include("src/usolve/usolve.jl") -function isolate(f; prec = 32, software="usolve") +function isolate(f; prec = 32, software="msolve") # Univariate isolation using usolve @assert is_univariate(f) "Not univariate polynomial" if software == "usolve" return usolve(f, precision = prec, uspath="src/usolve/usolve") + else + fvar = vars(f)[1] + return inter_solutions(Ideal(vcat([f], [ t for t in gens(parent(f)) if t!=fvar ])), precision=prec) end end @@ -12,6 +15,6 @@ function isolate_eval(f, ivar, val; prec=64) # univariate isolation of roots of a bivariate polynomial f # whose ivar-th variable is evaluated at val # uses msolve - sols = inter_solutions(Ideal([f, gens(R)[ivar] - val]), precision=prec) + sols = inter_solutions(Ideal([f, gens(parent(f))[ivar] - val]), precision=prec) return [ s[ivar%2+1] for s in sols ] end \ No newline at end of file diff --git a/src/connectcurves/tools,jl b/src/connectcurves/tools,jl deleted file mode 100644 index 2fbaa11..0000000 --- a/src/connectcurves/tools,jl +++ /dev/null @@ -1,27 +0,0 @@ -function order_permut2d(L) - # Create a list of tuples with elements and their corresponding indices - LL = [(L[i][j], (i, j)) for i in eachindex(L) for j in eachindex(L[i])] - # Sort the enumerated list based on the values - sorted_LL = sort(LL, by = x -> x[1]) - # Extract the sorted values and their corresponding indices - sorted_L = [pair[1] for pair in sorted_LL] - sorted_ind = [pair[2] for pair in sorted_LL] - - return sorted_L, sorted_ind -end - -function Arb_to_rat(x) - r = radius(x) - return map(simplest_rational_inside, [x-2*r, x+2*r]) -end - -function rat_to_Arb(x) - x1,x2 = x - xm, xd = RR((x1+x2)/2), RR(x2-x1) - return ball(xm,xd) -end - -function evaluate_Arb(f, x) - cf = coefficients_of_univariate(f) - return evalpoly(RR(x), cf) -end \ No newline at end of file diff --git a/src/connectcurves/tools.jl b/src/connectcurves/tools.jl index 7bfc2ef..2fbaa11 100644 --- a/src/connectcurves/tools.jl +++ b/src/connectcurves/tools.jl @@ -1,82 +1,27 @@ -#using Nemo -using Singular - -function randQQ(size=3) - fac = 10^(size) - return Nemo.QQ((-1)^(trunc(Int,rand()*10))*trunc(Int,rand()*fac),trunc(Int,rand()*fac)) -end - -function _mpoly_to_singular(f) - @assert Nemo.is_univariate(f) "Not univariate polynomial" - R, x = Singular.polynomial_ring(Singular.QQ, [:x]) - x = first(x) - cf = Nemo.coefficients_of_univariate(f) - return sum([ cf[j]*x^(j-1) for j = eachindex(cf) ]) -end - -function nb_roots_interval(f,a,b) - g = _mpoly_to_singular(f) - return Singular.LibRootsur.sturm(g, Singular.QQ(a), Singular.QQ(b)) -end - -""" - nb_roots_interval_partition(f, a, b) - -Compute the number of real roots of f(x) in the intervals: - (-infinity, a), (a,b), (b, +infinity) - -# Input: -* f: polynomial with involving one variable, with coeffients in QQ -* a,b: rational elements of QQ -# Output: -* [ n(-infinity, a), n(a,b), n(b, +infinity) ] - -""" -function nb_roots_interval_partition(f, a, b) - g = _mpoly_to_singular(f) - M = Singular.LibRootsur.maxabs(g) - a1, b1 = Singular.QQ(a), Singular.QQ(b) - M1, M2 = min(-M, a1), max(b1, M) - B = [ M1-1, a1, b1, M2+1 ] - return [ Singular.LibRootsur.sturm(g, B[i], B[i+1]) for i=1:3 ] -end - -function sturm_habicht_seq(f) - g = _mpoly_to_singular(f) - SH = map(Singular.coefficients_of_univariate, Singular.LibRootsur.sturmhaseq(g)) - return [ vcat(SH[k], [n_Q(0) for _=1:(k-length(SH[k]))]) for k in eachindex(SH) ] +function order_permut2d(L) + # Create a list of tuples with elements and their corresponding indices + LL = [(L[i][j], (i, j)) for i in eachindex(L) for j in eachindex(L[i])] + # Sort the enumerated list based on the values + sorted_LL = sort(LL, by = x -> x[1]) + # Extract the sorted values and their corresponding indices + sorted_L = [pair[1] for pair in sorted_LL] + sorted_ind = [pair[2] for pair in sorted_LL] + + return sorted_L, sorted_ind end -function subresultants_seq(f) - SH = sturm_habicht_seq(f) - d(k) = (-1)^((k*(k+1))>>1) - return [ d(length(SH)-1-k)*SH[k] for k=1:length(SH)-2 ] +function Arb_to_rat(x) + r = radius(x) + return map(simplest_rational_inside, [x-2*r, x+2*r]) end -function subresultants_seq_biv(f, iv) - iu = iv%2+1 - # Modern computer Algebra Th 6.51. - degs = degrees(f) - n, d = degs[iv], degs[iu] - degsmax = [ (2*n-1-2*k)*d for k=0:d-2 ] - Dmax = degsmax[end]>>1+1 - ## - xs = [ randQQ() for _=1:(degsmax[1]+1) ] - @time begin - Srev = [ subresultants_seq(evaluate(f,[iu],[xx])) for xx in xs ] - end - S,t = Nemo.polynomial_ring(Nemo.QQ,"t") - Sr = [ [ S(0) for _=1:i] for i=1:n-2 ] - for i = 1:n-2 - for j = 1:i - ys = [ Nemo.QQ(Srev[l][i][j]) for l=eachindex(Srev) ] - Sr[i][j] = Nemo.interpolate(S, xs, ys) - end - end - return Sr +function rat_to_Arb(x) + x1,x2 = x + xm, xd = RR((x1+x2)/2), RR(x2-x1) + return ball(xm,xd) end -#R, (x,y) = Nemo.polynomial_ring(Nemo.QQ, [:x,:y]) -#f = x^7+y^2*x^5-2*x*y^3+1+y^6 -#f = (x^2+y^2-1)*(2*x-y) -#Sr = subresultants_seq_biv(f, 1) +function evaluate_Arb(f, x) + cf = coefficients_of_univariate(f) + return evalpoly(RR(x), cf) +end \ No newline at end of file From 6f38113da3d86bff604dfaa76a4b281018f8296c Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 19:45:18 +0200 Subject: [PATCH 018/180] graph methods --- src/connectcurves/boxes.jl | 2 +- src/connectcurves/connectcurves.jl | 67 +++++++++++++----------------- src/connectcurves/graph.jl | 13 +++++- src/connectcurves/isolate.jl | 5 ++- src/connectcurves/plots.jl | 1 + src/connectcurves/tools.jl | 8 ++-- 6 files changed, 49 insertions(+), 47 deletions(-) diff --git a/src/connectcurves/boxes.jl b/src/connectcurves/boxes.jl index 648f5d1..ef6632e 100644 --- a/src/connectcurves/boxes.jl +++ b/src/connectcurves/boxes.jl @@ -52,7 +52,7 @@ end function refine_xboxes(f, LB, prec) # Implementation of refine_xboxes function goes here - xnew = isolate(f, prec=prec)[2] + xnew = isolate(f, prec=prec) for i in eachindex(LB) LB[i] = [ xnew[i], LB[i][2] ] end diff --git a/src/connectcurves/connectcurves.jl b/src/connectcurves/connectcurves.jl index ef86f09..7f14a6d 100644 --- a/src/connectcurves/connectcurves.jl +++ b/src/connectcurves/connectcurves.jl @@ -3,7 +3,7 @@ #using Plots, Colors #pythonplot() -export compute_graph +export compute_graph, connected_components, number_connected_components include("tools.jl") include("subresultants.jl") @@ -18,7 +18,7 @@ function compute_graph(f; generic=false, precx = 100) # Generic change of variables changemat = [1 0; 0 1] if !generic - changemat = rand(-500:500, 2, 2) + changemat = map(QQ,rand(-500:500, 2, 2)) end f = evaluate(f, collect(changemat*[x; y])); @@ -44,15 +44,14 @@ function compute_graph(f; generic=false, precx = 100) println("\nIsolating critical values at precision ", precx,"..") @time begin xcrit = [ isolate(first(p), prec=precx) for p in params ] - xcrit_usolve = getindex.(xcrit, 1) - xcrit = getindex.(xcrit, 2) _, xcritpermut = order_permut2d(xcrit); end println("\nComputing isolating critical boxes using Arb with precision ",max(precx,150),"..") @time begin - RR = ArbField(max(precx,150)) - Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1])/evaluate_Arb(params[i][3],xc[1])] for xc in xcrit[i]] for i in eachindex(xcrit) ] + #RR = ArbField(max(precx,150)) + precArb = max(precx,150) + Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1], precArb)/evaluate_Arb(params[i][3],xc[1],precArb)] for xc in xcrit[i]] for i in eachindex(xcrit) ] LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ] end @@ -136,19 +135,15 @@ function compute_graph(f; generic=false, precx = 100) end end - #print("\nGraph computation :") - #@time begin + println("Graph computation") # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot # And even remove this fiber for the graph Vert = [] Edg = [] Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ] Viso = [] - ite = 1 for ind in 1:length(xcritpermut) - global ite - local i i, j = xcritpermut[ind] if ind > 1 @@ -177,8 +172,7 @@ function compute_graph(f; generic=false, precx = 100) else for k in 1:length(I[1]) push!(Vert, [xcrit[i][j][1], sum(I[1][k])//2]) - push!(Corr[i][j][1], ite) - ite += 1 + push!(Corr[i][j][1], length(Vert)) end end ########################### @@ -186,25 +180,24 @@ function compute_graph(f; generic=false, precx = 100) if ind < length(xcritpermut) for k in 1:length(I[2]) push!(Vert, [(xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4]) - push!(Corr[i][j][3], ite) - ite += 1 + push!(Corr[i][j][3], length(Vert)) end else for k in 1:length(I[2]) push!(Vert, [xcrit[i][j][2], sum(I[2][k])//2]) - push!(Corr[i][j][3], ite) - ite += 1 + push!(Corr[i][j][3], length(Vert)) end end ########################### # Below the critical point - + #println() + #println(map(length,I)) + #println(vcat(nI[1], nI[2], [length(I[1])+1])) for k in 1:ymincrit-1 push!(Vert, [xcmid, sum(I[1][k] + I[2][k])// 4]) - push!(Corr[i][j][2][1], ite) - push!(Edg, [Corr[i][j][1][k], ite]) # left - push!(Edg, [ite, Corr[i][j][3][k]]) # right - ite += 1 + push!(Corr[i][j][2][1], length(Vert)) + push!(Edg, [Corr[i][j][1][k], length(Vert)]) # left + push!(Edg, [length(Vert), Corr[i][j][3][k]]) # right end ########################### # The critical point @@ -214,10 +207,9 @@ function compute_graph(f; generic=false, precx = 100) #pass # We can add the isolated vertex # push!(Vert, Pcrit[i][j]) - # push!(Corr[i][j][2][1], ite) + # push!(Corr[i][j][2][1], length(Vert)) # We will subsequently add the vertex in the graph - # push!(Viso, ite) - # ite += 1 + # push!(Viso, length(Vert)) ############################################ ## TO BE REPLACED BY APPSING IDENTIFICATOR ## ## works for space curves without nodes ## @@ -230,36 +222,35 @@ function compute_graph(f; generic=false, precx = 100) else # We can add the vertex push!(Vert, [xcmid, ycmid]) - push!(Corr[i][j][2][2], ite) + push!(Corr[i][j][2][2], length(Vert)) # We connect to the vertical left side of the critical box for k in nI[1] - push!(Edg, [Corr[i][j][1][k], ite]) + push!(Edg, [Corr[i][j][1][k], length(Vert)]) end # We connect to the vertical right side of the critical box for k in nI[2] - push!(Edg, [ite, Corr[i][j][3][k]]) + push!(Edg, [length(Vert), Corr[i][j][3][k]]) end - ite += 1 end ########################### # Above the critical point for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1 push!(Vert, [xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4]) - push!(Corr[i][j][2][3], ite) - push!(Edg, [Corr[i][j][1][end - k + 1], ite]) # left - push!(Edg, [ite, Corr[i][j][3][end - k + 1]]) # right - ite += 1 + push!(Corr[i][j][2][3], length(Vert)) + push!(Edg, [Corr[i][j][1][end - k + 1], length(Vert)]) # left + push!(Edg, [length(Vert), Corr[i][j][3][end - k + 1]]) # right end end - #end #EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] #plot_graph(Vert, EdgPlot) #gui() - CVert, CEdg = connected_components(Vert, Edg); - - println("\n## Lifted curve has ", length(CVert), " connected components ##") - #plot_graph_comp(Vert,CEdg) + # Operate inverse change of variable if necessary + if !(generic) + Vert = [ map(QQ,v) for v in Vert ] + end + + return Vert, Edg end \ No newline at end of file diff --git a/src/connectcurves/graph.jl b/src/connectcurves/graph.jl index f20cea3..6691e58 100644 --- a/src/connectcurves/graph.jl +++ b/src/connectcurves/graph.jl @@ -1,6 +1,11 @@ +## TODO : deal with isolated vertices (not appearing in the edges) +############################ + +function connected_components(G) + # Group the vert and edges w.r.t the connected components they belong to + ########### + vert, edges = G -## Graph functions -function connected_components(vert, edges) adj_list = Dict{Int, Vector{Int}}() visited = Set{Int}() components = Vector{Vector{Int}}() @@ -45,4 +50,8 @@ function connected_components(vert, edges) grouped_vert = [ [ vert[cv] for cv in c ] for c in components ] return grouped_vert, grouped_edges +end + +function number_connected_components(G) + return length(first(connected_components(G))) end \ No newline at end of file diff --git a/src/connectcurves/isolate.jl b/src/connectcurves/isolate.jl index 84314f0..414967e 100644 --- a/src/connectcurves/isolate.jl +++ b/src/connectcurves/isolate.jl @@ -4,10 +4,11 @@ function isolate(f; prec = 32, software="msolve") # Univariate isolation using usolve @assert is_univariate(f) "Not univariate polynomial" if software == "usolve" - return usolve(f, precision = prec, uspath="src/usolve/usolve") + return getindex.(usolve(f, precision = prec, uspath="src/usolve/usolve"),2) else fvar = vars(f)[1] - return inter_solutions(Ideal(vcat([f], [ t for t in gens(parent(f)) if t!=fvar ])), precision=prec) + sols = inter_solutions(Ideal(vcat([f], [ t for t in gens(parent(f)) if t!=fvar ])), precision=prec) + return getindex.(sols, var_index(fvar)) end end diff --git a/src/connectcurves/plots.jl b/src/connectcurves/plots.jl index b959033..040d70f 100644 --- a/src/connectcurves/plots.jl +++ b/src/connectcurves/plots.jl @@ -1,3 +1,4 @@ + ## Plot functions function plot_graph(V, E) println("Plotting the graph") diff --git a/src/connectcurves/tools.jl b/src/connectcurves/tools.jl index 2fbaa11..2a41af8 100644 --- a/src/connectcurves/tools.jl +++ b/src/connectcurves/tools.jl @@ -15,13 +15,13 @@ function Arb_to_rat(x) return map(simplest_rational_inside, [x-2*r, x+2*r]) end -function rat_to_Arb(x) +function rat_to_Arb(x, prec) x1,x2 = x - xm, xd = RR((x1+x2)/2), RR(x2-x1) + xm, xd = ArbField(prec)((x1+x2)/2), ArbField(prec)(x2-x1) return ball(xm,xd) end -function evaluate_Arb(f, x) +function evaluate_Arb(f, x, prec) cf = coefficients_of_univariate(f) - return evalpoly(RR(x), cf) + return evalpoly(ArbField(prec)(x), cf) end \ No newline at end of file From b9d0b12be0eb9a96d68204a8f204ab1bf3b8d577 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 12 May 2024 22:34:58 +0200 Subject: [PATCH 019/180] add dependancies --- Manifest.toml | 829 ++++++++++++++++++++++++++++- Project.toml | 10 +- src/AlgebraicSolving.jl | 5 +- src/connectcurves/boxes.jl | 4 +- src/connectcurves/connectcurves.jl | 19 +- src/connectcurves/graph.jl | 13 +- src/connectcurves/plots.jl | 51 +- src/imports.jl | 3 + 8 files changed, 900 insertions(+), 34 deletions(-) diff --git a/Manifest.toml b/Manifest.toml index be7ef88..8800004 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -2,7 +2,7 @@ julia_version = "1.10.1" manifest_format = "2.0" -project_hash = "92eb5777a40fb58f53c5c7597a7a312dbc129602" +project_hash = "7a6e412edf7e0069b27986b55a45575b55f508bb" [[deps.AbstractAlgebra]] deps = ["InteractiveUtils", "LinearAlgebra", "MacroTools", "Preferences", "Random", "RandomExtensions", "SparseArrays", "Test"] @@ -58,24 +58,77 @@ uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" [[deps.Base64]] uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" +[[deps.BitFlags]] +git-tree-sha1 = "2dc09997850d68179b69dafb58ae806167a32b1b" +uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35" +version = "0.1.8" + [[deps.BitTwiddlingConvenienceFunctions]] deps = ["Static"] git-tree-sha1 = "0c5f81f47bbbcf4aea7b2959135713459170798b" uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b" version = "0.1.5" +[[deps.Bzip2_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd" +uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" +version = "1.0.8+1" + [[deps.CPUSummary]] deps = ["CpuId", "IfElse", "PrecompileTools", "Static"] git-tree-sha1 = "601f7e7b3d36f18790e2caf83a882d88e9b71ff1" uuid = "2a0fbf3d-bb9c-48f3-b0a9-814d99fd7ab9" version = "0.2.4" +[[deps.Cairo_jll]] +deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] +git-tree-sha1 = "a4c43f59baa34011e303e76f5c8c91bf58415aaf" +uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" +version = "1.18.0+1" + [[deps.CloseOpenIntervals]] deps = ["Static", "StaticArrayInterface"] git-tree-sha1 = "70232f82ffaab9dc52585e0dd043b5e0c6b714f1" uuid = "fb6a15b2-703c-40df-9091-08a04967cfa9" version = "0.1.12" +[[deps.CodecZlib]] +deps = ["TranscodingStreams", "Zlib_jll"] +git-tree-sha1 = "59939d8a997469ee05c4b4944560a820f9ba0d73" +uuid = "944b1d66-785c-5afd-91f1-9de20f533193" +version = "0.7.4" + +[[deps.ColorSchemes]] +deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"] +git-tree-sha1 = "4b270d6465eb21ae89b732182c20dc165f8bf9f2" +uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4" +version = "3.25.0" + +[[deps.ColorTypes]] +deps = ["FixedPointNumbers", "Random"] +git-tree-sha1 = "b10d0b65641d57b8b4d5e234446582de5047050d" +uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f" +version = "0.11.5" + +[[deps.ColorVectorSpace]] +deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"] +git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249" +uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4" +version = "0.10.0" + + [deps.ColorVectorSpace.extensions] + SpecialFunctionsExt = "SpecialFunctions" + + [deps.ColorVectorSpace.weakdeps] + SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b" + +[[deps.Colors]] +deps = ["ColorTypes", "FixedPointNumbers", "Reexport"] +git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a" +uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" +version = "0.12.10" + [[deps.Compat]] deps = ["TOML", "UUIDs"] git-tree-sha1 = "b1c55339b7c6c350ee89f2c1604299660525b248" @@ -91,16 +144,44 @@ deps = ["Artifacts", "Libdl"] uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" version = "1.1.0+0" +[[deps.ConcurrentUtilities]] +deps = ["Serialization", "Sockets"] +git-tree-sha1 = "6cbbd4d241d7e6579ab354737f4dd95ca43946e1" +uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb" +version = "2.4.1" + +[[deps.Contour]] +git-tree-sha1 = "439e35b0b36e2e5881738abc8857bd92ad6ff9a8" +uuid = "d38c429a-6771-53c6-b99e-75d170b6e991" +version = "0.6.3" + [[deps.CpuId]] deps = ["Markdown"] git-tree-sha1 = "fcbb72b032692610bfbdb15018ac16a36cf2e406" uuid = "adafc99b-e345-5852-983c-f28acb93d879" version = "0.3.1" +[[deps.DataAPI]] +git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe" +uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a" +version = "1.16.0" + +[[deps.DataStructures]] +deps = ["Compat", "InteractiveUtils", "OrderedCollections"] +git-tree-sha1 = "1d0a14036acb104d9e89698bd408f63ab58cdc82" +uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8" +version = "0.18.20" + [[deps.Dates]] deps = ["Printf"] uuid = "ade2ca70-3891-5945-98fb-dc099432e06a" +[[deps.DelimitedFiles]] +deps = ["Mmap"] +git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae" +uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" +version = "1.9.1" + [[deps.DocStringExtensions]] deps = ["LibGit2"] git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d" @@ -112,6 +193,36 @@ deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"] uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6" version = "1.6.0" +[[deps.EpollShim_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "8e9441ee83492030ace98f9789a654a6d0b1f643" +uuid = "2702e6a9-849d-5ed8-8c21-79e8b8f9ee43" +version = "0.0.20230411+0" + +[[deps.ExceptionUnwrapping]] +deps = ["Test"] +git-tree-sha1 = "dcb08a0d93ec0b1cdc4af184b26b591e9695423a" +uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4" +version = "0.1.10" + +[[deps.Expat_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "1c6317308b9dc757616f0b5cb379db10494443a7" +uuid = "2e619515-83b5-522b-bb60-26c02a35a201" +version = "2.6.2+0" + +[[deps.FFMPEG]] +deps = ["FFMPEG_jll"] +git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8" +uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a" +version = "0.4.1" + +[[deps.FFMPEG_jll]] +deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"] +git-tree-sha1 = "466d45dc38e15794ec7d5d63ec03d776a9aff36e" +uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5" +version = "4.4.4+1" + [[deps.FLINT_jll]] deps = ["Artifacts", "GMP_jll", "JLLWrappers", "Libdl", "MPFR_jll", "OpenBLAS32_jll"] git-tree-sha1 = "4bde447e7bc6de73de36870fc942df02f4dd44b5" @@ -121,11 +232,93 @@ version = "300.100.300+0" [[deps.FileWatching]] uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee" +[[deps.FixedPointNumbers]] +deps = ["Statistics"] +git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc" +uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93" +version = "0.8.4" + +[[deps.Fontconfig_jll]] +deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Zlib_jll"] +git-tree-sha1 = "db16beca600632c95fc8aca29890d83788dd8b23" +uuid = "a3f928ae-7b40-5064-980b-68af3947d34b" +version = "2.13.96+0" + +[[deps.Format]] +git-tree-sha1 = "9c68794ef81b08086aeb32eeaf33531668d5f5fc" +uuid = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8" +version = "1.3.7" + +[[deps.FreeType2_jll]] +deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"] +git-tree-sha1 = "d8db6a5a2fe1381c1ea4ef2cab7c69c2de7f9ea0" +uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7" +version = "2.13.1+0" + +[[deps.FriBidi_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "1ed150b39aebcc805c26b93a8d0122c940f64ce2" +uuid = "559328eb-81f9-559d-9380-de523a88c83c" +version = "1.0.14+0" + +[[deps.GLFW_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"] +git-tree-sha1 = "ff38ba61beff76b8f4acad8ab0c97ef73bb670cb" +uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89" +version = "3.3.9+0" + [[deps.GMP_jll]] deps = ["Artifacts", "Libdl"] uuid = "781609d7-10c4-51f6-84f2-b8444358ff6d" version = "6.2.1+6" +[[deps.GR]] +deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"] +git-tree-sha1 = "ddda044ca260ee324c5fc07edb6d7cf3f0b9c350" +uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71" +version = "0.73.5" + +[[deps.GR_jll]] +deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"] +git-tree-sha1 = "278e5e0f820178e8a26df3184fcb2280717c79b1" +uuid = "d2c73de3-f751-5644-a686-071e5b155ba9" +version = "0.73.5+0" + +[[deps.Gettext_jll]] +deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"] +git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046" +uuid = "78b55507-aeef-58d4-861c-77aaff3498b1" +version = "0.21.0+0" + +[[deps.Glib_jll]] +deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"] +git-tree-sha1 = "359a1ba2e320790ddbe4ee8b4d54a305c0ea2aff" +uuid = "7746bdde-850d-59dc-9ae8-88ece973131d" +version = "2.80.0+0" + +[[deps.Graphite2_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011" +uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472" +version = "1.3.14+0" + +[[deps.Grisu]] +git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2" +uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe" +version = "1.0.2" + +[[deps.HTTP]] +deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"] +git-tree-sha1 = "d1d712be3164d61d1fb98e7ce9bcbc6cc06b45ed" +uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3" +version = "1.10.8" + +[[deps.HarfBuzz_jll]] +deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"] +git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3" +uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566" +version = "2.8.1+1" + [[deps.HostCPUFeatures]] deps = ["BitTwiddlingConvenienceFunctions", "IfElse", "Libdl", "Static"] git-tree-sha1 = "eb8fed28f4994600e29beef49744639d985a04b2" @@ -141,18 +334,78 @@ version = "0.1.1" deps = ["Markdown"] uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240" +[[deps.IrrationalConstants]] +git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2" +uuid = "92d709cd-6900-40b7-9082-c6be49f344b6" +version = "0.2.2" + +[[deps.JLFzf]] +deps = ["Pipe", "REPL", "Random", "fzf_jll"] +git-tree-sha1 = "a53ebe394b71470c7f97c2e7e170d51df21b17af" +uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c" +version = "0.1.7" + [[deps.JLLWrappers]] deps = ["Artifacts", "Preferences"] git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca" uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210" version = "1.5.0" +[[deps.JSON]] +deps = ["Dates", "Mmap", "Parsers", "Unicode"] +git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a" +uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6" +version = "0.21.4" + +[[deps.JpegTurbo_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "c84a835e1a09b289ffcd2271bf2a337bbdda6637" +uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8" +version = "3.0.3+0" + +[[deps.LAME_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "170b660facf5df5de098d866564877e119141cbd" +uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d" +version = "3.100.2+0" + +[[deps.LERC_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434" +uuid = "88015f11-f218-50d7-93a8-a6af411a945d" +version = "3.0.0+1" + [[deps.LLVMOpenMP_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "d986ce2d884d49126836ea94ed5bfb0f12679713" uuid = "1d63c593-3942-5779-bab2-d838dc0a180e" version = "15.0.7+0" +[[deps.LZO_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "70c5da094887fd2cae843b8db33920bac4b6f07d" +uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac" +version = "2.10.2+0" + +[[deps.LaTeXStrings]] +git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec" +uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" +version = "1.3.1" + +[[deps.Latexify]] +deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"] +git-tree-sha1 = "e0b5cd21dc1b44ec6e64f351976f961e6f31d6c4" +uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316" +version = "0.16.3" + + [deps.Latexify.extensions] + DataFramesExt = "DataFrames" + SymEngineExt = "SymEngine" + + [deps.Latexify.weakdeps] + DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" + SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8" + [[deps.LayoutPointers]] deps = ["ArrayInterface", "LinearAlgebra", "ManualMemory", "SIMDTypes", "Static", "StaticArrayInterface"] git-tree-sha1 = "62edfee3211981241b57ff1cedf4d74d79519277" @@ -186,13 +439,83 @@ version = "1.11.0+1" [[deps.Libdl]] uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb" +[[deps.Libffi_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290" +uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490" +version = "3.2.2+1" + +[[deps.Libgcrypt_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll"] +git-tree-sha1 = "9fd170c4bbfd8b935fdc5f8b7aa33532c991a673" +uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4" +version = "1.8.11+0" + +[[deps.Libglvnd_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"] +git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733" +uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29" +version = "1.6.0+0" + +[[deps.Libgpg_error_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "fbb1f2bef882392312feb1ede3615ddc1e9b99ed" +uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8" +version = "1.49.0+0" + +[[deps.Libiconv_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "f9557a255370125b405568f9767d6d195822a175" +uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531" +version = "1.17.0+0" + +[[deps.Libmount_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "0c4f9c4f1a50d8f35048fa0532dabbadf702f81e" +uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9" +version = "2.40.1+0" + +[[deps.Libtiff_jll]] +deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"] +git-tree-sha1 = "2da088d113af58221c52828a80378e16be7d037a" +uuid = "89763e89-9b03-5906-acba-b20f662cd828" +version = "4.5.1+1" + +[[deps.Libuuid_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "5ee6203157c120d79034c748a2acba45b82b8807" +uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700" +version = "2.40.1+0" + [[deps.LinearAlgebra]] deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"] uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +[[deps.LogExpFunctions]] +deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"] +git-tree-sha1 = "18144f3e9cbe9b15b070288eef858f71b291ce37" +uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688" +version = "0.3.27" + + [deps.LogExpFunctions.extensions] + LogExpFunctionsChainRulesCoreExt = "ChainRulesCore" + LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables" + LogExpFunctionsInverseFunctionsExt = "InverseFunctions" + + [deps.LogExpFunctions.weakdeps] + ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" + ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0" + InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112" + [[deps.Logging]] uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" +[[deps.LoggingExtras]] +deps = ["Dates", "Logging"] +git-tree-sha1 = "c1dd6d7978c12545b4179fb6153b9250c96b0075" +uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36" +version = "1.0.3" + [[deps.LoopVectorization]] deps = ["ArrayInterface", "CPUSummary", "CloseOpenIntervals", "DocStringExtensions", "HostCPUFeatures", "IfElse", "LayoutPointers", "LinearAlgebra", "OffsetArrays", "PolyesterWeave", "PrecompileTools", "SIMDTypes", "SLEEFPirates", "Static", "StaticArrayInterface", "ThreadingUtilities", "UnPack", "VectorizationBase"] git-tree-sha1 = "8f6786d8b2b3248d79db3ad359ce95382d5a6df8" @@ -228,15 +551,41 @@ version = "0.1.8" deps = ["Base64"] uuid = "d6f4376e-aef5-505a-96c1-9c027394607a" +[[deps.MbedTLS]] +deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"] +git-tree-sha1 = "c067a280ddc25f196b5e7df3877c6b226d390aaf" +uuid = "739be429-bea8-5141-9913-cc70e7f3736d" +version = "1.1.9" + [[deps.MbedTLS_jll]] deps = ["Artifacts", "Libdl"] uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1" version = "2.28.2+1" +[[deps.Measures]] +git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102" +uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e" +version = "0.3.2" + +[[deps.Missings]] +deps = ["DataAPI"] +git-tree-sha1 = "ec4f7fbeab05d7747bdf98eb74d130a2a2ed298d" +uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28" +version = "1.2.0" + +[[deps.Mmap]] +uuid = "a63ad114-7e13-5084-954f-fe012c677804" + [[deps.MozillaCACerts_jll]] uuid = "14a3606d-f60d-562e-9121-12d972cd8159" version = "2023.1.10" +[[deps.NaNMath]] +deps = ["OpenLibm_jll"] +git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4" +uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3" +version = "1.0.2" + [[deps.Nemo]] deps = ["AbstractAlgebra", "FLINT_jll", "Libdl", "LinearAlgebra", "Pkg", "Random", "RandomExtensions", "SHA"] git-tree-sha1 = "17b059f61e340a3a2e59826c3d182a1184a582d3" @@ -256,6 +605,12 @@ weakdeps = ["Adapt"] [deps.OffsetArrays.extensions] OffsetArraysAdaptExt = "Adapt" +[[deps.Ogg_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f" +uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051" +version = "1.3.5+1" + [[deps.OpenBLAS32_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"] git-tree-sha1 = "6065c4cff8fee6c6770b277af45d5082baacdba1" @@ -267,11 +622,93 @@ deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"] uuid = "4536629a-c528-5b80-bd46-f80d51c5b363" version = "0.3.23+4" +[[deps.OpenLibm_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "05823500-19ac-5b8b-9628-191a04bc5112" +version = "0.8.1+2" + +[[deps.OpenSSL]] +deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"] +git-tree-sha1 = "38cb508d080d21dc1128f7fb04f20387ed4c0af4" +uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c" +version = "1.4.3" + +[[deps.OpenSSL_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "3da7367955dcc5c54c1ba4d402ccdc09a1a3e046" +uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95" +version = "3.0.13+1" + +[[deps.Opus_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720" +uuid = "91d4177d-7536-5919-b921-800302f37372" +version = "1.3.2+0" + +[[deps.OrderedCollections]] +git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5" +uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d" +version = "1.6.3" + +[[deps.PCRE2_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15" +version = "10.42.0+1" + +[[deps.Parsers]] +deps = ["Dates", "PrecompileTools", "UUIDs"] +git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821" +uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0" +version = "2.8.1" + +[[deps.Pipe]] +git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d" +uuid = "b98c9c47-44ae-5843-9183-064241ee97a0" +version = "1.3.0" + +[[deps.Pixman_jll]] +deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl"] +git-tree-sha1 = "35621f10a7531bc8fa58f74610b1bfb70a3cfc6b" +uuid = "30392449-352a-5448-841d-b1acce4e97dc" +version = "0.43.4+0" + [[deps.Pkg]] deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"] uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" version = "1.10.0" +[[deps.PlotThemes]] +deps = ["PlotUtils", "Statistics"] +git-tree-sha1 = "1f03a2d339f42dca4a4da149c7e15e9b896ad899" +uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a" +version = "3.1.0" + +[[deps.PlotUtils]] +deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"] +git-tree-sha1 = "7b1a9df27f072ac4c9c7cbe5efb198489258d1f5" +uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043" +version = "1.4.1" + +[[deps.Plots]] +deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"] +git-tree-sha1 = "442e1e7ac27dd5ff8825c3fa62fbd1e86397974b" +uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +version = "1.40.4" + + [deps.Plots.extensions] + FileIOExt = "FileIO" + GeometryBasicsExt = "GeometryBasics" + IJuliaExt = "IJulia" + ImageInTerminalExt = "ImageInTerminal" + UnitfulExt = "Unitful" + + [deps.Plots.weakdeps] + FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549" + GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" + IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a" + ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254" + Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" + [[deps.PolyesterWeave]] deps = ["BitTwiddlingConvenienceFunctions", "CPUSummary", "IfElse", "Static", "ThreadingUtilities"] git-tree-sha1 = "240d7170f5ffdb285f9427b92333c3463bf65bf6" @@ -294,6 +731,12 @@ version = "1.4.3" deps = ["Unicode"] uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" +[[deps.Qt6Base_jll]] +deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Vulkan_Loader_jll", "Xorg_libSM_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_cursor_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "libinput_jll", "xkbcommon_jll"] +git-tree-sha1 = "37b7bb7aabf9a085e0044307e1717436117f2b3b" +uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56" +version = "6.5.3+1" + [[deps.REPL]] deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"] uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" @@ -308,6 +751,29 @@ git-tree-sha1 = "b8a399e95663485820000f26b6a43c794e166a49" uuid = "fb686558-2515-59ef-acaa-46db3789a887" version = "0.4.4" +[[deps.RecipesBase]] +deps = ["PrecompileTools"] +git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff" +uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01" +version = "1.3.4" + +[[deps.RecipesPipeline]] +deps = ["Dates", "NaNMath", "PlotUtils", "PrecompileTools", "RecipesBase"] +git-tree-sha1 = "45cf9fd0ca5839d06ef333c8201714e888486342" +uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c" +version = "0.6.12" + +[[deps.Reexport]] +git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b" +uuid = "189a3867-3050-52da-a836-e630ba90ab69" +version = "1.2.2" + +[[deps.RelocatableFolders]] +deps = ["SHA", "Scratch"] +git-tree-sha1 = "ffdaf70d81cf6ff22c2b6e733c900c3321cab864" +uuid = "05181044-ff0b-4ac5-8273-598c1e38db00" +version = "1.0.1" + [[deps.Requires]] deps = ["UUIDs"] git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7" @@ -329,12 +795,35 @@ git-tree-sha1 = "3aac6d68c5e57449f5b9b865c9ba50ac2970c4cf" uuid = "476501e8-09a2-5ece-8869-fb82de89a1fa" version = "0.6.42" +[[deps.Scratch]] +deps = ["Dates"] +git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386" +uuid = "6c6a2e73-6563-6170-7368-637461726353" +version = "1.2.1" + [[deps.Serialization]] uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" +[[deps.Showoff]] +deps = ["Dates", "Grisu"] 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"Pkg"] +git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" +uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" +version = "2.0.2+0" + +[[deps.libinput_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"] +git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce" +uuid = "36db933b-70db-51c0-b978-0f229ee0e533" +version = "1.18.0+0" + +[[deps.libpng_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"] +git-tree-sha1 = "d7015d2e18a5fd9a4f47de711837e980519781a4" +uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" +version = "1.6.43+1" + +[[deps.libvorbis_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] +git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c" +uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" +version = "1.3.7+1" + [[deps.msolve_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "FLINT_jll", "GMP_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl", "MPFR_jll"] git-tree-sha1 = "00d6ebe337ec3935bf6a356f6c6060933c8b73e8" uuid = "6d01cc9a-e8f6-580e-8c54-544227e08205" version = "0.600.501+0" +[[deps.mtdev_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11" +uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e" +version = "1.1.6+0" + [[deps.nghttp2_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" @@ -448,3 +1257,21 @@ version = "1.52.0+1" deps = ["Artifacts", "Libdl"] uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" version = "17.4.0+2" + +[[deps.x264_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" +uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" +version = "2021.5.5+0" + +[[deps.x265_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" +uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" +version = "3.5.0+0" + +[[deps.xkbcommon_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] +git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37" +uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" +version = "1.4.1+1" diff --git a/Project.toml b/Project.toml index db0396e..64fc080 100644 --- a/Project.toml +++ b/Project.toml @@ -4,11 +4,13 @@ authors = ["ederc ", "Mohab Safey El Din 2 - print((i,j)," ",npcside) precxtmp *= 2 println("\nRefine extreme boxes along x-axis to precision ", precxtmp) refine_xboxes(params[1][1], LBcrit[1], precxtmp) @@ -249,8 +258,8 @@ function compute_graph(f; generic=false, precx = 100) #plot_graph_comp(Vert,CEdg) # Operate inverse change of variable if necessary if !(generic) - Vert = [ map(QQ,v) for v in Vert ] + Vert = [ changemat*v for v in Vert ] end - + return Vert, Edg end \ No newline at end of file diff --git a/src/connectcurves/graph.jl b/src/connectcurves/graph.jl index 6691e58..c932ed2 100644 --- a/src/connectcurves/graph.jl +++ b/src/connectcurves/graph.jl @@ -1,8 +1,12 @@ ## TODO : deal with isolated vertices (not appearing in the edges) ############################ +function index_of(x, L) + return findfirst(t->t==x,L) +end + function connected_components(G) - # Group the vert and edges w.r.t the connected components they belong to + # Outputs subgraphs of the connected components ########### vert, edges = G @@ -42,16 +46,15 @@ function connected_components(G) for node in component for neighbor in adj_list[node] if neighbor > node && neighbor in component - push!(grouped_edges[idx], (node, neighbor)) + push!(grouped_edges[idx], (index_of(node,component), index_of(neighbor,component))) end end end end - grouped_vert = [ [ vert[cv] for cv in c ] for c in components ] - return grouped_vert, grouped_edges + return [ [[ vert[cv] for cv in components[i] ], grouped_edges[i]] for i in eachindex(components) ] end function number_connected_components(G) - return length(first(connected_components(G))) + return length(connected_components(G)) end \ No newline at end of file diff --git a/src/connectcurves/plots.jl b/src/connectcurves/plots.jl index 040d70f..d586e00 100644 --- a/src/connectcurves/plots.jl +++ b/src/connectcurves/plots.jl @@ -1,27 +1,50 @@ ## Plot functions -function plot_graph(V, E) +function plot_graph(G; color="red", width=3, vert = true) println("Plotting the graph") + V, E = G plot(legend=false) for e in E - xe, ye = map(Float64,[e[1][1], e[2][1]]), map(Float64,[e[1][2], e[2][2]]) - plot!(xe, ye, lc="red", lw=3) + v1, v2 = [ map(Float64, V[ee]) for ee in e ] + plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=color, lw=width) end - scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) - #plt.show(block=true) - plot!() + if vert + scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) + end + gui() end -function plot_graph_comp(V, CE) +function plot_graphs(CG; width=3, vert=true) println("Plotting the graph") plot(legend=false) - col = distinguishable_colors(length(CE)+2) - for j in eachindex(CE) - for e in CE[j] - v1, v2 = map(Float64, V[e[1]]), map(Float64, V[e[2]]) - plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=3) + col = distinguishable_colors(length(CG)+2) + for j in eachindex(CG) + V, E = CG[j] + for e in E + v1, v2 = [ map(Float64, V[ee]) for ee in e ] + plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) + end + if vert + scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) + end + end + gui() +end + +function plot_graph_comp(G; width=3, vert=true) + println("Plotting the graph") + plot(legend=false) + CG = connected_components(G) + col = distinguishable_colors(length(CG)+2) + for j in eachindex(CG) + V, E = CG[j] + for e in E + v1, v2 = [ map(Float64, V[ee]) for ee in e ] + plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) + end + if vert + scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) end end - #plt.show(block=true) - plot!() + gui() end \ No newline at end of file diff --git a/src/imports.jl b/src/imports.jl index ccf335a..492178b 100644 --- a/src/imports.jl +++ b/src/imports.jl @@ -6,6 +6,9 @@ using LinearAlgebra using StaticArrays using LoopVectorization +import Plots: plot, plot!, scatter!, gui, gr, pythonplot +import Colors: distinguishable_colors + import Random: MersenneTwister import Logging: ConsoleLogger, with_logger, Warn, Info import Printf: @sprintf From a57894477d62ca9b712beab9c9f8bb8f9dfc94e1 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Wed, 15 May 2024 15:38:29 +0200 Subject: [PATCH 020/180] compute boxes with msolve --- src/connectcurves/boxes.jl | 8 +++++- src/connectcurves/connectcurves.jl | 39 +++++++++++++++++++----------- src/connectcurves/tools.jl | 4 +-- 3 files changed, 34 insertions(+), 17 deletions(-) diff --git a/src/connectcurves/boxes.jl b/src/connectcurves/boxes.jl index 9b6885c..c78442e 100644 --- a/src/connectcurves/boxes.jl +++ b/src/connectcurves/boxes.jl @@ -51,9 +51,15 @@ function intersect_box(f, B; prec=100) end function refine_xboxes(f, LB, prec) - # Implementation of refine_xboxes function goes here + # Refine LB along first axis, being roots of f xnew = isolate(f, prec=prec) for i in eachindex(LB) LB[i] = [ xnew[i], LB[i][2] ] end end + +function refine_ith_xboxes(f, LB, i, prec) + # Refine only LB[i] along first axis, being i-th root of f + xnew = isolate(f, prec=prec) + LB[i] = [ xnew[i], LB[i][2] ] +end diff --git a/src/connectcurves/connectcurves.jl b/src/connectcurves/connectcurves.jl index d569ca2..0299839 100644 --- a/src/connectcurves/connectcurves.jl +++ b/src/connectcurves/connectcurves.jl @@ -12,11 +12,12 @@ include("boxes.jl") include("graph.jl") include("plots.jl") -function compute_graph(f; generic=false, precx = 100,v=0) +function compute_graph(f; generic=false, precx = 150,v=0, arb=false) println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") println("!! Careful: this is a WIP version !!") println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") +@time begin R = parent(f) x, y = gens(R) # Generic change of variables @@ -45,19 +46,28 @@ function compute_graph(f; generic=false, precx = 100,v=0) params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in group_sqr ]; end - # TODO : check that no overlap between different isolations - println("\nIsolating critical values at precision ", precx,"..") - @time begin - xcrit = [ isolate(first(p), prec=precx) for p in params ] - _, xcritpermut = order_permut2d(xcrit); - end + if arb + # TODO : check that no overlap between different isolations + println("\nIsolating critical values with precision ", precx,"..") + @time begin + xcrit = [ isolate(first(p), prec=precx) for p in params ] + xcritpermut = order_permut2d(xcrit); + end - println("\nComputing isolating critical boxes using Arb with precision ",max(precx,150),"..") - @time begin - #RR = ArbField(max(precx,150)) - precArb = max(precx,150) - Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1], precArb)/evaluate_Arb(params[i][3],xc[1],precArb)] for xc in xcrit[i]] for i in eachindex(xcrit) ] - LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ] + println("\nComputing isolating critical boxes using Arb with precision ",max(precx,150),"..") + @time begin + #RR = ArbField(max(precx,150)) + precArb =precx + Pcrit = [ [ [xc, evaluate_Arb(params[i][2], xc[1], precArb)/evaluate_Arb(params[i][3],xc[1],precArb)] for xc in xcrit[i]] for i in eachindex(xcrit) ] + LBcrit = [ [ [ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for pcrit in Pcrit ] + end + else + println("\nCompute critical boxes with msolve with precision ", precx,"..") + @time begin + LBcrit = [ sort(inter_solutions(AlgebraicSolving.Ideal([p[1], p[3]*y-p[2]]), precision=precx),by=t->t[1]) for p in params ] + xcrit = [ [ B[1] for B in lbcrit ] for lbcrit in LBcrit ] + xcritpermut = order_permut2d(xcrit); + end end print("\nTest for identifying singular boxes");ts=time(); @@ -260,6 +270,7 @@ function compute_graph(f; generic=false, precx = 100,v=0) if !(generic) Vert = [ changemat*v for v in Vert ] end - +println("Total time:") +end return Vert, Edg end \ No newline at end of file diff --git a/src/connectcurves/tools.jl b/src/connectcurves/tools.jl index 2a41af8..e7b0b25 100644 --- a/src/connectcurves/tools.jl +++ b/src/connectcurves/tools.jl @@ -4,10 +4,10 @@ function order_permut2d(L) # Sort the enumerated list based on the values sorted_LL = sort(LL, by = x -> x[1]) # Extract the sorted values and their corresponding indices - sorted_L = [pair[1] for pair in sorted_LL] + #sorted_L = [pair[1] for pair in sorted_LL] sorted_ind = [pair[2] for pair in sorted_LL] - return sorted_L, sorted_ind + return sorted_ind end function Arb_to_rat(x) From 43204b3cb36f5b103a4b22e58692a39b4c399913 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sun, 19 May 2024 00:44:01 +0200 Subject: [PATCH 021/180] improvements --- src/connectcurves/arbtools.jl | 20 ++++++++++++++++++++ src/connectcurves/connectcurves.jl | 1 + src/connectcurves/tools.jl | 24 ++++++++++++------------ 3 files changed, 33 insertions(+), 12 deletions(-) create mode 100644 src/connectcurves/arbtools.jl diff --git a/src/connectcurves/arbtools.jl b/src/connectcurves/arbtools.jl new file mode 100644 index 0000000..4721a75 --- /dev/null +++ b/src/connectcurves/arbtools.jl @@ -0,0 +1,20 @@ +function Arb_to_rat(x) + r = radius(x) + return map(simplest_rational_inside, [x-2*r, x+2*r]) +end + +function rat_to_Arb(x, prec) + x1,x2 = x + xm, xd = ArbField(prec)((x1+x2)/2), ArbField(prec)(x2-x1) + return ball(xm,xd) +end + +function evaluate_Arb(f, x, prec) + cf = coefficients_of_univariate(f) + return evalpoly(ArbField(prec)(x), cf) +end + +function Arb_eval(f, B, prec) + BA = [ rat_to_Arb(b, prec) for b in B ] + return evaluate(change_base_ring(ArbField(prec), f), BA) +end \ No newline at end of file diff --git a/src/connectcurves/connectcurves.jl b/src/connectcurves/connectcurves.jl index 0299839..6dfc2e8 100644 --- a/src/connectcurves/connectcurves.jl +++ b/src/connectcurves/connectcurves.jl @@ -11,6 +11,7 @@ include("isolate.jl") include("boxes.jl") include("graph.jl") include("plots.jl") +include("arbtools.jl") function compute_graph(f; generic=false, precx = 150,v=0, arb=false) println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") diff --git a/src/connectcurves/tools.jl b/src/connectcurves/tools.jl index e7b0b25..9bf0b0b 100644 --- a/src/connectcurves/tools.jl +++ b/src/connectcurves/tools.jl @@ -10,18 +10,18 @@ function order_permut2d(L) return sorted_ind end -function Arb_to_rat(x) - r = radius(x) - return map(simplest_rational_inside, [x-2*r, x+2*r]) +function diff(p, v, n) + dp = p + for j in 1:n + dp = derivative(dp, v) + end + return dp end -function rat_to_Arb(x, prec) - x1,x2 = x - xm, xd = ArbField(prec)((x1+x2)/2), ArbField(prec)(x2-x1) - return ball(xm,xd) -end - -function evaluate_Arb(f, x, prec) - cf = coefficients_of_univariate(f) - return evalpoly(ArbField(prec)(x), cf) +function diff_list(p, v, n) + Ldp = [p] + for j in 1:n + push!(Ldb,derivative(Ldp[end], v)) + end + return Ldp end \ No newline at end of file From 6e1a83697cb713101dc1e4eb2061fba5a49b19fa Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 20 May 2024 12:31:14 +0200 Subject: [PATCH 022/180] add interpolation parmetrization --- src/connectcurves/connectcurves.jl | 4 +- src/connectcurves/param-curve.jl | 79 ++++++++++++++++++++++++++++++ 2 files changed, 82 insertions(+), 1 deletion(-) create mode 100644 src/connectcurves/param-curve.jl diff --git a/src/connectcurves/connectcurves.jl b/src/connectcurves/connectcurves.jl index 6dfc2e8..141004b 100644 --- a/src/connectcurves/connectcurves.jl +++ b/src/connectcurves/connectcurves.jl @@ -3,7 +3,8 @@ #using Plots, Colors #pythonplot() -export compute_graph, connected_components, number_connected_components, plot_graph, plot_graphs, plot_graph_comp +export compute_graph, connected_components, number_connected_components, + plot_graph, plot_graphs, plot_graph_comp, compute_param include("tools.jl") include("subresultants.jl") @@ -12,6 +13,7 @@ include("boxes.jl") include("graph.jl") include("plots.jl") include("arbtools.jl") +include("param-curve.jl") function compute_graph(f; generic=false, precx = 150,v=0, arb=false) println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") diff --git a/src/connectcurves/param-curve.jl b/src/connectcurves/param-curve.jl new file mode 100644 index 0000000..e90092c --- /dev/null +++ b/src/connectcurves/param-curve.jl @@ -0,0 +1,79 @@ + +function repl_ind(L,i,x) + # replace by element x at index i + return [ L[1:i-1]; x; L[i+1:end] ] +end + +function rem_var(f, i, A) + CE = [collect(coefficients(f)), collect(exponent_vectors(f))] + CE[2] = [ rem_ind(e, i) for e in CE[2]] + return array_to_poly(CE, A) +end + +function deg_Alg(F, dim) + # Compute the degree of the the alg set of dimension dim + # defined by F + if dim <= 0 + r = rational_parametrization(AlgebraicSolving.Ideal(F)) + else + vars = gens(parent(first(F))) + planes = [ sum([ rand(-100:100)*v for v in vcat(vars,1) ]) for _ in 1:dim] + r = rational_parametrization(AlgebraicSolving.Ideal(vcat(F,planes))) + end + return degree(r.elim) +end + + +function compute_param(F) + varias = gens(parent(first(F))) + N = length(varias) + + if N == 2 + return F + end + + DEG = deg_Alg(F,1) + if deg_Alg(vcat(F,varias[N-1]-rand(-100:100)),0) != DEG + error("The curve is not in generic position") + end + + PARAM = [] + rr = 0 + _values, i = [], 1 + A, (s,t) = polynomial_ring(QQ,[:s,:t]) + while length(_values) < DEG+2 + try + Feval = [ evaluate(f, repl_ind(varias, N-1, QQ(i))) for f in F ] + Feval = [ rem_var(f, N-1, A) for f in Feval ] + r = rational_parametrization(AlgebraicSolving.Ideal(Feval)) + #ivev = findfirst(t->t==R.S[end-1],r.vars) + lc = leading_coefficient(r.elim) + rr = [ p/lc for p in vcat(r.elim,r.param) ] + push!(PARAM, rr) + push!(_values, QQ(i)) + i+=1 + catch + error("bad specialization choice") + end + end + + CURVEPARAM = [] + + T, (x1,x2) = polynomial_ring(QQ, [:x1,:x2]) + + for count in 1:N-1 + COEFFS = [] + for deg in 0:DEG + _evals = [ coeff(PARAM[i][count],deg) for i in 1:length(PARAM)] + S, u = polynomial_ring(QQ,"u") + push!(COEFFS, interpolate(S, map(QQ,_values[1:length(PARAM)]), _evals)) + end + + C = [ collect(coefficients(c)) for c in COEFFS ] + POL = sum([ C[i][j]*x1^(j-1)*x2^(i-1) for i in 1:length(C) for j in 1:length(C[i])]) + + push!(CURVEPARAM, POL) + end + + return CURVEPARAM +end From 880de67edf29496263abb5b7b5eeb46e1008fb83 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 20 May 2024 12:38:38 +0200 Subject: [PATCH 023/180] interface with parametrization --- src/connectcurves/connectcurves.jl | 16 ++++++++++++++-- 1 file changed, 14 insertions(+), 2 deletions(-) diff --git a/src/connectcurves/connectcurves.jl b/src/connectcurves/connectcurves.jl index 141004b..5f32ee6 100644 --- a/src/connectcurves/connectcurves.jl +++ b/src/connectcurves/connectcurves.jl @@ -15,8 +15,20 @@ include("plots.jl") include("arbtools.jl") include("param-curve.jl") -function compute_graph(f; generic=false, precx = 150,v=0, arb=false) - println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") +function compute_graph(F; param=false, generic=false, precx=150, v=0, arb=false) + + if !(param) + println("Compute rational parametrization...") + @time begin + Fparam = compute_param(F) + end + end + + return compute_graph_param(Fparam[1], generic=generic, precx=precx, v=v, arb=arb) +end + +function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) + println("\n!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") println("!! Careful: this is a WIP version !!") println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") From d1d6a60ccc19fdd8a2a3033517a4dd06576d02ed Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 21 May 2024 22:53:45 +0200 Subject: [PATCH 024/180] better change of variables --- src/connectcurves/connectcurves.jl | 6 +++--- src/connectcurves/param-curve.jl | 2 +- src/connectcurves/tools.jl | 8 ++++++++ 3 files changed, 12 insertions(+), 4 deletions(-) diff --git a/src/connectcurves/connectcurves.jl b/src/connectcurves/connectcurves.jl index 5f32ee6..92fe951 100644 --- a/src/connectcurves/connectcurves.jl +++ b/src/connectcurves/connectcurves.jl @@ -20,7 +20,7 @@ function compute_graph(F; param=false, generic=false, precx=150, v=0, arb=false) if !(param) println("Compute rational parametrization...") @time begin - Fparam = compute_param(F) + Fparam = compute_param(F, generic=generic) end end @@ -38,7 +38,7 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) # Generic change of variables changemat = [1 0; 0 1] if !generic - changemat = map(QQ,rand(-500:500, 2, 2)) + changemat = trimat_rand(QQ, 2, range=-500:500) end f = evaluate(f, collect(changemat*[x; y])); @@ -288,4 +288,4 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) println("Total time:") end return Vert, Edg -end \ No newline at end of file +end diff --git a/src/connectcurves/param-curve.jl b/src/connectcurves/param-curve.jl index e90092c..828c608 100644 --- a/src/connectcurves/param-curve.jl +++ b/src/connectcurves/param-curve.jl @@ -24,7 +24,7 @@ function deg_Alg(F, dim) end -function compute_param(F) +function compute_param(F; generic=false) varias = gens(parent(first(F))) N = length(varias) diff --git a/src/connectcurves/tools.jl b/src/connectcurves/tools.jl index 9bf0b0b..5e75709 100644 --- a/src/connectcurves/tools.jl +++ b/src/connectcurves/tools.jl @@ -24,4 +24,12 @@ function diff_list(p, v, n) push!(Ldb,derivative(Ldp[end], v)) end return Ldp +end + +function trimat_rand(A, n; up=true, range=-100:100) + if up + return [ i==j ? one(A) : (ij ? A(rand(range)) : zero(A)) for i in 1:3, j in 1:3 ] + end end \ No newline at end of file From f027e45ff5371560c9d8f7358316b9605446e98c Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 5 Aug 2024 21:10:33 +0200 Subject: [PATCH 025/180] maj code connectivity --- Manifest.toml | 335 ++++++------------ Project.toml | 8 +- src/AlgebraicSolving.jl | 7 +- src/connectcurves/param-curve.jl | 79 ----- src/connectivity/Cannytools.jl | 174 +++++++++ .../arbtools.jl | 0 src/{connectcurves => connectivity}/boxes.jl | 0 src/connectivity/computeRM.jl | 80 +++++ .../connectcurves.jl | 49 ++- src/{connectcurves => connectivity}/graph.jl | 0 .../isolate.jl | 4 +- src/connectivity/paramcurve.jl | 153 ++++++++ src/{connectcurves => connectivity}/plots.jl | 0 .../src/resultant/Makefile | 0 .../__pycache__/bresultant.cpython-310.pyc | Bin .../src/resultant/bresultant | Bin .../src/resultant/bresultant.jl | 0 .../src/resultant/bresultant.sage | 0 .../src/resultant/data.c | 0 .../src/resultant/data.h | 0 .../src/resultant/flint_euclide.c | 0 .../src/resultant/flint_resultant.c | 0 .../src/resultant/io.c | 0 .../src/resultant/main.c | 0 .../src/resultant/out.txt | 0 .../src/resultant/ratreconstruct.c | 0 .../src/usolve/usolve | Bin .../src/usolve/usolve.jl | 0 .../subresultants.jl | 0 src/{connectcurves => connectivity}/tools.jl | 0 src/imports.jl | 8 +- 31 files changed, 549 insertions(+), 348 deletions(-) delete mode 100644 src/connectcurves/param-curve.jl create mode 100644 src/connectivity/Cannytools.jl rename src/{connectcurves => connectivity}/arbtools.jl (100%) rename src/{connectcurves => connectivity}/boxes.jl (100%) create mode 100644 src/connectivity/computeRM.jl rename src/{connectcurves => connectivity}/connectcurves.jl (89%) rename src/{connectcurves => connectivity}/graph.jl (100%) rename src/{connectcurves => connectivity}/isolate.jl (73%) create mode 100644 src/connectivity/paramcurve.jl rename src/{connectcurves => connectivity}/plots.jl (100%) rename src/{connectcurves => connectivity}/src/resultant/Makefile (100%) rename src/{connectcurves => connectivity}/src/resultant/__pycache__/bresultant.cpython-310.pyc (100%) rename src/{connectcurves => connectivity}/src/resultant/bresultant (100%) rename src/{connectcurves => connectivity}/src/resultant/bresultant.jl (100%) rename src/{connectcurves => connectivity}/src/resultant/bresultant.sage (100%) rename src/{connectcurves => connectivity}/src/resultant/data.c (100%) rename src/{connectcurves => connectivity}/src/resultant/data.h (100%) rename src/{connectcurves => connectivity}/src/resultant/flint_euclide.c (100%) rename src/{connectcurves => connectivity}/src/resultant/flint_resultant.c (100%) rename src/{connectcurves => connectivity}/src/resultant/io.c (100%) rename src/{connectcurves => connectivity}/src/resultant/main.c (100%) rename src/{connectcurves => connectivity}/src/resultant/out.txt (100%) rename src/{connectcurves => connectivity}/src/resultant/ratreconstruct.c (100%) rename src/{connectcurves => connectivity}/src/usolve/usolve (100%) rename src/{connectcurves => connectivity}/src/usolve/usolve.jl (100%) rename src/{connectcurves => connectivity}/subresultants.jl (100%) rename src/{connectcurves => connectivity}/tools.jl (100%) diff --git a/Manifest.toml b/Manifest.toml index 8800004..34b82dd 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -2,56 +2,18 @@ julia_version = "1.10.1" manifest_format = "2.0" -project_hash = "7a6e412edf7e0069b27986b55a45575b55f508bb" +project_hash = "41b78713eea3ae65743b4a45ba2e4e27496d5a74" [[deps.AbstractAlgebra]] deps = ["InteractiveUtils", "LinearAlgebra", "MacroTools", "Preferences", "Random", "RandomExtensions", "SparseArrays", "Test"] -git-tree-sha1 = "3987905620fb20e5b852446b7cb156eb0f71cb49" +git-tree-sha1 = "82d5966bba732eaf9972d9b2e3e725de7288c9d7" uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d" -version = "0.41.4" - -[[deps.Adapt]] -deps = ["LinearAlgebra", "Requires"] -git-tree-sha1 = "6a55b747d1812e699320963ffde36f1ebdda4099" -uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" -version = "4.0.4" -weakdeps = ["StaticArrays"] - - [deps.Adapt.extensions] - AdaptStaticArraysExt = "StaticArrays" +version = "0.42.0" [[deps.ArgTools]] uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" version = "1.1.1" -[[deps.ArrayInterface]] -deps = ["Adapt", "LinearAlgebra", "SparseArrays", "SuiteSparse"] -git-tree-sha1 = "133a240faec6e074e07c31ee75619c90544179cf" -uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9" -version = "7.10.0" - - [deps.ArrayInterface.extensions] - ArrayInterfaceBandedMatricesExt = "BandedMatrices" - ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices" - ArrayInterfaceCUDAExt = "CUDA" - ArrayInterfaceCUDSSExt = "CUDSS" - ArrayInterfaceChainRulesExt = "ChainRules" - ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore" - ArrayInterfaceReverseDiffExt = "ReverseDiff" - ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore" - ArrayInterfaceTrackerExt = "Tracker" - - [deps.ArrayInterface.weakdeps] - BandedMatrices = "aae01518-5342-5314-be14-df237901396f" - BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0" - CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" - CUDSS = "45b445bb-4962-46a0-9369-b4df9d0f772e" - ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2" - GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527" - ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267" - StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c" - Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c" - [[deps.Artifacts]] uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" @@ -59,15 +21,9 @@ uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" [[deps.BitFlags]] -git-tree-sha1 = "2dc09997850d68179b69dafb58ae806167a32b1b" +git-tree-sha1 = "0691e34b3bb8be9307330f88d1a3c3f25466c24d" uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35" -version = "0.1.8" - -[[deps.BitTwiddlingConvenienceFunctions]] -deps = ["Static"] -git-tree-sha1 = "0c5f81f47bbbcf4aea7b2959135713459170798b" -uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b" -version = "0.1.5" +version = "0.1.9" [[deps.Bzip2_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] @@ -75,35 +31,23 @@ git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd" uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" version = "1.0.8+1" -[[deps.CPUSummary]] -deps = ["CpuId", "IfElse", "PrecompileTools", "Static"] -git-tree-sha1 = "601f7e7b3d36f18790e2caf83a882d88e9b71ff1" -uuid = "2a0fbf3d-bb9c-48f3-b0a9-814d99fd7ab9" -version = "0.2.4" - [[deps.Cairo_jll]] deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] -git-tree-sha1 = "a4c43f59baa34011e303e76f5c8c91bf58415aaf" +git-tree-sha1 = "a2f1c8c668c8e3cb4cca4e57a8efdb09067bb3fd" uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" -version = "1.18.0+1" - -[[deps.CloseOpenIntervals]] -deps = ["Static", "StaticArrayInterface"] -git-tree-sha1 = "70232f82ffaab9dc52585e0dd043b5e0c6b714f1" -uuid = "fb6a15b2-703c-40df-9091-08a04967cfa9" -version = "0.1.12" +version = "1.18.0+2" [[deps.CodecZlib]] deps = ["TranscodingStreams", "Zlib_jll"] -git-tree-sha1 = "59939d8a997469ee05c4b4944560a820f9ba0d73" +git-tree-sha1 = "b8fe8546d52ca154ac556809e10c75e6e7430ac8" uuid = "944b1d66-785c-5afd-91f1-9de20f533193" -version = "0.7.4" +version = "0.7.5" [[deps.ColorSchemes]] deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"] -git-tree-sha1 = "4b270d6465eb21ae89b732182c20dc165f8bf9f2" +git-tree-sha1 = "b5278586822443594ff615963b0c09755771b3e0" uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4" -version = "3.25.0" +version = "3.26.0" [[deps.ColorTypes]] deps = ["FixedPointNumbers", "Random"] @@ -125,9 +69,9 @@ version = "0.10.0" [[deps.Colors]] deps = ["ColorTypes", "FixedPointNumbers", "Reexport"] -git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a" +git-tree-sha1 = "362a287c3aa50601b0bc359053d5c2468f0e7ce0" uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" -version = "0.12.10" +version = "0.12.11" [[deps.Compat]] deps = ["TOML", "UUIDs"] @@ -146,21 +90,15 @@ version = "1.1.0+0" [[deps.ConcurrentUtilities]] deps = ["Serialization", "Sockets"] -git-tree-sha1 = "6cbbd4d241d7e6579ab354737f4dd95ca43946e1" +git-tree-sha1 = "ea32b83ca4fefa1768dc84e504cc0a94fb1ab8d1" uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb" -version = "2.4.1" +version = "2.4.2" [[deps.Contour]] git-tree-sha1 = "439e35b0b36e2e5881738abc8857bd92ad6ff9a8" uuid = "d38c429a-6771-53c6-b99e-75d170b6e991" version = "0.6.3" -[[deps.CpuId]] -deps = ["Markdown"] -git-tree-sha1 = "fcbb72b032692610bfbdb15018ac16a36cf2e406" -uuid = "adafc99b-e345-5852-983c-f28acb93d879" -version = "0.3.1" - [[deps.DataAPI]] git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe" uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a" @@ -176,6 +114,12 @@ version = "0.18.20" deps = ["Printf"] uuid = "ade2ca70-3891-5945-98fb-dc099432e06a" +[[deps.Dbus_jll]] +deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl"] +git-tree-sha1 = "fc173b380865f70627d7dd1190dc2fce6cc105af" +uuid = "ee1fde0b-3d02-5ea6-8484-8dfef6360eab" +version = "1.14.10+0" + [[deps.DelimitedFiles]] deps = ["Mmap"] git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae" @@ -234,9 +178,9 @@ uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee" [[deps.FixedPointNumbers]] deps = ["Statistics"] -git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc" +git-tree-sha1 = "05882d6995ae5c12bb5f36dd2ed3f61c98cbb172" uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93" -version = "0.8.4" +version = "0.8.5" [[deps.Fontconfig_jll]] deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Zlib_jll"] @@ -251,9 +195,9 @@ version = "1.3.7" [[deps.FreeType2_jll]] deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"] -git-tree-sha1 = "d8db6a5a2fe1381c1ea4ef2cab7c69c2de7f9ea0" +git-tree-sha1 = "5c1d8ae0efc6c2e7b1fc502cbe25def8f661b7bc" uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7" -version = "2.13.1+0" +version = "2.13.2+0" [[deps.FriBidi_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] @@ -262,10 +206,10 @@ uuid = "559328eb-81f9-559d-9380-de523a88c83c" version = "1.0.14+0" [[deps.GLFW_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"] -git-tree-sha1 = "ff38ba61beff76b8f4acad8ab0c97ef73bb670cb" +deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll", "libdecor_jll", "xkbcommon_jll"] +git-tree-sha1 = "532f9126ad901533af1d4f5c198867227a7bb077" uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89" -version = "3.3.9+0" +version = "3.4.0+1" [[deps.GMP_jll]] deps = ["Artifacts", "Libdl"] @@ -273,16 +217,16 @@ uuid = "781609d7-10c4-51f6-84f2-b8444358ff6d" version = "6.2.1+6" [[deps.GR]] -deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"] -git-tree-sha1 = "ddda044ca260ee324c5fc07edb6d7cf3f0b9c350" +deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"] +git-tree-sha1 = "629693584cef594c3f6f99e76e7a7ad17e60e8d5" uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71" -version = "0.73.5" +version = "0.73.7" [[deps.GR_jll]] deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"] -git-tree-sha1 = "278e5e0f820178e8a26df3184fcb2280717c79b1" +git-tree-sha1 = "a8863b69c2a0859f2c2c87ebdc4c6712e88bdf0d" uuid = "d2c73de3-f751-5644-a686-071e5b155ba9" -version = "0.73.5+0" +version = "0.73.7+0" [[deps.Gettext_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"] @@ -292,9 +236,9 @@ version = "0.21.0+0" [[deps.Glib_jll]] deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"] -git-tree-sha1 = "359a1ba2e320790ddbe4ee8b4d54a305c0ea2aff" +git-tree-sha1 = "7c82e6a6cd34e9d935e9aa4051b66c6ff3af59ba" uuid = "7746bdde-850d-59dc-9ae8-88ece973131d" -version = "2.80.0+0" +version = "2.80.2+0" [[deps.Graphite2_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] @@ -319,17 +263,6 @@ git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3" uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566" version = "2.8.1+1" -[[deps.HostCPUFeatures]] -deps = ["BitTwiddlingConvenienceFunctions", "IfElse", "Libdl", "Static"] -git-tree-sha1 = "eb8fed28f4994600e29beef49744639d985a04b2" -uuid = "3e5b6fbb-0976-4d2c-9146-d79de83f2fb0" -version = "0.1.16" - -[[deps.IfElse]] -git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1" -uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173" -version = "0.1.1" - [[deps.InteractiveUtils]] deps = ["Markdown"] uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240" @@ -394,9 +327,9 @@ version = "1.3.1" [[deps.Latexify]] deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"] -git-tree-sha1 = "e0b5cd21dc1b44ec6e64f351976f961e6f31d6c4" +git-tree-sha1 = "5b0d630f3020b82c0775a51d05895852f8506f50" uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316" -version = "0.16.3" +version = "0.16.4" [deps.Latexify.extensions] DataFramesExt = "DataFrames" @@ -406,12 +339,6 @@ version = "0.16.3" DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8" -[[deps.LayoutPointers]] -deps = ["ArrayInterface", "LinearAlgebra", "ManualMemory", "SIMDTypes", "Static", "StaticArrayInterface"] -git-tree-sha1 = "62edfee3211981241b57ff1cedf4d74d79519277" -uuid = "10f19ff3-798f-405d-979b-55457f8fc047" -version = "0.1.15" - [[deps.LibCURL]] deps = ["LibCURL_jll", "MozillaCACerts_jll"] uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21" @@ -493,9 +420,9 @@ uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" [[deps.LogExpFunctions]] deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"] -git-tree-sha1 = "18144f3e9cbe9b15b070288eef858f71b291ce37" +git-tree-sha1 = "a2d09619db4e765091ee5c6ffe8872849de0feea" uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688" -version = "0.3.27" +version = "0.3.28" [deps.LogExpFunctions.extensions] LogExpFunctionsChainRulesCoreExt = "ChainRulesCore" @@ -516,21 +443,6 @@ git-tree-sha1 = "c1dd6d7978c12545b4179fb6153b9250c96b0075" uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36" version = "1.0.3" -[[deps.LoopVectorization]] -deps = ["ArrayInterface", "CPUSummary", "CloseOpenIntervals", "DocStringExtensions", "HostCPUFeatures", "IfElse", "LayoutPointers", "LinearAlgebra", "OffsetArrays", "PolyesterWeave", "PrecompileTools", "SIMDTypes", "SLEEFPirates", "Static", "StaticArrayInterface", "ThreadingUtilities", "UnPack", "VectorizationBase"] -git-tree-sha1 = "8f6786d8b2b3248d79db3ad359ce95382d5a6df8" -uuid = "bdcacae8-1622-11e9-2a5c-532679323890" -version = "0.12.170" - - [deps.LoopVectorization.extensions] - ForwardDiffExt = ["ChainRulesCore", "ForwardDiff"] - SpecialFunctionsExt = "SpecialFunctions" - - [deps.LoopVectorization.weakdeps] - ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" - ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" - SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b" - [[deps.MPFR_jll]] deps = ["Artifacts", "GMP_jll", "Libdl"] uuid = "3a97d323-0669-5f0c-9066-3539efd106a3" @@ -542,11 +454,6 @@ git-tree-sha1 = "2fa9ee3e63fd3a4f7a9a4f4744a52f4856de82df" uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" version = "0.5.13" -[[deps.ManualMemory]] -git-tree-sha1 = "bcaef4fc7a0cfe2cba636d84cda54b5e4e4ca3cd" -uuid = "d125e4d3-2237-4719-b19c-fa641b8a4667" -version = "0.1.8" - [[deps.Markdown]] deps = ["Base64"] uuid = "d6f4376e-aef5-505a-96c1-9c027394607a" @@ -588,23 +495,14 @@ version = "1.0.2" [[deps.Nemo]] deps = ["AbstractAlgebra", "FLINT_jll", "Libdl", "LinearAlgebra", "Pkg", "Random", "RandomExtensions", "SHA"] -git-tree-sha1 = "17b059f61e340a3a2e59826c3d182a1184a582d3" +git-tree-sha1 = "df48747041f75651a434a42f1ee1b8bc61f9301a" uuid = "2edaba10-b0f1-5616-af89-8c11ac63239a" -version = "0.45.1" +version = "0.46.0" [[deps.NetworkOptions]] uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" version = "1.2.0" -[[deps.OffsetArrays]] -git-tree-sha1 = "e64b4f5ea6b7389f6f046d13d4896a8f9c1ba71e" -uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881" -version = "1.14.0" -weakdeps = ["Adapt"] - - [deps.OffsetArrays.extensions] - OffsetArraysAdaptExt = "Adapt" - [[deps.Ogg_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f" @@ -635,9 +533,9 @@ version = "1.4.3" [[deps.OpenSSL_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "3da7367955dcc5c54c1ba4d402ccdc09a1a3e046" +git-tree-sha1 = "a028ee3cb5641cccc4c24e90c36b0a4f7707bdf5" uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95" -version = "3.0.13+1" +version = "3.0.14+0" [[deps.Opus_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] @@ -655,6 +553,12 @@ deps = ["Artifacts", "Libdl"] uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15" version = "10.42.0+1" +[[deps.Pango_jll]] +deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"] +git-tree-sha1 = "cb5a2ab6763464ae0f19c86c56c63d4a2b0f5bda" +uuid = "36c8627f-9965-5494-a995-c6b170f724f3" +version = "1.52.2+0" + [[deps.Parsers]] deps = ["Dates", "PrecompileTools", "UUIDs"] git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821" @@ -679,9 +583,9 @@ version = "1.10.0" [[deps.PlotThemes]] deps = ["PlotUtils", "Statistics"] -git-tree-sha1 = "1f03a2d339f42dca4a4da149c7e15e9b896ad899" +git-tree-sha1 = "6e55c6841ce3411ccb3457ee52fc48cb698d6fb0" uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a" -version = "3.1.0" +version = "3.2.0" [[deps.PlotUtils]] deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"] @@ -690,10 +594,10 @@ uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043" version = "1.4.1" [[deps.Plots]] -deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"] -git-tree-sha1 = "442e1e7ac27dd5ff8825c3fa62fbd1e86397974b" +deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "TOML", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"] +git-tree-sha1 = "082f0c4b70c202c37784ce4bfbc33c9f437685bf" uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" -version = "1.40.4" +version = "1.40.5" [deps.Plots.extensions] FileIOExt = "FileIO" @@ -709,12 +613,6 @@ version = "1.40.4" ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254" Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" -[[deps.PolyesterWeave]] -deps = ["BitTwiddlingConvenienceFunctions", "CPUSummary", "IfElse", "Static", "ThreadingUtilities"] -git-tree-sha1 = "240d7170f5ffdb285f9427b92333c3463bf65bf6" -uuid = "1d0040c9-8b98-4ee7-8388-3f51789ca0ad" -version = "0.2.1" - [[deps.PrecompileTools]] deps = ["Preferences"] git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f" @@ -733,9 +631,27 @@ uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" [[deps.Qt6Base_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Vulkan_Loader_jll", "Xorg_libSM_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_cursor_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "libinput_jll", "xkbcommon_jll"] -git-tree-sha1 = "37b7bb7aabf9a085e0044307e1717436117f2b3b" +git-tree-sha1 = "492601870742dcd38f233b23c3ec629628c1d724" uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56" -version = "6.5.3+1" +version = "6.7.1+1" + +[[deps.Qt6Declarative_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll", "Qt6ShaderTools_jll"] +git-tree-sha1 = "e5dd466bf2569fe08c91a2cc29c1003f4797ac3b" +uuid = "629bc702-f1f5-5709-abd5-49b8460ea067" +version = "6.7.1+2" + +[[deps.Qt6ShaderTools_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll"] +git-tree-sha1 = "1a180aeced866700d4bebc3120ea1451201f16bc" +uuid = "ce943373-25bb-56aa-8eca-768745ed7b5a" +version = "6.7.1+1" + +[[deps.Qt6Wayland_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll", "Qt6Declarative_jll"] +git-tree-sha1 = "729927532d48cf79f49070341e1d918a65aba6b0" +uuid = "e99dba38-086e-5de3-a5b1-6e4c66e897c3" +version = "6.7.1+1" [[deps.REPL]] deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"] @@ -784,17 +700,6 @@ version = "1.3.0" uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" version = "0.7.0" -[[deps.SIMDTypes]] -git-tree-sha1 = "330289636fb8107c5f32088d2741e9fd7a061a5c" -uuid = "94e857df-77ce-4151-89e5-788b33177be4" -version = "0.1.0" - -[[deps.SLEEFPirates]] -deps = ["IfElse", "Static", "VectorizationBase"] -git-tree-sha1 = "3aac6d68c5e57449f5b9b865c9ba50ac2970c4cf" -uuid = "476501e8-09a2-5ece-8869-fb82de89a1fa" -version = "0.6.42" - [[deps.Scratch]] deps = ["Dates"] git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386" @@ -829,28 +734,11 @@ deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"] uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" version = "1.10.0" -[[deps.Static]] -deps = ["IfElse"] -git-tree-sha1 = "d2fdac9ff3906e27f7a618d47b676941baa6c80c" -uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3" -version = "0.8.10" - -[[deps.StaticArrayInterface]] -deps = ["ArrayInterface", "Compat", "IfElse", "LinearAlgebra", "PrecompileTools", "Requires", "SparseArrays", "Static", "SuiteSparse"] -git-tree-sha1 = "5d66818a39bb04bf328e92bc933ec5b4ee88e436" -uuid = "0d7ed370-da01-4f52-bd93-41d350b8b718" -version = "1.5.0" -weakdeps = ["OffsetArrays", "StaticArrays"] - - [deps.StaticArrayInterface.extensions] - StaticArrayInterfaceOffsetArraysExt = "OffsetArrays" - StaticArrayInterfaceStaticArraysExt = "StaticArrays" - [[deps.StaticArrays]] deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"] -git-tree-sha1 = "bf074c045d3d5ffd956fa0a461da38a44685d6b2" +git-tree-sha1 = "eeafab08ae20c62c44c8399ccb9354a04b80db50" uuid = "90137ffa-7385-5640-81b9-e52037218182" -version = "1.9.3" +version = "1.9.7" [deps.StaticArrays.extensions] StaticArraysChainRulesCoreExt = "ChainRulesCore" @@ -861,9 +749,9 @@ version = "1.9.3" Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" [[deps.StaticArraysCore]] -git-tree-sha1 = "36b3d696ce6366023a0ea192b4cd442268995a0d" +git-tree-sha1 = "192954ef1208c7019899fbf8049e717f92959682" uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c" -version = "1.4.2" +version = "1.4.3" [[deps.Statistics]] deps = ["LinearAlgebra", "SparseArrays"] @@ -882,10 +770,6 @@ git-tree-sha1 = "5cf7606d6cef84b543b483848d4ae08ad9832b21" uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" version = "0.34.3" -[[deps.SuiteSparse]] -deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"] -uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9" - [[deps.SuiteSparse_jll]] deps = ["Artifacts", "Libdl", "libblastrampoline_jll"] uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c" @@ -911,16 +795,10 @@ version = "0.1.1" deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" -[[deps.ThreadingUtilities]] -deps = ["ManualMemory"] -git-tree-sha1 = "eda08f7e9818eb53661b3deb74e3159460dfbc27" -uuid = "8290d209-cae3-49c0-8002-c8c24d57dab5" -version = "0.5.2" - [[deps.TranscodingStreams]] -git-tree-sha1 = "5d54d076465da49d6746c647022f3b3674e64156" +git-tree-sha1 = "96612ac5365777520c3c5396314c8cf7408f436a" uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa" -version = "0.10.8" +version = "0.11.1" weakdeps = ["Random", "Test"] [deps.TranscodingStreams.extensions] @@ -935,11 +813,6 @@ version = "1.5.1" deps = ["Random", "SHA"] uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" -[[deps.UnPack]] -git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b" -uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed" -version = "1.0.2" - [[deps.Unicode]] uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" @@ -951,9 +824,9 @@ version = "0.4.1" [[deps.Unitful]] deps = ["Dates", "LinearAlgebra", "Random"] -git-tree-sha1 = "3c793be6df9dd77a0cf49d80984ef9ff996948fa" +git-tree-sha1 = "d95fe458f26209c66a187b1114df96fd70839efd" uuid = "1986cc42-f94f-5a68-af5c-568840ba703d" -version = "1.19.0" +version = "1.21.0" [deps.Unitful.extensions] ConstructionBaseUnitfulExt = "ConstructionBase" @@ -965,21 +838,15 @@ version = "1.19.0" [[deps.UnitfulLatexify]] deps = ["LaTeXStrings", "Latexify", "Unitful"] -git-tree-sha1 = "e2d817cc500e960fdbafcf988ac8436ba3208bfd" +git-tree-sha1 = "975c354fcd5f7e1ddcc1f1a23e6e091d99e99bc8" uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728" -version = "1.6.3" +version = "1.6.4" [[deps.Unzip]] git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78" uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d" version = "0.2.0" -[[deps.VectorizationBase]] -deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static", "StaticArrayInterface"] -git-tree-sha1 = "6129a4faf6242e7c3581116fbe3270f3ab17c90d" -uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f" -version = "0.21.67" - [[deps.Vulkan_Loader_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"] git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59" @@ -1000,15 +867,15 @@ version = "1.31.0+0" [[deps.XML2_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"] -git-tree-sha1 = "532e22cf7be8462035d092ff21fada7527e2c488" +git-tree-sha1 = "d9717ce3518dc68a99e6b96300813760d887a01d" uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a" -version = "2.12.6+0" +version = "2.13.1+0" [[deps.XSLT_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"] -git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a" +deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "XML2_jll", "Zlib_jll"] +git-tree-sha1 = "a54ee957f4c86b526460a720dbc882fa5edcbefc" uuid = "aed1982a-8fda-507f-9586-7b0439959a61" -version = "1.1.34+0" +version = "1.1.41+0" [[deps.XZ_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] @@ -1096,9 +963,9 @@ version = "0.1.1+0" [[deps.Xorg_libxcb_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"] -git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d" +git-tree-sha1 = "bcd466676fef0878338c61e655629fa7bbc69d8e" uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b" -version = "1.15.0+0" +version = "1.17.0+0" [[deps.Xorg_libxkbfile_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"] @@ -1190,10 +1057,10 @@ uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70" version = "3.1.1+0" [[deps.libaom_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "1827acba325fdcdf1d2647fc8d5301dd9ba43a9d" uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b" -version = "3.4.0+0" +version = "3.9.0+0" [[deps.libass_jll]] deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] @@ -1206,6 +1073,12 @@ deps = ["Artifacts", "Libdl"] uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" version = "5.8.0+1" +[[deps.libdecor_jll]] +deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"] +git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f" +uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f" +version = "0.2.2+0" + [[deps.libevdev_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22" @@ -1232,15 +1105,15 @@ version = "1.6.43+1" [[deps.libvorbis_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] -git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c" +git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3" uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" -version = "1.3.7+1" +version = "1.3.7+2" [[deps.msolve_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "FLINT_jll", "GMP_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl", "MPFR_jll"] -git-tree-sha1 = "00d6ebe337ec3935bf6a356f6c6060933c8b73e8" +git-tree-sha1 = "b2e3c462bc0587672d3137d657a491c7b06751ea" uuid = "6d01cc9a-e8f6-580e-8c54-544227e08205" -version = "0.600.501+0" +version = "0.700.100+0" [[deps.mtdev_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] diff --git a/Project.toml b/Project.toml index 64fc080..18d20c8 100644 --- a/Project.toml +++ b/Project.toml @@ -1,13 +1,12 @@ name = "AlgebraicSolving" uuid = "66b61cbe-0446-4d5d-9090-1ff510639f9d" authors = ["ederc ", "Mohab Safey El Din "] -version = "0.4.15" +version = "0.6.0" [deps] Colors = "5ae59095-9a9b-59fe-a467-6f913c188581" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" -LoopVectorization = "bdcacae8-1622-11e9-2a5c-532679323890" Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" @@ -20,12 +19,11 @@ msolve_jll = "6d01cc9a-e8f6-580e-8c54-544227e08205" [compat] LinearAlgebra = "1.6" Logging = "1.6" -LoopVectorization = "0.12" Markdown = "1.6" -Nemo = "0.43, 0.44, 0.45" +Nemo = "0.43, 0.44, 0.45, 0.46" Printf = "1.6" Random = "1.6" StaticArrays = "1" Test = "1.6" julia = "1.6" -msolve_jll = "0.600.501" +msolve_jll = "0.700.100" diff --git a/src/AlgebraicSolving.jl b/src/AlgebraicSolving.jl index 0ff4474..ba4f00f 100644 --- a/src/AlgebraicSolving.jl +++ b/src/AlgebraicSolving.jl @@ -14,9 +14,12 @@ include("algorithms/normal-forms.jl") include("algorithms/solvers.jl") #= siggb =# include("siggb/siggb.jl") -#= Connectivity on alg. curves=# -include("connectcurves/connectcurves.jl") +#= connectivity =# +include("connectivity/computeRM.jl") +include("connectivity/paramcurve.jl") +include("connectivity/connectcurves.jl") #= examples =# include("examples/katsura.jl") include("examples/cyclic.jl") + end # module AlgebraicSolving diff --git a/src/connectcurves/param-curve.jl b/src/connectcurves/param-curve.jl deleted file mode 100644 index 828c608..0000000 --- a/src/connectcurves/param-curve.jl +++ /dev/null @@ -1,79 +0,0 @@ - -function repl_ind(L,i,x) - # replace by element x at index i - return [ L[1:i-1]; x; L[i+1:end] ] -end - -function rem_var(f, i, A) - CE = [collect(coefficients(f)), collect(exponent_vectors(f))] - CE[2] = [ rem_ind(e, i) for e in CE[2]] - return array_to_poly(CE, A) -end - -function deg_Alg(F, dim) - # Compute the degree of the the alg set of dimension dim - # defined by F - if dim <= 0 - r = rational_parametrization(AlgebraicSolving.Ideal(F)) - else - vars = gens(parent(first(F))) - planes = [ sum([ rand(-100:100)*v for v in vcat(vars,1) ]) for _ in 1:dim] - r = rational_parametrization(AlgebraicSolving.Ideal(vcat(F,planes))) - end - return degree(r.elim) -end - - -function compute_param(F; generic=false) - varias = gens(parent(first(F))) - N = length(varias) - - if N == 2 - return F - end - - DEG = deg_Alg(F,1) - if deg_Alg(vcat(F,varias[N-1]-rand(-100:100)),0) != DEG - error("The curve is not in generic position") - end - - PARAM = [] - rr = 0 - _values, i = [], 1 - A, (s,t) = polynomial_ring(QQ,[:s,:t]) - while length(_values) < DEG+2 - try - Feval = [ evaluate(f, repl_ind(varias, N-1, QQ(i))) for f in F ] - Feval = [ rem_var(f, N-1, A) for f in Feval ] - r = rational_parametrization(AlgebraicSolving.Ideal(Feval)) - #ivev = findfirst(t->t==R.S[end-1],r.vars) - lc = leading_coefficient(r.elim) - rr = [ p/lc for p in vcat(r.elim,r.param) ] - push!(PARAM, rr) - push!(_values, QQ(i)) - i+=1 - catch - error("bad specialization choice") - end - end - - CURVEPARAM = [] - - T, (x1,x2) = polynomial_ring(QQ, [:x1,:x2]) - - for count in 1:N-1 - COEFFS = [] - for deg in 0:DEG - _evals = [ coeff(PARAM[i][count],deg) for i in 1:length(PARAM)] - S, u = polynomial_ring(QQ,"u") - push!(COEFFS, interpolate(S, map(QQ,_values[1:length(PARAM)]), _evals)) - end - - C = [ collect(coefficients(c)) for c in COEFFS ] - POL = sum([ C[i][j]*x1^(j-1)*x2^(i-1) for i in 1:length(C) for j in 1:length(C[i])]) - - push!(CURVEPARAM, POL) - end - - return CURVEPARAM -end diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl new file mode 100644 index 0000000..6de2262 --- /dev/null +++ b/src/connectivity/Cannytools.jl @@ -0,0 +1,174 @@ + +function remfirstvars(F::Vector{P}, irem) where {P <: MPolyRingElem} + R = parent(first(F)) + istart = irem+1 + S, vars = polynomial_ring(base_ring(R), ["x$i" for i in istart:nvars(R)]) + res = typeof(first(F))[] + for f in F + ctx = MPolyBuildCtx(S) + for (e, c) in zip(exponent_vectors(f), coefficients(f)) + @assert(all([ e[i]==0 for i in 1:irem ]), "Occurence of first variable.s found!") + push_term!(ctx, c, e[istart:end]) + end + push!(res, finish(ctx)) + end + return res +end + +function remvars(F::Vector{P}; irem::Vector{Int64}) where {P <: MPolyRingElem} + R = parent(first(F)) + ikeep = [ i for i in 1:nvars(R) if !(i in irem) ] + S, vars = polynomial_ring(base_ring(R), ["x$i" for i in ikeep]) + res = typeof(first(F))[] + for f in F + ctx = MPolyBuildCtx(S) + for (e, c) in zip(exponent_vectors(f), coefficients(f)) + @assert(all([ e[i]==0 for i in irem ]), "Occurence of removed variable.s found!") + push_term!(ctx, c, [ e[i] for i in ikeep ]) + end + push!(res, finish(ctx)) + end + return res +end + +function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0) + # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj + @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" + R = parent(V) + n, hV = R.nvars, V.gens + c = n - dimV + + JW = [ derivative(f, k) for k=j+1:n, f in hV ] + sizeminors = c + dimproj - (j-1) + hW = vcat(hV, compute_minors(sizeminors, JW, R)) + output_functions = Dict( + "minors" => x -> x, + "groebner" => x -> groebner_basis(x, info_level=verb), + "real" => x -> real_solutions(x, info_level=verb), + "interval" => x -> real_solutions(x, interval=true, info_level=verb), + #"interval" => x -> inter_solutions(x, info_level=verb), + "parametric" => x -> rational_parametrization(x, info_level=verb) + ) + + return output_functions[output](AlgebraicSolving.Ideal(hW)) +end + +function compute_minors(p, A, R) + #Computes the p-minors of a matrix A + n, m = size(A) + rowsmins = collect(combinations(1:n, p)) + colsmins = collect(combinations(1:m, p)) + mins = Vector{eltype(A)}(undef, length(rowsmins) * length(colsmins)) + k = 1 + for rowsmin in rowsmins + for colsmin in colsmins + mins[k] = detmpoly(A[rowsmin, colsmin], R) + k += 1 + end + end + + return mins +end + +function combinations(a, n) + # Helper function to recursively generate combinations + function _combinations(a, n, start, chosen) + if length(chosen) == n + return [chosen] + elseif start > length(a) + return [] + else + # Include the current element and recurse + include_current = _combinations(a, n, start + 1, [chosen; a[start]]) + # Exclude the current element and recurse + exclude_current = _combinations(a, n, start + 1, chosen) + return vcat(include_current, exclude_current) + end + end + return _combinations(a, n, 1, []) +end + +function detmpoly(A::Matrix{QQMPolyRingElem}, R) + # Get the size of the matrix + n = size(A, 1) + if n != size(A, 2) + throw(ArgumentError("Matrix must be square")) + end + + if n == 1 + return A[1, 1] + end + + # Initialize the determinant polynomial + detA = QQMPolyRingElem(R,0) + + # Compute the determinant polynomial + for j = 1:n + submatrix = A[2:end, [i for i = 1:n if i != j]] + detA += (-1)^(1+j)*A[1, j] * detmpoly(submatrix, R) + end + + return detA +end + +function contfrac_convergents(x::Rational{Int}) + q = Rational{Int}[] + fpart, ipart = modf(x) + push!(q, ipart) + na, da, nb, db = Int(1), Int(0), Int(ipart), Int(1) + while true + fpart == 0 && return q + x = inv(fpart) + fpart, ipart = modf(x) + na, da, nb, db = nb, db, na+ipart*nb, da+ipart*db + push!(q, nb//db) + end +end + +function modfQQ(x::QQFieldElem) + ipart, fpart = [ f(numerator(x), denominator(x)) for f in [div, rem]] + return QQFieldElem(fpart, denominator(x)), ipart +end + +function small_mid_point(a::QQFieldElem,b::QQFieldElem) + a == b && return a + if b < a + a, b = b, a + end + x = (a+b)/ QQFieldElem(2) + fpart, ipart = modfQQ(x) + println("\n",fpart," , ", ipart) + q1, q2 = QQFieldElem(1//0), QQFieldElem(ipart,1) + while true + #println("(",q1," ; ",q2,")") + if numerator(fpart) == 0 || (q2 > a && q2 < b) + return q2 + end + x = inv(fpart) + fpart, ipart = modfQQ(x) + println(fpart," , ", ipart) + q1, q2 = q2, QQFieldElem(numerator(q1) + ipart*numerator(q2), denominator(q1) + ipart*denominator(q2)) + end +end + +function MidRationalPoints(S::Vector{Vector{QQFieldElem}}) + # S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] + # such that the [l_i, r_i] are rational and disjoint open intervals. + # + # It orders the [l_i,r_i] and computes the simplest + # rational points between these intervals. + n = length(S) + if n==0 + return Vector{QQFieldElem}(undef, 0) + end + S1 = sort(S, lt=(x, y) -> x[2] <= y[1]) + ratioP = Vector{QQFieldElem}(undef, n-1) + for i in 1:(n- 1) + ri, li1 = S1[i][2], S1[i+1][1] + @assert ri < li1 "The intervals are not disjoint." + #ratioP[i] = small_mid_point(ri, li1) + ratioP[i] = simplest_between(ri, li1) + end + return ratioP +end + diff --git a/src/connectcurves/arbtools.jl b/src/connectivity/arbtools.jl similarity index 100% rename from src/connectcurves/arbtools.jl rename to src/connectivity/arbtools.jl diff --git a/src/connectcurves/boxes.jl b/src/connectivity/boxes.jl similarity index 100% rename from src/connectcurves/boxes.jl rename to src/connectivity/boxes.jl diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl new file mode 100644 index 0000000..1cb7963 --- /dev/null +++ b/src/connectivity/computeRM.jl @@ -0,0 +1,80 @@ +#using Pkg +#Pkg.activate("AlgebraicSolving.jl") +#using Revise +#using AlgebraicSolving +#using Nemo + +export computeRM + +include("Cannytools.jl") + +function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{Vector{QQFieldElem}}([[]]) ) + # V is a variety of dimension dimV + # Q are base points with rational coefficients + # C are query points with rational coefficients + + A = parent(V) + varias, nvarias = gens(A), nvars(A) + hV = V.gens + #println(Q) + e = length(first(Q)) + fixvarias, newvarias = varias[1:e], varias[e+1:nvarias] + + R = Vector{AlgebraicSolving.Ideal{QQMPolyRingElem}}(undef,0) + + for q in Q + ## Fq ## + if e > 0 + hFq = remfirstvars([evaluate(h, fixvarias, q) for h in V.gens], e) + Fq = AlgebraicSolving.Ideal(hFq) + else + Fq = V + end + + if dimV - e <= 1 + push!(R, AlgebraicSolving.Ideal(vcat(Fq.gens, [fixvarias[j] - q[j] for j in 1:e]))) + + else + ## sing(Fq) ## + #println("Compute first the singular points") + singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=0) + @assert(length(singFq)==0, "Non-emtpy real sing locus!") + #@assert(degree(singFq.elim)==0, "Non-emtpy sing locus!") + + ## K(pi_1,Fq) ## + K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=0) + + ## K(pi_2, Fq) ## + K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors") + push!(R, AlgebraicSolving.Ideal(vcat(K2Fq.gens, [fixvarias[j] - q[j] for j in 1:e]))) + + ## Points with vertical tg in K(pi_2, Fq) ## + K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=0) + + ## New base points ## + K1W = vcat(K1Fq, K1WmFq) + K1WRat = MidRationalPoints(getindex.(K1W,1)) + newQ = [ vcat(q, [kv]) for kv in K1WRat ] + + RFq = computeRM(V, dimV, newQ) + + R = vcat(R, RFq) + end + end + + return R +end + +#= +## Test ## +R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) +#h = x1^2+x2^2+x3^2+x4^2-1 +h = (x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2) +h = evaluate(h,[x1,x2,x3],[x1+rand(-10:10)*x2+rand(-10:10)*x3+rand(-10:10)*x4,x2+rand(-10:10)*x3+rand(-10:10)*x4,x3+rand(-10:10)*x4]) +V = AlgebraicSolving.Ideal([h]) + +carte = (computeRM(V, 3, [Vector{QQFieldElem}(undef,0)])) +#println(carte) +=# + + diff --git a/src/connectcurves/connectcurves.jl b/src/connectivity/connectcurves.jl similarity index 89% rename from src/connectcurves/connectcurves.jl rename to src/connectivity/connectcurves.jl index 92fe951..b25379d 100644 --- a/src/connectcurves/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -13,18 +13,18 @@ include("boxes.jl") include("graph.jl") include("plots.jl") include("arbtools.jl") -include("param-curve.jl") function compute_graph(F; param=false, generic=false, precx=150, v=0, arb=false) - if !(param) println("Compute rational parametrization...") @time begin - Fparam = compute_param(F, generic=generic) + Fparam = compute_param(F)[3] end + else + Fparam = F[1] end - return compute_graph_param(Fparam[1], generic=generic, precx=precx, v=v, arb=arb) + return compute_graph_param(Fparam, generic=generic, precx=precx, v=v, arb=arb) end function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) @@ -32,7 +32,6 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) println("!! Careful: this is a WIP version !!") println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") -@time begin R = parent(f) x, y = gens(R) # Generic change of variables @@ -79,7 +78,7 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) else println("\nCompute critical boxes with msolve with precision ", precx,"..") @time begin - LBcrit = [ sort(inter_solutions(AlgebraicSolving.Ideal([p[1], p[3]*y-p[2]]), precision=precx),by=t->t[1]) for p in params ] + LBcrit = [ sort(real_solutions(AlgebraicSolving.Ideal([p[1], p[3]*y-p[2]]), precision=precx, interval=true),by=t->t[1]) for p in params ] xcrit = [ [ B[1] for B in lbcrit ] for lbcrit in LBcrit ] xcritpermut = order_permut2d(xcrit); end @@ -96,7 +95,6 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) # and change into npcside = [0,0,2,2] ## TODO : Refine only the intervals that need to be refined println("\nCompute intersections with critical boxes..") - @time begin LPCside = Array{Any}(undef,length(LBcrit)) ndig = maximum([Int(floor(log10(length(LB)))) for LB in LBcrit]) for i in eachindex(LBcrit) @@ -167,7 +165,6 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) end end end - end println("Graph computation") # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot @@ -236,23 +233,25 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) ########################### # The critical point ########################## - # if it is an isolated point - if isempty(nI[1]) && isempty(nI[2]) - #pass - # We can add the isolated vertex - # push!(Vert, Pcrit[i][j]) - # push!(Corr[i][j][2][1], length(Vert)) - # We will subsequently add the vertex in the graph - # push!(Viso, length(Vert)) - ############################################ - ## TO BE REPLACED BY APPSING IDENTIFICATOR ## - ## works for space curves without nodes ## - ############################################ # If we are dealing with a node - elseif i == 2 - # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 - push!(Edg, [Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]]]) - push!(Edg, [Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]]]) + if i == 2 + # if it is an isolated point + if isempty(nI[1]) && isempty(nI[2]) + #pass + # We can add the isolated vertex + # push!(Vert, [xcmid, ycmid]) + # push!(Corr[i][j][2][1], length(Vert)) + # We will subsequently add the vertex in the graph + # push!(Viso, length(Vert)) + ############################################ + ## TO BE REPLACED BY APPSING IDENTIFICATOR ## + ## works for space curves without nodes ## + ############################################ + else + # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 + push!(Edg, [Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]]]) + push!(Edg, [Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]]]) + end else # We can add the vertex push!(Vert, [xcmid, ycmid]) @@ -274,7 +273,6 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) push!(Edg, [Corr[i][j][1][end - k + 1], length(Vert)]) # left push!(Edg, [length(Vert), Corr[i][j][3][end - k + 1]]) # right end - end #EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] #plot_graph(Vert, EdgPlot) @@ -285,7 +283,6 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) if !(generic) Vert = [ changemat*v for v in Vert ] end -println("Total time:") end return Vert, Edg end diff --git a/src/connectcurves/graph.jl b/src/connectivity/graph.jl similarity index 100% rename from src/connectcurves/graph.jl rename to src/connectivity/graph.jl diff --git a/src/connectcurves/isolate.jl b/src/connectivity/isolate.jl similarity index 73% rename from src/connectcurves/isolate.jl rename to src/connectivity/isolate.jl index 414967e..4dce6ca 100644 --- a/src/connectcurves/isolate.jl +++ b/src/connectivity/isolate.jl @@ -7,7 +7,7 @@ function isolate(f; prec = 32, software="msolve") return getindex.(usolve(f, precision = prec, uspath="src/usolve/usolve"),2) else fvar = vars(f)[1] - sols = inter_solutions(Ideal(vcat([f], [ t for t in gens(parent(f)) if t!=fvar ])), precision=prec) + sols = real_solutions(Ideal(vcat([f], [ t for t in gens(parent(f)) if t!=fvar ])), precision=prec, interval=true) return getindex.(sols, var_index(fvar)) end end @@ -16,6 +16,6 @@ function isolate_eval(f, ivar, val; prec=64) # univariate isolation of roots of a bivariate polynomial f # whose ivar-th variable is evaluated at val # uses msolve - sols = inter_solutions(Ideal([f, gens(parent(f))[ivar] - val]), precision=prec) + sols = real_solutions(Ideal([f, gens(parent(f))[ivar] - val]), precision=prec, interval=true) return [ s[ivar%2+1] for s in sols ] end \ No newline at end of file diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl new file mode 100644 index 0000000..f71da3f --- /dev/null +++ b/src/connectivity/paramcurve.jl @@ -0,0 +1,153 @@ +#println("Loading libraries and data..") +#using Pkg +#using Revise +#Pkg.activate("AlgebraicSolving.jl-official") +#using AlgebraicSolving +#import Nemo: coefficients, exponent_vectors, coeff, interpolate, MPolyBuildCtx, push_term!, finish, gens + +export compute_param + +function rem_var(f, i) + # Remove the occurence of the ith variable + R = parent(f) + A, Avars = polynomial_ring(base_ring(R), rem_ind(R.S, i)) + CE = [collect(coefficients(f)), collect(exponent_vectors(f))] + CE[2] = [ rem_ind(e, i) for e in CE[2]] + + # Reconstruct the polynomial in the ring A + C = MPolyBuildCtx(A) + R = base_ring(A) + for i in eachindex(CE[1]) + push_term!(C, R(CE[1][i]), CE[2][i]); + end + return finish(C) +end + +function rem_ind(L,i::Int) + # remove element at index i + return [ L[1:i-1]; L[i+1:end] ] +end + +function deg_Alg(F, dim) + if dim <= 0 + r = rational_parametrization(Ideal(F)) + else + varias = gens(parent(first(F))) + planes = [ sum([ rand(-100:100)*v for v in vcat(varias,1) ]) for _ in 1:dim] + r = rational_parametrization(Ideal(vcat(F,planes))) + end + return degree(r.elim) +end + + +function compute_param(F) + R = parent(first(F)) + varias, N = gens(R), nvars(R) + + # Identification of two generic variables for the parametrization") + ivarias_gen = Vector{Int}(undef,0) + DEG = deg_Alg(F,1) + ind = N + while true + NEW_DEG = deg_Alg(vcat(F, varias[ind]-rand(-100:100)), 0) + if NEW_DEG == DEG + push!(ivarias_gen, ind) + end + (length(ivarias_gen) < 2 && ind > 0) || break + ind -= 1 + end + reverse!(ivarias_gen) + nb_lf = 2-length(ivarias_gen) + + if ivarias_gen != [N-1,N] + # Add new generic variables at the end if necessary + newvarias_S = [R.S[i] for i in vcat(setdiff(1:N, ivarias_gen), ivarias_gen)] + append!(newvarias_S, [:A,:B][nb_lf:-1:1] ) + + # We change the polynomial ring and add linear form(s) if necessary + Rold, Nold = R, N + R, varias = polynomial_ring(base_ring(Rold), newvarias_S) + N = length(varias) + + index_permut = Dict((v, i) for (i, v) in enumerate(newvarias_S)) + permut_varias = [ index_permut[v] for v in Rold.S ] + # TODO: permut exponents and use polynomial constructor + F = [ evaluate(f, [ varias[permut_varias[i]] for i in 1:Nold ]) for f in F ] + + if nb_lf > 0 + lf_cfs = [ rand(ZZ(-100):ZZ(100), N) for _ in 1:nb_lf] + append!(F, [ transpose(lf)*varias for lf in lf_cfs ]) + else + lf_cfs = Vector{Vector{ZZRingElem}}(undef,0) + end + else + lf_cfs = Vector{Vector{ZZRingElem}}(undef,0) + end + + # Compute DEG+1 evaluations of the param (whose deg is bounded by DEG) + PARAM = Vector{Vector{AlgebraicSolving.QQPolyRingElem}}(undef,0) + _values = Vector{QQFieldElem}(undef,0) + i = 1 + while length(_values) < DEG+2 + if i > 2*(DEG+2) + error("Too many bad specializations") + end + + #try + Feval = [ evaluate(f, [N-1], [QQ(i)]) for f in F ] + Feval = [ rem_var(f, N-1) for f in Feval ] + r = rational_parametrization(Ideal(Feval)) + # For lifting: the same variable must be chosen for the param + if r.vars == rem_ind(R.S, N-1) + lc = leading_coefficient(r.elim) + # TODO: why dividing by lc ? + rr = [ p/lc for p in vcat(r.elim, r.denom, r.param) ] + push!(PARAM, rr) + push!(_values, QQ(i)) + else + println("bad specialization: ", i) + end + #catch + # error("bad specialization: ", i) + #end + i += 1 + end + + # Interpolate each coefficient of each poly in the param + POLY_PARAM = Vector{QQMPolyRingElem}(undef,0) + T, (x,y) = polynomial_ring(QQ, [:x,:y]) + for count in 1:N + COEFFS = [] + for deg in 0:DEG + _evals = [ coeff(PARAM[i][count], deg) for i in 1:length(PARAM)] + push!(COEFFS, interpolate(polynomial_ring(QQ,"u")[1], _values, _evals)) + end + + C = [ collect(coefficients(c)) for c in COEFFS ] + POL_term = [C[i][j]*x^(j-1)*y^(i-1) for i in 1:length(C) for j in 1:length(C[i])] + POL = length(POL_term) > 0 ? sum(POL_term) : T(0) + + push!(POLY_PARAM, POL) + end + + return [R.S, lf_cfs, POLY_PARAM[1], POLY_PARAM[2], POLY_PARAM[3:end]] +end + +#= +# Tests +R, (a,b,c) = polynomial_ring(QQ, [:a,:b,:c]) +F = [-62*a^2-24*a*b+83*a*c-46*b^2-45*b*c+16*c^2+13*a-65*b-84*c-19, +92*a^2-a*b+39*a*c-16*b^2+61*b*c+78*c^2+17*a+49*b-97*c-56 +] + +R, (x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) +F = [ +x1^4 - 12*x1^3*x2 - 40*x1^3*x3 + 12*x1^3*x4 + 56*x1^2*x2^2 + 320*x1^2*x2*x3 - 148*x1^2*x2*x4 + 802*x1^2*x3^2 + 56*x1^2*x3*x4 + 288*x1^2*x4^2 - 20*x1^2 - 120*x1*x2^3 - 880*x1*x2^2*x3 + 576*x1*x2^2*x4 - 4012*x1*x2*x3^2 + 224*x1*x2*x3*x4 - 1968*x1*x2*x4^2 + 120*x1*x2 - 8040*x1*x3^3 - 3508*x1*x3^2*x4 - 3264*x1*x3*x4^2 + 400*x1*x3 + 1512*x1*x4^3 - 120*x1*x4 + 100*x2^4 + 800*x2^3*x3 - 760*x2^3*x4 + 5620*x2^2*x3^2 - 80*x2^2*x3*x4 + 3964*x2^2*x4^2 - 200*x2^2 + 16080*x2*x3^3 - 3436*x2*x3^2*x4 - 1168*x2*x3*x4^2 - 800*x2*x3 - 9576*x2*x4^3 + 760*x2*x4 + 40401*x3^4 + 59496*x3^3*x4 + 72556*x3^2*x4^2 - 4020*x3^2 + 37296*x3*x4^3 - 2960*x3*x4 + 15876*x4^4 - 2484*x4^2 + 64, + -40*x1^3 + 320*x1^2*x2 + 1604*x1^2*x3 + 56*x1^2*x4 - 880*x1*x2^2 - 8024*x1*x2*x3 + 224*x1*x2*x4 - 24120*x1*x3^2 - 7016*x1*x3*x4 - 3264*x1*x4^2 + 400*x1 + 800*x2^3 + 11240*x2^2*x3 - 80*x2^2*x4 + 48240*x2*x3^2 - 6872*x2*x3*x4 - 1168*x2*x4^2 - 800*x2 + 161604*x3^3 + 178488*x3^2*x4 + 145112*x3*x4^2 - 8040*x3 + 37296*x4^3 - 2960*x4, + 12*x1^3 - 148*x1^2*x2 + 56*x1^2*x3 + 576*x1^2*x4 + 576*x1*x2^2 + 224*x1*x2*x3 - 3936*x1*x2*x4 - 3508*x1*x3^2 - 6528*x1*x3*x4 + 4536*x1*x4^2 - 120*x1 - 760*x2^3 - 80*x2^2*x3 + 7928*x2^2*x4 - 3436*x2*x3^2 - 2336*x2*x3*x4 - 28728*x2*x4^2 + 760*x2 + 59496*x3^3 + 145112*x3^2*x4 + 111888*x3*x4^2 - 2960*x3 + 63504*x4^3 - 4968*x4 + ] + + @time begin + compute_param(F) + end +=# diff --git a/src/connectcurves/plots.jl b/src/connectivity/plots.jl similarity index 100% rename from src/connectcurves/plots.jl rename to src/connectivity/plots.jl diff --git a/src/connectcurves/src/resultant/Makefile b/src/connectivity/src/resultant/Makefile similarity index 100% rename from src/connectcurves/src/resultant/Makefile rename to src/connectivity/src/resultant/Makefile diff --git a/src/connectcurves/src/resultant/__pycache__/bresultant.cpython-310.pyc b/src/connectivity/src/resultant/__pycache__/bresultant.cpython-310.pyc similarity index 100% rename from src/connectcurves/src/resultant/__pycache__/bresultant.cpython-310.pyc rename to src/connectivity/src/resultant/__pycache__/bresultant.cpython-310.pyc diff --git a/src/connectcurves/src/resultant/bresultant b/src/connectivity/src/resultant/bresultant similarity index 100% rename from src/connectcurves/src/resultant/bresultant rename to src/connectivity/src/resultant/bresultant diff --git a/src/connectcurves/src/resultant/bresultant.jl b/src/connectivity/src/resultant/bresultant.jl similarity index 100% rename from src/connectcurves/src/resultant/bresultant.jl rename to src/connectivity/src/resultant/bresultant.jl diff --git a/src/connectcurves/src/resultant/bresultant.sage b/src/connectivity/src/resultant/bresultant.sage similarity index 100% rename from src/connectcurves/src/resultant/bresultant.sage rename to src/connectivity/src/resultant/bresultant.sage diff --git a/src/connectcurves/src/resultant/data.c b/src/connectivity/src/resultant/data.c similarity index 100% rename from src/connectcurves/src/resultant/data.c rename to src/connectivity/src/resultant/data.c diff --git a/src/connectcurves/src/resultant/data.h b/src/connectivity/src/resultant/data.h similarity index 100% rename from src/connectcurves/src/resultant/data.h rename to src/connectivity/src/resultant/data.h diff --git a/src/connectcurves/src/resultant/flint_euclide.c b/src/connectivity/src/resultant/flint_euclide.c similarity index 100% rename from src/connectcurves/src/resultant/flint_euclide.c rename to src/connectivity/src/resultant/flint_euclide.c diff --git a/src/connectcurves/src/resultant/flint_resultant.c b/src/connectivity/src/resultant/flint_resultant.c similarity index 100% rename from src/connectcurves/src/resultant/flint_resultant.c rename to src/connectivity/src/resultant/flint_resultant.c diff --git a/src/connectcurves/src/resultant/io.c b/src/connectivity/src/resultant/io.c similarity index 100% rename from src/connectcurves/src/resultant/io.c rename to src/connectivity/src/resultant/io.c diff --git a/src/connectcurves/src/resultant/main.c b/src/connectivity/src/resultant/main.c similarity index 100% rename from src/connectcurves/src/resultant/main.c rename to src/connectivity/src/resultant/main.c diff --git a/src/connectcurves/src/resultant/out.txt b/src/connectivity/src/resultant/out.txt similarity index 100% rename from src/connectcurves/src/resultant/out.txt rename to src/connectivity/src/resultant/out.txt diff --git a/src/connectcurves/src/resultant/ratreconstruct.c b/src/connectivity/src/resultant/ratreconstruct.c similarity index 100% rename from src/connectcurves/src/resultant/ratreconstruct.c rename to src/connectivity/src/resultant/ratreconstruct.c diff --git a/src/connectcurves/src/usolve/usolve b/src/connectivity/src/usolve/usolve similarity index 100% rename from src/connectcurves/src/usolve/usolve rename to src/connectivity/src/usolve/usolve diff --git a/src/connectcurves/src/usolve/usolve.jl b/src/connectivity/src/usolve/usolve.jl similarity index 100% rename from src/connectcurves/src/usolve/usolve.jl rename to src/connectivity/src/usolve/usolve.jl diff --git a/src/connectcurves/subresultants.jl b/src/connectivity/subresultants.jl similarity index 100% rename from src/connectcurves/subresultants.jl rename to src/connectivity/subresultants.jl diff --git a/src/connectcurves/tools.jl b/src/connectivity/tools.jl similarity index 100% rename from src/connectcurves/tools.jl rename to src/connectivity/tools.jl diff --git a/src/imports.jl b/src/imports.jl index 492178b..8731603 100644 --- a/src/imports.jl +++ b/src/imports.jl @@ -4,10 +4,11 @@ using msolve_jll using Nemo using LinearAlgebra using StaticArrays -using LoopVectorization -import Plots: plot, plot!, scatter!, gui, gr, pythonplot -import Colors: distinguishable_colors +using Plots, Colors +pythonplot() + +import Plots: plot import Random: MersenneTwister import Logging: ConsoleLogger, with_logger, Warn, Info @@ -35,6 +36,7 @@ import Nemo: is_probable_prime, is_square, is_unit, + is_zero, isqrtrem, jacobi_symbol, leading_coefficient, From 1ee72de883b246d8b65c256739e0308658a8b92c Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 13 Aug 2024 20:42:42 +0200 Subject: [PATCH 026/180] function for changing ring variables --- src/connectivity/Cannytools.jl | 61 +++++++++++++++++++++++----------- 1 file changed, 42 insertions(+), 19 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 6de2262..c17307a 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -1,36 +1,59 @@ - -function remfirstvars(F::Vector{P}, irem) where {P <: MPolyRingElem} +# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables +function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} R = parent(first(F)) - istart = irem+1 - S, vars = polynomial_ring(base_ring(R), ["x$i" for i in istart:nvars(R)]) + # Locate variables of R in newvarias + to_varias = Vector{Int}(undef,0) + for v in newvarias_S + ind = findfirst(x->x==v, R.S) + push!(to_varias, typeof(ind)==Nothing ? length(R.S)+1 : ind) + end + + ind_novarias = setdiff(eachindex(R.S), to_varias) + newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) + res = typeof(first(F))[] + ctx = MPolyBuildCtx(newR) + for f in F - ctx = MPolyBuildCtx(S) for (e, c) in zip(exponent_vectors(f), coefficients(f)) - @assert(all([ e[i]==0 for i in 1:irem ]), "Occurence of first variable.s found!") - push_term!(ctx, c, e[istart:end]) + @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") + push!(e, 0) + push_term!(ctx, c, [e[i] for i in to_varias ]) end push!(res, finish(ctx)) end - return res + + return res +end + +function change_ringvar(f::MPolyRingElem, newvarias_S::Vector{Symbol}) + return change_ringvar([f], newvarias_S) end -function remvars(F::Vector{P}; irem::Vector{Int64}) where {P <: MPolyRingElem} +function change_ringvar(F::Vector{P}, ind_newvarias::Vector{Int64}) where {P <: MPolyRingElem} R = parent(first(F)) - ikeep = [ i for i in 1:nvars(R) if !(i in irem) ] - S, vars = polynomial_ring(base_ring(R), ["x$i" for i in ikeep]) - res = typeof(first(F))[] + return change_ringvar(F, [R.S[i] for i in ind_newvarias]) +end + +function change_ringvar(f::MPolyRingElem, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {I <: Int64} + R = parent(f) + return change_ringvar([f], [R.S[i] for i in ind_newvarias]) +end + +# Return the polynomials in F, but injected in the polynomial ring with the variables occuring in F +function change_ringvar(F::Vector{P}) where {P <: MPolyRingElem} + union_varias = Set{Symbol}() for f in F - ctx = MPolyBuildCtx(S) - for (e, c) in zip(exponent_vectors(f), coefficients(f)) - @assert(all([ e[i]==0 for i in irem ]), "Occurence of removed variable.s found!") - push_term!(ctx, c, [ e[i] for i in ikeep ]) - end - push!(res, finish(ctx)) + union!(union_varias, map(Symbol, vars(f)) ) end - return res + return change_ringvar(F, collect(union_varias)) +end + +function change_ringvar(f::MPolyRingElem) + change_ringvar([f]) end + function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0) # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" From 1bb304c2094399de1682e096f668e8d12bcc3971 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 13 Aug 2024 20:43:13 +0200 Subject: [PATCH 027/180] adapt to new function --- src/connectivity/computeRM.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 1cb7963..2201ff2 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,7 +4,7 @@ #using AlgebraicSolving #using Nemo -export computeRM +export computeRM, computepolarproj include("Cannytools.jl") @@ -25,7 +25,7 @@ function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{V for q in Q ## Fq ## if e > 0 - hFq = remfirstvars([evaluate(h, fixvarias, q) for h in V.gens], e) + hFq = change_ringvar([evaluate(h, fixvarias, q) for h in V.gens], collect(1:e)) Fq = AlgebraicSolving.Ideal(hFq) else Fq = V From 7918a398a157a13106a18093b4da3ae37eefd7f1 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 13 Aug 2024 20:43:58 +0200 Subject: [PATCH 028/180] add option to force using new variables in parametrization --- src/connectivity/paramcurve.jl | 79 ++++++++++++++++++++-------------- 1 file changed, 46 insertions(+), 33 deletions(-) diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index f71da3f..643cdbf 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -40,50 +40,63 @@ function deg_Alg(F, dim) end -function compute_param(F) +function compute_param(F; lfs = false) R = parent(first(F)) varias, N = gens(R), nvars(R) - - # Identification of two generic variables for the parametrization") - ivarias_gen = Vector{Int}(undef,0) DEG = deg_Alg(F,1) - ind = N - while true - NEW_DEG = deg_Alg(vcat(F, varias[ind]-rand(-100:100)), 0) - if NEW_DEG == DEG - push!(ivarias_gen, ind) - end - (length(ivarias_gen) < 2 && ind > 0) || break - ind -= 1 - end - reverse!(ivarias_gen) - nb_lf = 2-length(ivarias_gen) - if ivarias_gen != [N-1,N] + if !lfs + # Identification of two generic variables for the parametrization") + ivarias_gen = Vector{Int}(undef,0) + ind = N + while true + NEW_DEG = deg_Alg(vcat(F, varias[ind]-rand(-100:100)), 0) + if NEW_DEG == DEG + push!(ivarias_gen, ind) + end + (length(ivarias_gen) < 2 && ind > 0) || break + ind -= 1 + end + reverse!(ivarias_gen) + nb_lf = 2-length(ivarias_gen) + + if ivarias_gen != [N-1,N] + # Add new generic variables at the end if necessary + newvarias_S = [R.S[i] for i in vcat(setdiff(1:N, ivarias_gen), ivarias_gen)] + append!(newvarias_S, [:A,:B][nb_lf:-1:1] ) + + # We change the polynomial ring and add linear form(s) if necessary + Rold, Nold = R, N + R, varias = polynomial_ring(base_ring(Rold), newvarias_S) + N = length(varias) + + index_permut = Dict((v, i) for (i, v) in enumerate(newvarias_S)) + permut_varias = [ index_permut[v] for v in Rold.S ] + # TODO: permut exponents and use polynomial constructor + F = [ evaluate(f, [ varias[permut_varias[i]] for i in 1:Nold ]) for f in F ] + + if nb_lf > 0 + lf_cfs = [ rand(ZZ(-100):ZZ(100), N) for _ in 1:nb_lf] + append!(F, [ transpose(lf)*varias for lf in lf_cfs ]) + else + lf_cfs = Vector{Vector{ZZRingElem}}(undef,0) + end + else + lf_cfs = Vector{Vector{ZZRingElem}}(undef,0) + end + else # Add new generic variables at the end if necessary - newvarias_S = [R.S[i] for i in vcat(setdiff(1:N, ivarias_gen), ivarias_gen)] - append!(newvarias_S, [:A,:B][nb_lf:-1:1] ) + newvarias_S = vcat(R.S, [:B,:A]) # We change the polynomial ring and add linear form(s) if necessary Rold, Nold = R, N R, varias = polynomial_ring(base_ring(Rold), newvarias_S) N = length(varias) - index_permut = Dict((v, i) for (i, v) in enumerate(newvarias_S)) - permut_varias = [ index_permut[v] for v in Rold.S ] - # TODO: permut exponents and use polynomial constructor - F = [ evaluate(f, [ varias[permut_varias[i]] for i in 1:Nold ]) for f in F ] - - if nb_lf > 0 - lf_cfs = [ rand(ZZ(-100):ZZ(100), N) for _ in 1:nb_lf] - append!(F, [ transpose(lf)*varias for lf in lf_cfs ]) - else - lf_cfs = Vector{Vector{ZZRingElem}}(undef,0) - end - else - lf_cfs = Vector{Vector{ZZRingElem}}(undef,0) + F = [ evaluate(f, [ varias[i] for i in 1:Nold ]) for f in F ] + lf_cfs = [ rand(ZZ(-100):ZZ(100), N) for _ in 1:2] + append!(F, [ transpose(lf)*varias for lf in lf_cfs ]) end - # Compute DEG+1 evaluations of the param (whose deg is bounded by DEG) PARAM = Vector{Vector{AlgebraicSolving.QQPolyRingElem}}(undef,0) _values = Vector{QQFieldElem}(undef,0) @@ -122,7 +135,7 @@ function compute_param(F) _evals = [ coeff(PARAM[i][count], deg) for i in 1:length(PARAM)] push!(COEFFS, interpolate(polynomial_ring(QQ,"u")[1], _values, _evals)) end - + C = [ collect(coefficients(c)) for c in COEFFS ] POL_term = [C[i][j]*x^(j-1)*y^(i-1) for i in 1:length(C) for j in 1:length(C[i])] POL = length(POL_term) > 0 ? sum(POL_term) : T(0) From db7ea307a5cc7161353ac59e3685c0182b61dc83 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 13 Aug 2024 20:45:01 +0200 Subject: [PATCH 029/180] add test for singular boxes : mutivariate evaluation --- src/connectivity/connectcurves.jl | 27 +++++++++++++++++++++++++-- 1 file changed, 25 insertions(+), 2 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index b25379d..92c3444 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -86,8 +86,28 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) print("\nTest for identifying singular boxes");ts=time(); ######################################################## - ### TODO ############################################### - ######################################################## + # For each mult of sing pts (keys) give the corresponding factors of the resultant (values) + ### DEBUG: for now, only nodes for singular points, hardcode below ### + mult_to_factor = Dict(2=>[2]) + ######################################################### + Lfyk = diff_list(f, 2, multmax) + for mult in keys(mult_to_factor) + for k in mult_to_factor[mult] + while true + flag = false + for j in eachindex(LBcrit[k]) + pcrit = arb ? Pcrit[k][j] : [ rat_to_Arb(c, prec) for c in LBcrit[k][j] ] + if contains_zero(evaluate(Lfyk[mult], pcrit)) + println("Refine singular boxes of multiplicity ", k) + refine_boxes(params[k], LBcrit[k]) + flag = true + break + end + end + flag || break + end + end + end # Could be improved by handling nodes as extreme boxes: # when npcside = [2,2,0,0] just take nearest below and above @@ -174,6 +194,7 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ] Viso = [] + println(LBcrit[2][1]) for ind in 1:length(xcritpermut) i, j = xcritpermut[ind] @@ -237,6 +258,7 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) if i == 2 # if it is an isolated point if isempty(nI[1]) && isempty(nI[2]) + println("Remove appsing ($i,$j) (isolated)") #pass # We can add the isolated vertex # push!(Vert, [xcmid, ycmid]) @@ -248,6 +270,7 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) ## works for space curves without nodes ## ############################################ else + println("Remove appsing ($i,$j) (node)") # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 push!(Edg, [Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]]]) push!(Edg, [Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]]]) From 6f7992ce3f7418dd6d1fe0d3479699969cd2a9d5 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 13 Aug 2024 20:45:40 +0200 Subject: [PATCH 030/180] comment pythonplot --- src/imports.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/imports.jl b/src/imports.jl index 5efece5..80314a7 100644 --- a/src/imports.jl +++ b/src/imports.jl @@ -5,7 +5,7 @@ using Nemo using LinearAlgebra using StaticArrays using Plots, Colors -pythonplot() +#pythonplot() import Plots: plot import Random: MersenneTwister From 1db1aae1b613b97ed84ff5a958d39cd7dc340b15 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 27 Aug 2024 17:21:45 +0200 Subject: [PATCH 031/180] integer coeff + display node removal + add control points at the end of the parametrization --- src/connectivity/arbtools.jl | 2 +- src/connectivity/connectcurves.jl | 68 +++++++++++++++++++++---------- src/connectivity/graph.jl | 19 ++++++++- src/connectivity/plots.jl | 17 +++++--- src/connectivity/tools.jl | 2 +- 5 files changed, 78 insertions(+), 30 deletions(-) diff --git a/src/connectivity/arbtools.jl b/src/connectivity/arbtools.jl index 4721a75..0e25ac1 100644 --- a/src/connectivity/arbtools.jl +++ b/src/connectivity/arbtools.jl @@ -1,6 +1,6 @@ function Arb_to_rat(x) r = radius(x) - return map(simplest_rational_inside, [x-2*r, x+2*r]) + return map(simplest_rational_inside, [x-r, x+r]) end function rat_to_Arb(x, prec) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 92c3444..2dacf85 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -14,7 +14,7 @@ include("graph.jl") include("plots.jl") include("arbtools.jl") -function compute_graph(F; param=false, generic=false, precx=150, v=0, arb=false) +function compute_graph(F, C=[]; param=true, generic=true, precx=150, v=0, arb=true, int_coeff=false) if !(param) println("Compute rational parametrization...") @time begin @@ -24,33 +24,38 @@ function compute_graph(F; param=false, generic=false, precx=150, v=0, arb=false) Fparam = F[1] end - return compute_graph_param(Fparam, generic=generic, precx=precx, v=v, arb=arb) + return compute_graph_param(Fparam, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff) end -function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) +function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, int_coeff=false) println("\n!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") println("!! Careful: this is a WIP version !!") println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") R = parent(f) x, y = gens(R) + + if int_coeff + CD = lcm(map(denominator, collect(coefficients(f)))) + f *= CD + end # Generic change of variables changemat = [1 0; 0 1] if !generic - changemat = trimat_rand(QQ, 2, range=-500:500) + changemat = trimat_rand(QQ, 2, range=-100:100) end f = evaluate(f, collect(changemat*[x; y])); println("\nCompute parametrization of critical pts...") @time begin - sr = subresultants(f, derivative(f,y), 2, list=true); + sr = subresultants(f, derivative(f,y), 2, list=true) # Take sqfree factors of the resultant sqr = collect(factor_squarefree(sr[1][1])) # Keep only deg>0 factors - filter(t->t[2]>0, sqr) + filter!(t->t[2]>0, sqr) # Order by multiplicity - sqr = sort(sqr, by=t->t[2]) + sort!(sqr, by=t->t[2]) # Group by multiplicity group_sqr = [ [R(1),i] for i in 1:sqr[end][2] ] for r in sqr @@ -58,6 +63,10 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) end # Construct the parametrization of the critical points params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in group_sqr ]; + + if length(C)>0 + push!(params, C) + end end if arb @@ -84,23 +93,25 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) end end - print("\nTest for identifying singular boxes");ts=time(); + @time begin + println("\nTest for identifying singular boxes");ts=time(); ######################################################## # For each mult of sing pts (keys) give the corresponding factors of the resultant (values) ### DEBUG: for now, only nodes for singular points, hardcode below ### mult_to_factor = Dict(2=>[2]) ######################################################### - Lfyk = diff_list(f, 2, multmax) - for mult in keys(mult_to_factor) - for k in mult_to_factor[mult] + mults = keys(mult_to_factor) + Lfyk = diff_list(f, 2, maximum(mults)) + for m in mults + for k in mult_to_factor[m] while true flag = false for j in eachindex(LBcrit[k]) - pcrit = arb ? Pcrit[k][j] : [ rat_to_Arb(c, prec) for c in LBcrit[k][j] ] - if contains_zero(evaluate(Lfyk[mult], pcrit)) + pcrit = [ rat_to_Arb(c, precx) for c in LBcrit[k][j] ] + if contains_zero(evaluate(Lfyk[m+1], pcrit)) println("Refine singular boxes of multiplicity ", k) - refine_boxes(params[k], LBcrit[k]) - flag = true + # TODO refine_boxes(params[k], LBcrit[k]) + #flag = true break end end @@ -108,7 +119,9 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) end end end + end + @time begin # Could be improved by handling nodes as extreme boxes: # when npcside = [2,2,0,0] just take nearest below and above # intersections b with the curves on the vertical sides @@ -185,16 +198,19 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) end end end + end - println("Graph computation") + println("\nGraph computation") # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot # And even remove this fiber for the graph Vert = [] Edg = [] Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ] Viso = [] + Vcon = [] + + Lapp = [[],[]] - println(LBcrit[2][1]) for ind in 1:length(xcritpermut) i, j = xcritpermut[ind] @@ -258,7 +274,7 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) if i == 2 # if it is an isolated point if isempty(nI[1]) && isempty(nI[2]) - println("Remove appsing ($i,$j) (isolated)") + push!(Lapp[1], (i,j)) #pass # We can add the isolated vertex # push!(Vert, [xcmid, ycmid]) @@ -270,10 +286,10 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) ## works for space curves without nodes ## ############################################ else - println("Remove appsing ($i,$j) (node)") # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 push!(Edg, [Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]]]) push!(Edg, [Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]]]) + push!(Lapp[2], (i,j)) end else # We can add the vertex @@ -287,6 +303,10 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) for k in nI[2] push!(Edg, [length(Vert), Corr[i][j][3][k]]) end + if length(C)>0 && i==length(params) + # If this is a control point + push!(Vcon, length(Vert)) + end end ########################### # Above the critical point @@ -296,7 +316,9 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) push!(Edg, [Corr[i][j][1][end - k + 1], length(Vert)]) # left push!(Edg, [length(Vert), Corr[i][j][3][end - k + 1]]) # right end + end + println("Removed apparent singularities: $(length(Lapp[1])) isolated $(length(Lapp[2])) nodes") #EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] #plot_graph(Vert, EdgPlot) #gui() @@ -306,6 +328,10 @@ function compute_graph_param(f; generic=false, precx = 150,v=0, arb=false) if !(generic) Vert = [ changemat*v for v in Vert ] end -end - return Vert, Edg + + if length(C)>0 + return (Vert, Edg), Vcon + else + return Vert, Edg + end end diff --git a/src/connectivity/graph.jl b/src/connectivity/graph.jl index c932ed2..1d79e19 100644 --- a/src/connectivity/graph.jl +++ b/src/connectivity/graph.jl @@ -5,7 +5,7 @@ function index_of(x, L) return findfirst(t->t==x,L) end -function connected_components(G) +function connected_components(G; Vemph=[]) # Outputs subgraphs of the connected components ########### vert, edges = G @@ -52,7 +52,22 @@ function connected_components(G) end end - return [ [[ vert[cv] for cv in components[i] ], grouped_edges[i]] for i in eachindex(components) ] + if length(Vemph)>0 + CVemph = [ [] for _ in eachindex(components) ] + for i in eachindex(components) + for j in eachindex(components[i]) + if components[i][j] in Vemph + push!(CVemph[i], j) + end + end + end + end + + if length(Vemph)>0 + return [ [[ vert[cv] for cv in components[i] ], grouped_edges[i], CVemph[i]] for i in eachindex(components) ] + else + return [ [[ vert[cv] for cv in components[i] ], grouped_edges[i]] for i in eachindex(components) ] + end end function number_connected_components(G) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index d586e00..00b4c62 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,6 +1,6 @@ ## Plot functions -function plot_graph(G; color="red", width=3, vert = true) +function plot_graph(G; Vemph=[], color="red", width=3, vert = true) println("Plotting the graph") V, E = G plot(legend=false) @@ -11,6 +11,7 @@ function plot_graph(G; color="red", width=3, vert = true) if vert scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) end + scatter!( map(Float64, [V[i][1] for i in Vemph]), map(Float64, [V[i][2] for i in Vemph]), mc=color, m=:diamond) gui() end @@ -19,7 +20,9 @@ function plot_graphs(CG; width=3, vert=true) plot(legend=false) col = distinguishable_colors(length(CG)+2) for j in eachindex(CG) - V, E = CG[j] + V = CG[j][1] + E = CG[j][2] + CVemph = length(CG[j])>2 ? CG[j][3] : [] for e in E v1, v2 = [ map(Float64, V[ee]) for ee in e ] plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) @@ -27,17 +30,20 @@ function plot_graphs(CG; width=3, vert=true) if vert scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) end + scatter!( map(Float64, [V[i][1] for i in Vemph]), map(Float64, [V[i][2] for i in Vemph]), mc=col[j+2], m=:diamond) end gui() end -function plot_graph_comp(G; width=3, vert=true) +function plot_graph_comp(G; Vemph=[], width=3, vert=true) println("Plotting the graph") plot(legend=false) - CG = connected_components(G) + CG = connected_components(G, Vemph=Vemph) col = distinguishable_colors(length(CG)+2) for j in eachindex(CG) - V, E = CG[j] + V = CG[j][1] + E = CG[j][2] + CVemph = length(CG[j])>2 ? CG[j][3] : [] for e in E v1, v2 = [ map(Float64, V[ee]) for ee in e ] plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) @@ -45,6 +51,7 @@ function plot_graph_comp(G; width=3, vert=true) if vert scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) end + scatter!( map(Float64, [V[i][1] for i in CVemph]), map(Float64, [V[i][2] for i in CVemph]), mc=col[j+2], m=:diamond) end gui() end \ No newline at end of file diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index 5e75709..4a067b6 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -21,7 +21,7 @@ end function diff_list(p, v, n) Ldp = [p] for j in 1:n - push!(Ldb,derivative(Ldp[end], v)) + push!(Ldp, derivative(Ldp[end], v)) end return Ldp end From 2109126606623217e499c650e3f22b0ece5053a9 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 27 Aug 2024 19:43:02 +0200 Subject: [PATCH 032/180] group abscissa index of control points w.r.t. component --- src/connectivity/connectcurves.jl | 14 +++++++++++++- src/connectivity/graph.jl | 15 ++++++++++++--- src/connectivity/plots.jl | 10 ++++------ 3 files changed, 29 insertions(+), 10 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 2dacf85..d716b1f 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -3,7 +3,7 @@ #using Plots, Colors #pythonplot() -export compute_graph, connected_components, number_connected_components, +export compute_graph, connected_components, number_connected_components, group_by_component, plot_graph, plot_graphs, plot_graph_comp, compute_param include("tools.jl") @@ -335,3 +335,15 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, return Vert, Edg end end + +function group_by_component(F::Vector{P}, C::Vector{P}; param=true, generic=true, precx=150, v=0, arb=true, int_coeff=false) where {P <: MPolyRingElem} + # Compute a graph homeomorphic to Z(F) and return the vertices identified by Z(C) + G, Vcon = compute_graph(F, C, param=param, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff) + # Compute the partition of the vertices in Vcon according to the connected component in G + sort!(Vcon) + CVcon = group_by_component(G, Vcon) + + # Convert the partition into abscissa order + index_map = Dict((val, idx) for (idx, val) in enumerate(Vcon)) + return [map(v -> index_map[v], C) for C in CVcon] +end \ No newline at end of file diff --git a/src/connectivity/graph.jl b/src/connectivity/graph.jl index 1d79e19..f5f1133 100644 --- a/src/connectivity/graph.jl +++ b/src/connectivity/graph.jl @@ -5,7 +5,7 @@ function index_of(x, L) return findfirst(t->t==x,L) end -function connected_components(G; Vemph=[]) +function connected_components(G; Vemph=[], ind_abs=false) # Outputs subgraphs of the connected components ########### vert, edges = G @@ -57,19 +57,28 @@ function connected_components(G; Vemph=[]) for i in eachindex(components) for j in eachindex(components[i]) if components[i][j] in Vemph - push!(CVemph[i], j) + if ind_abs + push!(CVemph[i], components[i][j]) + else + push!(CVemph[i], j) + end end end end end if length(Vemph)>0 - return [ [[ vert[cv] for cv in components[i] ], grouped_edges[i], CVemph[i]] for i in eachindex(components) ] + return [ [[[ vert[cv] for cv in components[i] ], grouped_edges[i]], CVemph[i]] for i in eachindex(components) ] else return [ [[ vert[cv] for cv in components[i] ], grouped_edges[i]] for i in eachindex(components) ] end end +function group_by_component(G, V) + CG = connected_components(G, Vemph=V, ind_abs=true) + return filter(c->length(c)>0, [ C[2] for C in CG ]) +end + function number_connected_components(G) return length(connected_components(G)) end \ No newline at end of file diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 00b4c62..7c60c28 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -20,9 +20,8 @@ function plot_graphs(CG; width=3, vert=true) plot(legend=false) col = distinguishable_colors(length(CG)+2) for j in eachindex(CG) - V = CG[j][1] - E = CG[j][2] - CVemph = length(CG[j])>2 ? CG[j][3] : [] + V, E = CG[j][1] + CVemph = length(Vemph)>1 ? CG[j][2] : [] for e in E v1, v2 = [ map(Float64, V[ee]) for ee in e ] plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) @@ -41,9 +40,8 @@ function plot_graph_comp(G; Vemph=[], width=3, vert=true) CG = connected_components(G, Vemph=Vemph) col = distinguishable_colors(length(CG)+2) for j in eachindex(CG) - V = CG[j][1] - E = CG[j][2] - CVemph = length(CG[j])>2 ? CG[j][3] : [] + V, E = CG[j][1] + CVemph = length(Vemph)>1 ? CG[j][2] : [] for e in E v1, v2 = [ map(Float64, V[ee]) for ee in e ] plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) From 6f351eec6846d43596447c9d15314a8d6949264c Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Wed, 28 Aug 2024 16:11:46 +0200 Subject: [PATCH 033/180] multiple bug fixes --- src/connectivity/Cannytools.jl | 2 +- src/connectivity/boxes.jl | 2 +- src/connectivity/computeRM.jl | 11 +++++++---- src/connectivity/connectcurves.jl | 18 +++++++++++------- src/connectivity/plots.jl | 11 ++++------- 5 files changed, 24 insertions(+), 20 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index c17307a..8d49eb6 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -30,7 +30,7 @@ function change_ringvar(f::MPolyRingElem, newvarias_S::Vector{Symbol}) return change_ringvar([f], newvarias_S) end -function change_ringvar(F::Vector{P}, ind_newvarias::Vector{Int64}) where {P <: MPolyRingElem} +function change_ringvar(F::Vector{P}, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {P <: MPolyRingElem, I <: Int64} R = parent(first(F)) return change_ringvar(F, [R.S[i] for i in ind_newvarias]) end diff --git a/src/connectivity/boxes.jl b/src/connectivity/boxes.jl index c78442e..2b09789 100644 --- a/src/connectivity/boxes.jl +++ b/src/connectivity/boxes.jl @@ -39,7 +39,7 @@ function intersect_box(f, B; prec=100) push!(L[i+2][2], j) elseif overlap_inter(l, B[2]) prec *= 2 - #println("Increase precision to ", prec) + println("Increase precision to ", prec) flag = true break end diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 2201ff2..847a1c7 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -5,6 +5,8 @@ #using Nemo export computeRM, computepolarproj +# DEBUG +export change_ringvar, compute_minors include("Cannytools.jl") @@ -25,15 +27,15 @@ function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{V for q in Q ## Fq ## if e > 0 - hFq = change_ringvar([evaluate(h, fixvarias, q) for h in V.gens], collect(1:e)) + hFq = change_ringvar([evaluate(h, fixvarias, q) for h in V.gens], e+1:nvarias) Fq = AlgebraicSolving.Ideal(hFq) else Fq = V end if dimV - e <= 1 - push!(R, AlgebraicSolving.Ideal(vcat(Fq.gens, [fixvarias[j] - q[j] for j in 1:e]))) - + curve = change_ringvar(Fq.gens, A.S) + push!(R, AlgebraicSolving.Ideal(vcat(curve, [fixvarias[j] - q[j] for j in 1:e]))) else ## sing(Fq) ## #println("Compute first the singular points") @@ -46,7 +48,8 @@ function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{V ## K(pi_2, Fq) ## K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors") - push!(R, AlgebraicSolving.Ideal(vcat(K2Fq.gens, [fixvarias[j] - q[j] for j in 1:e]))) + polar = change_ringvar(K2Fq.gens, A.S) + push!(R, AlgebraicSolving.Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) ## Points with vertical tg in K(pi_2, Fq) ## K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=0) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index d716b1f..853c9df 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -6,6 +6,9 @@ export compute_graph, connected_components, number_connected_components, group_by_component, plot_graph, plot_graphs, plot_graph_comp, compute_param + # DEBUG + export subresultants, diff, diff_list + include("tools.jl") include("subresultants.jl") include("isolate.jl") @@ -39,6 +42,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, CD = lcm(map(denominator, collect(coefficients(f)))) f *= CD end + #println(f) # Generic change of variables changemat = [1 0; 0 1] if !generic @@ -98,7 +102,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, ######################################################## # For each mult of sing pts (keys) give the corresponding factors of the resultant (values) ### DEBUG: for now, only nodes for singular points, hardcode below ### - mult_to_factor = Dict(2=>[2]) + mult_to_factor = Dict(2=>2:length(group_sqr)) ######################################################### mults = keys(mult_to_factor) Lfyk = diff_list(f, 2, maximum(mults)) @@ -129,9 +133,9 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, ## TODO : Refine only the intervals that need to be refined println("\nCompute intersections with critical boxes..") LPCside = Array{Any}(undef,length(LBcrit)) - ndig = maximum([Int(floor(log10(length(LB)))) for LB in LBcrit]) + ndig = maximum([Int(floor(log10(max(1,length(LB))))) for LB in LBcrit]) for i in eachindex(LBcrit) - ndigi = Int(floor(log10(length(LBcrit[i])))) + ndigi = Int(floor(log10(max(1,length(LBcrit[i]))))) LPCside[i] = Array{Any}(undef, length(LBcrit[i])) precxtmp = precx while true @@ -177,7 +181,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, # If it intersects on the bottom side if nPCside[1] == 1 # yinf: the intersection with the vertical side just below the extreme point - yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[2]]) + yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[1]]) # We vertically enlarge the box until it intersects on the horizontal side push!(LPCside[1][j][s + 2][2], yinf) LPCside[1][j][1][2] = [] @@ -188,7 +192,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, # If it intersects on the top side if nPCside[2] == 1 # ymax: the intersection with the vertical side just above the extreme point - ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[1]]) + ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[2]]) # We vertically enlarge the box until it intersects on the horizontal side push!(LPCside[1][j][s + 2][2], ymax) LPCside[1][j][2][2] = [] @@ -260,7 +264,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, # Below the critical point #println() #println(map(length,I)) - #println(vcat(nI[1], nI[2], [length(I[1])+1])) + #println(nI[1],", ", nI[2], ", ", [length(I[1])+1]) for k in 1:ymincrit-1 push!(Vert, [xcmid, sum(I[1][k] + I[2][k])// 4]) push!(Corr[i][j][2][1], length(Vert)) @@ -271,7 +275,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, # The critical point ########################## # If we are dealing with a node - if i == 2 + if length(group_sqr)>1 && i == 2 # if it is an isolated point if isempty(nI[1]) && isempty(nI[2]) push!(Lapp[1], (i,j)) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 7c60c28..9ebe189 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,6 +1,6 @@ ## Plot functions -function plot_graph(G; Vemph=[], color="red", width=3, vert = true) +function plot_graph(G, Vemph=[]; color="red", width=3, vert = true) println("Plotting the graph") V, E = G plot(legend=false) @@ -20,8 +20,7 @@ function plot_graphs(CG; width=3, vert=true) plot(legend=false) col = distinguishable_colors(length(CG)+2) for j in eachindex(CG) - V, E = CG[j][1] - CVemph = length(Vemph)>1 ? CG[j][2] : [] + V, E = CG[j] for e in E v1, v2 = [ map(Float64, V[ee]) for ee in e ] plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) @@ -29,19 +28,17 @@ function plot_graphs(CG; width=3, vert=true) if vert scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) end - scatter!( map(Float64, [V[i][1] for i in Vemph]), map(Float64, [V[i][2] for i in Vemph]), mc=col[j+2], m=:diamond) end gui() end -function plot_graph_comp(G; Vemph=[], width=3, vert=true) +function plot_graph_comp(G, Vemph=[]; width=3, vert=true) println("Plotting the graph") plot(legend=false) CG = connected_components(G, Vemph=Vemph) col = distinguishable_colors(length(CG)+2) for j in eachindex(CG) - V, E = CG[j][1] - CVemph = length(Vemph)>1 ? CG[j][2] : [] + (V, E), CVemph = length(Vemph)>1 ? CG[j] : (CG[j], []) for e in E v1, v2 = [ map(Float64, V[ee]) for ee in e ] plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) From 76769759a68f5beabd04fe988a10c172302bca50 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Wed, 28 Aug 2024 21:40:08 +0200 Subject: [PATCH 034/180] choose the linear form for param --- src/connectivity/connectcurves.jl | 6 ++++-- src/connectivity/paramcurve.jl | 6 +++--- 2 files changed, 7 insertions(+), 5 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 853c9df..c597591 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -42,7 +42,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, CD = lcm(map(denominator, collect(coefficients(f)))) f *= CD end - #println(f) + println(f) # Generic change of variables changemat = [1 0; 0 1] if !generic @@ -322,7 +322,9 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, end end - println("Removed apparent singularities: $(length(Lapp[1])) isolated $(length(Lapp[2])) nodes") + if Lapp != [[],[]] + println("Removed apparent singularities: $(length(Lapp[1])) isolated $(length(Lapp[2])) nodes") + end #EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] #plot_graph(Vert, EdgPlot) #gui() diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index 643cdbf..8dae408 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -40,12 +40,12 @@ function deg_Alg(F, dim) end -function compute_param(F; lfs = false) +function compute_param(F; use_lfs = false, lfs = []) R = parent(first(F)) varias, N = gens(R), nvars(R) DEG = deg_Alg(F,1) - if !lfs + if !use_lfs && length(lfs)==0 # Identification of two generic variables for the parametrization") ivarias_gen = Vector{Int}(undef,0) ind = N @@ -94,7 +94,7 @@ function compute_param(F; lfs = false) N = length(varias) F = [ evaluate(f, [ varias[i] for i in 1:Nold ]) for f in F ] - lf_cfs = [ rand(ZZ(-100):ZZ(100), N) for _ in 1:2] + lf_cfs = vcat(lfs, [ rand(ZZ(-100):ZZ(100), N) for _ in 1:2-length(lfs)]) append!(F, [ transpose(lf)*varias for lf in lf_cfs ]) end # Compute DEG+1 evaluations of the param (whose deg is bounded by DEG) From 600ea29638c3e08e31906787364c85e705752f41 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 29 Aug 2024 21:29:01 +0200 Subject: [PATCH 035/180] change_ringvars univariate + manage multiple Pcontrol + fix bug refine --- src/connectivity/Cannytools.jl | 14 ++++++++++---- src/connectivity/connectcurves.jl | 21 ++++++--------------- 2 files changed, 16 insertions(+), 19 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 8d49eb6..22219c9 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -26,8 +26,13 @@ function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: M return res end -function change_ringvar(f::MPolyRingElem, newvarias_S::Vector{Symbol}) - return change_ringvar([f], newvarias_S) +function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: PolyRingElem} + A, (x,) = polynomial_ring(QQ, [parent(first(F)).S]) + return change_ringvar([ evaluate(f, x) for f in F ], newvarias_S) +end + +function change_ringvar(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) + return first(change_ringvar([f], newvarias_S)) end function change_ringvar(F::Vector{P}, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {P <: MPolyRingElem, I <: Int64} @@ -37,7 +42,7 @@ end function change_ringvar(f::MPolyRingElem, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {I <: Int64} R = parent(f) - return change_ringvar([f], [R.S[i] for i in ind_newvarias]) + return first(change_ringvar([f], [R.S[i] for i in ind_newvarias])) end # Return the polynomials in F, but injected in the polynomial ring with the variables occuring in F @@ -50,10 +55,11 @@ function change_ringvar(F::Vector{P}) where {P <: MPolyRingElem} end function change_ringvar(f::MPolyRingElem) - change_ringvar([f]) + return first(change_ringvar([f])) end + function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0) # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index c597591..aed00e8 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -42,7 +42,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, CD = lcm(map(denominator, collect(coefficients(f)))) f *= CD end - println(f) + #println(f) # Generic change of variables changemat = [1 0; 0 1] if !generic @@ -67,10 +67,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, end # Construct the parametrization of the critical points params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in group_sqr ]; - - if length(C)>0 - push!(params, C) - end + append!(params, C) end if arb @@ -144,16 +141,10 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, print("mult=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp) npcside = [length(n) for (I, n) in pcside] - if i == 1 && sum(npcside) > 2 - precxtmp *= 2 - println("\nRefine extreme boxes along x-axis to precision ", precxtmp) - refine_xboxes(params[1][1], LBcrit[1], precxtmp) - flag = true - break - elseif i > 1 && sum(npcside[1:2]) != 0 + if (i == 1 && sum(npcside) > 2) || (i > 1 && sum(npcside[1:2]) != 0) precxtmp *= 2 - println("\nRefine singular boxes along x-axis to precision ", precxtmp) - refine_xboxes(params[2][1], LBcrit[2], precxtmp) + println("\nRefine boxes along x-axis to precision ", precxtmp) + refine_xboxes(params[i][1], LBcrit[i], precxtmp) flag = true break end @@ -307,7 +298,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, for k in nI[2] push!(Edg, [length(Vert), Corr[i][j][3][k]]) end - if length(C)>0 && i==length(params) + if i > length(params)-length(C) # If this is a control point push!(Vcon, length(Vert)) end From b6756c441cc500ec9bab1a9d43cea5cbe74c43b1 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 30 Aug 2024 01:38:45 +0200 Subject: [PATCH 036/180] bugfix msolve + manage rational critical coordinates v0 + full subres seq + fix arbeval zeropoly --- src/algorithms/solvers.jl | 2 +- src/connectivity/arbtools.jl | 8 ++++++-- src/connectivity/connectcurves.jl | 16 ++++++++++++++++ src/connectivity/plots.jl | 2 +- src/connectivity/subresultants.jl | 2 +- 5 files changed, 25 insertions(+), 5 deletions(-) diff --git a/src/algorithms/solvers.jl b/src/algorithms/solvers.jl index 11152bf..b8ffd62 100644 --- a/src/algorithms/solvers.jl +++ b/src/algorithms/solvers.jl @@ -147,7 +147,7 @@ function _core_msolve( jl_vnames = Base.unsafe_wrap(Array, res_vnames[], jl_rp_nr_vars) vsymbols = [Symbol(unsafe_string(jl_vnames[i])) for i in 1:jl_rp_nr_vars] #= get possible variable permutation, ignoring additional variables=# - perm = sortperm(vsymbols[1:nr_vars]) + perm = findfirst.(isequal.(R.S), Ref(vsymbols)) rat_param = _get_rational_parametrization(jl_ld, jl_len, jl_cf, jl_cf_lf, jl_rp_nr_vars) diff --git a/src/connectivity/arbtools.jl b/src/connectivity/arbtools.jl index 0e25ac1..5fa4073 100644 --- a/src/connectivity/arbtools.jl +++ b/src/connectivity/arbtools.jl @@ -10,8 +10,12 @@ function rat_to_Arb(x, prec) end function evaluate_Arb(f, x, prec) - cf = coefficients_of_univariate(f) - return evalpoly(ArbField(prec)(x), cf) + if is_zero(f) + return ArbField(prec)(0) + else + cf = coefficients_of_univariate(f) + return evalpoly(ArbField(prec)(x), cf) + end end function Arb_eval(f, B, prec) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index aed00e8..9fbcfec 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -75,6 +75,13 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, println("\nIsolating critical values with precision ", precx,"..") @time begin xcrit = [ isolate(first(p), prec=precx) for p in params ] + for i in eachindex(xcrit) + for j in eachindex(xcrit[i]) + if xcrit[i][j][1]==xcrit[i][j][2] + xcrit[i][j] = [xcrit[i][j][1]-1//ZZ(1)<t[1]) for p in params ] + for i in eachindex(LBcrit) + for j in eachindex(LBcrit[i]) + for k in eachindex(LBcrit[i][j]) + if LBcrit[i][j][k][1]==LBcrit[i][j][k][2] + LBcrit[i][j][k] = [LBcrit[i][j][k][1]-1//ZZ(1)< Date: Fri, 30 Aug 2024 12:31:07 +0200 Subject: [PATCH 037/180] control points in plot_graphS --- src/connectivity/plots.jl | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 6f19a7b..421a272 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -20,14 +20,15 @@ function plot_graphs(CG; width=3, vert=true) plot(legend=false) col = distinguishable_colors(length(CG)+2) for j in eachindex(CG) - V, E = CG[j] + (V, E), CVemph = length(CG[j][1])==2 ? CG[j] : (CG[j], []) for e in E v1, v2 = [ map(Float64, V[ee]) for ee in e ] plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) end if vert - scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc=col[j+2], m=:diamond) + scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) end + scatter!( map(Float64, [V[i][1] for i in CVemph]), map(Float64, [V[i][2] for i in CVemph]), mc=col[j+2], m=:diamond) end gui() end From 11b9c7d5780fcbe507f54043b83011bcee42c978 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 30 Aug 2024 12:31:47 +0200 Subject: [PATCH 038/180] multiple lists of vertices for multiple Pcontrols --- src/connectivity/connectcurves.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 9fbcfec..0ec558c 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -218,7 +218,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, Edg = [] Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ] Viso = [] - Vcon = [] + Vcon = [ [] for _ in 1:length(C) ] Lapp = [[],[]] @@ -316,7 +316,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, end if i > length(params)-length(C) # If this is a control point - push!(Vcon, length(Vert)) + push!(Vcon[i + length(C) - length(params)], length(Vert)) end end ########################### From 1d1dc838bffe71669f3ea1d8aa93f6eb8263fedd Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 30 Aug 2024 12:32:16 +0200 Subject: [PATCH 039/180] fix bug in variable order for param --- src/connectivity/paramcurve.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index 8dae408..0f51ab7 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -137,7 +137,7 @@ function compute_param(F; use_lfs = false, lfs = []) end C = [ collect(coefficients(c)) for c in COEFFS ] - POL_term = [C[i][j]*x^(j-1)*y^(i-1) for i in 1:length(C) for j in 1:length(C[i])] + POL_term = [C[i][j]*x^(i-1)*y^(j-1) for i in 1:length(C) for j in 1:length(C[i])] POL = length(POL_term) > 0 ? sum(POL_term) : T(0) push!(POLY_PARAM, POL) From babe94334c95850d9576f72578e0d7288f52608f Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 3 Sep 2024 00:31:00 +0200 Subject: [PATCH 040/180] type of list --- src/connectivity/Cannytools.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 22219c9..5e9d489 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -105,7 +105,7 @@ function combinations(a, n) if length(chosen) == n return [chosen] elseif start > length(a) - return [] + return Vector{Int}([]) else # Include the current element and recurse include_current = _combinations(a, n, start + 1, [chosen; a[start]]) @@ -114,7 +114,7 @@ function combinations(a, n) return vcat(include_current, exclude_current) end end - return _combinations(a, n, 1, []) + return _combinations(a, n, 1, Vector{Int}([])) end function detmpoly(A::Matrix{QQMPolyRingElem}, R) From fc8a149c7b9ca3995f1a5a4543de418321477130 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 3 Sep 2024 00:31:24 +0200 Subject: [PATCH 041/180] heuristic for fibers --- src/connectivity/computeRM.jl | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 847a1c7..9f02732 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -6,7 +6,7 @@ export computeRM, computepolarproj # DEBUG -export change_ringvar, compute_minors +export change_ringvar, compute_minors, detmpoly include("Cannytools.jl") @@ -58,6 +58,8 @@ function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{V K1W = vcat(K1Fq, K1WmFq) K1WRat = MidRationalPoints(getindex.(K1W,1)) newQ = [ vcat(q, [kv]) for kv in K1WRat ] + # Heuristic to be proven + # newQ = newQ[2:end-1] RFq = computeRM(V, dimV, newQ) From e8c807984a5c61cb94a8078eac666a1fbf896d64 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 3 Sep 2024 00:32:15 +0200 Subject: [PATCH 042/180] float output + display control + other methods depending the input --- src/connectivity/connectcurves.jl | 54 ++++++++++++++++--------------- 1 file changed, 28 insertions(+), 26 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 0ec558c..9b07538 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -3,7 +3,7 @@ #using Plots, Colors #pythonplot() -export compute_graph, connected_components, number_connected_components, group_by_component, +export compute_graph, connected_components, number_connected_components, group_by_component, merge_graphs, plot_graph, plot_graphs, plot_graph_comp, compute_param # DEBUG @@ -17,20 +17,7 @@ include("graph.jl") include("plots.jl") include("arbtools.jl") -function compute_graph(F, C=[]; param=true, generic=true, precx=150, v=0, arb=true, int_coeff=false) - if !(param) - println("Compute rational parametrization...") - @time begin - Fparam = compute_param(F)[3] - end - else - Fparam = F[1] - end - - return compute_graph_param(Fparam, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff) -end - -function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, int_coeff=false) +function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf=true) where (P <: MPolyRingElem) println("\n!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") println("!! Careful: this is a WIP version !!") println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") @@ -149,12 +136,13 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, ndig = maximum([Int(floor(log10(max(1,length(LB))))) for LB in LBcrit]) for i in eachindex(LBcrit) ndigi = Int(floor(log10(max(1,length(LBcrit[i]))))) + Ptype = i > length(LBcrit) - length(C) ? "Pcon" : "mult" LPCside[i] = Array{Any}(undef, length(LBcrit[i])) precxtmp = precx while true flag = false for j in eachindex(LBcrit[i]) - print("mult=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") + print("$Ptype=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp) npcside = [length(n) for (I, n) in pcside] if (i == 1 && sum(npcside) > 2) || (i > 1 && sum(npcside[1:2]) != 0) @@ -214,6 +202,8 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, println("\nGraph computation") # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot # And even remove this fiber for the graph + fct = outf ? Float64 : identity + Vert = [] Edg = [] Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ] @@ -237,8 +227,8 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, I = [ l[1] for l in PCside[3:end] ] nI = [ l[2] for l in PCside[3:end] ] - xcmid = sum(LBcrit[i][j][1])//2 - ycmid = sum(LBcrit[i][j][2])//2 + xcmid = sum(LBcrit[i][j][1])//2 |> fct + ycmid = sum(LBcrit[i][j][2])//2 |> fct ymincrit = minimum(vcat(nI[1], nI[2], [length(I[1])+1])) # Construct vertices @@ -250,7 +240,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, end else for k in 1:length(I[1]) - push!(Vert, [xcrit[i][j][1], sum(I[1][k])//2]) + push!(Vert, map(fct, [xcrit[i][j][1], sum(I[1][k])//2])) push!(Corr[i][j][1], length(Vert)) end end @@ -258,12 +248,12 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, # On the vertical right side if ind < length(xcritpermut) for k in 1:length(I[2]) - push!(Vert, [(xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4]) + push!(Vert, map(fct, [(xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4])) push!(Corr[i][j][3], length(Vert)) end else for k in 1:length(I[2]) - push!(Vert, [xcrit[i][j][2], sum(I[2][k])//2]) + push!(Vert, map(fct, [xcrit[i][j][2], sum(I[2][k])//2])) push!(Corr[i][j][3], length(Vert)) end end @@ -273,7 +263,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, #println(map(length,I)) #println(nI[1],", ", nI[2], ", ", [length(I[1])+1]) for k in 1:ymincrit-1 - push!(Vert, [xcmid, sum(I[1][k] + I[2][k])// 4]) + push!(Vert, map(fct, [xcmid, sum(I[1][k] + I[2][k])// 4])) push!(Corr[i][j][2][1], length(Vert)) push!(Edg, [Corr[i][j][1][k], length(Vert)]) # left push!(Edg, [length(Vert), Corr[i][j][3][k]]) # right @@ -322,7 +312,7 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, ########################### # Above the critical point for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1 - push!(Vert, [xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4]) + push!(Vert, map(fct,[xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4])) push!(Corr[i][j][2][3], length(Vert)) push!(Edg, [Corr[i][j][1][end - k + 1], length(Vert)]) # left push!(Edg, [length(Vert), Corr[i][j][3][end - k + 1]]) # right @@ -349,9 +339,21 @@ function compute_graph_param(f, C=[]; generic=true, precx = 150, v=0, arb=true, end end -function group_by_component(F::Vector{P}, C::Vector{P}; param=true, generic=true, precx=150, v=0, arb=true, int_coeff=false) where {P <: MPolyRingElem} +function compute_graph(f::P, C::Dict{Int,Vector{P}}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) + G, Vcon = compute_graph(f, collect(values(C)), generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf) + VC = Dict([ k => Vcon[i] for (i,k) in enumerate(keys(C)) ]) + return G, VC +end + +function compute_graph(f::P, C::Vector{P}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) + G, (Vcon,) = compute_graph(f, [C], generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf = outf) + return G, Vcon +end + +################################################################ +function group_by_component(f::P, C::Vector{P}; generic=true, precx=150, v=0, arb=true, int_coeff=false) where {P <: MPolyRingElem} # Compute a graph homeomorphic to Z(F) and return the vertices identified by Z(C) - G, Vcon = compute_graph(F, C, param=param, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff) + G, Vcon = compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff) # Compute the partition of the vertices in Vcon according to the connected component in G sort!(Vcon) CVcon = group_by_component(G, Vcon) @@ -359,4 +361,4 @@ function group_by_component(F::Vector{P}, C::Vector{P}; param=true, generic=true # Convert the partition into abscissa order index_map = Dict((val, idx) for (idx, val) in enumerate(Vcon)) return [map(v -> index_map[v], C) for C in CVcon] -end \ No newline at end of file +end From c5b02d892e1f7c8ce944ebd7b2a22399a0570b51 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 3 Sep 2024 00:32:36 +0200 Subject: [PATCH 043/180] function for merging graphs --- src/connectivity/graph.jl | 44 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 44 insertions(+) diff --git a/src/connectivity/graph.jl b/src/connectivity/graph.jl index f5f1133..85c8bc8 100644 --- a/src/connectivity/graph.jl +++ b/src/connectivity/graph.jl @@ -81,4 +81,48 @@ end function number_connected_components(G) return length(connected_components(G)) +end + + +function merge_graphs(LG, VC) + # Initialize merged graph with the vertices and edges of the first graph + V_merged, E_merged = deepcopy(LG[1]) + + # To keep track of the mapping of vertices from each graph to the merged graph + all_vertex_maps = [Dict(i => i for i in 1:length(V_merged))] + + # Iterate over each graph G_i in LG starting from the second graph + for i in 2:length(LG) + V_i, E_i = LG[i] # Vertices and edges of the current graph + VC_i = VC[i] # Dictionary of common vertices for the current graph + + # Dictionary to map vertices of G_i to their new indices in V_merged + vertex_index_map = Dict() + + # Step 1: Map common vertices from G_i to existing vertices in V_merged + for (k, common_indices) in VC_i + if k < i + # Map each common vertex in G_i to its corresponding vertex in G_k (already merged) + for (j, idx) in enumerate(common_indices) + vertex_index_map[idx] = all_vertex_maps[k][VC[k][i][j]] + end + end + end + + # Step 2: Add non-common vertices from G_i to V_merged + for idx in 1:length(V_i) + if !haskey(vertex_index_map, idx) # If not already mapped, it's a new vertex + vertex_index_map[idx] = push!(V_merged, V_i[idx]) |> length + end + end + + # Step 3: Merge edges of G_i into the merged graph + new_edges = [(vertex_index_map[i], vertex_index_map[j]) for (i, j) in E_i] + append!(E_merged, new_edges) + + # Store the vertex index mapping for G_i for future merges + push!(all_vertex_maps, vertex_index_map) + end + + return V_merged, E_merged end \ No newline at end of file From a0f60f7d0b127792793b52899f411cfba3574680 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 3 Sep 2024 00:33:29 +0200 Subject: [PATCH 044/180] function for forcing parametric variable.s for msolve --- src/connectivity/paramcurve.jl | 12 +++++++++++- 1 file changed, 11 insertions(+), 1 deletion(-) diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index 0f51ab7..2f6a719 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -5,7 +5,7 @@ #using AlgebraicSolving #import Nemo: coefficients, exponent_vectors, coeff, interpolate, MPolyBuildCtx, push_term!, finish, gens -export compute_param +export compute_param, param_newvars function rem_var(f, i) # Remove the occurence of the ith variable @@ -146,6 +146,16 @@ function compute_param(F; use_lfs = false, lfs = []) return [R.S, lf_cfs, POLY_PARAM[1], POLY_PARAM[2], POLY_PARAM[3:end]] end +function param_newvars(F::Vector{P} where P <: MPolyRingElem, Svars::Vector{Symbol}, cfs_lf::Vector{Vector{I}} where I<:Union{ZZRingElem, QQFieldElem}) + eq = change_ringvar(F, Svars) + newvarias = gens(parent(first(eq))) + neweq = vcat(eq, [ transpose(lf)*newvarias for lf in cfs_lf ]) + + C = rational_parametrization(Ideal(neweq)) + return change_ringvar([C.elim, C.elim == -1 ? C.elim : C.param[end], C.denom], [:x,:y]) +end + + #= # Tests R, (a,b,c) = polynomial_ring(QQ, [:a,:b,:c]) From 3eff83db8d4526a3ffe041d078451017ff8e7e42 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 3 Sep 2024 11:52:43 +0200 Subject: [PATCH 045/180] adapted data types --- src/connectivity/connectcurves.jl | 38 +++++++++++++++---------------- 1 file changed, 19 insertions(+), 19 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 9b07538..5bbda3f 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -202,10 +202,10 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t println("\nGraph computation") # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot # And even remove this fiber for the graph - fct = outf ? Float64 : identity - - Vert = [] - Edg = [] + fct, typeout = outf ? (Float64, Float64) : (identity, QQFieldElem) + + Vert = Vector{Tuple{typeout, typeout}}() + Edg = Vector{Tuple{Int, Int}}() Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ] Viso = [] Vcon = [ [] for _ in 1:length(C) ] @@ -240,7 +240,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t end else for k in 1:length(I[1]) - push!(Vert, map(fct, [xcrit[i][j][1], sum(I[1][k])//2])) + push!(Vert, (xcrit[i][j][1], sum(I[1][k])//2) .|> fct) push!(Corr[i][j][1], length(Vert)) end end @@ -248,12 +248,12 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t # On the vertical right side if ind < length(xcritpermut) for k in 1:length(I[2]) - push!(Vert, map(fct, [(xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4])) + push!(Vert, ((xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4) .|> fct) push!(Corr[i][j][3], length(Vert)) end else for k in 1:length(I[2]) - push!(Vert, map(fct, [xcrit[i][j][2], sum(I[2][k])//2])) + push!(Vert, (xcrit[i][j][2], sum(I[2][k])//2) .|> fct) push!(Corr[i][j][3], length(Vert)) end end @@ -263,10 +263,10 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t #println(map(length,I)) #println(nI[1],", ", nI[2], ", ", [length(I[1])+1]) for k in 1:ymincrit-1 - push!(Vert, map(fct, [xcmid, sum(I[1][k] + I[2][k])// 4])) + push!(Vert, (xcmid, sum(I[1][k] + I[2][k])// 4) .|> fct) push!(Corr[i][j][2][1], length(Vert)) - push!(Edg, [Corr[i][j][1][k], length(Vert)]) # left - push!(Edg, [length(Vert), Corr[i][j][3][k]]) # right + push!(Edg, (Corr[i][j][1][k], length(Vert))) # left + push!(Edg, (length(Vert), Corr[i][j][3][k])) # right end ########################### # The critical point @@ -288,21 +288,21 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t ############################################ else # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 - push!(Edg, [Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]]]) - push!(Edg, [Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]]]) + push!(Edg, (Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]])) + push!(Edg, (Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]])) push!(Lapp[2], (i,j)) end else # We can add the vertex - push!(Vert, [xcmid, ycmid]) + push!(Vert, (xcmid, ycmid)) push!(Corr[i][j][2][2], length(Vert)) # We connect to the vertical left side of the critical box for k in nI[1] - push!(Edg, [Corr[i][j][1][k], length(Vert)]) + push!(Edg, (Corr[i][j][1][k], length(Vert))) end # We connect to the vertical right side of the critical box for k in nI[2] - push!(Edg, [length(Vert), Corr[i][j][3][k]]) + push!(Edg, (length(Vert), Corr[i][j][3][k])) end if i > length(params)-length(C) # If this is a control point @@ -312,10 +312,10 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t ########################### # Above the critical point for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1 - push!(Vert, map(fct,[xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4])) + push!(Vert, (xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4) .|> fct) push!(Corr[i][j][2][3], length(Vert)) - push!(Edg, [Corr[i][j][1][end - k + 1], length(Vert)]) # left - push!(Edg, [length(Vert), Corr[i][j][3][end - k + 1]]) # right + push!(Edg, (Corr[i][j][1][end - k + 1], length(Vert))) # left + push!(Edg, (length(Vert), Corr[i][j][3][end - k + 1])) # right end end @@ -341,7 +341,7 @@ end function compute_graph(f::P, C::Dict{Int,Vector{P}}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) G, Vcon = compute_graph(f, collect(values(C)), generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf) - VC = Dict([ k => Vcon[i] for (i,k) in enumerate(keys(C)) ]) + VC = Dict{Int64, Vector{Int}}([ k => Vcon[i] for (i,k) in enumerate(keys(C)) ]) return G, VC end From e22a70be84c2c108d2b890e031d14e49b02fe4a8 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 3 Sep 2024 11:53:05 +0200 Subject: [PATCH 046/180] merge list of graphs --- src/connectivity/graph.jl | 50 +++++++++++++++++++-------------------- 1 file changed, 24 insertions(+), 26 deletions(-) diff --git a/src/connectivity/graph.jl b/src/connectivity/graph.jl index 85c8bc8..5f50f4e 100644 --- a/src/connectivity/graph.jl +++ b/src/connectivity/graph.jl @@ -5,7 +5,7 @@ function index_of(x, L) return findfirst(t->t==x,L) end -function connected_components(G; Vemph=[], ind_abs=false) +function connected_components(G, Vemph=[]; ind_abs=false) # Outputs subgraphs of the connected components ########### vert, edges = G @@ -57,11 +57,7 @@ function connected_components(G; Vemph=[], ind_abs=false) for i in eachindex(components) for j in eachindex(components[i]) if components[i][j] in Vemph - if ind_abs - push!(CVemph[i], components[i][j]) - else - push!(CVemph[i], j) - end + push!(CVemph[i], ind_abs ? components[i][j] : j) end end end @@ -75,7 +71,7 @@ function connected_components(G; Vemph=[], ind_abs=false) end function group_by_component(G, V) - CG = connected_components(G, Vemph=V, ind_abs=true) + CG = connected_components(G, V, ind_abs=true) return filter(c->length(c)>0, [ C[2] for C in CG ]) end @@ -84,45 +80,47 @@ function number_connected_components(G) end -function merge_graphs(LG, VC) +function merge_graphs(LG::Vector{Tuple{Vector{Tuple{T,T}}, Vector{Tuple{Int,Int}}}} where T<:Union{Float64, QQFieldElem}, LVC::Vector{Dict{Int, Vector{Int}}}) # Initialize merged graph with the vertices and edges of the first graph - V_merged, E_merged = deepcopy(LG[1]) + Vtot, Etot = deepcopy(LG[1]) # To keep track of the mapping of vertices from each graph to the merged graph - all_vertex_maps = [Dict(i => i for i in 1:length(V_merged))] + all_vertex_maps = [Dict(i => i for i in 1:length(Vtot))] # Iterate over each graph G_i in LG starting from the second graph for i in 2:length(LG) - V_i, E_i = LG[i] # Vertices and edges of the current graph - VC_i = VC[i] # Dictionary of common vertices for the current graph + Vi, Ei = LG[i] # Vertices and edges of the current graph - # Dictionary to map vertices of G_i to their new indices in V_merged + # Dictionary to map vertices of Gi to their new indices in Vtot vertex_index_map = Dict() - # Step 1: Map common vertices from G_i to existing vertices in V_merged - for (k, common_indices) in VC_i + # Step 1: Map common vertices from Gi to existing vertices in Vtot + for (k, common_indices) in LVC[i] if k < i - # Map each common vertex in G_i to its corresponding vertex in G_k (already merged) + # Map each common vertex in Gi to its corresponding vertex in Gk (already merged) for (j, idx) in enumerate(common_indices) - vertex_index_map[idx] = all_vertex_maps[k][VC[k][i][j]] + vertex_index_map[idx] = all_vertex_maps[k][LVC[k][i][j]] end end end - # Step 2: Add non-common vertices from G_i to V_merged - for idx in 1:length(V_i) + # Step 2: Add non-common vertices from Gi to Vtot + for idx in 1:length(Vi) if !haskey(vertex_index_map, idx) # If not already mapped, it's a new vertex - vertex_index_map[idx] = push!(V_merged, V_i[idx]) |> length + vertex_index_map[idx] = push!(Vtot, Vi[idx]) |> length end end + # Step 3: Merge edges of Gi into the merged graph + new_edges = [(vertex_index_map[i], vertex_index_map[j]) for (i, j) in Ei] + append!(Etot, new_edges) - # Step 3: Merge edges of G_i into the merged graph - new_edges = [(vertex_index_map[i], vertex_index_map[j]) for (i, j) in E_i] - append!(E_merged, new_edges) - - # Store the vertex index mapping for G_i for future merges + # Store the vertex index mapping for Gi for future merges push!(all_vertex_maps, vertex_index_map) end - return V_merged, E_merged + return Vtot, Etot +end + +function merge_graphs(LGVC::Vector{Tuple{Tuple{Vector{Tuple{T, T}}, Vector{Tuple{Int64, Int64}}}, Dict{Int64, Vector{Int64}}}} where T<:Union{Float64, QQFieldElem}) + return merge_graphs(first.(LGVC), last.(LGVC)) end \ No newline at end of file From aba9c462824842652fa56c6d976ec0908ec3b521 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 3 Sep 2024 11:53:44 +0200 Subject: [PATCH 047/180] more flexible plot functions --- src/connectivity/plots.jl | 57 +++++++++++++++++++-------------------- 1 file changed, 27 insertions(+), 30 deletions(-) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 421a272..495b51d 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,9 +1,12 @@ ## Plot functions -function plot_graph(G, Vemph=[]; color="red", width=3, vert = true) - println("Plotting the graph") +function plot_graph(G, Vemph::Vector{Vector{T}}=Vector{Vector{T}}(); color="red", width=3, vert=true, subplt=false) where T<:Any + if !subplt + println("Plotting the graph") + plot(legend=false) + end V, E = G - plot(legend=false) + #col = distinguishable_colors(length(Vemph)+2) for e in E v1, v2 = [ map(Float64, V[ee]) for ee in e ] plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=color, lw=width) @@ -11,24 +14,29 @@ function plot_graph(G, Vemph=[]; color="red", width=3, vert = true) if vert scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) end - scatter!( map(Float64, [V[i][1] for i in Vemph]), map(Float64, [V[i][2] for i in Vemph]), mc=color, m=:diamond) - gui() + for i in 1:length(Vemph) + scatter!( map(Float64, [V[j][1] for j in Vemph[i]]), map(Float64, [V[j][2] for j in Vemph[i]]), mc=color, m=:diamond) + end + #gui() end -function plot_graphs(CG; width=3, vert=true) - println("Plotting the graph") - plot(legend=false) +function plot_graph(G, Vemph::Vector{T} where T<:Any; color="red", width=3, vert=true, subplt=false) + plot_graph(G, [Vemph], color=color, width=width, vert=vert, subplt=subplt) +end + +function plot_graph(G, Vemph::Dict{Int, Vector{T}} where T<:Any; color="red", width=3, vert=true, subplt=false) + plot_graph(G, Vemph|>values|>collect, color=color, width=width, vert=vert, subplt=subplt) +end + +function plot_graphs(CG; width=3, vert=true, subplt=false) + if !subplt + println("Plotting the graph") + plot(legend=false) + end col = distinguishable_colors(length(CG)+2) for j in eachindex(CG) - (V, E), CVemph = length(CG[j][1])==2 ? CG[j] : (CG[j], []) - for e in E - v1, v2 = [ map(Float64, V[ee]) for ee in e ] - plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) - end - if vert - scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) - end - scatter!( map(Float64, [V[i][1] for i in CVemph]), map(Float64, [V[i][2] for i in CVemph]), mc=col[j+2], m=:diamond) + G, CVemph = length(CG[j][1])==2 ? CG[j] : (CG[j], Vector{Int}()) + plot_graph(G, CVemph, color=col[j+2], subplt=true) end gui() end @@ -36,18 +44,7 @@ end function plot_graph_comp(G, Vemph=[]; width=3, vert=true) println("Plotting the graph") plot(legend=false) - CG = connected_components(G, Vemph=Vemph) - col = distinguishable_colors(length(CG)+2) - for j in eachindex(CG) - (V, E), CVemph = length(Vemph)>1 ? CG[j] : (CG[j], []) - for e in E - v1, v2 = [ map(Float64, V[ee]) for ee in e ] - plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=col[j+2], lw=width) - end - if vert - scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) - end - scatter!( map(Float64, [V[i][1] for i in CVemph]), map(Float64, [V[i][2] for i in CVemph]), mc=col[j+2], m=:diamond) - end + CG = connected_components(G, Vemph) + plot_graphs(CG, width=width, vert=vert, subplt=true) gui() end \ No newline at end of file From bf2cee10209147b702d5dc3d71116f0464be1122 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sat, 7 Sep 2024 10:44:52 +0200 Subject: [PATCH 048/180] multi-threading with msolve --- src/connectivity/Cannytools.jl | 10 +++++----- src/connectivity/computeRM.jl | 10 +++++----- 2 files changed, 10 insertions(+), 10 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 5e9d489..6dc5a85 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -60,7 +60,7 @@ end -function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0) +function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" R = parent(V) @@ -72,11 +72,11 @@ function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; d hW = vcat(hV, compute_minors(sizeminors, JW, R)) output_functions = Dict( "minors" => x -> x, - "groebner" => x -> groebner_basis(x, info_level=verb), - "real" => x -> real_solutions(x, info_level=verb), - "interval" => x -> real_solutions(x, interval=true, info_level=verb), + "groebner" => x -> groebner_basis(x, info_level=verb,nr_thrds=nr_thrds), + "real" => x -> real_solutions(x, info_level=verb,nr_thrds=nr_thrds), + "interval" => x -> real_solutions(x, interval=true, info_level=verb,nr_thrds=nr_thrds), #"interval" => x -> inter_solutions(x, info_level=verb), - "parametric" => x -> rational_parametrization(x, info_level=verb) + "parametric" => x -> rational_parametrization(x, info_level=verb,nr_thrds=nr_thrds) ) return output_functions[output](AlgebraicSolving.Ideal(hW)) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 9f02732..65ab9c8 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -10,7 +10,7 @@ export change_ringvar, compute_minors, detmpoly include("Cannytools.jl") -function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{Vector{QQFieldElem}}([[]]) ) +function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{Vector{QQFieldElem}}([[]]) ; v=0) # V is a variety of dimension dimV # Q are base points with rational coefficients # C are query points with rational coefficients @@ -39,20 +39,20 @@ function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{V else ## sing(Fq) ## #println("Compute first the singular points") - singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=0) + singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=v, nr_thrds=Threads.nthreads()) @assert(length(singFq)==0, "Non-emtpy real sing locus!") #@assert(degree(singFq.elim)==0, "Non-emtpy sing locus!") ## K(pi_1,Fq) ## - K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=0) + K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=v, nr_thrds=Threads.nthreads()) ## K(pi_2, Fq) ## - K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors") + K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors", verb=v, nr_thrds=Threads.nthreads()) polar = change_ringvar(K2Fq.gens, A.S) push!(R, AlgebraicSolving.Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) ## Points with vertical tg in K(pi_2, Fq) ## - K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=0) + K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=v, nr_thrds=Threads.nthreads()) ## New base points ## K1W = vcat(K1Fq, K1WmFq) From 2921fe716096ae281b58a25f335357c48786b7a6 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sat, 7 Sep 2024 10:46:15 +0200 Subject: [PATCH 049/180] multi-threading for curve parametrization --- src/connectivity/paramcurve.jl | 39 ++++++++++++++++++++++------------ 1 file changed, 25 insertions(+), 14 deletions(-) diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index 2f6a719..7ad5595 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -98,10 +98,13 @@ function compute_param(F; use_lfs = false, lfs = []) append!(F, [ transpose(lf)*varias for lf in lf_cfs ]) end # Compute DEG+1 evaluations of the param (whose deg is bounded by DEG) - PARAM = Vector{Vector{AlgebraicSolving.QQPolyRingElem}}(undef,0) - _values = Vector{QQFieldElem}(undef,0) - i = 1 - while length(_values) < DEG+2 + println("Parametrization step...") + @time begin + PARAM = Vector{Vector{AlgebraicSolving.QQPolyRingElem}}(undef,DEG+2) + _values = Vector{QQFieldElem}(undef,DEG+2) + i, c = 1, 0 + while c < DEG+2 + #println("$c/ $(DEG+2)") if i > 2*(DEG+2) error("Too many bad specializations") end @@ -109,14 +112,15 @@ function compute_param(F; use_lfs = false, lfs = []) #try Feval = [ evaluate(f, [N-1], [QQ(i)]) for f in F ] Feval = [ rem_var(f, N-1) for f in Feval ] - r = rational_parametrization(Ideal(Feval)) + r = rational_parametrization(Ideal(Feval), nr_thrds=Threads.nthreads()) # For lifting: the same variable must be chosen for the param if r.vars == rem_ind(R.S, N-1) lc = leading_coefficient(r.elim) # TODO: why dividing by lc ? rr = [ p/lc for p in vcat(r.elim, r.denom, r.param) ] - push!(PARAM, rr) - push!(_values, QQ(i)) + PARAM[i] = rr + _values[i] = QQ(i) + c += 1 else println("bad specialization: ", i) end @@ -125,22 +129,29 @@ function compute_param(F; use_lfs = false, lfs = []) #end i += 1 end + end # Interpolate each coefficient of each poly in the param - POLY_PARAM = Vector{QQMPolyRingElem}(undef,0) + println("Interpolation step...") + @time begin + POLY_PARAM = Vector{QQMPolyRingElem}(undef,N) T, (x,y) = polynomial_ring(QQ, [:x,:y]) - for count in 1:N - COEFFS = [] - for deg in 0:DEG - _evals = [ coeff(PARAM[i][count], deg) for i in 1:length(PARAM)] - push!(COEFFS, interpolate(polynomial_ring(QQ,"u")[1], _values, _evals)) + A, u = polynomial_ring(QQ, :u) + Threads.@threads for count in 1:N + #println("$count/$N") + COEFFS = Vector{QQPolyRingElem}(undef, DEG+1) + Threads.@threads for deg in 0:DEG + #println("$deg/$DEG") + _evals = [coeff(PARAM[i][count], deg) for i in 1:length(PARAM)] + COEFFS[deg+1] = interpolate(A, _values, _evals) end C = [ collect(coefficients(c)) for c in COEFFS ] POL_term = [C[i][j]*x^(i-1)*y^(j-1) for i in 1:length(C) for j in 1:length(C[i])] POL = length(POL_term) > 0 ? sum(POL_term) : T(0) - push!(POLY_PARAM, POL) + POLY_PARAM[count] = POL + end end return [R.S, lf_cfs, POLY_PARAM[1], POLY_PARAM[2], POLY_PARAM[3:end]] From 22339b9939ff373da805a14e2cccbf914d474b01 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sat, 7 Sep 2024 10:46:32 +0200 Subject: [PATCH 050/180] multi-modular subresultant --- Manifest.toml | 13 ++++++++++++- Project.toml | 1 + src/connectivity/connectcurves.jl | 2 +- src/connectivity/subresultants.jl | 27 ++++++++++++++++++++++++++- src/imports.jl | 1 + 5 files changed, 41 insertions(+), 3 deletions(-) diff --git a/Manifest.toml b/Manifest.toml index 34b82dd..230d183 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -2,7 +2,7 @@ julia_version = "1.10.1" manifest_format = "2.0" -project_hash = "41b78713eea3ae65743b4a45ba2e4e27496d5a74" +project_hash = "4d3be6417b0dd2907e17a74f5ed176639eddabae" [[deps.AbstractAlgebra]] deps = ["InteractiveUtils", "LinearAlgebra", "MacroTools", "Preferences", "Random", "RandomExtensions", "SparseArrays", "Test"] @@ -263,6 +263,11 @@ git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3" uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566" version = "2.8.1+1" +[[deps.IntegerMathUtils]] +git-tree-sha1 = "b8ffb903da9f7b8cf695a8bead8e01814aa24b30" +uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235" +version = "0.1.2" + [[deps.InteractiveUtils]] deps = ["Markdown"] uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240" @@ -625,6 +630,12 @@ git-tree-sha1 = "9306f6085165d270f7e3db02af26a400d580f5c6" uuid = "21216c6a-2e73-6563-6e65-726566657250" version = "1.4.3" +[[deps.Primes]] +deps = ["IntegerMathUtils"] +git-tree-sha1 = "cb420f77dc474d23ee47ca8d14c90810cafe69e7" +uuid = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae" +version = "0.5.6" + [[deps.Printf]] deps = ["Unicode"] uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" diff --git a/Project.toml b/Project.toml index 0f312c7..f50a22d 100644 --- a/Project.toml +++ b/Project.toml @@ -10,6 +10,7 @@ Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +Primes = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae" Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 5bbda3f..ed4c30c 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -7,7 +7,7 @@ export compute_graph, connected_components, number_connected_components, group_b plot_graph, plot_graphs, plot_graph_comp, compute_param # DEBUG - export subresultants, diff, diff_list + export mmod_subresultants, subresultants, diff, diff_list include("tools.jl") include("subresultants.jl") diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index da237e5..db56743 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -49,6 +49,7 @@ function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingEl while true d = degree(A) e = degree(B) + println("($d,$e)") if iszero(B) return S end @@ -85,7 +86,7 @@ function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingEl if e == 0 return S end - B = pseudorem(A,-B) / (s^delta * leading_coefficient(A)) + @time B = pseudorem(A,-B) / (s^delta * leading_coefficient(A)) A = copy(C) s = leading_coefficient(A) end @@ -135,3 +136,27 @@ function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false return newsr end + +function mmod_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false) where T <: RingElement + prim = nextprime(2^(30)) + L1, primprod = [], ZZ(1) + i=1 + while true + print("$i, ") + if !all([ divides(ZZ(prim), evaluate(leading_coefficient(l, 2),[0,0]))[1] for l in [P,Q] ]) + L2 = deepcopy(L1) + Pprim, Qprim = [ change_coefficient_ring(GF(prim), poly) for poly in [P,Q] ] + sr = subresultants(Pprim, Qprim, idx)[1] + L1 = lift.(Ref(ZZ), coefficients_of_univariate(sr)) + if L2 != [] + L1 = [ crt(L2[i], primprod, L1[i], ZZ(prim), true) for i in 1:length(L2) ] + end + primprod *= ZZ(prim) + L1 != L2 || break + end + prim = nextprime(prim+1) + i+=1 + end + println() + return L1 +end diff --git a/src/imports.jl b/src/imports.jl index 80314a7..fd2ac19 100644 --- a/src/imports.jl +++ b/src/imports.jl @@ -5,6 +5,7 @@ using Nemo using LinearAlgebra using StaticArrays using Plots, Colors +using Primes #pythonplot() import Plots: plot From d5e8033066c18c411c5473756794d2ea9f56e69a Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 16 Sep 2024 13:07:54 +0200 Subject: [PATCH 051/180] tranpose of jac + polarphi --- src/connectivity/Cannytools.jl | 31 +++++++++++++++++++++++++++---- 1 file changed, 27 insertions(+), 4 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 6dc5a85..70b8138 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -58,8 +58,6 @@ function change_ringvar(f::MPolyRingElem) return first(change_ringvar([f])) end - - function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" @@ -67,7 +65,7 @@ function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; d n, hV = R.nvars, V.gens c = n - dimV - JW = [ derivative(f, k) for k=j+1:n, f in hV ] + JW = transpose([ derivative(f, k) for k=j+1:n, f in hV ]) sizeminors = c + dimproj - (j-1) hW = vcat(hV, compute_minors(sizeminors, JW, R)) output_functions = Dict( @@ -75,7 +73,32 @@ function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; d "groebner" => x -> groebner_basis(x, info_level=verb,nr_thrds=nr_thrds), "real" => x -> real_solutions(x, info_level=verb,nr_thrds=nr_thrds), "interval" => x -> real_solutions(x, interval=true, info_level=verb,nr_thrds=nr_thrds), - #"interval" => x -> inter_solutions(x, info_level=verb), + "parametric" => x -> rational_parametrization(x, info_level=verb,nr_thrds=nr_thrds) + ) + + return output_functions[output](AlgebraicSolving.Ideal(hW)) +end + +function computepolarphi(j::Int, V::AlgebraicSolving.Ideal, phi::MPolyRingElem, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) + # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj + @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" + R = parent(V) + n, hV = R.nvars, V.gens + c = n - dimV + + if j==0 + JW = transpose([ derivative(f, k) for k=1:n, f in hV ]) + sizeminors = c + else + JW = transpose([ derivative(f, k) for k=j:n, f in [hV;[phi]] ]) + sizeminors = c + 1 + dimproj - (j-1) + end + hW = vcat(hV, compute_minors(sizeminors, JW, R)) + output_functions = Dict( + "minors" => x -> x, + "groebner" => x -> groebner_basis(x, info_level=verb,nr_thrds=nr_thrds), + "real" => x -> real_solutions(x, info_level=verb,nr_thrds=nr_thrds), + "interval" => x -> real_solutions(x, interval=true, info_level=verb,nr_thrds=nr_thrds), "parametric" => x -> rational_parametrization(x, info_level=verb,nr_thrds=nr_thrds) ) From c7207d7b80b856ab168c1f05af48c87b5e236198 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 16 Sep 2024 13:08:42 +0200 Subject: [PATCH 052/180] export some functions --- src/connectivity/computeRM.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 65ab9c8..9e5ce48 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,7 +4,7 @@ #using AlgebraicSolving #using Nemo -export computeRM, computepolarproj +export computeRM, computepolarproj, computepolarphi # DEBUG export change_ringvar, compute_minors, detmpoly From 5ec905cee030171ce71918e180f9a391576013c3 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 16 Sep 2024 13:09:19 +0200 Subject: [PATCH 053/180] fix invert variable change --- src/connectivity/connectcurves.jl | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index ed4c30c..6b3a7fb 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -7,7 +7,7 @@ export compute_graph, connected_components, number_connected_components, group_b plot_graph, plot_graphs, plot_graph_comp, compute_param # DEBUG - export mmod_subresultants, subresultants, diff, diff_list + export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd include("tools.jl") include("subresultants.jl") @@ -329,7 +329,11 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t #plot_graph_comp(Vert,CEdg) # Operate inverse change of variable if necessary if !(generic) - Vert = [ changemat*v for v in Vert ] + for i in eachindex(Vert) + vx,vy = Vert[i] + vx,vy = Float64.(changemat*[vx, vy]) + Vert = [ (vx, vy) for v in Vert ] + end end if length(C)>0 From 7249b75487408ac1a602f1726c1fcd613d5c8d4a Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 16 Sep 2024 13:09:54 +0200 Subject: [PATCH 054/180] handle ideal parametrization --- src/connectivity/paramcurve.jl | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index 7ad5595..d2e5f6e 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -39,8 +39,11 @@ function deg_Alg(F, dim) return degree(r.elim) end +function compute_param(I::Ideal{P} where P<:MPolyRingElem; use_lfs = false, lfs = []) + return compute_param(I.gens, use_lfs = use_lfs, lfs = lfs) +end -function compute_param(F; use_lfs = false, lfs = []) +function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs = []) R = parent(first(F)) varias, N = gens(R), nvars(R) DEG = deg_Alg(F,1) From 7ea060ae9a40cf1b2d5a4c4e6f2ab76be115db00 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 16 Sep 2024 13:10:24 +0200 Subject: [PATCH 055/180] fix subplots and gui display --- src/connectivity/plots.jl | 12 ++++++++---- 1 file changed, 8 insertions(+), 4 deletions(-) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 495b51d..d3d8739 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,6 +1,6 @@ ## Plot functions -function plot_graph(G, Vemph::Vector{Vector{T}}=Vector{Vector{T}}(); color="red", width=3, vert=true, subplt=false) where T<:Any +function plot_graph(G, Vemph::Vector{Vector{T}} where T<:Any; color="red", width=3, vert=true, subplt=false) if !subplt println("Plotting the graph") plot(legend=false) @@ -17,7 +17,11 @@ function plot_graph(G, Vemph::Vector{Vector{T}}=Vector{Vector{T}}(); color="red" for i in 1:length(Vemph) scatter!( map(Float64, [V[j][1] for j in Vemph[i]]), map(Float64, [V[j][2] for j in Vemph[i]]), mc=color, m=:diamond) end - #gui() + subplt || gui() +end + +function plot_graph(G; color="red", width=3, vert=true, subplt=false) + plot_graph(G, Vector{Vector{QQMPolyRingElem}}(); color=color, width=width, vert=vert, subplt=subplt) end function plot_graph(G, Vemph::Vector{T} where T<:Any; color="red", width=3, vert=true, subplt=false) @@ -38,7 +42,7 @@ function plot_graphs(CG; width=3, vert=true, subplt=false) G, CVemph = length(CG[j][1])==2 ? CG[j] : (CG[j], Vector{Int}()) plot_graph(G, CVemph, color=col[j+2], subplt=true) end - gui() + subplt || gui() end function plot_graph_comp(G, Vemph=[]; width=3, vert=true) @@ -46,5 +50,5 @@ function plot_graph_comp(G, Vemph=[]; width=3, vert=true) plot(legend=false) CG = connected_components(G, Vemph) plot_graphs(CG, width=width, vert=vert, subplt=true) - gui() + subplt || gui() end \ No newline at end of file From 49d3293e497b4217204e5eb0c2b2b0033d8386d1 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 16 Sep 2024 13:12:14 +0200 Subject: [PATCH 056/180] begin interpolation subresultant + fact gcd --- src/connectivity/subresultants.jl | 49 ++++++++++++++++++++++++++++--- 1 file changed, 45 insertions(+), 4 deletions(-) diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index db56743..b03e647 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -49,7 +49,7 @@ function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingEl while true d = degree(A) e = degree(B) - println("($d,$e)") + #println("($d,$e)") if iszero(B) return S end @@ -86,7 +86,8 @@ function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingEl if e == 0 return S end - @time B = pseudorem(A,-B) / (s^delta * leading_coefficient(A)) + #@time + B = pseudorem(A,-B) / (s^delta * leading_coefficient(A)) A = copy(C) s = leading_coefficient(A) end @@ -137,13 +138,40 @@ function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false return newsr end +function interp_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, iv; list=false) where T <: RingElement + R = parent(P) + A = coefficient_ring(R) + iu = iv%2+1 + Vu, Vv = [:x, :y] + # Modern computer Algebra Th 6.51. + degs = degrees(P) + n, d = degs[iv], degs[iu] + degsmax = [ (2*n-1-2*k)*d for k=0:d-2 ] + Dmax = degsmax[end]>>1+1 + ## + xs = [ rand(A) for _=1:(degsmax[1]+1) ] + @time begin + Srev = [ subresultants(change_ringvar(evaluate(P,[iu],[xx]),[Vv]), change_ringvar(evaluate(Q,[iu],[xx]),[Vv])) for xx in xs ] + end + S,t = Nemo.polynomial_ring(A,Vu) + Sr = [ [ S(0) for _=1:i] for i=1:n-2 ] + for i = 1:n-2 + for j = 1:i + ys = [ A(Srev[l][i][j]) for l=eachindex(Srev) ] + Sr[i][j] = interpolate(S, xs, ys) + end + end + return Sr +end + function mmod_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false) where T <: RingElement prim = nextprime(2^(30)) L1, primprod = [], ZZ(1) i=1 while true - print("$i, ") if !all([ divides(ZZ(prim), evaluate(leading_coefficient(l, 2),[0,0]))[1] for l in [P,Q] ]) + print("$i: ") + @time begin L2 = deepcopy(L1) Pprim, Qprim = [ change_coefficient_ring(GF(prim), poly) for poly in [P,Q] ] sr = subresultants(Pprim, Qprim, idx)[1] @@ -153,10 +181,23 @@ function mmod_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list= end primprod *= ZZ(prim) L1 != L2 || break + i+=1 + end end prim = nextprime(prim+1) - i+=1 end println() return L1 end + +function fact_gcd(delta, Lsr, mult) + Lphi = [gcd(delta, Lsr[1])] + Ldelta = [delta/Lphi[1]] + i = 2 + while idegree(s[2])>0, Dict(enumerate(Ldelta))) +end \ No newline at end of file From 9e1a71605c3ca70bfb776ab6f5e0b1f6a2e97bd8 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 17 Sep 2024 20:32:11 +0200 Subject: [PATCH 057/180] fix problem arb, refine critical boxes + fix inverse coordinate change --- src/connectivity/arbtools.jl | 16 +++++-- src/connectivity/connectcurves.jl | 72 +++++++++++++++++++------------ 2 files changed, 57 insertions(+), 31 deletions(-) diff --git a/src/connectivity/arbtools.jl b/src/connectivity/arbtools.jl index 5fa4073..cafa221 100644 --- a/src/connectivity/arbtools.jl +++ b/src/connectivity/arbtools.jl @@ -9,12 +9,22 @@ function rat_to_Arb(x, prec) return ball(xm,xd) end -function evaluate_Arb(f, x, prec) +function evaluate_Arb(f, x::ArbFieldElem) if is_zero(f) - return ArbField(prec)(0) + return zero(parent(x)) else cf = coefficients_of_univariate(f) - return evalpoly(ArbField(prec)(x), cf) + return evalpoly(x, cf) + end +end + +function evaluate_Arb(f, g, x::ArbFieldElem) + @assert !is_zero(g) "Denominator must be non-zero" + if is_zero(f) + return zero(parent(x)) + else + cf, cg = coefficients_of_univariate.([f, g]) + return evalpoly(x, cf) / evalpoly(x, cg) end end diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 6b3a7fb..4920c38 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -4,10 +4,11 @@ #pythonplot() export compute_graph, connected_components, number_connected_components, group_by_component, merge_graphs, - plot_graph, plot_graphs, plot_graph_comp, compute_param + plot_graph, plot_graphs, plot_graph_comp, compute_param, Bresultant # DEBUG - export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd + export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, + rat_to_Arb, evaluate_Arb, evaluate_Arb_rat, int_coeffs include("tools.jl") include("subresultants.jl") @@ -16,8 +17,9 @@ include("boxes.jl") include("graph.jl") include("plots.jl") include("arbtools.jl") +include("src/resultant/bresultant.jl") -function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf=true) where (P <: MPolyRingElem) +function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) println("\n!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") println("!! Careful: this is a WIP version !!") println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") @@ -39,10 +41,11 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t println("\nCompute parametrization of critical pts...") - @time begin - sr = subresultants(f, derivative(f,y), 2, list=true) + @time sr = subresultants(change_coefficient_ring(ZZ,f), change_coefficient_ring(ZZ,derivative(f,y)), 2, list=true) + sr = [ [ change_coefficient_ring(QQ,p) for p in srp ] for srp in sr ] # Take sqfree factors of the resultant sqr = collect(factor_squarefree(sr[1][1])) + #println(sqr) # Keep only deg>0 factors filter!(t->t[2]>0, sqr) # Order by multiplicity @@ -52,37 +55,48 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t for r in sqr group_sqr[r[2]][1] *= r[1] end + #filter!(t->total_degree(t[1])>0, group_sqr) + iparam = Dict([1=>2, 2=>2, 3=>2]) # Construct the parametrization of the critical points - params = [ [ q[1], -sr[2][1], sr[2][2] ] for q in group_sqr ]; + params = [ [ q[1], -sr[iparam[q[2]]][1], (iparam[q[2]]-1)*sr[iparam[q[2]]][2] ] for q in group_sqr ]; + #println(params) append!(params, C) - end if arb - # TODO : check that no overlap between different isolations - println("\nIsolating critical values with precision ", precx,"..") - @time begin - xcrit = [ isolate(first(p), prec=precx) for p in params ] - for i in eachindex(xcrit) - for j in eachindex(xcrit[i]) - if xcrit[i][j][1]==xcrit[i][j][2] - xcrit[i][j] = [xcrit[i][j][1]-1//ZZ(1)<t[1]) for p in params ] + # TODO: parameter -I + LBcrit = [ sort(real_solutions(AlgebraicSolving.Ideal([p[1], p[3]*y-p[2]]), precision=precx, info_level=2,interval=true),by=t->t[1]) for p in params ] for i in eachindex(LBcrit) for j in eachindex(LBcrit[i]) for k in eachindex(LBcrit[i][j]) @@ -96,7 +110,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t xcritpermut = order_permut2d(xcrit); end end - + @time begin println("\nTest for identifying singular boxes");ts=time(); ######################################################## @@ -199,6 +213,8 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t end end + #return LnPCside + println("\nGraph computation") # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot # And even remove this fiber for the graph @@ -332,7 +348,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t for i in eachindex(Vert) vx,vy = Vert[i] vx,vy = Float64.(changemat*[vx, vy]) - Vert = [ (vx, vy) for v in Vert ] + Vert[i] = (vx, vy) end end From 4009bf087ec95dec74e1c1e8530ce6165ac7a2f0 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 17 Sep 2024 20:32:51 +0200 Subject: [PATCH 058/180] significant improvement of isolation + use default usolve --- src/connectivity/isolate.jl | 25 +++++++++++++++++-------- 1 file changed, 17 insertions(+), 8 deletions(-) diff --git a/src/connectivity/isolate.jl b/src/connectivity/isolate.jl index 4dce6ca..bd8cb25 100644 --- a/src/connectivity/isolate.jl +++ b/src/connectivity/isolate.jl @@ -1,21 +1,30 @@ include("src/usolve/usolve.jl") -function isolate(f; prec = 32, software="msolve") +function isolate(f; prec = 32, software="usolve") # Univariate isolation using usolve + if total_degree(f) == 0 + return [] + end @assert is_univariate(f) "Not univariate polynomial" if software == "usolve" - return getindex.(usolve(f, precision = prec, uspath="src/usolve/usolve"),2) + return usolve(f, precision = prec, uspath="AlgebraicSolving.jl/src/connectivity/src/usolve/usolve", output="inter") else - fvar = vars(f)[1] - sols = real_solutions(Ideal(vcat([f], [ t for t in gens(parent(f)) if t!=fvar ])), precision=prec, interval=true) - return getindex.(sols, var_index(fvar)) + #println(f) + sols = real_solutions(Ideal([change_ringvar(f)]), precision=prec, interval=true) + return getindex.(sols, 1) end end -function isolate_eval(f, ivar, val; prec=64) +function isolate_eval(f, ivar, val; prec=64, software="usolve") + #print(val) # univariate isolation of roots of a bivariate polynomial f # whose ivar-th variable is evaluated at val # uses msolve - sols = real_solutions(Ideal([f, gens(parent(f))[ivar] - val]), precision=prec, interval=true) - return [ s[ivar%2+1] for s in sols ] + fev = change_ringvar(evaluate(f, [ivar], [val])) + CD = lcm(map(denominator, collect(coefficients(fev)))) + fev *= CD + + return isolate(fev, prec=prec, software=software) + + end \ No newline at end of file From 71dd357287e4aab40c7f93f8163489dbe267dd03 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 17 Sep 2024 20:33:18 +0200 Subject: [PATCH 059/180] fix subplt --- src/connectivity/plots.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index d3d8739..5661d21 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -45,7 +45,7 @@ function plot_graphs(CG; width=3, vert=true, subplt=false) subplt || gui() end -function plot_graph_comp(G, Vemph=[]; width=3, vert=true) +function plot_graph_comp(G, Vemph=[]; width=3, vert=true, subplt=false) println("Plotting the graph") plot(legend=false) CG = connected_components(G, Vemph) From f723e201e1db174a1c7491fd158eadeea16bf791 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 17 Sep 2024 20:34:45 +0200 Subject: [PATCH 060/180] multiple bugfixes + multi threading on multi-modular subresultants --- src/connectivity/subresultants.jl | 61 ++++++++++++++++++++++--------- 1 file changed, 43 insertions(+), 18 deletions(-) diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index b03e647..c94cb42 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -164,29 +164,54 @@ function interp_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, iv; list return Sr end -function mmod_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false) where T <: RingElement - prim = nextprime(2^(30)) +function mmod_subresultants(P::QQMPolyRingElem, Q::QQMPolyRingElem, idx; list=false) + CD = [ lcm(map(denominator, collect(coefficients(f)))) for f in [P,Q] ] + PZ, QZ = change_coefficient_ring.(Ref(ZZ), [P,Q] .* CD) + #println(PZ,"\n",QZ) + sr = mmod_subresultants(PZ, QZ, idx; list=list) + return sr + if list + return [ change_coefficient_ring.(Ref(QQ),srp) for srp in sr ] + else + return change_coefficient_ring.(Ref(QQ),sr) + end +end + +function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=false) + prim = ZZ(2)<<(60) L1, primprod = [], ZZ(1) + lcpq = [ evaluate(leading_coefficient(l, 2),[0,0]) for l in [P,Q] ] i=1 + step=Threads.nthreads() while true - if !all([ divides(ZZ(prim), evaluate(leading_coefficient(l, 2),[0,0]))[1] for l in [P,Q] ]) - print("$i: ") - @time begin - L2 = deepcopy(L1) - Pprim, Qprim = [ change_coefficient_ring(GF(prim), poly) for poly in [P,Q] ] - sr = subresultants(Pprim, Qprim, idx)[1] - L1 = lift.(Ref(ZZ), coefficients_of_univariate(sr)) - if L2 != [] - L1 = [ crt(L2[i], primprod, L1[i], ZZ(prim), true) for i in 1:length(L2) ] - end - primprod *= ZZ(prim) - L1 != L2 || break - i+=1 + print("$i primes ") + LP, LQ, Lprim = MPolyRingElem[], MPolyRingElem[], ZZRingElem[] + while length(Lprim) < step + prim = next_prime(prim) + if !any(getindex.(divides.(Ref(prim), lcpq),1)) + Pprim, Qprim = [ change_coefficient_ring(residue_ring(ZZ, prim)[1], poly) for poly in [P,Q] ] + push!.([LP,LQ,Lprim], [Pprim,Qprim,prim]) end end - prim = nextprime(prim+1) + Ltemp = Vector{Vector{ZZRingElem}}(undef,step) + Threads.@threads for j in 1:step + sr = subresultants(LP[j], LQ[j], idx)[1] + Ltemp[j] = lift.(Ref(ZZ), coefficients_of_univariate(sr)) + end + if L1 != [] + push!.([Ltemp, Lprim], [L1, primprod]) + end + nLt = length(first(Ltemp)) + @assert all(length.(Ltemp) .== nLt) "Specialization problem" + L2 = deepcopy(L1) + L1 = [ crt(getindex.(Ltemp,i), Lprim, true) for i in 1:nLt ] + + L1 != L2 || break + #println(L1) + primprod = prod(Lprim) + i+=step + println(ndigits(primprod, 10), " digits") end - println() return L1 end @@ -199,5 +224,5 @@ function fact_gcd(delta, Lsr, mult) push!(Ldelta, Ldelta[i-1]/Lphi[i]) i+=1 end - return filter(s->degree(s[2])>0, Dict(enumerate(Ldelta))) + return filter(s->degree(s[2])>0, (enumerate(Ldelta))) end \ No newline at end of file From 4628d5cb32359ffeceea5b532d99da0f3fe421ab Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 17 Sep 2024 20:35:06 +0200 Subject: [PATCH 061/180] integer coefficient function tool --- src/connectivity/tools.jl | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index 4a067b6..fc4e1ce 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -32,4 +32,11 @@ function trimat_rand(A, n; up=true, range=-100:100) else return [ i==j ? one(A) : (i>j ? A(rand(range)) : zero(A)) for i in 1:3, j in 1:3 ] end -end \ No newline at end of file +end + +function int_coeffs(F::Vector{P} where P <: QQMPolyRingElem) + CD = [ lcm(map(denominator, collect(coefficients(f)))) for f in F ] + return (F .* CD) +end + +int_coeffs(f::QQMPolyRingElem) = int_coeffs([f])[1] \ No newline at end of file From a49b6c848d0b954fe1bf40b39c5517fcff0b8f4c Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 17 Sep 2024 20:35:19 +0200 Subject: [PATCH 062/180] use nextprime from Nemo --- src/imports.jl | 1 - 1 file changed, 1 deletion(-) diff --git a/src/imports.jl b/src/imports.jl index fd2ac19..80314a7 100644 --- a/src/imports.jl +++ b/src/imports.jl @@ -5,7 +5,6 @@ using Nemo using LinearAlgebra using StaticArrays using Plots, Colors -using Primes #pythonplot() import Plots: plot From d1700e14cc7b1cb4a1bbff2f8cec7c422534c752 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 24 Sep 2024 16:14:12 +0200 Subject: [PATCH 063/180] start managing conditionnal printing --- src/connectivity/connectcurves.jl | 29 +++++++++-------------------- 1 file changed, 9 insertions(+), 20 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 4920c38..63cc6a3 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -4,7 +4,7 @@ #pythonplot() export compute_graph, connected_components, number_connected_components, group_by_component, merge_graphs, - plot_graph, plot_graphs, plot_graph_comp, compute_param, Bresultant + plot_graph, plot_graphs, plot_graph_comp, compute_param, Bresultant, param_crit_split # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, @@ -20,28 +20,17 @@ include("arbtools.jl") include("src/resultant/bresultant.jl") function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - println("\n!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") - println("!! Careful: this is a WIP version !!") - println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!") - R = parent(f) x, y = gens(R) - if int_coeff - CD = lcm(map(denominator, collect(coefficients(f)))) - f *= CD - end - #println(f) - # Generic change of variables - changemat = [1 0; 0 1] - if !generic - changemat = trimat_rand(QQ, 2, range=-100:100) - end + # Pre-processing the input + f = int_coeff ? int_coeffs(f) : f + changemat = generic ? [1 0; 0 1] : trimat_rand(QQ, 2, range=-100:100) f = evaluate(f, collect(changemat*[x; y])); - + v > 1 && println(f) - println("\nCompute parametrization of critical pts...") - @time sr = subresultants(change_coefficient_ring(ZZ,f), change_coefficient_ring(ZZ,derivative(f,y)), 2, list=true) + v > 0 && println("\nCompute parametrization of critical pts...") + @iftime v > 0 sr = subresultants(change_coefficient_ring(ZZ,f), change_coefficient_ring(ZZ,derivative(f,y)), 2, list=true) sr = [ [ change_coefficient_ring(QQ,p) for p in srp ] for srp in sr ] # Take sqfree factors of the resultant sqr = collect(factor_squarefree(sr[1][1])) @@ -56,7 +45,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t group_sqr[r[2]][1] *= r[1] end #filter!(t->total_degree(t[1])>0, group_sqr) - iparam = Dict([1=>2, 2=>2, 3=>2]) + iparam = Dict([1=>2, 2=>2, 3=>2, 4=>2, 5=>2, 6=>3]) # Construct the parametrization of the critical points params = [ [ q[1], -sr[iparam[q[2]]][1], (iparam[q[2]]-1)*sr[iparam[q[2]]][2] ] for q in group_sqr ]; #println(params) @@ -96,7 +85,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t println("\nCompute critical boxes with msolve with precision ", precx,"..") @time begin # TODO: parameter -I - LBcrit = [ sort(real_solutions(AlgebraicSolving.Ideal([p[1], p[3]*y-p[2]]), precision=precx, info_level=2,interval=true),by=t->t[1]) for p in params ] + LBcrit = [ sort(real_solutions(AlgebraicSolving.Ideal([p[1], p[3]*y-p[2]]), precision=precx,interval=true),by=t->t[1]) for p in params ] for i in eachindex(LBcrit) for j in eachindex(LBcrit[i]) for k in eachindex(LBcrit[i][j]) From 3c53de2c8c14418bc6e767ef9574f3260c1fa016 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 24 Sep 2024 16:14:56 +0200 Subject: [PATCH 064/180] minor things --- src/connectivity/isolate.jl | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/src/connectivity/isolate.jl b/src/connectivity/isolate.jl index bd8cb25..08fd793 100644 --- a/src/connectivity/isolate.jl +++ b/src/connectivity/isolate.jl @@ -10,7 +10,7 @@ function isolate(f; prec = 32, software="usolve") return usolve(f, precision = prec, uspath="AlgebraicSolving.jl/src/connectivity/src/usolve/usolve", output="inter") else #println(f) - sols = real_solutions(Ideal([change_ringvar(f)]), precision=prec, interval=true) + sols = real_solutions(Ideal([change_ringvar(f)]), precision=prec, interval=true, info_level=0) return getindex.(sols, 1) end end @@ -20,6 +20,7 @@ function isolate_eval(f, ivar, val; prec=64, software="usolve") # univariate isolation of roots of a bivariate polynomial f # whose ivar-th variable is evaluated at val # uses msolve + #println(ivar,"\n", val,"\n", f) fev = change_ringvar(evaluate(f, [ivar], [val])) CD = lcm(map(denominator, collect(coefficients(fev)))) fev *= CD From 2aa49785b415a0578edf151e9c1095172a7a2c83 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 24 Sep 2024 16:15:58 +0200 Subject: [PATCH 065/180] generalize int_coeffs + macro for conditionnal timing --- src/connectivity/tools.jl | 14 ++++++++++++-- 1 file changed, 12 insertions(+), 2 deletions(-) diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index fc4e1ce..4f0aeea 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -34,9 +34,19 @@ function trimat_rand(A, n; up=true, range=-100:100) end end -function int_coeffs(F::Vector{P} where P <: QQMPolyRingElem) +function int_coeffs(F::Vector{P} where P <: Union{QQMPolyRingElem, QQPolyRingElem}) CD = [ lcm(map(denominator, collect(coefficients(f)))) for f in F ] return (F .* CD) end -int_coeffs(f::QQMPolyRingElem) = int_coeffs([f])[1] \ No newline at end of file +int_coeffs(f::Union{QQMPolyRingElem, QQPolyRingElem}) = int_coeffs([f])[1] + +macro iftime(v, ex) + quote + if $(esc(v)) + @time $(esc(ex)) + else + $(esc(ex)) + end + end +end \ No newline at end of file From 0e9f10d16733cab803b42fdd24626b3e6f02cc10 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 24 Sep 2024 16:17:28 +0200 Subject: [PATCH 066/180] subresultant interpolation + big changes in mmod_subresultant + fix fact_gcd + param_crit_split --- src/connectivity/subresultants.jl | 175 ++++++++++++++++++++++-------- 1 file changed, 131 insertions(+), 44 deletions(-) diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index c94cb42..dafef92 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -146,29 +146,33 @@ function interp_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, iv; list # Modern computer Algebra Th 6.51. degs = degrees(P) n, d = degs[iv], degs[iu] - degsmax = [ (2*n-1-2*k)*d for k=0:d-2 ] - Dmax = degsmax[end]>>1+1 + degsmax = [ (2*n-1-2*k)*d for k=0:d-1 ] + #Dmax = degsmax[end]>>1+1 ## - xs = [ rand(A) for _=1:(degsmax[1]+1) ] - @time begin - Srev = [ subresultants(change_ringvar(evaluate(P,[iu],[xx]),[Vv]), change_ringvar(evaluate(Q,[iu],[xx]),[Vv])) for xx in xs ] - end - S,t = Nemo.polynomial_ring(A,Vu) - Sr = [ [ S(0) for _=1:i] for i=1:n-2 ] - for i = 1:n-2 - for j = 1:i - ys = [ A(Srev[l][i][j]) for l=eachindex(Srev) ] - Sr[i][j] = interpolate(S, xs, ys) - end + B,t =polynomial_ring(A, Vv) + xs = A.(0:degsmax[1]) + Srev = Vector{Vector{typeof(t)}}(undef, length(xs)) + evPQ = [ [B(coefficients_of_univariate(evaluate(pq,[iu],[xx]))) for pq in [P,Q] ] for xx in xs] + Threads.@threads for i in 1:length(xs) + Srev[i] = subresultants(evPQ[i][1], evPQ[i][2]) + end + Srev = [ [ collect(coefficients(ss)) for ss in s] for s in Srev ] + C, = Nemo.polynomial_ring(A,Vu) + Sr = [ [ C(0) for _=1:i] for i=1:n ] + Lys = [ [ [ (try A(Srev[l][i][j]) catch; A(0) end) for l in eachindex(Srev) ] for j in 1:i ] for i in 1:n ] + for i = 1:n + # For the i-th subresultant + Threads.@threads for j in 1:i + # Each coefficient is interpolated + Sr[i][j] = interpolate(C, xs, Lys[i][j]) + end end return Sr end -function mmod_subresultants(P::QQMPolyRingElem, Q::QQMPolyRingElem, idx; list=false) - CD = [ lcm(map(denominator, collect(coefficients(f)))) for f in [P,Q] ] - PZ, QZ = change_coefficient_ring.(Ref(ZZ), [P,Q] .* CD) - #println(PZ,"\n",QZ) - sr = mmod_subresultants(PZ, QZ, idx; list=list) +function mmod_subresultants(P::QQMPolyRingElem, Q::QQMPolyRingElem, idx; list=false, n_threads=Threads.nthreads(), n_ssr=-1,v=0) + PZ, QZ = change_coefficient_ring.(Ref(ZZ), int_coeffs.([P,Q])) + sr = mmod_subresultants(PZ, QZ, idx; list=list, n_threads=n_threads, n_ssr=n_ssr, v=v) return sr if list return [ change_coefficient_ring.(Ref(QQ),srp) for srp in sr ] @@ -177,52 +181,135 @@ function mmod_subresultants(P::QQMPolyRingElem, Q::QQMPolyRingElem, idx; list=fa end end -function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=false) - prim = ZZ(2)<<(60) +function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=false, n_threads=Threads.nthreads(), n_ssr=0, v=0) + prim = ZZ(1)<<(61) L1, primprod = [], ZZ(1) + Ltemp = Vector{Vector{Vector{Vector{ZZRingElem}}}}(undef,n_threads+1) lcpq = [ evaluate(leading_coefficient(l, 2),[0,0]) for l in [P,Q] ] - i=1 - step=Threads.nthreads() + compt=n_threads while true - print("$i primes ") + v > 0 && print("$compt primes ") LP, LQ, Lprim = MPolyRingElem[], MPolyRingElem[], ZZRingElem[] - while length(Lprim) < step + while length(Lprim) < n_threads prim = next_prime(prim) - if !any(getindex.(divides.(Ref(prim), lcpq),1)) + if !any(getindex.(divides.(lcpq, Ref(prim)),1)) Pprim, Qprim = [ change_coefficient_ring(residue_ring(ZZ, prim)[1], poly) for poly in [P,Q] ] + #Pprim, Qprim = [ change_coefficient_ring(GF(prim), poly) for poly in [P,Q] ] push!.([LP,LQ,Lprim], [Pprim,Qprim,prim]) + else + return prim, lcpq end end - Ltemp = Vector{Vector{ZZRingElem}}(undef,step) - Threads.@threads for j in 1:step - sr = subresultants(LP[j], LQ[j], idx)[1] - Ltemp[j] = lift.(Ref(ZZ), coefficients_of_univariate(sr)) + Threads.@threads for j in 1:n_threads + sr = subresultants(LP[j], LQ[j], idx, list=true) + Ltemp[j] = [ [ lift.(Ref(ZZ), coefficients_of_univariate(srii)) for srii in sri ] for sri in sr ] + #sr = interp_subresultants(LP[j], LQ[j], idx)[1][1] + #Ltemp[j] = lift.(Ref(ZZ), coefficients(sr)) + end + + if n_ssr > 0 + for j in 1:n_threads + for k in eachindex(Ltemp[j]) + Ltemp[j][k] = Ltemp[j][k][end-min(k,n_ssr)+1:end] + end + end end + if L1 != [] - push!.([Ltemp, Lprim], [L1, primprod]) + Ltemp[n_threads+1] = copy(L1) + push!(Lprim, primprod) end - nLt = length(first(Ltemp)) - @assert all(length.(Ltemp) .== nLt) "Specialization problem" + #@assert allequal(length.(Ltemp[1:nthreads])) "Specialization problem" + Nssr = n_ssr<0 ? length(last(first(Ltemp))) : n_ssr + #println(Ltemp) L2 = deepcopy(L1) - L1 = [ crt(getindex.(Ltemp,i), Lprim, true) for i in 1:nLt ] - - L1 != L2 || break + L1 = Vector{Vector{Vector{ZZRingElem}}}(undef, length(first(Ltemp))) + Threads.@threads for i in eachindex(L1) + L1[i] = Vector{Vector{ZZRingElem}}(undef, min(i, Nssr)) + Threads.@threads for j in eachindex(L1[i]) + #println("($i,$j)") + L1[i][j] = Vector{ZZRingElem}(undef, length(Ltemp[1][i][j])) + Threads.@threads for k in eachindex(L1[i][j]) + cfs = [ try Ltemp[p][i][j][k] catch; ZZ(0) end for p in eachindex(Lprim) ] + L1[i][j][k] = crt(cfs, Lprim, true) + end + end + end #println(L1) primprod = prod(Lprim) - i+=step - println(ndigits(primprod, 10), " digits") + compt+=n_threads + v > 0 && println(ndigits(primprod, 10), " digits") + L1 != L2 || break + #compt < 20 || break end - return L1 + + uvar = parent(P).S[(idx+1)%2] + A, = polynomial_ring(ZZ, uvar) + sr = [ [ change_ringvar(A(ss),[uvar]) for ss in s ] for s in L1 ] + return sr end -function fact_gcd(delta, Lsr, mult) - Lphi = [gcd(delta, Lsr[1])] +function fact_gcd(delta::T, LP::Vector{T}) where (T <:PolyRingElem) + # delta : poly to factor w.r.t the polynomials in LP + Lphi = [gcd(delta, LP[1])] Ldelta = [delta/Lphi[1]] i = 2 - while i0 + push!(Lphi, gcd(Lphi[i-1], LP[i])) + push!(Ldelta, Lphi[i-1]/Lphi[i]) i+=1 end - return filter(s->degree(s[2])>0, (enumerate(Ldelta))) + return filter(s->degree(s[2])>0, Dict(enumerate(Ldelta))) +end + +function fact_gcd(delta::T, LP::Vector{T}) where (T <:MPolyRingElem) + @assert is_univariate(delta) && all(is_univariate.(LP)) "Not univariate polynomial" + R = parent(delta) + A, = polynomial_ring(coefficient_ring(R), first(R.S)) + out = fact_gcd(A(coefficients_of_univariate(delta)), A.(coefficients_of_univariate.(LP))) + return Dict([ (i, change_ringvar(f, [first(R.S)]) ) for (i,f) in out ]) +end + +function param_crit_split(f) + # Compute subresultants and factor the first subresultant + if total_degree(f) > 30 + @time sr = mmod_subresultants(f, derivative(f, 2), 2, list=true, n_ssr=2) + else + @time sr = subresultants(f, derivative(f, 2), 2, list=true) + end + sqr = collect(factor_squarefree(sr[1][1])) + + # Filter out factors with zero multiplicity and sort by multiplicity + sqr = sort!(filter(t -> t[2] > 0, sqr), by = t -> t[2]) + + # Group factors by multiplicity + sqrmult = unique(getindex.(sqr, 2)) + # TODO: no product, manage each subfactor + group_sqr = Dict(m => prod([r[1] for r in sqr if r[2] == m]) for m in sqrmult) + + # Initalization + singmult = filter(p->p*(p-1)<=sqrmult[end], 1:sqrmult[end]) + param_crit = Dict(p => Vector{MPolyRingElem}[] for p in singmult) + lsr = [ s[end] for s in sr[2:singmult[end]] ] + + # Critical points : multiplicity 1 in res + (1 in sqrmult) && push!(param_crit[1], [group_sqr[1], -sr[2][end-1], sr[2][end]]) + # Nodes : multiplicity 2 in res + (2 in sqrmult) && push!(param_crit[2], [group_sqr[2], -sr[2][end-1], sr[2][end]]) + # Other sing + filter!(m->!(m in [1,2]), sqrmult) + #TODO: simpler criterion for mult=p*(p-1)? + Ld = Vector{Dict{Int, MPolyRingElem}}(undef, length(sqrmult)) + #Threads.@threads + for k in eachindex(sqrmult) + Ld[k] = fact_gcd(group_sqr[sqrmult[k]], lsr) + end + for k in eachindex(Ld) + for (i, dji) in Ld[k] + push!(param_crit[i+1], [dji, -sr[i+1][end-1], i*sr[i+1][end]]) + end + end + + filter!(p->length(p[2])>0, param_crit) + return param_crit end \ No newline at end of file From 45e146f3d6eb515a49c7a19338e7f379a152e733 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 24 Sep 2024 17:13:37 +0200 Subject: [PATCH 067/180] no product of sqfree factors in param_crit_split --- src/connectivity/subresultants.jl | 30 ++++++++++++++++-------------- 1 file changed, 16 insertions(+), 14 deletions(-) diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index dafef92..a8cbe6e 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -281,35 +281,37 @@ function param_crit_split(f) # Filter out factors with zero multiplicity and sort by multiplicity sqr = sort!(filter(t -> t[2] > 0, sqr), by = t -> t[2]) - # Group factors by multiplicity sqrmult = unique(getindex.(sqr, 2)) - # TODO: no product, manage each subfactor - group_sqr = Dict(m => prod([r[1] for r in sqr if r[2] == m]) for m in sqrmult) - + group_sqr = Dict(m => [r[1] for r in sqr if r[2] == m] for m in sqrmult) + # Initalization - singmult = filter(p->p*(p-1)<=sqrmult[end], 1:sqrmult[end]) - param_crit = Dict(p => Vector{MPolyRingElem}[] for p in singmult) - lsr = [ s[end] for s in sr[2:singmult[end]] ] + singmult = filter(p->p*(p-1)<=sqrmult[end], 2:sqrmult[end]) + param_crit = Dict(p => [QQMPolyRingElem[], -sr[p][end-1], (p-1)*sr[p][end]] for p in singmult) + lsr = [ sr[p][end] for p in singmult ] # Critical points : multiplicity 1 in res - (1 in sqrmult) && push!(param_crit[1], [group_sqr[1], -sr[2][end-1], sr[2][end]]) + (1 in sqrmult) && push!(param_crit, 1=>[group_sqr[1], -sr[2][end-1], sr[2][end]]) # Nodes : multiplicity 2 in res - (2 in sqrmult) && push!(param_crit[2], [group_sqr[2], -sr[2][end-1], sr[2][end]]) + (2 in sqrmult) && append!(param_crit[2][1], group_sqr[2]) # Other sing filter!(m->!(m in [1,2]), sqrmult) #TODO: simpler criterion for mult=p*(p-1)? - Ld = Vector{Dict{Int, MPolyRingElem}}(undef, length(sqrmult)) + Ld = Vector{Vector{Dict{Int, QQMPolyRingElem}}}(undef, length(sqrmult)) #Threads.@threads for k in eachindex(sqrmult) - Ld[k] = fact_gcd(group_sqr[sqrmult[k]], lsr) + for l in eachindex(group_sqr[sqrmult[k]]) + Ld[k][l] = fact_gcd(group_sqr[sqrmult[k]][l], lsr) + end end for k in eachindex(Ld) - for (i, dji) in Ld[k] - push!(param_crit[i+1], [dji, -sr[i+1][end-1], i*sr[i+1][end]]) + for l in eachindex(Ld[k]) + for (i, dji) in Ld[k][l] + push!(param_crit[i+1][1], dji) + end end end - filter!(p->length(p[2])>0, param_crit) + filter!(p->length(p[2][1])>0, param_crit) return param_crit end \ No newline at end of file From 325be8945b0d02c802032cd7839ebab7864fabae Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 24 Sep 2024 17:57:48 +0200 Subject: [PATCH 068/180] maj connect curve with paramcritsplit BUT no refinements yet --- src/connectivity/connectcurves.jl | 85 ++++++++++++------------------- src/connectivity/isolate.jl | 4 +- 2 files changed, 34 insertions(+), 55 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 63cc6a3..2186fa6 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -30,35 +30,18 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t v > 1 && println(f) v > 0 && println("\nCompute parametrization of critical pts...") - @iftime v > 0 sr = subresultants(change_coefficient_ring(ZZ,f), change_coefficient_ring(ZZ,derivative(f,y)), 2, list=true) - sr = [ [ change_coefficient_ring(QQ,p) for p in srp ] for srp in sr ] - # Take sqfree factors of the resultant - sqr = collect(factor_squarefree(sr[1][1])) - #println(sqr) - # Keep only deg>0 factors - filter!(t->t[2]>0, sqr) - # Order by multiplicity - sort!(sqr, by=t->t[2]) - # Group by multiplicity - group_sqr = [ [R(1),i] for i in 1:sqr[end][2] ] - for r in sqr - group_sqr[r[2]][1] *= r[1] - end - #filter!(t->total_degree(t[1])>0, group_sqr) - iparam = Dict([1=>2, 2=>2, 3=>2, 4=>2, 5=>2, 6=>3]) - # Construct the parametrization of the critical points - params = [ [ q[1], -sr[iparam[q[2]]][1], (iparam[q[2]]-1)*sr[iparam[q[2]]][2] ] for q in group_sqr ]; + @iftime (v > 0) params = param_crit_split(f) #println(params) - append!(params, C) - + #append!(params, C) if arb - while true - try + compt = 1 + while compt < 5 + #try # TODO : check that no overlap between different isolations println("\nIsolating critical values with precision ", precx,"..") @time begin - xcrit = [ isolate(first(p), prec=precx) for p in params ] - for i in eachindex(xcrit) + xcrit = Dict(p[1]=> reduce(vcat, [isolate(pp, prec=precx) for pp in p[2][1]]) for p in params) + for i in keys(xcrit) for j in eachindex(xcrit[i]) if xcrit[i][j][1]==xcrit[i][j][2] xcrit[i][j] = [xcrit[i][j][1]-1//ZZ(1)< [[xc, evaluate_Arb(params[i][2], params[i][3], rat_to_Arb(xc, precArb))] for xc in xcrit[i]] for i in keys(xcrit)) + LBcrit =Dict( i=> [[ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for (i, pcrit) in Pcrit) end - catch - precx *= 2 - println("Refine x-precision to $precx") - else + #catch + # precx *= 2 + # println("Refine x-precision to $precx") + # compt += 1 + #else break - end + #end end else println("\nCompute critical boxes with msolve with precision ", precx,"..") @@ -104,26 +88,21 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t println("\nTest for identifying singular boxes");ts=time(); ######################################################## # For each mult of sing pts (keys) give the corresponding factors of the resultant (values) - ### DEBUG: for now, only nodes for singular points, hardcode below ### - mult_to_factor = Dict(2=>2:length(group_sqr)) ######################################################### - mults = keys(mult_to_factor) - Lfyk = diff_list(f, 2, maximum(mults)) - for m in mults - for k in mult_to_factor[m] - while true - flag = false - for j in eachindex(LBcrit[k]) - pcrit = [ rat_to_Arb(c, precx) for c in LBcrit[k][j] ] - if contains_zero(evaluate(Lfyk[m+1], pcrit)) - println("Refine singular boxes of multiplicity ", k) - # TODO refine_boxes(params[k], LBcrit[k]) - #flag = true - break - end + Lfyk = diff_list(f, 2, maximum(keys(LBcrit))) + for m in keys(LBcrit) + while true + flag = false + for j in eachindex(LBcrit[m]) + pcrit = [ rat_to_Arb(c, precx) for c in LBcrit[m][j] ] + if contains_zero(evaluate(Lfyk[m+1], pcrit)) + println("Refine singular boxes of multiplicity ", m) + # TODO refine_boxes(params[k], LBcrit[k]) + #flag = true + break end - flag || break end + flag || break end end end @@ -277,7 +256,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t # The critical point ########################## # If we are dealing with a node - if length(group_sqr)>1 && i == 2 + if i == 2 # if it is an isolated point if isempty(nI[1]) && isempty(nI[2]) push!(Lapp[1], (i,j)) @@ -309,10 +288,10 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t for k in nI[2] push!(Edg, (length(Vert), Corr[i][j][3][k])) end - if i > length(params)-length(C) - # If this is a control point - push!(Vcon[i + length(C) - length(params)], length(Vert)) - end + #if i > length(params)-length(C) + # # If this is a control point + # push!(Vcon[i + length(C) - length(params)], length(Vert)) + #end end ########################### # Above the critical point diff --git a/src/connectivity/isolate.jl b/src/connectivity/isolate.jl index 08fd793..9540765 100644 --- a/src/connectivity/isolate.jl +++ b/src/connectivity/isolate.jl @@ -1,6 +1,6 @@ include("src/usolve/usolve.jl") -function isolate(f; prec = 32, software="usolve") +function isolate(f; prec = 32, software="msolve") # Univariate isolation using usolve if total_degree(f) == 0 return [] @@ -15,7 +15,7 @@ function isolate(f; prec = 32, software="usolve") end end -function isolate_eval(f, ivar, val; prec=64, software="usolve") +function isolate_eval(f, ivar, val; prec=64, software="msolve") #print(val) # univariate isolation of roots of a bivariate polynomial f # whose ivar-th variable is evaluated at val From 2067d20683d09e0ef6f59c31ac8e159e2a98f635 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Wed, 25 Sep 2024 18:07:43 +0200 Subject: [PATCH 069/180] fix infinite refinement --- src/connectivity/connectcurves.jl | 17 ++++++++++------- 1 file changed, 10 insertions(+), 7 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 2186fa6..5dd04c2 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -36,7 +36,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t if arb compt = 1 while compt < 5 - #try + try # TODO : check that no overlap between different isolations println("\nIsolating critical values with precision ", precx,"..") @time begin @@ -57,13 +57,16 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t Pcrit = Dict( i => [[xc, evaluate_Arb(params[i][2], params[i][3], rat_to_Arb(xc, precArb))] for xc in xcrit[i]] for i in keys(xcrit)) LBcrit =Dict( i=> [[ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for (i, pcrit) in Pcrit) end - #catch - # precx *= 2 - # println("Refine x-precision to $precx") - # compt += 1 - #else + catch + precx *= 2 + println("Refine x-precision to $precx") + compt += 1 + else break - #end + end + end + if compt == 5 + error("Problem in isolating critical boxes") end else println("\nCompute critical boxes with msolve with precision ", precx,"..") From ac9dc10f826af56ee0ea422434d1f3077c2f00d2 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 00:36:41 +0200 Subject: [PATCH 070/180] refine boxes for many parametrizations --- src/connectivity/boxes.jl | 11 ++++++++++- 1 file changed, 10 insertions(+), 1 deletion(-) diff --git a/src/connectivity/boxes.jl b/src/connectivity/boxes.jl index 2b09789..9012c4e 100644 --- a/src/connectivity/boxes.jl +++ b/src/connectivity/boxes.jl @@ -50,7 +50,7 @@ function intersect_box(f, B; prec=100) return L end -function refine_xboxes(f, LB, prec) +function refine_xboxes(f::T where T<:Union{PolyRingElem, MPolyRingElem}, LB, prec) # Refine LB along first axis, being roots of f xnew = isolate(f, prec=prec) for i in eachindex(LB) @@ -58,6 +58,15 @@ function refine_xboxes(f, LB, prec) end end +function refine_xboxes(F::Vector{T} where T<:Union{PolyRingElem, MPolyRingElem}, LB, prec) + # Refine LB along first axis, being roots of the polynomial in F + # The order in F is assumed to match the one in LB + xnew = reduce(vcat, [isolate(f, prec=prec) for f in F]) + for i in eachindex(LB) + LB[i] = [ xnew[i], LB[i][2] ] + end +end + function refine_ith_xboxes(f, LB, i, prec) # Refine only LB[i] along first axis, being i-th root of f xnew = isolate(f, prec=prec) From bf4ab72905230ee9eeff87452958ea395441ceca Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 00:37:17 +0200 Subject: [PATCH 071/180] verbose usolve --- src/connectivity/isolate.jl | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/src/connectivity/isolate.jl b/src/connectivity/isolate.jl index 9540765..4b1f060 100644 --- a/src/connectivity/isolate.jl +++ b/src/connectivity/isolate.jl @@ -7,7 +7,7 @@ function isolate(f; prec = 32, software="msolve") end @assert is_univariate(f) "Not univariate polynomial" if software == "usolve" - return usolve(f, precision = prec, uspath="AlgebraicSolving.jl/src/connectivity/src/usolve/usolve", output="inter") + return usolve(f, precision = prec, uspath="AlgebraicSolving.jl/src/connectivity/src/usolve/usolve", output="inter", v=2) else #println(f) sols = real_solutions(Ideal([change_ringvar(f)]), precision=prec, interval=true, info_level=0) @@ -15,7 +15,7 @@ function isolate(f; prec = 32, software="msolve") end end -function isolate_eval(f, ivar, val; prec=64, software="msolve") +function isolate_eval(f, ivar, val; prec=64, software="usolve") #print(val) # univariate isolation of roots of a bivariate polynomial f # whose ivar-th variable is evaluated at val @@ -27,5 +27,4 @@ function isolate_eval(f, ivar, val; prec=64, software="msolve") return isolate(fev, prec=prec, software=software) - end \ No newline at end of file From 37c968fabe279f87681779043f06a86705ebea1b Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 00:38:04 +0200 Subject: [PATCH 072/180] trailing spaces --- src/connectivity/paramcurve.jl | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index d2e5f6e..44994a5 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -75,8 +75,8 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs index_permut = Dict((v, i) for (i, v) in enumerate(newvarias_S)) permut_varias = [ index_permut[v] for v in Rold.S ] - # TODO: permut exponents and use polynomial constructor - F = [ evaluate(f, [ varias[permut_varias[i]] for i in 1:Nold ]) for f in F ] + # TODO: permut exponents and use polynomial constructor + F = [ evaluate(f, [ varias[permut_varias[i]] for i in 1:Nold ]) for f in F ] if nb_lf > 0 lf_cfs = [ rand(ZZ(-100):ZZ(100), N) for _ in 1:nb_lf] @@ -96,7 +96,7 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs R, varias = polynomial_ring(base_ring(Rold), newvarias_S) N = length(varias) - F = [ evaluate(f, [ varias[i] for i in 1:Nold ]) for f in F ] + F = [ evaluate(f, [ varias[i] for i in 1:Nold ]) for f in F ] lf_cfs = vcat(lfs, [ rand(ZZ(-100):ZZ(100), N) for _ in 1:2-length(lfs)]) append!(F, [ transpose(lf)*varias for lf in lf_cfs ]) end @@ -134,7 +134,7 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs end end - # Interpolate each coefficient of each poly in the param + # Interpolate each coefficient of each poly in the param println("Interpolation step...") @time begin POLY_PARAM = Vector{QQMPolyRingElem}(undef,N) @@ -151,8 +151,8 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs C = [ collect(coefficients(c)) for c in COEFFS ] POL_term = [C[i][j]*x^(i-1)*y^(j-1) for i in 1:length(C) for j in 1:length(C[i])] - POL = length(POL_term) > 0 ? sum(POL_term) : T(0) - + POL = length(POL_term) > 0 ? sum(POL_term) : T(0) + POLY_PARAM[count] = POL end end @@ -173,7 +173,7 @@ end #= # Tests R, (a,b,c) = polynomial_ring(QQ, [:a,:b,:c]) -F = [-62*a^2-24*a*b+83*a*c-46*b^2-45*b*c+16*c^2+13*a-65*b-84*c-19, +F = [-62*a^2-24*a*b+83*a*c-46*b^2-45*b*c+16*c^2+13*a-65*b-84*c-19, 92*a^2-a*b+39*a*c-16*b^2+61*b*c+78*c^2+17*a+49*b-97*c-56 ] From ebce03052f3de642126760eae491ace324fdd4ae Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 00:38:22 +0200 Subject: [PATCH 073/180] Vertices to subplots Transmit vertices to the subplots --- src/connectivity/plots.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 5661d21..c6153c0 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -40,7 +40,7 @@ function plot_graphs(CG; width=3, vert=true, subplt=false) col = distinguishable_colors(length(CG)+2) for j in eachindex(CG) G, CVemph = length(CG[j][1])==2 ? CG[j] : (CG[j], Vector{Int}()) - plot_graph(G, CVemph, color=col[j+2], subplt=true) + plot_graph(G, CVemph, color=col[j+2], vert=vert, subplt=true) end subplt || gui() end @@ -50,5 +50,5 @@ function plot_graph_comp(G, Vemph=[]; width=3, vert=true, subplt=false) plot(legend=false) CG = connected_components(G, Vemph) plot_graphs(CG, width=width, vert=vert, subplt=true) - subplt || gui() + subplt || gui()#savefig("/tmp/test.html") end \ No newline at end of file From 65b0b24379530a7cfb61572a39c8375e62399464 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 00:39:43 +0200 Subject: [PATCH 074/180] Add zero coefficients when not generic subresultant --- src/connectivity/subresultants.jl | 60 +++++++++++++++++++------------ 1 file changed, 38 insertions(+), 22 deletions(-) diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index a8cbe6e..0e7742f 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -15,14 +15,14 @@ function add_ind(L,i,x) end function parray_asvar(LP, idx) - # takes the above representation of a poly P + # takes the above representation of a poly P # and outputs a representation of P seen as a univariate poly in the i-th variable deg = sort(LP[2], by= x->x[idx])[end][idx] NLP = [ [[],[]] for _ in 1:deg+1 ] for i in eachindex(LP[2]) di = LP[2][i][idx]+1 push!(NLP[di][1], LP[1][i]) - push!(NLP[di][2], rem_ind(LP[2][i], idx)) + push!(NLP[di][2], rem_ind(LP[2][i], idx)) end return NLP end @@ -86,7 +86,7 @@ function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingEl if e == 0 return S end - #@time + #@time B = pseudorem(A,-B) / (s^delta * leading_coefficient(A)) A = copy(C) s = leading_coefficient(A) @@ -109,13 +109,17 @@ function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false Lsr = [ [collect(coefficients(csr)) for csr in coefficients(sr)] for sr in sr] newsr = [] if list - for lsr in Lsr + for (k,lsr) in enumerate(Lsr) mlsr = [] - for i in 1:length(lsr) + for i in 1:k#length(lsr) tmp = [[],[]] - for j in 1:length(lsr[i]) - push!(tmp[1], lsr[i][j]) - push!(tmp[2],add_ind([j-1],idx, 0)) + if i in eachindex(lsr) + for j in 1:length(lsr[i]) + push!(tmp[1], lsr[i][j]) + push!(tmp[2],add_ind([j-1],idx, 0)) + end + else + tmp = [[P|>parent|>base_ring|>zero], [[0,0]]] end push!(mlsr, tmp) end @@ -125,7 +129,7 @@ function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false else for lsr in Lsr mlsr = [[],[]] - for i in 1:length(lsr) + for i in 1:i#length(lsr) for j in 1:length(lsr[i]) push!(mlsr[1], lsr[i][j]) push!(mlsr[2],add_ind([j-1],idx, i-1)) @@ -146,7 +150,7 @@ function interp_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, iv; list # Modern computer Algebra Th 6.51. degs = degrees(P) n, d = degs[iv], degs[iu] - degsmax = [ (2*n-1-2*k)*d for k=0:d-1 ] + degsmax = [ (2*n-1-2*k)*d for k=0:d-1 ] #Dmax = degsmax[end]>>1+1 ## B,t =polynomial_ring(A, Vv) @@ -192,7 +196,7 @@ function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=fa LP, LQ, Lprim = MPolyRingElem[], MPolyRingElem[], ZZRingElem[] while length(Lprim) < n_threads prim = next_prime(prim) - if !any(getindex.(divides.(lcpq, Ref(prim)),1)) + if !any(getindex.(divides.(lcpq, Ref(prim)),1)) Pprim, Qprim = [ change_coefficient_ring(residue_ring(ZZ, prim)[1], poly) for poly in [P,Q] ] #Pprim, Qprim = [ change_coefficient_ring(GF(prim), poly) for poly in [P,Q] ] push!.([LP,LQ,Lprim], [Pprim,Qprim,prim]) @@ -214,13 +218,13 @@ function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=fa end end end - + if L1 != [] Ltemp[n_threads+1] = copy(L1) push!(Lprim, primprod) end - #@assert allequal(length.(Ltemp[1:nthreads])) "Specialization problem" - Nssr = n_ssr<0 ? length(last(first(Ltemp))) : n_ssr + #@assert allequal(length.(Ltemp[1:nthreads])) "Specialization problem" + Nssr = n_ssr<0 ? length(last(first(Ltemp))) : n_ssr #println(Ltemp) L2 = deepcopy(L1) L1 = Vector{Vector{Vector{ZZRingElem}}}(undef, length(first(Ltemp))) @@ -255,6 +259,7 @@ function fact_gcd(delta::T, LP::Vector{T}) where (T <:PolyRingElem) Ldelta = [delta/Lphi[1]] i = 2 while degree(Lphi[end])>0 + #println.([Lphi,Ldelta,""]) push!(Lphi, gcd(Lphi[i-1], LP[i])) push!(Ldelta, Lphi[i-1]/Lphi[i]) i+=1 @@ -273,10 +278,15 @@ end function param_crit_split(f) # Compute subresultants and factor the first subresultant if total_degree(f) > 30 - @time sr = mmod_subresultants(f, derivative(f, 2), 2, list=true, n_ssr=2) + sr = mmod_subresultants(f, derivative(f, 2), 2, list=true, n_ssr=2) else - @time sr = subresultants(f, derivative(f, 2), 2, list=true) + sr = subresultants(f, derivative(f, 2), 2, list=true) + end + + if total_degree(sr[1][1]) == 0 + return Dict() end + sqr = collect(factor_squarefree(sr[1][1])) # Filter out factors with zero multiplicity and sort by multiplicity @@ -284,22 +294,29 @@ function param_crit_split(f) # Group factors by multiplicity sqrmult = unique(getindex.(sqr, 2)) group_sqr = Dict(m => [r[1] for r in sqr if r[2] == m] for m in sqrmult) - + #println(group_sqr) + # Initalization singmult = filter(p->p*(p-1)<=sqrmult[end], 2:sqrmult[end]) param_crit = Dict(p => [QQMPolyRingElem[], -sr[p][end-1], (p-1)*sr[p][end]] for p in singmult) - lsr = [ sr[p][end] for p in singmult ] # Critical points : multiplicity 1 in res (1 in sqrmult) && push!(param_crit, 1=>[group_sqr[1], -sr[2][end-1], sr[2][end]]) + + if length(singmult) == 0 + return filter(p->length(p[2][1])>0, param_crit) + end + # Nodes : multiplicity 2 in res - (2 in sqrmult) && append!(param_crit[2][1], group_sqr[2]) + (2 in sqrmult) && push!(param_crit, -1=>[group_sqr[2], -sr[2][end-1], sr[2][end]]) # Other sing filter!(m->!(m in [1,2]), sqrmult) #TODO: simpler criterion for mult=p*(p-1)? + lsr = [ try sr[p][end] catch; one(parent(f)) end for p in 2:(singmult[end]+1) ] Ld = Vector{Vector{Dict{Int, QQMPolyRingElem}}}(undef, length(sqrmult)) - #Threads.@threads + #Threads.@threads for k in eachindex(sqrmult) + Ld[k] = Vector{Dict{Int, QQMPolyRingElem}}(undef,length(group_sqr[sqrmult[k]])) for l in eachindex(group_sqr[sqrmult[k]]) Ld[k][l] = fact_gcd(group_sqr[sqrmult[k]][l], lsr) end @@ -312,6 +329,5 @@ function param_crit_split(f) end end - filter!(p->length(p[2][1])>0, param_crit) - return param_crit + return filter(p->length(p[2][1])>0, param_crit) end \ No newline at end of file From 81c3ea0d94f324f583c57d0304d7a6cbe21e9635 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 00:40:26 +0200 Subject: [PATCH 075/180] Update with new dict data structure; allow having diverse mult; node are -1 --- src/connectivity/connectcurves.jl | 120 ++++++++++++++++-------------- 1 file changed, 66 insertions(+), 54 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 5dd04c2..c7e67a6 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -41,7 +41,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t println("\nIsolating critical values with precision ", precx,"..") @time begin xcrit = Dict(p[1]=> reduce(vcat, [isolate(pp, prec=precx) for pp in p[2][1]]) for p in params) - for i in keys(xcrit) + for i in eachindex(xcrit) for j in eachindex(xcrit[i]) if xcrit[i][j][1]==xcrit[i][j][2] xcrit[i][j] = [xcrit[i][j][1]-1//ZZ(1)< [[xc, evaluate_Arb(params[i][2], params[i][3], rat_to_Arb(xc, precArb))] for xc in xcrit[i]] for i in keys(xcrit)) + Pcrit = Dict( i => [[xc, evaluate_Arb(params[i][2], params[i][3], rat_to_Arb(xc, precArb))] for xc in xcrit[i]] for i in eachindex(xcrit)) LBcrit =Dict( i=> [[ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for (i, pcrit) in Pcrit) + for i in eachindex(LBcrit) + for j in eachindex(LBcrit[i]) + if LBcrit[i][j][2][1]==LBcrit[i][j][2][2] + LBcrit[i][j][2] = [LBcrit[i][j][2][1]-1//ZZ(1)<t[1]) for p in params ] + LBcrit = Dict(p[1]=>reduce(vcat,[ sort(real_solutions(AlgebraicSolving.Ideal([pp, p[2][3]*y-p[2][2]]), precision=precx,interval=true),by=t->t[1]) for pp in p[2][1] ]) for p in params) for i in eachindex(LBcrit) for j in eachindex(LBcrit[i]) for k in eachindex(LBcrit[i][j]) @@ -82,22 +89,24 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t end end end - xcrit = [ [ B[1] for B in lbcrit ] for lbcrit in LBcrit ] + xcrit = Dict(lbcrit[1]=>[ B[1] for B in lbcrit[2] ] for lbcrit in LBcrit) xcritpermut = order_permut2d(xcrit); end end - + @time begin println("\nTest for identifying singular boxes");ts=time(); ######################################################## # For each mult of sing pts (keys) give the corresponding factors of the resultant (values) ######################################################### - Lfyk = diff_list(f, 2, maximum(keys(LBcrit))) - for m in keys(LBcrit) + Lfyk = diff_list(f, 2, max(maximum(eachindex(LBcrit)),2)) + for ind in eachindex(LBcrit) + ind!=1 || continue # extreme pts + m = ind==-1 ? 2 : ind # nodes have mult 2 while true flag = false - for j in eachindex(LBcrit[m]) - pcrit = [ rat_to_Arb(c, precx) for c in LBcrit[m][j] ] + for j in eachindex(LBcrit[ind]) + pcrit = [ rat_to_Arb(c, precx) for c in LBcrit[ind][j] ] if contains_zero(evaluate(Lfyk[m+1], pcrit)) println("Refine singular boxes of multiplicity ", m) # TODO refine_boxes(params[k], LBcrit[k]) @@ -117,20 +126,21 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t # and change into npcside = [0,0,2,2] ## TODO : Refine only the intervals that need to be refined println("\nCompute intersections with critical boxes..") - LPCside = Array{Any}(undef,length(LBcrit)) - ndig = maximum([Int(floor(log10(max(1,length(LB))))) for LB in LBcrit]) + LPCside = Dict{Int,Any}() + ndig = maximum([ndigits(length(LBcrit[i])) for i in eachindex(LBcrit)]) for i in eachindex(LBcrit) - ndigi = Int(floor(log10(max(1,length(LBcrit[i]))))) - Ptype = i > length(LBcrit) - length(C) ? "Pcon" : "mult" LPCside[i] = Array{Any}(undef, length(LBcrit[i])) - precxtmp = precx + ndigi = Int(floor(log10(max(1,length(LBcrit[i]))))) + Ptype = (i > length(LBcrit)-length(C)) ? "Pcon" : "mult" + precxtmp = precx while true flag = false for j in eachindex(LBcrit[i]) print("$Ptype=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp) npcside = [length(n) for (I, n) in pcside] - if (i == 1 && sum(npcside) > 2) || (i > 1 && sum(npcside[1:2]) != 0) + #println("($i, $j): $npcside") + if (i == 1 && sum(npcside) > 2) || (i != 1 && sum(npcside[1:2]) != 0) precxtmp *= 2 println("\nRefine boxes along x-axis to precision ", precxtmp) refine_xboxes(params[i][1], LBcrit[i], precxtmp) @@ -143,42 +153,44 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t end println("") end - LnPCside = [ [[length(indI) for (L, indI) in PB] for PB in lpcside] for lpcside in LPCside ] + LnPCside = Dict(i => [[length(indI) for (L, indI) in PB] for PB in LPCside[i]] for i in eachindex(LPCside)) # Update extreme boxes - for j in eachindex(LBcrit[1]) - # If the curve does not intersect the box only on vertical sides - if !(LnPCside[1][j][1:2] == [0, 0]) - PCside, nPCside = LPCside[1][j], LnPCside[1][j] - I = [ l[1] for l in PCside[3:end] ] - nI = [ l[2] for l in PCside[3:end] ] - # Locate the orientation of the extreme point - # s is the index on the side where there are more branches - # s=1: left; s=2: right - s = argmax([length(I[1]), length(I[2])]) - # Ordinate range of the extreme point - ycrit = LBcrit[1][j][2] - # If it intersects on the bottom side - if nPCside[1] == 1 - # yinf: the intersection with the vertical side just below the extreme point - yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[1]]) - # We vertically enlarge the box until it intersects on the horizontal side - push!(LPCside[1][j][s + 2][2], yinf) - LPCside[1][j][1][2] = [] - # We update the intersection numbers - LnPCside[1][j][s + 2] += 1 - LnPCside[1][j][1] = 0 - end - # If it intersects on the top side - if nPCside[2] == 1 - # ymax: the intersection with the vertical side just above the extreme point - ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[2]]) - # We vertically enlarge the box until it intersects on the horizontal side - push!(LPCside[1][j][s + 2][2], ymax) - LPCside[1][j][2][2] = [] - # We update the intersection numbers - LnPCside[1][j][s + 2] += 1 - LnPCside[1][j][2] = 0 + if haskey(LBcrit, 1) + for j in eachindex(LBcrit[1]) + # If the curve does not intersect the box only on vertical sides + if !(LnPCside[1][j][1:2] == [0, 0]) + PCside, nPCside = LPCside[1][j], LnPCside[1][j] + I = [ l[1] for l in PCside[3:end] ] + nI = [ l[2] for l in PCside[3:end] ] + # Locate the orientation of the extreme point + # s is the index on the side where there are more branches + # s=1: left; s=2: right + s = argmax([length(I[1]), length(I[2])]) + # Ordinate range of the extreme point + ycrit = LBcrit[1][j][2] + # If it intersects on the bottom side + if nPCside[1] == 1 + # yinf: the intersection with the vertical side just below the extreme point + yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[1]]) + # We vertically enlarge the box until it intersects on the horizontal side + push!(LPCside[1][j][s + 2][2], yinf) + LPCside[1][j][1][2] = [] + # We update the intersection numbers + LnPCside[1][j][s + 2] += 1 + LnPCside[1][j][1] = 0 + end + # If it intersects on the top side + if nPCside[2] == 1 + # ymax: the intersection with the vertical side just above the extreme point + ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[2]]) + # We vertically enlarge the box until it intersects on the horizontal side + push!(LPCside[1][j][s + 2][2], ymax) + LPCside[1][j][2][2] = [] + # We update the intersection numbers + LnPCside[1][j][s + 2] += 1 + LnPCside[1][j][2] = 0 + end end end end @@ -193,13 +205,13 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t Vert = Vector{Tuple{typeout, typeout}}() Edg = Vector{Tuple{Int, Int}}() - Corr = [[[[], [[], [], []], []] for j in xcrit[i] ] for i in eachindex(xcrit) ] + Corr = Dict( m => [[[], [[], [], []], []] for j in xcrit[m] ] for m in eachindex(xcrit)) Viso = [] Vcon = [ [] for _ in 1:length(C) ] Lapp = [[],[]] - for ind in 1:length(xcritpermut) + for ind in eachindex(xcritpermut) i, j = xcritpermut[ind] if ind > 1 @@ -259,7 +271,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t # The critical point ########################## # If we are dealing with a node - if i == 2 + if i == -1 # if it is an isolated point if isempty(nI[1]) && isempty(nI[2]) push!(Lapp[1], (i,j)) @@ -318,7 +330,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t if !(generic) for i in eachindex(Vert) vx,vy = Vert[i] - vx,vy = Float64.(changemat*[vx, vy]) + vx,vy = fct.(changemat*[vx, vy]) Vert[i] = (vx, vy) end end @@ -348,7 +360,7 @@ function group_by_component(f::P, C::Vector{P}; generic=true, precx=150, v=0, ar # Compute the partition of the vertices in Vcon according to the connected component in G sort!(Vcon) CVcon = group_by_component(G, Vcon) - + # Convert the partition into abscissa order index_map = Dict((val, idx) for (idx, val) in enumerate(Vcon)) return [map(v -> index_map[v], C) for C in CVcon] From 38f5a520991d78e0c2baa69897918d1867e16ecc Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 00:45:57 +0200 Subject: [PATCH 076/180] maj deps --- Manifest.toml | 112 +++++++++++++++++++++++++------------------------- 1 file changed, 55 insertions(+), 57 deletions(-) diff --git a/Manifest.toml b/Manifest.toml index 230d183..05ed0fc 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -2,13 +2,13 @@ julia_version = "1.10.1" manifest_format = "2.0" -project_hash = "4d3be6417b0dd2907e17a74f5ed176639eddabae" +project_hash = "4db683e8f9f80c8c42d885d685c8810868b9b1a4" [[deps.AbstractAlgebra]] deps = ["InteractiveUtils", "LinearAlgebra", "MacroTools", "Preferences", "Random", "RandomExtensions", "SparseArrays", "Test"] -git-tree-sha1 = "82d5966bba732eaf9972d9b2e3e725de7288c9d7" +git-tree-sha1 = "45e46834b8fcfd59389939445267047577b19df5" uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d" -version = "0.42.0" +version = "0.43.1" [[deps.ArgTools]] uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" @@ -39,9 +39,9 @@ version = "1.18.0+2" [[deps.CodecZlib]] deps = ["TranscodingStreams", "Zlib_jll"] -git-tree-sha1 = "b8fe8546d52ca154ac556809e10c75e6e7430ac8" +git-tree-sha1 = "bce6804e5e6044c6daab27bb533d1295e4a2e759" uuid = "944b1d66-785c-5afd-91f1-9de20f533193" -version = "0.7.5" +version = "0.7.6" [[deps.ColorSchemes]] deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"] @@ -75,9 +75,9 @@ version = "0.12.11" [[deps.Compat]] deps = ["TOML", "UUIDs"] -git-tree-sha1 = "b1c55339b7c6c350ee89f2c1604299660525b248" +git-tree-sha1 = "8ae8d32e09f0dcf42a36b90d4e17f5dd2e4c4215" uuid = "34da2185-b29b-5c13-b0c7-acf172513d20" -version = "4.15.0" +version = "4.16.0" weakdeps = ["Dates", "LinearAlgebra"] [deps.Compat.extensions] @@ -157,9 +157,9 @@ version = "2.6.2+0" [[deps.FFMPEG]] deps = ["FFMPEG_jll"] -git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8" +git-tree-sha1 = "53ebe7511fa11d33bec688a9178fac4e49eeee00" uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a" -version = "0.4.1" +version = "0.4.2" [[deps.FFMPEG_jll]] deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"] @@ -258,10 +258,10 @@ uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3" version = "1.10.8" [[deps.HarfBuzz_jll]] -deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"] -git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3" +deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll"] +git-tree-sha1 = "401e4f3f30f43af2c8478fc008da50096ea5240f" uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566" -version = "2.8.1+1" +version = "8.3.1+0" [[deps.IntegerMathUtils]] git-tree-sha1 = "b8ffb903da9f7b8cf695a8bead8e01814aa24b30" @@ -279,15 +279,15 @@ version = "0.2.2" [[deps.JLFzf]] deps = ["Pipe", "REPL", "Random", "fzf_jll"] -git-tree-sha1 = "a53ebe394b71470c7f97c2e7e170d51df21b17af" +git-tree-sha1 = "39d64b09147620f5ffbf6b2d3255be3c901bec63" uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c" -version = "0.1.7" +version = "0.1.8" [[deps.JLLWrappers]] deps = ["Artifacts", "Preferences"] -git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca" +git-tree-sha1 = "f389674c99bfcde17dc57454011aa44d5a260a40" uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210" -version = "1.5.0" +version = "1.6.0" [[deps.JSON]] deps = ["Dates", "Mmap", "Parsers", "Unicode"] @@ -297,9 +297,9 @@ version = "0.21.4" [[deps.JpegTurbo_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "c84a835e1a09b289ffcd2271bf2a337bbdda6637" +git-tree-sha1 = "25ee0be4d43d0269027024d75a24c24d6c6e590c" uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8" -version = "3.0.3+0" +version = "3.0.4+0" [[deps.LAME_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] @@ -315,15 +315,15 @@ version = "3.0.0+1" [[deps.LLVMOpenMP_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "d986ce2d884d49126836ea94ed5bfb0f12679713" +git-tree-sha1 = "78211fb6cbc872f77cad3fc0b6cf647d923f4929" uuid = "1d63c593-3942-5779-bab2-d838dc0a180e" -version = "15.0.7+0" +version = "18.1.7+0" [[deps.LZO_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "70c5da094887fd2cae843b8db33920bac4b6f07d" +git-tree-sha1 = "854a9c268c43b77b0a27f22d7fab8d33cdb3a731" uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac" -version = "2.10.2+0" +version = "2.10.2+1" [[deps.LaTeXStrings]] git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec" @@ -332,16 +332,18 @@ version = "1.3.1" [[deps.Latexify]] deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"] -git-tree-sha1 = "5b0d630f3020b82c0775a51d05895852f8506f50" +git-tree-sha1 = "ce5f5621cac23a86011836badfedf664a612cee4" uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316" -version = "0.16.4" +version = "0.16.5" [deps.Latexify.extensions] DataFramesExt = "DataFrames" + SparseArraysExt = "SparseArrays" SymEngineExt = "SymEngine" [deps.Latexify.weakdeps] DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" + SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8" [[deps.LibCURL]] @@ -500,9 +502,9 @@ version = "1.0.2" [[deps.Nemo]] deps = ["AbstractAlgebra", "FLINT_jll", "Libdl", "LinearAlgebra", "Pkg", "Random", "RandomExtensions", "SHA"] -git-tree-sha1 = "df48747041f75651a434a42f1ee1b8bc61f9301a" +git-tree-sha1 = "a644b4943424d9f1ffe7a7a1cdda617053bac5c0" uuid = "2edaba10-b0f1-5616-af89-8c11ac63239a" -version = "0.46.0" +version = "0.47.1" [[deps.NetworkOptions]] uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" @@ -538,15 +540,15 @@ version = "1.4.3" [[deps.OpenSSL_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "a028ee3cb5641cccc4c24e90c36b0a4f7707bdf5" +git-tree-sha1 = "7493f61f55a6cce7325f197443aa80d32554ba10" uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95" -version = "3.0.14+0" +version = "3.0.15+1" [[deps.Opus_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "6703a85cb3781bd5909d48730a67205f3f31a575" uuid = "91d4177d-7536-5919-b921-800302f37372" -version = "1.3.2+0" +version = "1.3.3+0" [[deps.OrderedCollections]] git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5" @@ -560,9 +562,9 @@ version = "10.42.0+1" [[deps.Pango_jll]] deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"] -git-tree-sha1 = "cb5a2ab6763464ae0f19c86c56c63d4a2b0f5bda" +git-tree-sha1 = "e127b609fb9ecba6f201ba7ab753d5a605d53801" uuid = "36c8627f-9965-5494-a995-c6b170f724f3" -version = "1.52.2+0" +version = "1.54.1+0" [[deps.Parsers]] deps = ["Dates", "PrecompileTools", "UUIDs"] @@ -600,9 +602,9 @@ version = "1.4.1" [[deps.Plots]] deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "TOML", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"] -git-tree-sha1 = "082f0c4b70c202c37784ce4bfbc33c9f437685bf" +git-tree-sha1 = "45470145863035bb124ca51b320ed35d071cc6c2" uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" -version = "1.40.5" +version = "1.40.8" [deps.Plots.extensions] FileIOExt = "FileIO" @@ -727,9 +729,9 @@ uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f" version = "1.0.3" [[deps.SimpleBufferStream]] -git-tree-sha1 = "874e8867b33a00e784c8a7e4b60afe9e037b74e1" +git-tree-sha1 = "f305871d2f381d21527c770d4788c06c097c9bc1" uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7" -version = "1.1.0" +version = "1.2.0" [[deps.Sockets]] uuid = "6462fe0b-24de-5631-8697-dd941f90decc" @@ -807,13 +809,9 @@ deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [[deps.TranscodingStreams]] -git-tree-sha1 = "96612ac5365777520c3c5396314c8cf7408f436a" +git-tree-sha1 = "e84b3a11b9bece70d14cce63406bbc79ed3464d2" uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa" -version = "0.11.1" -weakdeps = ["Random", "Test"] - - [deps.TranscodingStreams.extensions] - TestExt = ["Test", "Random"] +version = "0.11.2" [[deps.URIs]] git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b" @@ -878,9 +876,9 @@ version = "1.31.0+0" [[deps.XML2_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"] -git-tree-sha1 = "d9717ce3518dc68a99e6b96300813760d887a01d" +git-tree-sha1 = "1165b0443d0eca63ac1e32b8c0eb69ed2f4f8127" uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a" -version = "2.13.1+0" +version = "2.13.3+0" [[deps.XSLT_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "XML2_jll", "Zlib_jll"] @@ -1045,9 +1043,9 @@ version = "1.2.13+1" [[deps.Zstd_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "e678132f07ddb5bfa46857f0d7620fb9be675d3b" +git-tree-sha1 = "555d1076590a6cc2fdee2ef1469451f872d8b41b" uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" -version = "1.5.6+0" +version = "1.5.6+1" [[deps.eudev_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"] @@ -1057,9 +1055,9 @@ version = "3.2.9+0" [[deps.fzf_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8" +git-tree-sha1 = "936081b536ae4aa65415d869287d43ef3cb576b2" uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09" -version = "0.43.0+0" +version = "0.53.0+0" [[deps.gperf_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] @@ -1074,10 +1072,10 @@ uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b" version = "3.9.0+0" [[deps.libass_jll]] -deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] -git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" +deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"] +git-tree-sha1 = "e17c115d55c5fbb7e52ebedb427a0dca79d4484e" uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" -version = "0.15.1+0" +version = "0.15.2+0" [[deps.libblastrampoline_jll]] deps = ["Artifacts", "Libdl"] @@ -1097,10 +1095,10 @@ uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc" version = "1.11.0+0" [[deps.libfdk_aac_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "8a22cf860a7d27e4f3498a0fe0811a7957badb38" uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" -version = "2.0.2+0" +version = "2.0.3+0" [[deps.libinput_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"] @@ -1122,9 +1120,9 @@ version = "1.3.7+2" [[deps.msolve_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "FLINT_jll", "GMP_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl", "MPFR_jll"] -git-tree-sha1 = "b2e3c462bc0587672d3137d657a491c7b06751ea" +git-tree-sha1 = "7324fd011ebc4b9e43d9aa365c79797860459d0a" uuid = "6d01cc9a-e8f6-580e-8c54-544227e08205" -version = "0.700.100+0" +version = "0.700.200+0" [[deps.mtdev_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] From c9dd99eb6d0d1c5480ce174ee9378ead66d06751 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 10:12:46 +0200 Subject: [PATCH 077/180] manage exact roots when refinment --- src/connectivity/boxes.jl | 10 ++++++++++ src/connectivity/connectcurves.jl | 4 ++-- src/connectivity/isolate.jl | 2 +- 3 files changed, 13 insertions(+), 3 deletions(-) diff --git a/src/connectivity/boxes.jl b/src/connectivity/boxes.jl index 9012c4e..37f9dd3 100644 --- a/src/connectivity/boxes.jl +++ b/src/connectivity/boxes.jl @@ -53,6 +53,11 @@ end function refine_xboxes(f::T where T<:Union{PolyRingElem, MPolyRingElem}, LB, prec) # Refine LB along first axis, being roots of f xnew = isolate(f, prec=prec) + for i in eachindex(xnew) + if xnew[i][1]==xnew[i][2] + xnew[i] = [xnew[i][1]-1//ZZ(1)< Date: Thu, 26 Sep 2024 15:53:10 +0200 Subject: [PATCH 078/180] trailing spaces --- src/connectivity/Cannytools.jl | 24 ++++++++++++------------ src/connectivity/computeRM.jl | 4 ++-- src/connectivity/tools.jl | 4 ++-- 3 files changed, 16 insertions(+), 16 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 70b8138..a177f6f 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -5,7 +5,7 @@ function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: M to_varias = Vector{Int}(undef,0) for v in newvarias_S ind = findfirst(x->x==v, R.S) - push!(to_varias, typeof(ind)==Nothing ? length(R.S)+1 : ind) + push!(to_varias, typeof(ind)==Nothing ? length(R.S)+1 : ind) end ind_novarias = setdiff(eachindex(R.S), to_varias) @@ -22,8 +22,8 @@ function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: M end push!(res, finish(ctx)) end - - return res + + return res end function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: PolyRingElem} @@ -45,13 +45,13 @@ function change_ringvar(f::MPolyRingElem, ind_newvarias::Union{Vector{I}, UnitRa return first(change_ringvar([f], [R.S[i] for i in ind_newvarias])) end -# Return the polynomials in F, but injected in the polynomial ring with the variables occuring in F +# Return the polynomials in F, but injected in the polynomial ring with the variables occuring in F function change_ringvar(F::Vector{P}) where {P <: MPolyRingElem} union_varias = Set{Symbol}() for f in F union!(union_varias, map(Symbol, vars(f)) ) end - return change_ringvar(F, collect(union_varias)) + return change_ringvar(F, collect(union_varias)) end function change_ringvar(f::MPolyRingElem) @@ -146,20 +146,20 @@ function detmpoly(A::Matrix{QQMPolyRingElem}, R) if n != size(A, 2) throw(ArgumentError("Matrix must be square")) end - + if n == 1 return A[1, 1] end - + # Initialize the determinant polynomial detA = QQMPolyRingElem(R,0) - + # Compute the determinant polynomial for j = 1:n submatrix = A[2:end, [i for i = 1:n if i != j]] detA += (-1)^(1+j)*A[1, j] * detmpoly(submatrix, R) end - + return detA end @@ -173,7 +173,7 @@ function contfrac_convergents(x::Rational{Int}) x = inv(fpart) fpart, ipart = modf(x) na, da, nb, db = nb, db, na+ipart*nb, da+ipart*db - push!(q, nb//db) + push!(q, nb//db) end end @@ -199,7 +199,7 @@ function small_mid_point(a::QQFieldElem,b::QQFieldElem) x = inv(fpart) fpart, ipart = modfQQ(x) println(fpart," , ", ipart) - q1, q2 = q2, QQFieldElem(numerator(q1) + ipart*numerator(q2), denominator(q1) + ipart*denominator(q2)) + q1, q2 = q2, QQFieldElem(numerator(q1) + ipart*numerator(q2), denominator(q1) + ipart*denominator(q2)) end end @@ -222,5 +222,5 @@ function MidRationalPoints(S::Vector{Vector{QQFieldElem}}) ratioP[i] = simplest_between(ri, li1) end return ratioP -end +end diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 9e5ce48..248e3bf 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -19,7 +19,7 @@ function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{V varias, nvarias = gens(A), nvars(A) hV = V.gens #println(Q) - e = length(first(Q)) + e = length(first(Q)) fixvarias, newvarias = varias[1:e], varias[e+1:nvarias] R = Vector{AlgebraicSolving.Ideal{QQMPolyRingElem}}(undef,0) @@ -32,7 +32,7 @@ function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{V else Fq = V end - + if dimV - e <= 1 curve = change_ringvar(Fq.gens, A.S) push!(R, AlgebraicSolving.Ideal(vcat(curve, [fixvarias[j] - q[j] for j in 1:e]))) diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index 4f0aeea..0daad6d 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -6,8 +6,8 @@ function order_permut2d(L) # Extract the sorted values and their corresponding indices #sorted_L = [pair[1] for pair in sorted_LL] sorted_ind = [pair[2] for pair in sorted_LL] - - return sorted_ind + + return sorted_in end function diff(p, v, n) From 926318b40491bdb6ca3e355605d89fee2061d2e3 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 15:53:26 +0200 Subject: [PATCH 079/180] remove printing --- src/connectivity/plots.jl | 5 +---- 1 file changed, 1 insertion(+), 4 deletions(-) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index c6153c0..5b43ab8 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,8 +1,7 @@ ## Plot functions function plot_graph(G, Vemph::Vector{Vector{T}} where T<:Any; color="red", width=3, vert=true, subplt=false) - if !subplt - println("Plotting the graph") + if !subplt plot(legend=false) end V, E = G @@ -34,7 +33,6 @@ end function plot_graphs(CG; width=3, vert=true, subplt=false) if !subplt - println("Plotting the graph") plot(legend=false) end col = distinguishable_colors(length(CG)+2) @@ -46,7 +44,6 @@ function plot_graphs(CG; width=3, vert=true, subplt=false) end function plot_graph_comp(G, Vemph=[]; width=3, vert=true, subplt=false) - println("Plotting the graph") plot(legend=false) CG = connected_components(G, Vemph) plot_graphs(CG, width=width, vert=vert, subplt=true) From 7bab4af59d652be68d413009d2ee03008f658fd9 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 15:54:16 +0200 Subject: [PATCH 080/180] Manage printing levels + new shortcut functions : plot and nb of components --- src/connectivity/boxes.jl | 20 ++++++-- src/connectivity/connectcurves.jl | 85 +++++++++++++++++++++---------- 2 files changed, 72 insertions(+), 33 deletions(-) diff --git a/src/connectivity/boxes.jl b/src/connectivity/boxes.jl index 37f9dd3..11d9713 100644 --- a/src/connectivity/boxes.jl +++ b/src/connectivity/boxes.jl @@ -7,12 +7,13 @@ function overlap_inter(I,J) end # To try/do : isolate with usolve, call msolve with only one variable -function intersect_box(f, B; prec=100) +function intersect_box(f, B; prec=100, v=0) L = Array{Any}(undef, 4) for i in 1:2 # Lxi L[i] = Array{Any}(undef,2) - while true + compt = 0 + while compt < 5 flag = false L[i][1] = isolate_eval(f, 2, B[2][i], prec=prec) L[i][2] = [] @@ -21,16 +22,21 @@ function intersect_box(f, B; prec=100) push!(L[i][2], j) elseif overlap_inter(l, B[1]) prec *= 2 - println("Increase precision to ", prec) + v > 0 && println("Increase precision to ", prec) flag = true + compt += 1 break end end flag || break end + if compt >= 5 + error("Problem when isolating on one side of a box") + end # Lyi L[i+2] = Array{Any}(undef,2) - while true + compt = 0 + while compt < 5 flag = false L[i+2][1] = isolate_eval(f, 1, B[1][i], prec=prec) L[i+2][2] = [] @@ -39,13 +45,17 @@ function intersect_box(f, B; prec=100) push!(L[i+2][2], j) elseif overlap_inter(l, B[2]) prec *= 2 - println("Increase precision to ", prec) + v > 0 && println("Increase precision to ", prec) flag = true + compt += 1 break end end flag || break end + if compt >= 5 + error("Problem when isolating on one side of a box") + end end return L end diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 1aea7d8..9a23ab9 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -34,12 +34,12 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t #println(params) #append!(params, C) if arb - compt = 1 + compt = 0 while compt < 5 try # TODO : check that no overlap between different isolations - println("\nIsolating critical values with precision ", precx,"..") - @time begin + v > 0 && println("\nIsolating critical values with precision ", precx,"..") + @iftime (v > 0) begin xcrit = Dict(p[1]=> reduce(vcat, [isolate(pp, prec=precx) for pp in p[2][1]]) for p in params) for i in eachindex(xcrit) for j in eachindex(xcrit[i]) @@ -49,10 +49,10 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t end end xcritpermut = order_permut2d(xcrit); - end + end - println("\nComputing isolating critical boxes using Arb with precision ",max(precx,150),"..") - @time begin + v > 0 && println("\nComputing isolating critical boxes using Arb with precision ",max(precx,150),"..") + @iftime (v > 0) begin precArb = precx Pcrit = Dict( i => [[xc, evaluate_Arb(params[i][2], params[i][3], rat_to_Arb(xc, precArb))] for xc in xcrit[i]] for i in eachindex(xcrit)) LBcrit =Dict( i=> [[ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for (i, pcrit) in Pcrit) @@ -63,21 +63,21 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t end end end - end + end catch precx *= 2 - println("Refine x-precision to $precx") + v > 0 && println("Refine x-precision to $precx") compt += 1 else break end end - if compt == 5 + if compt >= 5 error("Problem in isolating critical boxes") end else - println("\nCompute critical boxes with msolve with precision ", precx,"..") - @time begin + v > 0 && println("\nCompute critical boxes with msolve with precision ", precx,"..") + @iftime (v > 0) begin # TODO: parameter -I LBcrit = Dict(p[1]=>reduce(vcat,[ sort(real_solutions(AlgebraicSolving.Ideal([pp, p[2][3]*y-p[2][2]]), precision=precx,interval=true),by=t->t[1]) for pp in p[2][1] ]) for p in params) for i in eachindex(LBcrit) @@ -91,11 +91,11 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t end xcrit = Dict(lbcrit[1]=>[ B[1] for B in lbcrit[2] ] for lbcrit in LBcrit) xcritpermut = order_permut2d(xcrit); - end + end end - @time begin - println("\nTest for identifying singular boxes");ts=time(); + v > 0 && println("\nTest for identifying singular boxes") +@iftime (v > 0) begin ######################################################## # For each mult of sing pts (keys) give the corresponding factors of the resultant (values) ######################################################### @@ -108,7 +108,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t for j in eachindex(LBcrit[ind]) pcrit = [ rat_to_Arb(c, precx) for c in LBcrit[ind][j] ] if contains_zero(evaluate(Lfyk[m+1], pcrit)) - println("Refine singular boxes of multiplicity ", m) + (v > 0) && println("Refine singular boxes of multiplicity ", m) # TODO refine_boxes(params[k], LBcrit[k]) #flag = true break @@ -117,15 +117,15 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t flag || break end end - end +end - @time begin - # Could be improved by handling nodes as extreme boxes: + v > 0 && println("\nCompute intersections with critical boxes..") +@iftime (v > 0) begin + # Could be improved by handling nodes (or even any ordinary sing) as extreme boxes: # when npcside = [2,2,0,0] just take nearest below and above # intersections b with the curves on the vertical sides # and change into npcside = [0,0,2,2] ## TODO : Refine only the intervals that need to be refined - println("\nCompute intersections with critical boxes..") LPCside = Dict{Int,Any}() ndig = maximum([ndigits(length(LBcrit[i])) for i in eachindex(LBcrit)]) for i in eachindex(LBcrit) @@ -133,25 +133,30 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t ndigi = Int(floor(log10(max(1,length(LBcrit[i]))))) Ptype = (i > length(LBcrit)-length(C)) ? "Pcon" : "mult" precxtmp = precx - while true + compt = 0 + while compt < 5 flag = false for j in eachindex(LBcrit[i]) - print("$Ptype=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") - pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp) + v > 0 && print("$Ptype=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") + pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp,v=v) npcside = [length(n) for (I, n) in pcside] #println("($i, $j): $npcside") if (i == 1 && sum(npcside) > 2) || (i != 1 && sum(npcside[1:2]) != 0) precxtmp *= 2 - println("\nRefine boxes along x-axis to precision ", precxtmp) + v > 0 && println("\nRefine boxes along x-axis to precision ", precxtmp) refine_xboxes(params[i][1], LBcrit[i], precxtmp) flag = true + compt += 1 break end LPCside[i][j] = pcside end flag || break end - println("") + v > 0 && println("") + if compt >= 5 + error("Problem in computing intersections with boxes") + end end LnPCside = Dict(i => [[length(indI) for (L, indI) in PB] for PB in LPCside[i]] for i in eachindex(LPCside)) @@ -194,11 +199,11 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t end end end - end +end #return LnPCside - println("\nGraph computation") + #println("\nGraph computation") # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot # And even remove this fiber for the graph fct, typeout = outf ? (Float64, Float64) : (identity, QQFieldElem) @@ -318,7 +323,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t end end - if Lapp != [[],[]] + if v > 0 && Lapp != [[],[]] println("Removed apparent singularities: $(length(Lapp[1])) isolated $(length(Lapp[2])) nodes") end #EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] @@ -361,7 +366,31 @@ function group_by_component(f::P, C::Vector{P}; generic=true, precx=150, v=0, ar sort!(Vcon) CVcon = group_by_component(G, Vcon) - # Convert the partition into abscissa order + # Convert the partition into abscissa order index_map = Dict((val, idx) for (idx, val) in enumerate(Vcon)) return [map(v -> index_map[v], C) for C in CVcon] end + +function plot_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + plot_graph(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +end + +function plot_graph(f::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + plot_graph(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +end + +function plot_graph_comp(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + plot_graph_comp(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +end + +function plot_graph_comp(f::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + plot_graph_comp(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +end + +function number_connected_components(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + number_connected_components(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +end + +function number_connected_components(f::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + number_connected_components(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +end \ No newline at end of file From bd26082735be4633033f180c90308377668a319f Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 26 Sep 2024 16:12:00 +0200 Subject: [PATCH 081/180] fix typo --- src/connectivity/tools.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index 0daad6d..9515c84 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -7,7 +7,7 @@ function order_permut2d(L) #sorted_L = [pair[1] for pair in sorted_LL] sorted_ind = [pair[2] for pair in sorted_LL] - return sorted_in + return sorted_ind end function diff(p, v, n) From 775c90e5b35c2707aad94961d3e07232c2541868 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 27 Sep 2024 16:03:15 +0200 Subject: [PATCH 082/180] minor --- src/connectivity/isolate.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/isolate.jl b/src/connectivity/isolate.jl index 6bbf867..2f83b28 100644 --- a/src/connectivity/isolate.jl +++ b/src/connectivity/isolate.jl @@ -1,6 +1,7 @@ include("src/usolve/usolve.jl") function isolate(f; prec = 32, software="msolve") + #println(f) # Univariate isolation using usolve if total_degree(f) == 0 return [] @@ -9,7 +10,6 @@ function isolate(f; prec = 32, software="msolve") if software == "usolve" return usolve(f, precision = prec, uspath="AlgebraicSolving.jl/src/connectivity/src/usolve/usolve", output="inter", v=2) else - #println(f) sols = real_solutions(Ideal([change_ringvar(f)]), precision=prec, interval=true, info_level=0) return getindex.(sols, 1) end From 36ab10c1e01927c344ce3164a1ca5541ca7124c1 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 27 Sep 2024 16:04:00 +0200 Subject: [PATCH 083/180] change variable order in param --- src/connectivity/paramcurve.jl | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index 44994a5..f41455c 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -105,8 +105,8 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs @time begin PARAM = Vector{Vector{AlgebraicSolving.QQPolyRingElem}}(undef,DEG+2) _values = Vector{QQFieldElem}(undef,DEG+2) - i, c = 1, 0 - while c < DEG+2 + i, c = 1, 1 + while c <= DEG+2 #println("$c/ $(DEG+2)") if i > 2*(DEG+2) error("Too many bad specializations") @@ -121,10 +121,11 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs lc = leading_coefficient(r.elim) # TODO: why dividing by lc ? rr = [ p/lc for p in vcat(r.elim, r.denom, r.param) ] - PARAM[i] = rr - _values[i] = QQ(i) + PARAM[c] = rr + _values[c] = QQ(i) c += 1 else + #println(r.vars, rem_ind(R.S, N-1)) println("bad specialization: ", i) end #catch @@ -150,7 +151,7 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs end C = [ collect(coefficients(c)) for c in COEFFS ] - POL_term = [C[i][j]*x^(i-1)*y^(j-1) for i in 1:length(C) for j in 1:length(C[i])] + POL_term = [C[i][j]*y^(i-1)*x^(j-1) for i in 1:length(C) for j in 1:length(C[i])] POL = length(POL_term) > 0 ? sum(POL_term) : T(0) POLY_PARAM[count] = POL From 854164a725c69a0fc4915034ad7acb19ae6dd559 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 27 Sep 2024 16:04:13 +0200 Subject: [PATCH 084/180] apparent singularities --- src/connectivity/connectcurves.jl | 30 +++++++++++++++--------------- src/connectivity/subresultants.jl | 21 +++++++++++++++++---- 2 files changed, 32 insertions(+), 19 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 9a23ab9..3993a53 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -8,7 +8,7 @@ export compute_graph, connected_components, number_connected_components, group_b # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, - rat_to_Arb, evaluate_Arb, evaluate_Arb_rat, int_coeffs + rat_to_Arb, evaluate_Arb, evaluate_Arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array include("tools.jl") include("subresultants.jl") @@ -19,7 +19,7 @@ include("plots.jl") include("arbtools.jl") include("src/resultant/bresultant.jl") -function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) +function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) R = parent(f) x, y = gens(R) @@ -30,7 +30,7 @@ function compute_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=t v > 1 && println(f) v > 0 && println("\nCompute parametrization of critical pts...") - @iftime (v > 0) params = param_crit_split(f) + @iftime (v > 0) params = param_crit_split(f,g) #println(params) #append!(params, C) if arb @@ -371,26 +371,26 @@ function group_by_component(f::P, C::Vector{P}; generic=true, precx=150, v=0, ar return [map(v -> index_map[v], C) for C in CVcon] end -function plot_graph(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - plot_graph(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +function plot_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + plot_graph(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) end -function plot_graph(f::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - plot_graph(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +function plot_graph(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + plot_graph(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) end -function plot_graph_comp(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - plot_graph_comp(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +function plot_graph_comp(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + plot_graph_comp(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) end -function plot_graph_comp(f::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - plot_graph_comp(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +function plot_graph_comp(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + plot_graph_comp(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) end -function number_connected_components(f::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - number_connected_components(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +function number_connected_components(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + number_connected_components(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) end -function number_connected_components(f::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - number_connected_components(compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +function number_connected_components(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) + number_connected_components(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) end \ No newline at end of file diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index 0e7742f..6a0c607 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -129,7 +129,7 @@ function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false else for lsr in Lsr mlsr = [[],[]] - for i in 1:i#length(lsr) + for i in 1:length(lsr) for j in 1:length(lsr[i]) push!(mlsr[1], lsr[i][j]) push!(mlsr[2],add_ind([j-1],idx, i-1)) @@ -275,7 +275,7 @@ function fact_gcd(delta::T, LP::Vector{T}) where (T <:MPolyRingElem) return Dict([ (i, change_ringvar(f, [first(R.S)]) ) for (i,f) in out ]) end -function param_crit_split(f) +function param_crit_split(f,g) # Compute subresultants and factor the first subresultant if total_degree(f) > 30 sr = mmod_subresultants(f, derivative(f, 2), 2, list=true, n_ssr=2) @@ -308,7 +308,13 @@ function param_crit_split(f) end # Nodes : multiplicity 2 in res - (2 in sqrmult) && push!(param_crit, -1=>[group_sqr[2], -sr[2][end-1], sr[2][end]]) + if 2 in sqrmult + A = derivative(derivative(f,2),2)*derivative(g,1) - derivative(derivative(f,1),2)*derivative(g,2) + A1 = numerator(evaluate(A, [2], [-sr[2][end-1]//sr[2][end]])) + dA = gcd.(group_sqr[2], Ref(A1)) + push!(param_crit, -1=>[group_sqr[2]./dA, -sr[2][end-1], sr[2][end]]) + append!(param_crit[2][1], dA) + end # Other sing filter!(m->!(m in [1,2]), sqrmult) #TODO: simpler criterion for mult=p*(p-1)? @@ -324,10 +330,17 @@ function param_crit_split(f) for k in eachindex(Ld) for l in eachindex(Ld[k]) for (i, dji) in Ld[k][l] - push!(param_crit[i+1][1], dji) + if haskey(param_crit, i+1) + push!(param_crit[i+1][1], dji) + else + error("Curve not in generic position") + end end end end + for i in eachindex(param_crit) + filter!(p->total_degree(p)>0, param_crit[i][1]) + end return filter(p->length(p[2][1])>0, param_crit) end \ No newline at end of file From dcdbc9d29efa57211638880f47fdc624522c44a3 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 30 Sep 2024 14:24:50 +0200 Subject: [PATCH 085/180] add change_ringvar for modular base rings --- src/connectivity/Cannytools.jl | 45 +++++++++++++++++++++++++++++++++- 1 file changed, 44 insertions(+), 1 deletion(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index a177f6f..c3dbba3 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -27,7 +27,8 @@ function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: M end function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: PolyRingElem} - A, (x,) = polynomial_ring(QQ, [parent(first(F)).S]) + R = parent(first(F)) + A, (x,) = polynomial_ring(base_ring(R), [R.S]) return change_ringvar([ evaluate(f, x) for f in F ], newvarias_S) end @@ -58,6 +59,48 @@ function change_ringvar(f::MPolyRingElem) return first(change_ringvar([f])) end +# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables +function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} + R = parent(first(F)) + # Locate variables of R in newvarias + to_varias = Vector{Int}(undef,0) + for v in newvarias_S + ind = findfirst(x->x==v, oldvarias_S) + push!(to_varias, typeof(ind)==Nothing ? length(oldvarias_S)+1 : ind) + end + + ind_novarias = setdiff(eachindex(oldvarias_S), to_varias) + newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) + + res = typeof(first(F))[] + ctx = MPolyBuildCtx(newR) + + for f in F + for (e, c) in zip(exponent_vectors(f), coefficients(f)) + @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") + push!(e, 0) + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res +end + +function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: PolyRingElem} + R = parent(first(F)) + A, (x,) = polynomial_ring(base_ring(R), oldvarias_S) + return change_ringvar_mod([ evaluate(f, x) for f in F ], newvarias_S, oldvarias_S) +end + +function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) + return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) +end + +#function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) +# return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) +#end + function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" From bafbee1237909018dde3c97f724abb3ccaa01888 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 30 Sep 2024 14:25:13 +0200 Subject: [PATCH 086/180] export change_ringvar_mod --- src/connectivity/computeRM.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 248e3bf..bfa182a 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -6,7 +6,7 @@ export computeRM, computepolarproj, computepolarphi # DEBUG -export change_ringvar, compute_minors, detmpoly +export change_ringvar, compute_minors, detmpoly, change_ringvar_mod include("Cannytools.jl") From 7a102f9aa54079d2ea00c7c5b984b662d19b39b5 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 30 Sep 2024 14:26:56 +0200 Subject: [PATCH 087/180] remove variable --- src/connectivity/paramcurve.jl | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index f41455c..df4f9ed 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -23,6 +23,22 @@ function rem_var(f, i) return finish(C) end +function rem_var(f, i, S) + # Remove the occurence of the ith variable + R = parent(f) + A, Avars = polynomial_ring(base_ring(R), rem_ind(S, i)) + CE = [collect(coefficients(f)), collect(exponent_vectors(f))] + CE[2] = [ rem_ind(e, i) for e in CE[2]] + + # Reconstruct the polynomial in the ring A + C = MPolyBuildCtx(A) + R = base_ring(A) + for i in eachindex(CE[1]) + push_term!(C, R(CE[1][i]), CE[2][i]); + end + return finish(C) +end + function rem_ind(L,i::Int) # remove element at index i return [ L[1:i-1]; L[i+1:end] ] From 8b00196269601021f0d25bb37f4a3d7e501156cd Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 30 Sep 2024 14:29:02 +0200 Subject: [PATCH 088/180] add detection for app sing, with several modular speedups --- src/connectivity/subresultants.jl | 125 +++++++++++++++++++++++++++--- 1 file changed, 113 insertions(+), 12 deletions(-) diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index 6a0c607..ddabd91 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -1,4 +1,24 @@ # Some tools + +function homogenize(P::MPolyRingElem, i::Int, S::Vector{T} where T<:Union{Symbol, String}) + A = base_ring(parent(P)) + if iszero(P) + return zero(polynomial_ring(A, S)[1]) + end + # Homogenize w.r.t to the i-th variables + LPc, LPe = poly_to_array(P) + deg, N = maximum(getindex.(LPe, i)), length(LPe[1]) + for j in eachindex(LPe) + push!(LPe[j], deg-LPe[j][i]) + end + R, = polynomial_ring(A, S) + return array_to_poly([LPc,LPe], R) +end + +function homogenize(LP::Vector{P} where P<:MPolyRingElem, i::Int, S::Vector{T} where T<:Union{Symbol, String}) + return [ homogenize(lp, 2, S) for lp in LP ] +end + function poly_to_array(P::MPolyRingElem) # return P as two lists ci and vi of resp. coeffs and exponents return [collect(coefficients(P)), collect(exponent_vectors(P))] @@ -14,6 +34,19 @@ function add_ind(L,i,x) return [ L[1:i-1]; [x]; L[i:end] ] end +function parray_asvarcoeff(LP, idx) + # takes the above representation of a poly P + # and outputs a representation of P with univariate coeffs in the i-th variable + A = parent(LP[1][1]) + NLP = [ Vector{typeof(LP[1][1])}[], [] ] + for (c,e) in zip(LP[1], LP[2]) + vcat(zeros(A, e[idx]), [c]) + push!(NLP[1], vcat(zeros(A, e[idx]), [c])) + push!(NLP[2], rem_ind(e, idx)) + end + return NLP +end + function parray_asvar(LP, idx) # takes the above representation of a poly P # and outputs a representation of P seen as a univariate poly in the i-th variable @@ -275,12 +308,72 @@ function fact_gcd(delta::T, LP::Vector{T}) where (T <:MPolyRingElem) return Dict([ (i, change_ringvar(f, [first(R.S)]) ) for (i,f) in out ]) end -function param_crit_split(f,g) +function num_biv_rat_mod(A, P, RS) + # Computes the numerator of the polynomial A(x,a(x)//b(x)) mod q + # where P = [q, a, b] + B = base_ring(parent(A)) + + T, = polynomial_ring(B, RS[1]) + Puniv = [ T(coefficients_of_univariate(p)) for p in P ] + + U, fU = Nemo.residue_ring(T, Puniv[1]) + amod, bmod = fU.(Puniv[2:end]) + + newv = vcat(RS, [:t]) + Tbiv, = polynomial_ring(T, newv[2:end]) + Ah = homogenize(A, 2, newv) + Ah1 = array_to_poly(parray_asvarcoeff(poly_to_array(Ah), 1), Tbiv) + Ahmod = change_coefficient_ring(U, Ah1) + + Aeval = evaluate(Ahmod, [amod, bmod]) + return change_ringvar_mod(lift(Aeval), RS, newv) +end + +function intersect_biv(P::Vector{T} where T<:Any, A::MPolyRingElem) + # P = [Lq, a, b] encodes sets (x,a(x)/b(x)) where Lq[i](x)=0 + # Compute divisor dA of q that encodes intersection with A(x,y)=0 + compt = 0 + RS = parent(A).S + dA, dAf = [], [] + pprod, p = 1, ZZ(1) << 60 + while compt<12 + #print("$compt,") + if compt>0 + dAfold, dAold = copy(dAf), copy(dA) + end + p = next_prime(p) + Pp = change_coefficient_ring.(Ref(GF(p)), P) + Ap = change_coefficient_ring(GF(p), A) + #@time "Eval" + Apev = num_biv_rat_mod(Ap, Pp, RS) + dAp = gcd(Pp[1], Apev) + dA = lift.(Ref(ZZ), coefficients_of_univariate(dAp)) + if compt>0 + dA = [ crt([d1, d2], [pprod, p], true) for (d1, d2) in zip(dAold, dA) ] + end + if length(filter!(!is_zero, dA)) <= 1 + #println("Trivial gcd") + return one(parent(P[1])) + end + pprod = pprod*p + dAf = [ reconstruct(c, pprod) for c in dA ] + if compt>0 + dAf != dAfold || break + end + compt += 1 + end + #println() + B, = polynomial_ring(QQ, RS[1]) + return change_ringvar(B(dAf), RS) +end + +function param_crit_split(f, g; v=1, detect_app=true) # Compute subresultants and factor the first subresultant + v>0 && println("Compute subresultant sequence") if total_degree(f) > 30 - sr = mmod_subresultants(f, derivative(f, 2), 2, list=true, n_ssr=2) + @iftime v>0 sr = mmod_subresultants(f, derivative(f, 2), 2, list=true, n_ssr=2) else - sr = subresultants(f, derivative(f, 2), 2, list=true) + @iftime v>0 sr = subresultants(f, derivative(f, 2), 2, list=true) end if total_degree(sr[1][1]) == 0 @@ -296,6 +389,8 @@ function param_crit_split(f,g) group_sqr = Dict(m => [r[1] for r in sqr if r[2] == m] for m in sqrmult) #println(group_sqr) + v>0 && println("Compute crit partition w.r.t to multiplicity") +@iftime v>0 begin # Initalization singmult = filter(p->p*(p-1)<=sqrmult[end], 2:sqrmult[end]) param_crit = Dict(p => [QQMPolyRingElem[], -sr[p][end-1], (p-1)*sr[p][end]] for p in singmult) @@ -308,20 +403,24 @@ function param_crit_split(f,g) end # Nodes : multiplicity 2 in res + v>0 && println("Compute apparent singularities") if 2 in sqrmult - A = derivative(derivative(f,2),2)*derivative(g,1) - derivative(derivative(f,1),2)*derivative(g,2) - A1 = numerator(evaluate(A, [2], [-sr[2][end-1]//sr[2][end]])) - dA = gcd.(group_sqr[2], Ref(A1)) - push!(param_crit, -1=>[group_sqr[2]./dA, -sr[2][end-1], sr[2][end]]) - append!(param_crit[2][1], dA) + if detect_app + A = derivative(derivative(f,2),2)*derivative(g,1) - derivative(derivative(f,1),2)*derivative(g,2) + dA = [ int_coeffs(intersect_biv([q, -sr[2][end-1], sr[2][end]], A)) for q in group_sqr[2] ] + @time "Division" push!(param_crit, -1=>[group_sqr[2]./dA, -sr[2][end-1], sr[2][end]]) + append!(param_crit[2][1], dA) + else + push!(param_crit, -1=>[group_sqr[2], -sr[2][end-1], sr[2][end]]) + end end # Other sing filter!(m->!(m in [1,2]), sqrmult) #TODO: simpler criterion for mult=p*(p-1)? lsr = [ try sr[p][end] catch; one(parent(f)) end for p in 2:(singmult[end]+1) ] Ld = Vector{Vector{Dict{Int, QQMPolyRingElem}}}(undef, length(sqrmult)) - #Threads.@threads - for k in eachindex(sqrmult) + println("Compute gcd decomposition") + Threads.@threads for k in eachindex(sqrmult) Ld[k] = Vector{Dict{Int, QQMPolyRingElem}}(undef,length(group_sqr[sqrmult[k]])) for l in eachindex(group_sqr[sqrmult[k]]) Ld[k][l] = fact_gcd(group_sqr[sqrmult[k]][l], lsr) @@ -338,9 +437,11 @@ function param_crit_split(f,g) end end end - +end for i in eachindex(param_crit) filter!(p->total_degree(p)>0, param_crit[i][1]) end return filter(p->length(p[2][1])>0, param_crit) -end \ No newline at end of file +end + +param_crit_split(f; v=1) = param_crit_split(f, zero(parent(f)), v=v, detect_app=false) \ No newline at end of file From 18f33240647e18657d1879456200aab13a66a88d Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 30 Sep 2024 14:29:25 +0200 Subject: [PATCH 089/180] export appsing related functions for debug --- src/connectivity/connectcurves.jl | 6 +----- 1 file changed, 1 insertion(+), 5 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 3993a53..4890279 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -8,7 +8,7 @@ export compute_graph, connected_components, number_connected_components, group_b # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, - rat_to_Arb, evaluate_Arb, evaluate_Arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array + rat_to_Arb, evaluate_Arb, evaluate_Arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, intersect_biv, num_biv_rat_mod, parray_asvarcoeff include("tools.jl") include("subresultants.jl") @@ -286,10 +286,6 @@ end # push!(Corr[i][j][2][1], length(Vert)) # We will subsequently add the vertex in the graph # push!(Viso, length(Vert)) - ############################################ - ## TO BE REPLACED BY APPSING IDENTIFICATOR ## - ## works for space curves without nodes ## - ############################################ else # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 push!(Edg, (Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]])) From cec5ddf31270f165f727ba01caaead930b17013b Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 17 Oct 2024 00:46:06 +0200 Subject: [PATCH 090/180] build Mpoly function + maj --- src/connectivity/Cannytools.jl | 56 +++++++++++++++++++++++++++++----- 1 file changed, 48 insertions(+), 8 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index c3dbba3..c7a04a1 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -28,8 +28,22 @@ end function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: PolyRingElem} R = parent(first(F)) - A, (x,) = polynomial_ring(base_ring(R), [R.S]) - return change_ringvar([ evaluate(f, x) for f in F ], newvarias_S) + to_varias = [ v==R.S ? 1 : 2 for v in newvarias_S] + newR, = polynomial_ring(base_ring(R), newvarias_S) + + res = typeof(zero(newR))[] + ctx = MPolyBuildCtx(newR) + + LcF = [ filter!(t->t[2]!=0, collect(enumerate(coefficients(f)))) for f in F ] + for f in LcF + for (ef, c) in f + e = [ef-1, 0] + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res end function change_ringvar(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) @@ -101,7 +115,32 @@ end # return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) #end +function MPolyBuild(F::Vector{Vector{P}}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} + A = parent(first(first(F))) + R, = polynomial_ring(A, newvarias_S) + to_varias = [ i==idx ? 1 : 2 for i in eachindex(newvarias_S) ] + + res = typeof(zero(R))[] + ctx = MPolyBuildCtx(R) + + LcF = [ filter!(t->t[2]!=0, collect(enumerate(f))) for f in F ] + for f in LcF + for (ef, c) in f + e = [ef-1, 0] + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res +end + +function MPolyBuild(f::Vector{P}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} + return first(MPolyBuild([f], newvarias_S, idx)) +end + function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) + #println("$j $V $dimV") # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" R = parent(V) @@ -111,6 +150,7 @@ function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; d JW = transpose([ derivative(f, k) for k=j+1:n, f in hV ]) sizeminors = c + dimproj - (j-1) hW = vcat(hV, compute_minors(sizeminors, JW, R)) + filter!(!iszero, hW) output_functions = Dict( "minors" => x -> x, "groebner" => x -> groebner_basis(x, info_level=verb,nr_thrds=nr_thrds), @@ -122,19 +162,19 @@ function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; d return output_functions[output](AlgebraicSolving.Ideal(hW)) end -function computepolarphi(j::Int, V::AlgebraicSolving.Ideal, phi::MPolyRingElem, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) +function computepolarphi(j::Int, V::AlgebraicSolving.Ideal, phi::Vector{T} where T<:MPolyRingElem, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" R = parent(V) - n, hV = R.nvars, V.gens + n, hV = nvars(R), V.gens c = n - dimV if j==0 JW = transpose([ derivative(f, k) for k=1:n, f in hV ]) sizeminors = c else - JW = transpose([ derivative(f, k) for k=j:n, f in [hV;[phi]] ]) - sizeminors = c + 1 + dimproj - (j-1) + JW = transpose([ derivative(f, k) for k=1:n, f in vcat(hV,phi) ]) + sizeminors = c + j + dimproj - (j-1) end hW = vcat(hV, compute_minors(sizeminors, JW, R)) output_functions = Dict( @@ -183,7 +223,7 @@ function combinations(a, n) return _combinations(a, n, 1, Vector{Int}([])) end -function detmpoly(A::Matrix{QQMPolyRingElem}, R) +function detmpoly(A::Matrix{T} where T<:MPolyRingElem, R) # Get the size of the matrix n = size(A, 1) if n != size(A, 2) @@ -195,7 +235,7 @@ function detmpoly(A::Matrix{QQMPolyRingElem}, R) end # Initialize the determinant polynomial - detA = QQMPolyRingElem(R,0) + detA = zero(R) # Compute the determinant polynomial for j = 1:n From a5c68c425c54d485133019b988e2b705b25685b9 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 17 Oct 2024 00:46:31 +0200 Subject: [PATCH 091/180] some verbose --- src/connectivity/computeRM.jl | 15 +++++++++------ 1 file changed, 9 insertions(+), 6 deletions(-) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index bfa182a..303af35 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -6,7 +6,7 @@ export computeRM, computepolarproj, computepolarphi # DEBUG -export change_ringvar, compute_minors, detmpoly, change_ringvar_mod +export change_ringvar, compute_minors, detmpoly, change_ringvar_mod, MPolyBuild include("Cannytools.jl") @@ -38,21 +38,24 @@ function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{V push!(R, AlgebraicSolving.Ideal(vcat(curve, [fixvarias[j] - q[j] for j in 1:e]))) else ## sing(Fq) ## - #println("Compute first the singular points") - singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=v, nr_thrds=Threads.nthreads()) + v>0 && println("Compute first the singular points") + singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=v-1, nr_thrds=Threads.nthreads()) @assert(length(singFq)==0, "Non-emtpy real sing locus!") #@assert(degree(singFq.elim)==0, "Non-emtpy sing locus!") ## K(pi_1,Fq) ## - K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=v, nr_thrds=Threads.nthreads()) + v >0 && println("First critical points") + K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=v-1, nr_thrds=Threads.nthreads()) ## K(pi_2, Fq) ## - K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors", verb=v, nr_thrds=Threads.nthreads()) + v >0 && println("Second critical points") + K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors", verb=v-1, nr_thrds=Threads.nthreads()) polar = change_ringvar(K2Fq.gens, A.S) push!(R, AlgebraicSolving.Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) ## Points with vertical tg in K(pi_2, Fq) ## - K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=v, nr_thrds=Threads.nthreads()) + v >0 && println("Vertical tg points") + K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=v-1, nr_thrds=Threads.nthreads()) ## New base points ## K1W = vcat(K1Fq, K1WmFq) From a47835f47059cd49b68397d60efaeb23e45ee472 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 17 Oct 2024 00:48:06 +0200 Subject: [PATCH 092/180] fix bresultant interface --- src/connectivity/src/resultant/bresultant.jl | 66 ++++++++++++++++---- 1 file changed, 54 insertions(+), 12 deletions(-) diff --git a/src/connectivity/src/resultant/bresultant.jl b/src/connectivity/src/resultant/bresultant.jl index 67162ad..e343185 100644 --- a/src/connectivity/src/resultant/bresultant.jl +++ b/src/connectivity/src/resultant/bresultant.jl @@ -1,3 +1,5 @@ +export parse_poly + function PolyToBRstring(f) fc, fe = map(collect, [coefficients(f), exponent_vectors(f)]) s = string(length(fc), " 2\n") @@ -38,31 +40,71 @@ function ToBresultant(f, g, finput="/tmp/in.bs") close(ff) end +function parse_poly(poly_str) + # Regular expression to match terms of the form "ax^n", "bx", or constants + term_pattern = r"([+-]?[ ]*\d*)[\*]?x\^(\d+)|([+-]?[ ]*\d*)[\*]?x|([+-]?[ ]*\d+)" + + # Initialize a dictionary to store the coefficients with their exponents + coeffs = Dict{Int, BigInt}() + + # Use the regular expression to find all matches + for m in eachmatch(term_pattern, poly_str) + #println(m) + if !isnothing(m.captures[1]) && !isnothing(m.captures[2]) # Matches ax^n + s = m.captures[1] * (m.captures[1] in ["","-","+"] ? "1" : "") + coeffs[parse(Int, m.captures[2])] = parse(BigInt, s) + elseif !isnothing(m.captures[3]) # Matches bx (degree 1 term) + s = m.captures[3] * (m.captures[3] in ["","-","+"] ? "1" : "") + coeffs[1] = parse(BigInt, s) + elseif !isnothing(m.captures[4]) # Matches constant term + coeffs[0] = parse(BigInt, m.captures[4]) + end + end + + # Get the highest degree + max_degree = maximum(keys(coeffs)) + # Create the list of coefficients starting from the highest degree + result = [get(coeffs, i, 0) for i in 0:max_degree] + + return result +end + function FromBresultant(output="p", foutput="/tmp/out.bs") #x, y = symbols("x y") - #A, (x, y) = ZZ[], PolynomialRing(ZZ, ["x", "y"]) - ff = open(foutput, "r") + A, x = polynomial_ring(QQ, :x) + ff = open(foutput, "r+") s = read(ff, String) - s = replace(s, "\n" => "", ":" => "", ";" => "") - L = eval(Meta.parse(s)) - close(ff) - return L + #println(s) + Ls = split.(split(replace(s, r":|;\n|\[\n\[|\]\n\]" => ""), "],\n["), Ref(",\n")) + Lcs = [ parse_poly.(ls) for ls in Ls ] + #println(Lcs) + return [ A.(ls) for ls in Lcs ] end function Bresultant(f, g; fname1="/tmp/in.bs", fname2="/tmp/out.bs", bspath="./bresultant", v=0) - ToBresultant(f, g, fname1) - out = run(pipeline(`$bspath -f $fname1 -o $fname2`, stderr="/tmp/err.log.bs")) + @time ToBresultant(f, g, fname1) + #err = Pipe() + @time process = run(pipeline(`$bspath -f $fname1 -o $fname2`)) + + #= + #close(err.in) if v > 0 - ff = open("/tmp/err.log.bs", "r") - println(read(ff, String)) - close(ff) + c=0 + while c <100 + out = @async String(read(err)) + println(out) + c +=1 + end end #if v == 1 # println(split(stderr(out), '\n')[end - 1] |> x -> split(x, ": ")[end] * "s") #elseif v == 2 # println(stderr(out)) #end - return FromBresultant(fname2) + wait(process) + =# + + return @time FromBresultant(fname2) end #using Nemo From dfe825acd301d3208d6eeb16d43d66375fe1bce6 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 17 Oct 2024 00:48:18 +0200 Subject: [PATCH 093/180] typo --- src/connectivity/tools.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index 9515c84..3a0c8cc 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -49,4 +49,4 @@ macro iftime(v, ex) $(esc(ex)) end end -end \ No newline at end of file +end From 68f6a4140b1fd15a22d456cdad411fe046cdf406 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 17 Oct 2024 00:48:45 +0200 Subject: [PATCH 094/180] temp savefig --- src/connectivity/plots.jl | 33 ++++++++++++++++++++++++++++++++- 1 file changed, 32 insertions(+), 1 deletion(-) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 5b43ab8..020c5a4 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -40,12 +40,43 @@ function plot_graphs(CG; width=3, vert=true, subplt=false) G, CVemph = length(CG[j][1])==2 ? CG[j] : (CG[j], Vector{Int}()) plot_graph(G, CVemph, color=col[j+2], vert=vert, subplt=true) end - subplt || gui() + #subplt || gui() + savefig("/home/remi/Documents/gittravail/test.html") + replace_width_height_in_file("/home/remi/Documents/gittravail/test.html", 1000, 750) end function plot_graph_comp(G, Vemph=[]; width=3, vert=true, subplt=false) plot(legend=false) CG = connected_components(G, Vemph) + println(Vemph) plot_graphs(CG, width=width, vert=vert, subplt=true) subplt || gui()#savefig("/tmp/test.html") +end + +function replace_width_height_in_file(filename, x, y) + # Open the file and read its content as a string + content = read(filename, String) + + # Build the patterns to search for and the replacements + width_pattern = "\"width\": 600" + height_pattern = "\"height\": 400" + + # Create the replacement strings with new values of x and y + new_width = "\"width\": $x" + new_height = "\"height\": $y" + + # Replace the last occurrence of "width": 600 + last_width_pos = findlast(occursin(width_pattern), split(content, "\n")) + if last_width_pos !== nothing + content = replace(content, width_pattern => new_width; count=1) + end + + # Replace the last occurrence of "height": 400 + last_height_pos = findlast(occursin(height_pattern), split(content, "\n")) + if last_height_pos !== nothing + content = replace(content, height_pattern => new_height; count=1) + end + + # Write the modified content back to the file + write(filename, content) end \ No newline at end of file From 154d3d6289feaa3bcc719ba12e6f2eda5852d20f Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 17 Oct 2024 00:49:52 +0200 Subject: [PATCH 095/180] parrallelize + fix param_newvars --- src/connectivity/paramcurve.jl | 55 ++++++++++++++++++++-------------- 1 file changed, 33 insertions(+), 22 deletions(-) diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index df4f9ed..ede2dc8 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -121,33 +121,42 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs @time begin PARAM = Vector{Vector{AlgebraicSolving.QQPolyRingElem}}(undef,DEG+2) _values = Vector{QQFieldElem}(undef,DEG+2) - i, c = 1, 1 - while c <= DEG+2 - #println("$c/ $(DEG+2)") + i = 1 + free_ind = collect(1:DEG+2) + used_ind = zeros(Bool, DEG+2) + while length(free_ind) > 0 + #println("$(DEG+2-length(free_ind))/ $(DEG+2)") if i > 2*(DEG+2) error("Too many bad specializations") end - - #try - Feval = [ evaluate(f, [N-1], [QQ(i)]) for f in F ] - Feval = [ rem_var(f, N-1) for f in Feval ] - r = rational_parametrization(Ideal(Feval), nr_thrds=Threads.nthreads()) + LFeval = Vector{AlgebraicSolving.Ideal}(undef, length(free_ind)) + Threads.@threads for j in 1:length(free_ind) + LFeval[i+j-1] = Ideal([ rem_var(evaluate(f, [N-1], [QQ(i+j-1)]), N-1) for f in F ]) + end + Lr = Vector{AlgebraicSolving.RationalParametrization}(undef, length(free_ind)) + for j in 1:length(free_ind) + #println("$(i+j-1)/$(DEG+2)") + Lr[i+j-1] = rational_parametrization(LFeval[i+j-1], nr_thrds=Threads.nthreads()) + end + for j in 1:length(free_ind) # For lifting: the same variable must be chosen for the param - if r.vars == rem_ind(R.S, N-1) - lc = leading_coefficient(r.elim) - # TODO: why dividing by lc ? - rr = [ p/lc for p in vcat(r.elim, r.denom, r.param) ] - PARAM[c] = rr - _values[c] = QQ(i) - c += 1 + if Lr[j].vars == rem_ind(R.S, N-1) + lc = leading_coefficient(Lr[j].elim) + # TODO: why dividing by lc ? To get a unique representative? + rr = [ p/lc for p in vcat(Lr[j].elim, Lr[j].denom, Lr[j].param) ] + PARAM[j] = rr + _values[j] = QQ(i+j-1) + used_ind[j] = true + #println("Good specialization: ",i+j-1) else #println(r.vars, rem_ind(R.S, N-1)) - println("bad specialization: ", i) + println("bad specialization: ", i+j-1) end - #catch - # error("bad specialization: ", i) - #end - i += 1 + end + + i += length(free_ind) + free_ind = [ free_ind[j] for j in eachindex(free_ind) if !used_ind[j] ] + used_ind = zeros(Bool, length(free_ind)) end end @@ -178,9 +187,11 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs end function param_newvars(F::Vector{P} where P <: MPolyRingElem, Svars::Vector{Symbol}, cfs_lf::Vector{Vector{I}} where I<:Union{ZZRingElem, QQFieldElem}) - eq = change_ringvar(F, Svars) + Svarsbis = vcat(Svars[1:end-2], reverse!(Svars[end-1:end])) + eq = change_ringvar(F, Svarsbis) newvarias = gens(parent(first(eq))) - neweq = vcat(eq, [ transpose(lf)*newvarias for lf in cfs_lf ]) + newvariasbis = vcat(newvarias[1:end-2], reverse!(newvarias[end-1:end])) + neweq = vcat(eq, [ transpose(lf)*newvariasbis for lf in cfs_lf ]) C = rational_parametrization(Ideal(neweq)) return change_ringvar([C.elim, C.elim == -1 ? C.elim : C.param[end], C.denom], [:x,:y]) From c8f3ad96e603e06e70a2069f135d0cfafd6af57b Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 17 Oct 2024 00:50:16 +0200 Subject: [PATCH 096/180] fix control points --- src/connectivity/graph.jl | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/src/connectivity/graph.jl b/src/connectivity/graph.jl index 5f50f4e..026eda0 100644 --- a/src/connectivity/graph.jl +++ b/src/connectivity/graph.jl @@ -53,11 +53,13 @@ function connected_components(G, Vemph=[]; ind_abs=false) end if length(Vemph)>0 - CVemph = [ [] for _ in eachindex(components) ] + CVemph = [ Dict(k=>[] for k in eachindex(Vemph)) for _ in eachindex(components) ] for i in eachindex(components) for j in eachindex(components[i]) - if components[i][j] in Vemph - push!(CVemph[i], ind_abs ? components[i][j] : j) + for k in eachindex(Vemph) + if components[i][j] in Vemph[k] + push!(CVemph[i][k], ind_abs ? components[i][j] : j) + end end end end From 4103f48cbfc3b56e2574efb9a09e431fdc9cccf5 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 17 Oct 2024 00:50:43 +0200 Subject: [PATCH 097/180] tmp --- src/connectivity/isolate.jl | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/src/connectivity/isolate.jl b/src/connectivity/isolate.jl index 2f83b28..4c3eb00 100644 --- a/src/connectivity/isolate.jl +++ b/src/connectivity/isolate.jl @@ -1,6 +1,6 @@ include("src/usolve/usolve.jl") -function isolate(f; prec = 32, software="msolve") +function isolate(f; prec = 32, software="usolve") #println(f) # Univariate isolation using usolve if total_degree(f) == 0 @@ -15,7 +15,7 @@ function isolate(f; prec = 32, software="msolve") end end -function isolate_eval(f, ivar, val; prec=64, software="msolve") +function isolate_eval(f, ivar, val; prec=64, software="usolve") #print(val) # univariate isolation of roots of a bivariate polynomial f # whose ivar-th variable is evaluated at val @@ -25,6 +25,7 @@ function isolate_eval(f, ivar, val; prec=64, software="msolve") CD = lcm(map(denominator, collect(coefficients(fev)))) fev *= CD - return isolate(fev, prec=prec, software=software) + tmp = isolate(fev, prec=prec, software=software) + return tmp end \ No newline at end of file From 9ba84d72716577af5aaf72c4d9c97854b1b001a5 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 17 Oct 2024 00:51:06 +0200 Subject: [PATCH 098/180] add new function for param + several improvements --- src/connectivity/subresultants.jl | 194 ++++++++++++++++++++++++------ 1 file changed, 159 insertions(+), 35 deletions(-) diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index ddabd91..a8caca1 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -175,7 +175,7 @@ function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false return newsr end -function interp_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, iv; list=false) where T <: RingElement +function interp_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, iv; list=false, Dmax=nothing) where T <: RingElement R = parent(P) A = coefficient_ring(R) iu = iv%2+1 @@ -183,27 +183,39 @@ function interp_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, iv; list # Modern computer Algebra Th 6.51. degs = degrees(P) n, d = degs[iv], degs[iu] - degsmax = [ (2*n-1-2*k)*d for k=0:d-1 ] + if isnothing(Dmax) + Dmax = [ (2*n-1-2*k)*d for k=0:d-1 ][1] #Dmax = degsmax[end]>>1+1 + end ## B,t =polynomial_ring(A, Vv) - xs = A.(0:degsmax[1]) + xs = A.(-Dmax//2:Dmax//2) Srev = Vector{Vector{typeof(t)}}(undef, length(xs)) - evPQ = [ [B(coefficients_of_univariate(evaluate(pq,[iu],[xx]))) for pq in [P,Q] ] for xx in xs] + evPQ = [ [ B(0) for pq in [P,Q] ] for xx in xs] +@time begin + Threads.@threads for i in eachindex(xs) + evPQ[i][1] = B(coefficients_of_univariate(evaluate(P,[iu],[xs[i]]))) + evPQ[i][2] = B(coefficients_of_univariate(evaluate(Q,[iu],[xs[i]]))) + end +end +@time begin Threads.@threads for i in 1:length(xs) Srev[i] = subresultants(evPQ[i][1], evPQ[i][2]) end +end Srev = [ [ collect(coefficients(ss)) for ss in s] for s in Srev ] C, = Nemo.polynomial_ring(A,Vu) Sr = [ [ C(0) for _=1:i] for i=1:n ] Lys = [ [ [ (try A(Srev[l][i][j]) catch; A(0) end) for l in eachindex(Srev) ] for j in 1:i ] for i in 1:n ] - for i = 1:n +@time begin + Threads.@threads for i = 1:2 # For the i-th subresultant - Threads.@threads for j in 1:i + Threads.@threads for j in 0:i-1 # Each coefficient is interpolated - Sr[i][j] = interpolate(C, xs, Lys[i][j]) + Sr[i][end-j] = interpolate(C, xs, Lys[i][end-j]) end end +end return Sr end @@ -223,7 +235,7 @@ function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=fa L1, primprod = [], ZZ(1) Ltemp = Vector{Vector{Vector{Vector{ZZRingElem}}}}(undef,n_threads+1) lcpq = [ evaluate(leading_coefficient(l, 2),[0,0]) for l in [P,Q] ] - compt=n_threads + compt = n_threads while true v > 0 && print("$compt primes ") LP, LQ, Lprim = MPolyRingElem[], MPolyRingElem[], ZZRingElem[] @@ -237,12 +249,14 @@ function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=fa return prim, lcpq end end + @iftime v>1 begin Threads.@threads for j in 1:n_threads sr = subresultants(LP[j], LQ[j], idx, list=true) Ltemp[j] = [ [ lift.(Ref(ZZ), coefficients_of_univariate(srii)) for srii in sri ] for sri in sr ] #sr = interp_subresultants(LP[j], LQ[j], idx)[1][1] #Ltemp[j] = lift.(Ref(ZZ), coefficients(sr)) end + end if n_ssr > 0 for j in 1:n_threads @@ -261,6 +275,7 @@ function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=fa #println(Ltemp) L2 = deepcopy(L1) L1 = Vector{Vector{Vector{ZZRingElem}}}(undef, length(first(Ltemp))) + @iftime v>1 begin Threads.@threads for i in eachindex(L1) L1[i] = Vector{Vector{ZZRingElem}}(undef, min(i, Nssr)) Threads.@threads for j in eachindex(L1[i]) @@ -272,6 +287,7 @@ function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=fa end end end + end #println(L1) primprod = prod(Lprim) compt+=n_threads @@ -280,12 +296,98 @@ function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=fa #compt < 20 || break end - uvar = parent(P).S[(idx+1)%2] - A, = polynomial_ring(ZZ, uvar) - sr = [ [ change_ringvar(A(ss),[uvar]) for ss in s ] for s in L1 ] + v>1 && println("Convert the coefficients into polynomials") + L1Q = [ [QQ.(ss) for ss in s ] for s in L1 ] + @iftime v>0 sr = [ MPolyBuild(s, parent(P).S, (idx+1)%2) for s in L1Q ] return sr end +function mmod_param_crit(P::QQMPolyRingElem, Q::QQMPolyRingElem; n_threads=Threads.nthreads(), detect_app=true, v=0) + PZ, QZ = change_coefficient_ring.(Ref(ZZ), int_coeffs.([P,Q])) + pc = mmod_param_crit(PZ, QZ, n_threads=n_threads, detect_app=detect_app, v=v) + return pc + if list + return [ change_coefficient_ring.(Ref(QQ),srp) for srp in sr ] + else + return change_coefficient_ring.(Ref(QQ),sr) + end +end + +function mmod_param_crit(P::ZZMPolyRingElem, Q::ZZMPolyRingElem; n_threads=Threads.nthreads(), v=0, detect_app=true) + prim = ZZ(1)<<(61) + RS = parent(P).S + L1, L1f, primprod = [], [], ZZ(1) + Ltemp = Vector{Vector{Vector{Vector{ZZRingElem}}}}(undef,n_threads+1) + dP = derivative(P, 2) + lcpq = [ evaluate(leading_coefficient(l, 2),[0,0]) for l in [P,dP,Q] ] + compt = n_threads + while true + v > 0 && print("$compt primes ") + LP, LQ, Lprim = MPolyRingElem[], MPolyRingElem[], ZZRingElem[] + while length(Lprim) < n_threads + prim = next_prime(prim) + if !any(getindex.(divides.(lcpq, Ref(prim)),1)) + #Pprim, Qprim = [ change_coefficient_ring(residue_ring(ZZ, prim)[1], poly) for poly in [P,Q] ] + Pprim, Qprim = [ change_coefficient_ring(GF(prim), poly) for poly in [P,Q] ] + push!.([LP,LQ,Lprim], [Pprim,Qprim,prim]) + end + end + @iftime v>1 begin + Threads.@threads for j in 1:n_threads + pc = param_crit_split(LP[j], LQ[j], RS = RS, v=v-2, detect_app=detect_app) + Ltemp[j] = Vector{Vector{ZZMPolyRingElem}}(undef, length(pc)) + for (ik, k) in enumerate(eachindex(pc)) + q, a, b = pc[k] + q = first(q) + dq = derivative(q,1) + Pnum = mod(dq*gcdinv(b,q)[2]*a, q) + Ltemp[j][ik] = [ lift.(Ref(ZZ), coefficients_of_univariate(poly)) for poly in [q, Pnum, dq] ] + end + #sr = interp_subresultants(LP[j], LQ[j], idx)[1][1] + #Ltemp[j] = lift.(Ref(ZZ), coefficients(sr)) + end + end + + if L1 != [] + Ltemp[n_threads+1] = copy(L1) + push!(Lprim, primprod) + end + #println(Ltemp) + L1 = Vector{Vector{Vector{ZZRingElem}}}(undef, length(Ltemp[1])) + @iftime v>1 begin + Threads.@threads for i in eachindex(L1) + #println("($i,$j)") + L1[i] = Vector{ZZRingElem}(undef, length(Ltemp[1][i])) + Threads.@threads for j in eachindex(L1[i]) + L1[i][j] = Vector{ZZRingElem}(undef, length(Ltemp[1][i][j])) + for k in eachindex(L1[i][j]) + cfs = [ try Ltemp[p][i][j][k] catch; ZZ(0) end for p in eachindex(Lprim) ] + L1[i][j][k] = crt(cfs, Lprim, false) + end + end + end + end + primprod = prod(Lprim) + L2f = deepcopy(L1f) + try + @iftime v>1 L1f = [ [ [ reconstruct(c, primprod) for c in poly ] for poly in param ] for param in L1 ] + #println(L1f) + L1f != L2f || break + catch + println("No rational rec") + end + compt+=n_threads + v > 0 && println(ndigits(primprod, 10), " digits") + #compt < 20 || break + end + + v>1 && println("Convert the coefficients into polynomials") + L1Q = [ [ QQ.(poly) for poly in param ] for param in L1f ] + @iftime v>0 param = Dict( m => vcat([[int_coeffs(MPolyBuild(param[1], parent(P).S, 1))]], [ int_coeffs(MPolyBuild(poly, parent(P).S, 1)) for poly in param[2:end] ]) for (m, param) in zip([-1,1], L1Q)) + return param +end + + function fact_gcd(delta::T, LP::Vector{T}) where (T <:PolyRingElem) # delta : poly to factor w.r.t the polynomials in LP Lphi = [gcd(delta, LP[1])] @@ -300,12 +402,12 @@ function fact_gcd(delta::T, LP::Vector{T}) where (T <:PolyRingElem) return filter(s->degree(s[2])>0, Dict(enumerate(Ldelta))) end -function fact_gcd(delta::T, LP::Vector{T}) where (T <:MPolyRingElem) +function fact_gcd(delta::T, LP::Vector{T}, RS::Vector{Symbol}) where (T <:MPolyRingElem) @assert is_univariate(delta) && all(is_univariate.(LP)) "Not univariate polynomial" R = parent(delta) - A, = polynomial_ring(coefficient_ring(R), first(R.S)) + A, = polynomial_ring(coefficient_ring(R), first(RS)) out = fact_gcd(A(coefficients_of_univariate(delta)), A.(coefficients_of_univariate.(LP))) - return Dict([ (i, change_ringvar(f, [first(R.S)]) ) for (i,f) in out ]) + return Dict([ (i, change_ringvar(f, [first(RS)]) ) for (i,f) in out ]) end function num_biv_rat_mod(A, P, RS) @@ -329,9 +431,17 @@ function num_biv_rat_mod(A, P, RS) return change_ringvar_mod(lift(Aeval), RS, newv) end +function intersect_biv_mod(P::Vector{T} where T<:Any, A::MPolyRingElem, RS::Vector{Symbol}) + Aev = num_biv_rat_mod(A, P, RS) + return gcd(P[1], Aev) +end + function intersect_biv(P::Vector{T} where T<:Any, A::MPolyRingElem) # P = [Lq, a, b] encodes sets (x,a(x)/b(x)) where Lq[i](x)=0 # Compute divisor dA of q that encodes intersection with A(x,y)=0 + if iszero(A) + return P[1] + end compt = 0 RS = parent(A).S dA, dAf = [], [] @@ -349,29 +459,37 @@ function intersect_biv(P::Vector{T} where T<:Any, A::MPolyRingElem) dAp = gcd(Pp[1], Apev) dA = lift.(Ref(ZZ), coefficients_of_univariate(dAp)) if compt>0 - dA = [ crt([d1, d2], [pprod, p], true) for (d1, d2) in zip(dAold, dA) ] + dA = [ crt([d1, d2], [pprod, p], false) for (d1, d2) in zip(dAold, dA) ] end - if length(filter!(!is_zero, dA)) <= 1 + if length(filter(!is_zero, dA)) <= 1 #println("Trivial gcd") - return one(parent(P[1])) + return one(polynomial_ring(QQ, RS)[1]) end pprod = pprod*p - dAf = [ reconstruct(c, pprod) for c in dA ] - if compt>0 - dAf != dAfold || break + try + dAf = [ reconstruct(c, pprod) for c in dA ] + if compt>0 + dAf != dAfold || break + end + catch + println("No rational rec..") end compt += 1 end #println() B, = polynomial_ring(QQ, RS[1]) - return change_ringvar(B(dAf), RS) + return int_coeffs(change_ringvar(B(dAf), RS)) end -function param_crit_split(f, g; v=1, detect_app=true) +function param_crit_split(f, g; v=0, detect_app=true, RS = nothing) + @assert (f|>parent|>base_ring|>characteristic == 0 || !isnothing(RS)) "Variable names must be provided when char>0" + if f|>parent|>base_ring|>characteristic == 0 + RS = parent(f).S + end # Compute subresultants and factor the first subresultant v>0 && println("Compute subresultant sequence") - if total_degree(f) > 30 - @iftime v>0 sr = mmod_subresultants(f, derivative(f, 2), 2, list=true, n_ssr=2) + if total_degree(f) > 30 && f|>parent|>base_ring|>characteristic == 0 + @iftime v>0 sr = mmod_subresultants(f, derivative(f, 2), 2, list=true, n_ssr=2, v=v-1) else @iftime v>0 sr = subresultants(f, derivative(f, 2), 2, list=true) end @@ -380,7 +498,8 @@ function param_crit_split(f, g; v=1, detect_app=true) return Dict() end - sqr = collect(factor_squarefree(sr[1][1])) + v>1 && println("Square-free factorization") + @iftime v>1 sqr = collect(factor_squarefree(sr[1][1])) # Filter out factors with zero multiplicity and sort by multiplicity sqr = sort!(filter(t -> t[2] > 0, sqr), by = t -> t[2]) @@ -390,14 +509,12 @@ function param_crit_split(f, g; v=1, detect_app=true) #println(group_sqr) v>0 && println("Compute crit partition w.r.t to multiplicity") -@iftime v>0 begin # Initalization singmult = filter(p->p*(p-1)<=sqrmult[end], 2:sqrmult[end]) - param_crit = Dict(p => [QQMPolyRingElem[], -sr[p][end-1], (p-1)*sr[p][end]] for p in singmult) + param_crit = Dict(p => [[], -sr[p][end-1], (p-1)*sr[p][end]] for p in singmult) # Critical points : multiplicity 1 in res (1 in sqrmult) && push!(param_crit, 1=>[group_sqr[1], -sr[2][end-1], sr[2][end]]) - if length(singmult) == 0 return filter(p->length(p[2][1])>0, param_crit) end @@ -406,24 +523,31 @@ function param_crit_split(f, g; v=1, detect_app=true) v>0 && println("Compute apparent singularities") if 2 in sqrmult if detect_app + @iftime v>0 begin A = derivative(derivative(f,2),2)*derivative(g,1) - derivative(derivative(f,1),2)*derivative(g,2) - dA = [ int_coeffs(intersect_biv([q, -sr[2][end-1], sr[2][end]], A)) for q in group_sqr[2] ] - @time "Division" push!(param_crit, -1=>[group_sqr[2]./dA, -sr[2][end-1], sr[2][end]]) + if f|>parent|>base_ring|>characteristic > 0 + dA = [ (intersect_biv_mod([q, -sr[2][end-1], sr[2][end]], A, RS)) for q in group_sqr[2] ] + else + dA = [ (intersect_biv([q, -sr[2][end-1], sr[2][end]], A)) for q in group_sqr[2] ] + end + push!(param_crit, 0=>[group_sqr[2]./dA, -sr[2][end-1], sr[2][end]]) append!(param_crit[2][1], dA) + end else - push!(param_crit, -1=>[group_sqr[2], -sr[2][end-1], sr[2][end]]) + push!(param_crit, 0=>[group_sqr[2], -sr[2][end-1], sr[2][end]]) end end # Other sing filter!(m->!(m in [1,2]), sqrmult) #TODO: simpler criterion for mult=p*(p-1)? lsr = [ try sr[p][end] catch; one(parent(f)) end for p in 2:(singmult[end]+1) ] - Ld = Vector{Vector{Dict{Int, QQMPolyRingElem}}}(undef, length(sqrmult)) - println("Compute gcd decomposition") + Ld = Vector{Vector{Dict{Int, MPolyRingElem}}}(undef, length(sqrmult)) + v>0 && println("Compute gcd decomposition") +@iftime v>0 begin Threads.@threads for k in eachindex(sqrmult) - Ld[k] = Vector{Dict{Int, QQMPolyRingElem}}(undef,length(group_sqr[sqrmult[k]])) + Ld[k] = Vector{Dict{Int, MPolyRingElem}}(undef,length(group_sqr[sqrmult[k]])) for l in eachindex(group_sqr[sqrmult[k]]) - Ld[k][l] = fact_gcd(group_sqr[sqrmult[k]][l], lsr) + Ld[k][l] = fact_gcd(group_sqr[sqrmult[k]][l], lsr, RS) end end for k in eachindex(Ld) From 67a58ab95db57e4bd687ec74b8ff057f166a9949 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 17 Oct 2024 00:51:27 +0200 Subject: [PATCH 099/180] other param comp (commented) + fix control points --- src/connectivity/connectcurves.jl | 70 ++++++++++++++++--------------- 1 file changed, 37 insertions(+), 33 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 4890279..2034a94 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -8,7 +8,8 @@ export compute_graph, connected_components, number_connected_components, group_b # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, - rat_to_Arb, evaluate_Arb, evaluate_Arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, intersect_biv, num_biv_rat_mod, parray_asvarcoeff + rat_to_Arb, evaluate_Arb, evaluate_Arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, + intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit include("tools.jl") include("subresultants.jl") @@ -22,17 +23,25 @@ include("src/resultant/bresultant.jl") function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) R = parent(f) x, y = gens(R) - + intC = int_coeff ? int_coeffs : identity # Pre-processing the input - f = int_coeff ? int_coeffs(f) : f + f, g = intC([f,g]) changemat = generic ? [1 0; 0 1] : trimat_rand(QQ, 2, range=-100:100) f = evaluate(f, collect(changemat*[x; y])); v > 1 && println(f) - v > 0 && println("\nCompute parametrization of critical pts...") - @iftime (v > 0) params = param_crit_split(f,g) - #println(params) - #append!(params, C) + v > 0 && println("Compute parametrization of critical pts...") + @iftime (v > 0) params = param_crit_split(f,g,v=v-1, detect_app=true) + #@iftime (v > 0) params = mmod_param_crit(f, g,v=v-1, detect_app=false) + #=params = Bresultant(f, derivative(f,2), bspath="AlgebraicSolving.jl/src/connectivity/src/resultant/bresultant",v=2); + params = change_ringvar.(params, Ref([:x,:y])) + params = [ [[p[1]], p[3], p[2]] for p in params] + params = Dict(1=>params[1], -1=>params[2])=# + + for i in 1:length(C) + params[-i] = [ [C[i][1] |> intC], C[i][2], C[i][3] ] + end + #println(keys(params)) if arb compt = 0 while compt < 5 @@ -66,7 +75,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen end catch precx *= 2 - v > 0 && println("Refine x-precision to $precx") + v > 0 && println("\nRefine x-precision to $precx") compt += 1 else break @@ -93,6 +102,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen xcritpermut = order_permut2d(xcrit); end end + #println(xcrit) v > 0 && println("\nTest for identifying singular boxes") @iftime (v > 0) begin @@ -101,8 +111,8 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen ######################################################### Lfyk = diff_list(f, 2, max(maximum(eachindex(LBcrit)),2)) for ind in eachindex(LBcrit) - ind!=1 || continue # extreme pts - m = ind==-1 ? 2 : ind # nodes have mult 2 + ind>1 || ind==0 || continue # extreme and control pts + m = ind==0 ? 2 : ind # nodes have mult 2 while true flag = false for j in eachindex(LBcrit[ind]) @@ -130,7 +140,7 @@ end ndig = maximum([ndigits(length(LBcrit[i])) for i in eachindex(LBcrit)]) for i in eachindex(LBcrit) LPCside[i] = Array{Any}(undef, length(LBcrit[i])) - ndigi = Int(floor(log10(max(1,length(LBcrit[i]))))) + ndigi = ndigits(length(LBcrit[i])) Ptype = (i > length(LBcrit)-length(C)) ? "Pcon" : "mult" precxtmp = precx compt = 0 @@ -275,10 +285,8 @@ end ########################### # The critical point ########################## - # If we are dealing with a node - if i == -1 - # if it is an isolated point - if isempty(nI[1]) && isempty(nI[2]) + # If we are dealing with a isolated node + if i in [0,2] && isempty(nI[1]) && isempty(nI[2]) push!(Lapp[1], (i,j)) #pass # We can add the isolated vertex @@ -286,12 +294,12 @@ end # push!(Corr[i][j][2][1], length(Vert)) # We will subsequently add the vertex in the graph # push!(Viso, length(Vert)) - else - # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 - push!(Edg, (Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]])) - push!(Edg, (Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]])) - push!(Lapp[2], (i,j)) - end + # If we are dealing with an apparent singularity + elseif i == 0 + # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 + push!(Edg, (Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]])) + push!(Edg, (Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]])) + push!(Lapp[2], (i,j)) else # We can add the vertex push!(Vert, (xcmid, ycmid)) @@ -304,10 +312,10 @@ end for k in nI[2] push!(Edg, (length(Vert), Corr[i][j][3][k])) end - #if i > length(params)-length(C) - # # If this is a control point - # push!(Vcon[i + length(C) - length(params)], length(Vert)) - #end + if i < 0 + # If this is a control point + push!(Vcon[-i], length(Vert)) + end end ########################### # Above the critical point @@ -322,11 +330,7 @@ end if v > 0 && Lapp != [[],[]] println("Removed apparent singularities: $(length(Lapp[1])) isolated $(length(Lapp[2])) nodes") end - #EdgPlot = [[Vert[k] for k in [i, j]] for (i, j) in Edg] - #plot_graph(Vert, EdgPlot) - #gui() - #plot_graph_comp(Vert,CEdg) # Operate inverse change of variable if necessary if !(generic) for i in eachindex(Vert) @@ -343,14 +347,14 @@ end end end -function compute_graph(f::P, C::Dict{Int,Vector{P}}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) - G, Vcon = compute_graph(f, collect(values(C)), generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf) +function compute_graph(f::P, g::P, C::Dict{Int,Vector{P}}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) + G, Vcon = compute_graph(f, g, collect(values(C)), generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf) VC = Dict{Int64, Vector{Int}}([ k => Vcon[i] for (i,k) in enumerate(keys(C)) ]) return G, VC end -function compute_graph(f::P, C::Vector{P}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) - G, (Vcon,) = compute_graph(f, [C], generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf = outf) +function compute_graph(f::P, g::P, C::Vector{P}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) + G, (Vcon,) = compute_graph(f, g, [C], generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf = outf) return G, Vcon end From 9a02642a12a8828dbe976a1ac28d70002c6db5da Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 31 Mar 2025 01:05:32 +0200 Subject: [PATCH 100/180] maj (mainly verbose) --- Manifest.toml | 68 +++++++++++++++------------ Project.toml | 2 +- src/connectivity/Cannytools.jl | 8 ++-- src/connectivity/computeRM.jl | 10 ++-- src/connectivity/connectcurves.jl | 6 +++ src/connectivity/paramcurve.jl | 19 ++++---- src/connectivity/plots.jl | 12 ++--- src/connectivity/src/usolve/usolve.jl | 4 +- src/connectivity/subresultants.jl | 2 +- 9 files changed, 72 insertions(+), 59 deletions(-) diff --git a/Manifest.toml b/Manifest.toml index 05ed0fc..7faf1d8 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -2,13 +2,13 @@ julia_version = "1.10.1" manifest_format = "2.0" -project_hash = "4db683e8f9f80c8c42d885d685c8810868b9b1a4" +project_hash = "11eb6a443ca7f27cf646ae7e6a1882d5932bc885" [[deps.AbstractAlgebra]] deps = ["InteractiveUtils", "LinearAlgebra", "MacroTools", "Preferences", "Random", "RandomExtensions", "SparseArrays", "Test"] -git-tree-sha1 = "45e46834b8fcfd59389939445267047577b19df5" +git-tree-sha1 = "709a09fbc20ae499657a9cd2e832c9946809ece8" uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d" -version = "0.43.1" +version = "0.43.6" [[deps.ArgTools]] uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" @@ -33,9 +33,9 @@ version = "1.0.8+1" [[deps.Cairo_jll]] deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] -git-tree-sha1 = "a2f1c8c668c8e3cb4cca4e57a8efdb09067bb3fd" +git-tree-sha1 = "009060c9a6168704143100f36ab08f06c2af4642" uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" -version = "1.18.0+2" +version = "1.18.2+1" [[deps.CodecZlib]] deps = ["TranscodingStreams", "Zlib_jll"] @@ -218,15 +218,15 @@ version = "6.2.1+6" [[deps.GR]] deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"] -git-tree-sha1 = "629693584cef594c3f6f99e76e7a7ad17e60e8d5" +git-tree-sha1 = "ee28ddcd5517d54e417182fec3886e7412d3926f" uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71" -version = "0.73.7" +version = "0.73.8" [[deps.GR_jll]] deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"] -git-tree-sha1 = "a8863b69c2a0859f2c2c87ebdc4c6712e88bdf0d" +git-tree-sha1 = "f31929b9e67066bee48eec8b03c0df47d31a74b3" uuid = "d2c73de3-f751-5644-a686-071e5b155ba9" -version = "0.73.7+0" +version = "0.73.8+0" [[deps.Gettext_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"] @@ -236,9 +236,9 @@ version = "0.21.0+0" [[deps.Glib_jll]] deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"] -git-tree-sha1 = "7c82e6a6cd34e9d935e9aa4051b66c6ff3af59ba" +git-tree-sha1 = "674ff0db93fffcd11a3573986e550d66cd4fd71f" uuid = "7746bdde-850d-59dc-9ae8-88ece973131d" -version = "2.80.2+0" +version = "2.80.5+0" [[deps.Graphite2_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] @@ -285,9 +285,9 @@ version = "0.1.8" [[deps.JLLWrappers]] deps = ["Artifacts", "Preferences"] -git-tree-sha1 = "f389674c99bfcde17dc57454011aa44d5a260a40" +git-tree-sha1 = "be3dc50a92e5a386872a493a10050136d4703f9b" uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210" -version = "1.6.0" +version = "1.6.1" [[deps.JSON]] deps = ["Dates", "Mmap", "Parsers", "Unicode"] @@ -308,10 +308,10 @@ uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d" version = "3.100.2+0" [[deps.LERC_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "36bdbc52f13a7d1dcb0f3cd694e01677a515655b" uuid = "88015f11-f218-50d7-93a8-a6af411a945d" -version = "3.0.0+1" +version = "4.0.0+0" [[deps.LLVMOpenMP_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] @@ -326,9 +326,9 @@ uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac" version = "2.10.2+1" [[deps.LaTeXStrings]] -git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec" +git-tree-sha1 = "dda21b8cbd6a6c40d9d02a73230f9d70fed6918c" uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" -version = "1.3.1" +version = "1.4.0" [[deps.Latexify]] deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"] @@ -411,9 +411,9 @@ version = "2.40.1+0" [[deps.Libtiff_jll]] deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"] -git-tree-sha1 = "2da088d113af58221c52828a80378e16be7d037a" +git-tree-sha1 = "b404131d06f7886402758c9ce2214b636eb4d54a" uuid = "89763e89-9b03-5906-acba-b20f662cd828" -version = "4.5.1+1" +version = "4.7.0+0" [[deps.Libuuid_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] @@ -502,9 +502,9 @@ version = "1.0.2" [[deps.Nemo]] deps = ["AbstractAlgebra", "FLINT_jll", "Libdl", "LinearAlgebra", "Pkg", "Random", "RandomExtensions", "SHA"] -git-tree-sha1 = "a644b4943424d9f1ffe7a7a1cdda617053bac5c0" +git-tree-sha1 = "b02de63b9379b37f75488c299f2f1f49da666d84" uuid = "2edaba10-b0f1-5616-af89-8c11ac63239a" -version = "0.47.1" +version = "0.47.2" [[deps.NetworkOptions]] uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" @@ -595,10 +595,10 @@ uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a" version = "3.2.0" [[deps.PlotUtils]] -deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"] -git-tree-sha1 = "7b1a9df27f072ac4c9c7cbe5efb198489258d1f5" +deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "StableRNGs", "Statistics"] +git-tree-sha1 = "650a022b2ce86c7dcfbdecf00f78afeeb20e5655" uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043" -version = "1.4.1" +version = "1.4.2" [[deps.Plots]] deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "TOML", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"] @@ -747,6 +747,12 @@ deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"] uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" version = "1.10.0" +[[deps.StableRNGs]] +deps = ["Random"] +git-tree-sha1 = "83e6cce8324d49dfaf9ef059227f91ed4441a8e5" +uuid = "860ef19b-820b-49d6-a774-d7a799459cd3" +version = "1.0.2" + [[deps.StaticArrays]] deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"] git-tree-sha1 = "eeafab08ae20c62c44c8399ccb9354a04b80db50" @@ -809,9 +815,9 @@ deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [[deps.TranscodingStreams]] -git-tree-sha1 = "e84b3a11b9bece70d14cce63406bbc79ed3464d2" +git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742" uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa" -version = "0.11.2" +version = "0.11.3" [[deps.URIs]] git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b" @@ -1108,9 +1114,9 @@ version = "1.18.0+0" [[deps.libpng_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"] -git-tree-sha1 = "d7015d2e18a5fd9a4f47de711837e980519781a4" +git-tree-sha1 = "b70c870239dc3d7bc094eb2d6be9b73d27bef280" uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" -version = "1.6.43+1" +version = "1.6.44+0" [[deps.libvorbis_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] @@ -1120,9 +1126,9 @@ version = "1.3.7+2" [[deps.msolve_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "FLINT_jll", "GMP_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl", "MPFR_jll"] -git-tree-sha1 = "7324fd011ebc4b9e43d9aa365c79797860459d0a" +git-tree-sha1 = "31d4b30cc109d1e49293ce94d468a73932093aac" uuid = "6d01cc9a-e8f6-580e-8c54-544227e08205" -version = "0.700.200+0" +version = "0.700.300+0" [[deps.mtdev_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] diff --git a/Project.toml b/Project.toml index 0d8fa27..0937d3d 100644 --- a/Project.toml +++ b/Project.toml @@ -27,4 +27,4 @@ Random = "1.6" StaticArrays = "1" Test = "1.6" julia = "1.6" -msolve_jll = "0.700.200" +msolve_jll = "0.700.300" diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index c7a04a1..27b970b 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -290,13 +290,13 @@ function MidRationalPoints(S::Vector{Vector{QQFieldElem}}) # S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] # such that the [l_i, r_i] are rational and disjoint open intervals. # - # It orders the [l_i,r_i] and computes the simplest + # It orders the [l_i,r_i], removes repetitions and computes the simplest # rational points between these intervals. - n = length(S) - if n==0 - return Vector{QQFieldElem}(undef, 0) + if isempty(S) + return QQFieldElem[] end S1 = sort(S, lt=(x, y) -> x[2] <= y[1]) + n = unique!(S1) |> length ratioP = Vector{QQFieldElem}(undef, n-1) for i in 1:(n- 1) ri, li1 = S1[i][2], S1[i+1][1] diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 303af35..00cc00f 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -39,27 +39,27 @@ function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{V else ## sing(Fq) ## v>0 && println("Compute first the singular points") - singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=v-1, nr_thrds=Threads.nthreads()) + singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=max(v-1,0), nr_thrds=Threads.nthreads()) @assert(length(singFq)==0, "Non-emtpy real sing locus!") #@assert(degree(singFq.elim)==0, "Non-emtpy sing locus!") ## K(pi_1,Fq) ## v >0 && println("First critical points") - K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=v-1, nr_thrds=Threads.nthreads()) + K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=max(v-1,0), nr_thrds=Threads.nthreads()) ## K(pi_2, Fq) ## v >0 && println("Second critical points") - K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors", verb=v-1, nr_thrds=Threads.nthreads()) + K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors", verb=max(v-1,0), nr_thrds=Threads.nthreads()) polar = change_ringvar(K2Fq.gens, A.S) push!(R, AlgebraicSolving.Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) ## Points with vertical tg in K(pi_2, Fq) ## v >0 && println("Vertical tg points") - K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=v-1, nr_thrds=Threads.nthreads()) + K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=max(v-1,0), nr_thrds=Threads.nthreads()) ## New base points ## K1W = vcat(K1Fq, K1WmFq) - K1WRat = MidRationalPoints(getindex.(K1W,1)) + K1WRat = MidRationalPoints(getindex(K1W, 1)) newQ = [ vcat(q, [kv]) for kv in K1WRat ] # Heuristic to be proven # newQ = newQ[2:end-1] diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 2034a94..9dce70d 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -50,6 +50,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen v > 0 && println("\nIsolating critical values with precision ", precx,"..") @iftime (v > 0) begin xcrit = Dict(p[1]=> reduce(vcat, [isolate(pp, prec=precx) for pp in p[2][1]]) for p in params) + # Enlarge exact isolating root intervals for i in eachindex(xcrit) for j in eachindex(xcrit[i]) if xcrit[i][j][1]==xcrit[i][j][2] @@ -65,6 +66,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen precArb = precx Pcrit = Dict( i => [[xc, evaluate_Arb(params[i][2], params[i][3], rat_to_Arb(xc, precArb))] for xc in xcrit[i]] for i in eachindex(xcrit)) LBcrit =Dict( i=> [[ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for (i, pcrit) in Pcrit) + # Enlarge exact isolating box vertical side (horizontal lines) for i in eachindex(LBcrit) for j in eachindex(LBcrit[i]) if LBcrit[i][j][2][1]==LBcrit[i][j][2][2] @@ -89,6 +91,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen @iftime (v > 0) begin # TODO: parameter -I LBcrit = Dict(p[1]=>reduce(vcat,[ sort(real_solutions(AlgebraicSolving.Ideal([pp, p[2][3]*y-p[2][2]]), precision=precx,interval=true),by=t->t[1]) for pp in p[2][1] ]) for p in params) + # Enlarge each exact isolating box side for i in eachindex(LBcrit) for j in eachindex(LBcrit[i]) for k in eachindex(LBcrit[i][j]) @@ -117,6 +120,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen flag = false for j in eachindex(LBcrit[ind]) pcrit = [ rat_to_Arb(c, precx) for c in LBcrit[ind][j] ] + # Check if the the mult(pcrit)-th derivative of f vanishes on pcrit if contains_zero(evaluate(Lfyk[m+1], pcrit)) (v > 0) && println("Refine singular boxes of multiplicity ", m) # TODO refine_boxes(params[k], LBcrit[k]) @@ -140,8 +144,10 @@ end ndig = maximum([ndigits(length(LBcrit[i])) for i in eachindex(LBcrit)]) for i in eachindex(LBcrit) LPCside[i] = Array{Any}(undef, length(LBcrit[i])) + # Data printing part ndigi = ndigits(length(LBcrit[i])) Ptype = (i > length(LBcrit)-length(C)) ? "Pcon" : "mult" + ### precxtmp = precx compt = 0 while compt < 5 diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl index ede2dc8..3ad2cbe 100644 --- a/src/connectivity/paramcurve.jl +++ b/src/connectivity/paramcurve.jl @@ -59,7 +59,7 @@ function compute_param(I::Ideal{P} where P<:MPolyRingElem; use_lfs = false, lfs return compute_param(I.gens, use_lfs = use_lfs, lfs = lfs) end -function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs = []) +function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs = [], v=0) R = parent(first(F)) varias, N = gens(R), nvars(R) DEG = deg_Alg(F,1) @@ -73,7 +73,7 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs if NEW_DEG == DEG push!(ivarias_gen, ind) end - (length(ivarias_gen) < 2 && ind > 0) || break + (length(ivarias_gen) < 2 && ind > 1) || break ind -= 1 end reverse!(ivarias_gen) @@ -116,9 +116,10 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs lf_cfs = vcat(lfs, [ rand(ZZ(-100):ZZ(100), N) for _ in 1:2-length(lfs)]) append!(F, [ transpose(lf)*varias for lf in lf_cfs ]) end + println(varias) # Compute DEG+1 evaluations of the param (whose deg is bounded by DEG) - println("Parametrization step...") - @time begin + v > 0 && println("Parametrization step...") + #@iftime v>0 begin PARAM = Vector{Vector{AlgebraicSolving.QQPolyRingElem}}(undef,DEG+2) _values = Vector{QQFieldElem}(undef,DEG+2) i = 1 @@ -150,7 +151,7 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs #println("Good specialization: ",i+j-1) else #println(r.vars, rem_ind(R.S, N-1)) - println("bad specialization: ", i+j-1) + v>1 && println("bad specialization: ", i+j-1) end end @@ -158,11 +159,11 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs free_ind = [ free_ind[j] for j in eachindex(free_ind) if !used_ind[j] ] used_ind = zeros(Bool, length(free_ind)) end - end + #end # Interpolate each coefficient of each poly in the param - println("Interpolation step...") - @time begin + v > 0 && println("Interpolation step...") + #@iftime v>0 begin POLY_PARAM = Vector{QQMPolyRingElem}(undef,N) T, (x,y) = polynomial_ring(QQ, [:x,:y]) A, u = polynomial_ring(QQ, :u) @@ -181,7 +182,7 @@ function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs POLY_PARAM[count] = POL end - end + #end return [R.S, lf_cfs, POLY_PARAM[1], POLY_PARAM[2], POLY_PARAM[3:end]] end diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 020c5a4..ba1f3c6 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -40,15 +40,15 @@ function plot_graphs(CG; width=3, vert=true, subplt=false) G, CVemph = length(CG[j][1])==2 ? CG[j] : (CG[j], Vector{Int}()) plot_graph(G, CVemph, color=col[j+2], vert=vert, subplt=true) end - #subplt || gui() - savefig("/home/remi/Documents/gittravail/test.html") - replace_width_height_in_file("/home/remi/Documents/gittravail/test.html", 1000, 750) + subplt || gui() + #savefig("/home/remi/Documents/gittravail/test.html") + #replace_width_height_in_file("/home/remi/Documents/gittravail/test.html", 1000, 750) end function plot_graph_comp(G, Vemph=[]; width=3, vert=true, subplt=false) plot(legend=false) CG = connected_components(G, Vemph) - println(Vemph) + #println(Vemph) plot_graphs(CG, width=width, vert=vert, subplt=true) subplt || gui()#savefig("/tmp/test.html") end @@ -66,13 +66,13 @@ function replace_width_height_in_file(filename, x, y) new_height = "\"height\": $y" # Replace the last occurrence of "width": 600 - last_width_pos = findlast(occursin(width_pattern), split(content, "\n")) + last_width_pos = findlast(occursin(width_pattern), Base.split(content, "\n")) if last_width_pos !== nothing content = replace(content, width_pattern => new_width; count=1) end # Replace the last occurrence of "height": 400 - last_height_pos = findlast(occursin(height_pattern), split(content, "\n")) + last_height_pos = findlast(occursin(height_pattern), Base.split(content, "\n")) if last_height_pos !== nothing content = replace(content, height_pattern => new_height; count=1) end diff --git a/src/connectivity/src/usolve/usolve.jl b/src/connectivity/src/usolve/usolve.jl index f9c6b28..33fd8f2 100644 --- a/src/connectivity/src/usolve/usolve.jl +++ b/src/connectivity/src/usolve/usolve.jl @@ -23,8 +23,8 @@ end function usolve_out_to_tuple(foutput="/tmp/out.us") ff = open(foutput, "r") s = read(ff, String) - Ls = split(s, "\n")[1:end-1] - Ls = [ split(ls, " ") for ls in Ls[2:end] ] + Ls = Base.split(s, "\n")[1:end-1] + Ls = [ Base.split(ls, " ") for ls in Ls[2:end] ] return [ [eval(Meta.parse("ZZ($l)")) for l in ls] for ls in Ls ] end diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index a8caca1..046286d 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -472,7 +472,7 @@ function intersect_biv(P::Vector{T} where T<:Any, A::MPolyRingElem) dAf != dAfold || break end catch - println("No rational rec..") + #println("No rational rec..") end compt += 1 end From cdd9fdfb5fdb73339462a5d731f4148630e9272c Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 10 Apr 2025 10:16:46 +0200 Subject: [PATCH 101/180] first attempt to add query points --- src/connectivity/computeRM.jl | 24 +++++++++++++----------- 1 file changed, 13 insertions(+), 11 deletions(-) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 00cc00f..504fc95 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -10,11 +10,11 @@ export change_ringvar, compute_minors, detmpoly, change_ringvar_mod, MPolyBuild include("Cannytools.jl") -function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{Vector{QQFieldElem}}([[]]) ; v=0) +function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int; Q=Vector{Vector{QQFieldElem}}([[]]), C=Vector{Vector{QQFieldElem}}([]), v=0) # V is a variety of dimension dimV # Q are base points with rational coefficients # C are query points with rational coefficients - + println(Q) A = parent(V) varias, nvarias = gens(A), nvars(A) hV = V.gens @@ -41,32 +41,34 @@ function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int, Q=Vector{V v>0 && println("Compute first the singular points") singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=max(v-1,0), nr_thrds=Threads.nthreads()) @assert(length(singFq)==0, "Non-emtpy real sing locus!") - #@assert(degree(singFq.elim)==0, "Non-emtpy sing locus!") ## K(pi_1,Fq) ## - v >0 && println("First critical points") + v>0 && println("First critical points") K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=max(v-1,0), nr_thrds=Threads.nthreads()) ## K(pi_2, Fq) ## - v >0 && println("Second critical points") + v>0 && println("Second critical points") K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors", verb=max(v-1,0), nr_thrds=Threads.nthreads()) polar = change_ringvar(K2Fq.gens, A.S) push!(R, AlgebraicSolving.Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) ## Points with vertical tg in K(pi_2, Fq) ## - v >0 && println("Vertical tg points") + v>0 && println("Vertical tg points") K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=max(v-1,0), nr_thrds=Threads.nthreads()) ## New base points ## K1W = vcat(K1Fq, K1WmFq) K1WRat = MidRationalPoints(getindex(K1W, 1)) - newQ = [ vcat(q, [kv]) for kv in K1WRat ] # Heuristic to be proven - # newQ = newQ[2:end-1] - - RFq = computeRM(V, dimV, newQ) + #K1WRat = K1WRat[2:end-1] + ########## + append!(K1WRat, [ c[e+1] for c in C if c[1:e]==q && !(c[e+1] in K1WRat) ]) |> sort! + newQ = [ vcat(q, [kv]) for kv in K1WRat ] - R = vcat(R, RFq) + if !isempty(newQ) + RFq = computeRM(V, dimV, Q=newQ, C=C) + R = vcat(R, RFq) + end end end From f2d5b93c65bc682114b4f33e31d38db9c25a69a1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Fri, 18 Apr 2025 15:33:34 +0200 Subject: [PATCH 102/180] add current files --- src/connectivity/Cannytools.jl | 309 +++++++++++++++++++++++++++++++++ src/connectivity/computeRM.jl | 90 ++++++++++ 2 files changed, 399 insertions(+) create mode 100644 src/connectivity/Cannytools.jl create mode 100644 src/connectivity/computeRM.jl diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl new file mode 100644 index 0000000..27b970b --- /dev/null +++ b/src/connectivity/Cannytools.jl @@ -0,0 +1,309 @@ +# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables +function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} + R = parent(first(F)) + # Locate variables of R in newvarias + to_varias = Vector{Int}(undef,0) + for v in newvarias_S + ind = findfirst(x->x==v, R.S) + push!(to_varias, typeof(ind)==Nothing ? length(R.S)+1 : ind) + end + + ind_novarias = setdiff(eachindex(R.S), to_varias) + newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) + + res = typeof(first(F))[] + ctx = MPolyBuildCtx(newR) + + for f in F + for (e, c) in zip(exponent_vectors(f), coefficients(f)) + @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") + push!(e, 0) + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res +end + +function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: PolyRingElem} + R = parent(first(F)) + to_varias = [ v==R.S ? 1 : 2 for v in newvarias_S] + newR, = polynomial_ring(base_ring(R), newvarias_S) + + res = typeof(zero(newR))[] + ctx = MPolyBuildCtx(newR) + + LcF = [ filter!(t->t[2]!=0, collect(enumerate(coefficients(f)))) for f in F ] + for f in LcF + for (ef, c) in f + e = [ef-1, 0] + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res +end + +function change_ringvar(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) + return first(change_ringvar([f], newvarias_S)) +end + +function change_ringvar(F::Vector{P}, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {P <: MPolyRingElem, I <: Int64} + R = parent(first(F)) + return change_ringvar(F, [R.S[i] for i in ind_newvarias]) +end + +function change_ringvar(f::MPolyRingElem, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {I <: Int64} + R = parent(f) + return first(change_ringvar([f], [R.S[i] for i in ind_newvarias])) +end + +# Return the polynomials in F, but injected in the polynomial ring with the variables occuring in F +function change_ringvar(F::Vector{P}) where {P <: MPolyRingElem} + union_varias = Set{Symbol}() + for f in F + union!(union_varias, map(Symbol, vars(f)) ) + end + return change_ringvar(F, collect(union_varias)) +end + +function change_ringvar(f::MPolyRingElem) + return first(change_ringvar([f])) +end + +# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables +function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} + R = parent(first(F)) + # Locate variables of R in newvarias + to_varias = Vector{Int}(undef,0) + for v in newvarias_S + ind = findfirst(x->x==v, oldvarias_S) + push!(to_varias, typeof(ind)==Nothing ? length(oldvarias_S)+1 : ind) + end + + ind_novarias = setdiff(eachindex(oldvarias_S), to_varias) + newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) + + res = typeof(first(F))[] + ctx = MPolyBuildCtx(newR) + + for f in F + for (e, c) in zip(exponent_vectors(f), coefficients(f)) + @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") + push!(e, 0) + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res +end + +function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: PolyRingElem} + R = parent(first(F)) + A, (x,) = polynomial_ring(base_ring(R), oldvarias_S) + return change_ringvar_mod([ evaluate(f, x) for f in F ], newvarias_S, oldvarias_S) +end + +function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) + return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) +end + +#function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) +# return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) +#end + +function MPolyBuild(F::Vector{Vector{P}}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} + A = parent(first(first(F))) + R, = polynomial_ring(A, newvarias_S) + to_varias = [ i==idx ? 1 : 2 for i in eachindex(newvarias_S) ] + + res = typeof(zero(R))[] + ctx = MPolyBuildCtx(R) + + LcF = [ filter!(t->t[2]!=0, collect(enumerate(f))) for f in F ] + for f in LcF + for (ef, c) in f + e = [ef-1, 0] + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res +end + +function MPolyBuild(f::Vector{P}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} + return first(MPolyBuild([f], newvarias_S, idx)) +end + +function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) + #println("$j $V $dimV") + # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj + @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" + R = parent(V) + n, hV = R.nvars, V.gens + c = n - dimV + + JW = transpose([ derivative(f, k) for k=j+1:n, f in hV ]) + sizeminors = c + dimproj - (j-1) + hW = vcat(hV, compute_minors(sizeminors, JW, R)) + filter!(!iszero, hW) + output_functions = Dict( + "minors" => x -> x, + "groebner" => x -> groebner_basis(x, info_level=verb,nr_thrds=nr_thrds), + "real" => x -> real_solutions(x, info_level=verb,nr_thrds=nr_thrds), + "interval" => x -> real_solutions(x, interval=true, info_level=verb,nr_thrds=nr_thrds), + "parametric" => x -> rational_parametrization(x, info_level=verb,nr_thrds=nr_thrds) + ) + + return output_functions[output](AlgebraicSolving.Ideal(hW)) +end + +function computepolarphi(j::Int, V::AlgebraicSolving.Ideal, phi::Vector{T} where T<:MPolyRingElem, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) + # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj + @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" + R = parent(V) + n, hV = nvars(R), V.gens + c = n - dimV + + if j==0 + JW = transpose([ derivative(f, k) for k=1:n, f in hV ]) + sizeminors = c + else + JW = transpose([ derivative(f, k) for k=1:n, f in vcat(hV,phi) ]) + sizeminors = c + j + dimproj - (j-1) + end + hW = vcat(hV, compute_minors(sizeminors, JW, R)) + output_functions = Dict( + "minors" => x -> x, + "groebner" => x -> groebner_basis(x, info_level=verb,nr_thrds=nr_thrds), + "real" => x -> real_solutions(x, info_level=verb,nr_thrds=nr_thrds), + "interval" => x -> real_solutions(x, interval=true, info_level=verb,nr_thrds=nr_thrds), + "parametric" => x -> rational_parametrization(x, info_level=verb,nr_thrds=nr_thrds) + ) + + return output_functions[output](AlgebraicSolving.Ideal(hW)) +end + +function compute_minors(p, A, R) + #Computes the p-minors of a matrix A + n, m = size(A) + rowsmins = collect(combinations(1:n, p)) + colsmins = collect(combinations(1:m, p)) + mins = Vector{eltype(A)}(undef, length(rowsmins) * length(colsmins)) + k = 1 + for rowsmin in rowsmins + for colsmin in colsmins + mins[k] = detmpoly(A[rowsmin, colsmin], R) + k += 1 + end + end + + return mins +end + +function combinations(a, n) + # Helper function to recursively generate combinations + function _combinations(a, n, start, chosen) + if length(chosen) == n + return [chosen] + elseif start > length(a) + return Vector{Int}([]) + else + # Include the current element and recurse + include_current = _combinations(a, n, start + 1, [chosen; a[start]]) + # Exclude the current element and recurse + exclude_current = _combinations(a, n, start + 1, chosen) + return vcat(include_current, exclude_current) + end + end + return _combinations(a, n, 1, Vector{Int}([])) +end + +function detmpoly(A::Matrix{T} where T<:MPolyRingElem, R) + # Get the size of the matrix + n = size(A, 1) + if n != size(A, 2) + throw(ArgumentError("Matrix must be square")) + end + + if n == 1 + return A[1, 1] + end + + # Initialize the determinant polynomial + detA = zero(R) + + # Compute the determinant polynomial + for j = 1:n + submatrix = A[2:end, [i for i = 1:n if i != j]] + detA += (-1)^(1+j)*A[1, j] * detmpoly(submatrix, R) + end + + return detA +end + +function contfrac_convergents(x::Rational{Int}) + q = Rational{Int}[] + fpart, ipart = modf(x) + push!(q, ipart) + na, da, nb, db = Int(1), Int(0), Int(ipart), Int(1) + while true + fpart == 0 && return q + x = inv(fpart) + fpart, ipart = modf(x) + na, da, nb, db = nb, db, na+ipart*nb, da+ipart*db + push!(q, nb//db) + end +end + +function modfQQ(x::QQFieldElem) + ipart, fpart = [ f(numerator(x), denominator(x)) for f in [div, rem]] + return QQFieldElem(fpart, denominator(x)), ipart +end + +function small_mid_point(a::QQFieldElem,b::QQFieldElem) + a == b && return a + if b < a + a, b = b, a + end + x = (a+b)/ QQFieldElem(2) + fpart, ipart = modfQQ(x) + println("\n",fpart," , ", ipart) + q1, q2 = QQFieldElem(1//0), QQFieldElem(ipart,1) + while true + #println("(",q1," ; ",q2,")") + if numerator(fpart) == 0 || (q2 > a && q2 < b) + return q2 + end + x = inv(fpart) + fpart, ipart = modfQQ(x) + println(fpart," , ", ipart) + q1, q2 = q2, QQFieldElem(numerator(q1) + ipart*numerator(q2), denominator(q1) + ipart*denominator(q2)) + end +end + +function MidRationalPoints(S::Vector{Vector{QQFieldElem}}) + # S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] + # such that the [l_i, r_i] are rational and disjoint open intervals. + # + # It orders the [l_i,r_i], removes repetitions and computes the simplest + # rational points between these intervals. + if isempty(S) + return QQFieldElem[] + end + S1 = sort(S, lt=(x, y) -> x[2] <= y[1]) + n = unique!(S1) |> length + ratioP = Vector{QQFieldElem}(undef, n-1) + for i in 1:(n- 1) + ri, li1 = S1[i][2], S1[i+1][1] + @assert ri < li1 "The intervals are not disjoint." + #ratioP[i] = small_mid_point(ri, li1) + ratioP[i] = simplest_between(ri, li1) + end + return ratioP +end + diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl new file mode 100644 index 0000000..504fc95 --- /dev/null +++ b/src/connectivity/computeRM.jl @@ -0,0 +1,90 @@ +#using Pkg +#Pkg.activate("AlgebraicSolving.jl") +#using Revise +#using AlgebraicSolving +#using Nemo + +export computeRM, computepolarproj, computepolarphi +# DEBUG +export change_ringvar, compute_minors, detmpoly, change_ringvar_mod, MPolyBuild + +include("Cannytools.jl") + +function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int; Q=Vector{Vector{QQFieldElem}}([[]]), C=Vector{Vector{QQFieldElem}}([]), v=0) + # V is a variety of dimension dimV + # Q are base points with rational coefficients + # C are query points with rational coefficients + println(Q) + A = parent(V) + varias, nvarias = gens(A), nvars(A) + hV = V.gens + #println(Q) + e = length(first(Q)) + fixvarias, newvarias = varias[1:e], varias[e+1:nvarias] + + R = Vector{AlgebraicSolving.Ideal{QQMPolyRingElem}}(undef,0) + + for q in Q + ## Fq ## + if e > 0 + hFq = change_ringvar([evaluate(h, fixvarias, q) for h in V.gens], e+1:nvarias) + Fq = AlgebraicSolving.Ideal(hFq) + else + Fq = V + end + + if dimV - e <= 1 + curve = change_ringvar(Fq.gens, A.S) + push!(R, AlgebraicSolving.Ideal(vcat(curve, [fixvarias[j] - q[j] for j in 1:e]))) + else + ## sing(Fq) ## + v>0 && println("Compute first the singular points") + singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=max(v-1,0), nr_thrds=Threads.nthreads()) + @assert(length(singFq)==0, "Non-emtpy real sing locus!") + + ## K(pi_1,Fq) ## + v>0 && println("First critical points") + K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=max(v-1,0), nr_thrds=Threads.nthreads()) + + ## K(pi_2, Fq) ## + v>0 && println("Second critical points") + K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors", verb=max(v-1,0), nr_thrds=Threads.nthreads()) + polar = change_ringvar(K2Fq.gens, A.S) + push!(R, AlgebraicSolving.Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) + + ## Points with vertical tg in K(pi_2, Fq) ## + v>0 && println("Vertical tg points") + K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=max(v-1,0), nr_thrds=Threads.nthreads()) + + ## New base points ## + K1W = vcat(K1Fq, K1WmFq) + K1WRat = MidRationalPoints(getindex(K1W, 1)) + # Heuristic to be proven + #K1WRat = K1WRat[2:end-1] + ########## + append!(K1WRat, [ c[e+1] for c in C if c[1:e]==q && !(c[e+1] in K1WRat) ]) |> sort! + newQ = [ vcat(q, [kv]) for kv in K1WRat ] + + if !isempty(newQ) + RFq = computeRM(V, dimV, Q=newQ, C=C) + R = vcat(R, RFq) + end + end + end + + return R +end + +#= +## Test ## +R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) +#h = x1^2+x2^2+x3^2+x4^2-1 +h = (x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2) +h = evaluate(h,[x1,x2,x3],[x1+rand(-10:10)*x2+rand(-10:10)*x3+rand(-10:10)*x4,x2+rand(-10:10)*x3+rand(-10:10)*x4,x3+rand(-10:10)*x4]) +V = AlgebraicSolving.Ideal([h]) + +carte = (computeRM(V, 3, [Vector{QQFieldElem}(undef,0)])) +#println(carte) +=# + + From 85d734c485cde27f0f1a481d3d895bcf5b992eef Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Fri, 18 Apr 2025 17:18:53 +0200 Subject: [PATCH 103/180] simplify computepolar + remove useless functions + remove useless checks --- src/AlgebraicSolving.jl | 2 + src/connectivity/Cannytools.jl | 215 +++------------------------------ src/connectivity/computeRM.jl | 142 ++++++++++++---------- 3 files changed, 96 insertions(+), 263 deletions(-) diff --git a/src/AlgebraicSolving.jl b/src/AlgebraicSolving.jl index 5cab42f..9c66519 100644 --- a/src/AlgebraicSolving.jl +++ b/src/AlgebraicSolving.jl @@ -18,6 +18,8 @@ include("algorithms/paramcurve.jl") include("algorithms/hilbert.jl") #= siggb =# include("siggb/siggb.jl") +#= connectivity =# +include("connectivity/computeRM.jl") #= examples =# include("examples/katsura.jl") include("examples/cyclic.jl") diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 27b970b..16c274a 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -1,191 +1,22 @@ -# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables -function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} - R = parent(first(F)) - # Locate variables of R in newvarias - to_varias = Vector{Int}(undef,0) - for v in newvarias_S - ind = findfirst(x->x==v, R.S) - push!(to_varias, typeof(ind)==Nothing ? length(R.S)+1 : ind) - end - - ind_novarias = setdiff(eachindex(R.S), to_varias) - newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) - - res = typeof(first(F))[] - ctx = MPolyBuildCtx(newR) - - for f in F - for (e, c) in zip(exponent_vectors(f), coefficients(f)) - @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") - push!(e, 0) - push_term!(ctx, c, [e[i] for i in to_varias ]) - end - push!(res, finish(ctx)) - end - - return res -end - -function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: PolyRingElem} - R = parent(first(F)) - to_varias = [ v==R.S ? 1 : 2 for v in newvarias_S] - newR, = polynomial_ring(base_ring(R), newvarias_S) - - res = typeof(zero(newR))[] - ctx = MPolyBuildCtx(newR) - - LcF = [ filter!(t->t[2]!=0, collect(enumerate(coefficients(f)))) for f in F ] - for f in LcF - for (ef, c) in f - e = [ef-1, 0] - push_term!(ctx, c, [e[i] for i in to_varias ]) - end - push!(res, finish(ctx)) - end - - return res -end - -function change_ringvar(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) - return first(change_ringvar([f], newvarias_S)) -end - -function change_ringvar(F::Vector{P}, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {P <: MPolyRingElem, I <: Int64} - R = parent(first(F)) - return change_ringvar(F, [R.S[i] for i in ind_newvarias]) -end - -function change_ringvar(f::MPolyRingElem, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {I <: Int64} - R = parent(f) - return first(change_ringvar([f], [R.S[i] for i in ind_newvarias])) -end - -# Return the polynomials in F, but injected in the polynomial ring with the variables occuring in F -function change_ringvar(F::Vector{P}) where {P <: MPolyRingElem} - union_varias = Set{Symbol}() - for f in F - union!(union_varias, map(Symbol, vars(f)) ) - end - return change_ringvar(F, collect(union_varias)) -end - -function change_ringvar(f::MPolyRingElem) - return first(change_ringvar([f])) -end - -# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables -function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} - R = parent(first(F)) - # Locate variables of R in newvarias - to_varias = Vector{Int}(undef,0) - for v in newvarias_S - ind = findfirst(x->x==v, oldvarias_S) - push!(to_varias, typeof(ind)==Nothing ? length(oldvarias_S)+1 : ind) - end - - ind_novarias = setdiff(eachindex(oldvarias_S), to_varias) - newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) - - res = typeof(first(F))[] - ctx = MPolyBuildCtx(newR) - - for f in F - for (e, c) in zip(exponent_vectors(f), coefficients(f)) - @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") - push!(e, 0) - push_term!(ctx, c, [e[i] for i in to_varias ]) - end - push!(res, finish(ctx)) - end - - return res -end - -function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: PolyRingElem} - R = parent(first(F)) - A, (x,) = polynomial_ring(base_ring(R), oldvarias_S) - return change_ringvar_mod([ evaluate(f, x) for f in F ], newvarias_S, oldvarias_S) -end - -function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) - return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) -end - -#function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) -# return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) -#end - -function MPolyBuild(F::Vector{Vector{P}}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} - A = parent(first(first(F))) - R, = polynomial_ring(A, newvarias_S) - to_varias = [ i==idx ? 1 : 2 for i in eachindex(newvarias_S) ] - - res = typeof(zero(R))[] - ctx = MPolyBuildCtx(R) - - LcF = [ filter!(t->t[2]!=0, collect(enumerate(f))) for f in F ] - for f in LcF - for (ef, c) in f - e = [ef-1, 0] - push_term!(ctx, c, [e[i] for i in to_varias ]) - end - push!(res, finish(ctx)) - end - - return res -end - -function MPolyBuild(f::Vector{P}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} - return first(MPolyBuild([f], newvarias_S, idx)) -end - -function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) - #println("$j $V $dimV") - # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj - @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" +# Compute the set of points x where phi_j(T_x(V)) has dimension < dimproj +function computepolar( + j::Int, # j-th first coordinate images of phi + V::Ideal{P}; # input ideal + phi::Vector{P} = P[], # polynomial map in consideration (completed by sufficiently many projections) + dimproj = j-1, # maximum dimension of tangent space of phi + v=0, # verbosity level + ) where (P <: MPolyRingElem) + V.dim == -1 && dimension(V) R = parent(V) - n, hV = R.nvars, V.gens - c = n - dimV + n = nvars(R) + c = n - V.dim + nphi = length(phi) - JW = transpose([ derivative(f, k) for k=j+1:n, f in hV ]) - sizeminors = c + dimproj - (j-1) - hW = vcat(hV, compute_minors(sizeminors, JW, R)) - filter!(!iszero, hW) - output_functions = Dict( - "minors" => x -> x, - "groebner" => x -> groebner_basis(x, info_level=verb,nr_thrds=nr_thrds), - "real" => x -> real_solutions(x, info_level=verb,nr_thrds=nr_thrds), - "interval" => x -> real_solutions(x, interval=true, info_level=verb,nr_thrds=nr_thrds), - "parametric" => x -> rational_parametrization(x, info_level=verb,nr_thrds=nr_thrds) - ) + JW = transpose([ derivative(f, k) for k=max(j+1-nphi,0):n, f in vcat(V.gens, phi[1:min(j,nphi)])]) + sizeminors = c + min(nphi,j) + min(dimproj,j-1) - (j-1) + minors = compute_minors(sizeminors, JW, R) - return output_functions[output](AlgebraicSolving.Ideal(hW)) -end - -function computepolarphi(j::Int, V::AlgebraicSolving.Ideal, phi::Vector{T} where T<:MPolyRingElem, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) - # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj - @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" - R = parent(V) - n, hV = nvars(R), V.gens - c = n - dimV - - if j==0 - JW = transpose([ derivative(f, k) for k=1:n, f in hV ]) - sizeminors = c - else - JW = transpose([ derivative(f, k) for k=1:n, f in vcat(hV,phi) ]) - sizeminors = c + j + dimproj - (j-1) - end - hW = vcat(hV, compute_minors(sizeminors, JW, R)) - output_functions = Dict( - "minors" => x -> x, - "groebner" => x -> groebner_basis(x, info_level=verb,nr_thrds=nr_thrds), - "real" => x -> real_solutions(x, info_level=verb,nr_thrds=nr_thrds), - "interval" => x -> real_solutions(x, interval=true, info_level=verb,nr_thrds=nr_thrds), - "parametric" => x -> rational_parametrization(x, info_level=verb,nr_thrds=nr_thrds) - ) - - return output_functions[output](AlgebraicSolving.Ideal(hW)) + return Ideal(vcat(V.gens, minors)) end function compute_minors(p, A, R) @@ -246,20 +77,6 @@ function detmpoly(A::Matrix{T} where T<:MPolyRingElem, R) return detA end -function contfrac_convergents(x::Rational{Int}) - q = Rational{Int}[] - fpart, ipart = modf(x) - push!(q, ipart) - na, da, nb, db = Int(1), Int(0), Int(ipart), Int(1) - while true - fpart == 0 && return q - x = inv(fpart) - fpart, ipart = modf(x) - na, da, nb, db = nb, db, na+ipart*nb, da+ipart*db - push!(q, nb//db) - end -end - function modfQQ(x::QQFieldElem) ipart, fpart = [ f(numerator(x), denominator(x)) for f in [div, rem]] return QQFieldElem(fpart, denominator(x)), ipart diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 504fc95..418a4fb 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,75 +4,89 @@ #using AlgebraicSolving #using Nemo -export computeRM, computepolarproj, computepolarphi +export computeRM, computepolarproj, computepolarphi, computepolar # DEBUG -export change_ringvar, compute_minors, detmpoly, change_ringvar_mod, MPolyBuild +export compute_minors, detmpoly, change_ringvar_mod, MPolyBuild include("Cannytools.jl") -function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int; Q=Vector{Vector{QQFieldElem}}([[]]), C=Vector{Vector{QQFieldElem}}([]), v=0) - # V is a variety of dimension dimV - # Q are base points with rational coefficients - # C are query points with rational coefficients - println(Q) - A = parent(V) - varias, nvarias = gens(A), nvars(A) - hV = V.gens - #println(Q) - e = length(first(Q)) - fixvarias, newvarias = varias[1:e], varias[e+1:nvarias] - - R = Vector{AlgebraicSolving.Ideal{QQMPolyRingElem}}(undef,0) - - for q in Q - ## Fq ## - if e > 0 - hFq = change_ringvar([evaluate(h, fixvarias, q) for h in V.gens], e+1:nvarias) - Fq = AlgebraicSolving.Ideal(hFq) - else - Fq = V - end - - if dimV - e <= 1 - curve = change_ringvar(Fq.gens, A.S) - push!(R, AlgebraicSolving.Ideal(vcat(curve, [fixvarias[j] - q[j] for j in 1:e]))) - else - ## sing(Fq) ## - v>0 && println("Compute first the singular points") - singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=max(v-1,0), nr_thrds=Threads.nthreads()) - @assert(length(singFq)==0, "Non-emtpy real sing locus!") - - ## K(pi_1,Fq) ## - v>0 && println("First critical points") - K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=max(v-1,0), nr_thrds=Threads.nthreads()) - - ## K(pi_2, Fq) ## - v>0 && println("Second critical points") - K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors", verb=max(v-1,0), nr_thrds=Threads.nthreads()) - polar = change_ringvar(K2Fq.gens, A.S) - push!(R, AlgebraicSolving.Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) - - ## Points with vertical tg in K(pi_2, Fq) ## - v>0 && println("Vertical tg points") - K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=max(v-1,0), nr_thrds=Threads.nthreads()) - - ## New base points ## - K1W = vcat(K1Fq, K1WmFq) - K1WRat = MidRationalPoints(getindex(K1W, 1)) - # Heuristic to be proven - #K1WRat = K1WRat[2:end-1] - ########## - append!(K1WRat, [ c[e+1] for c in C if c[1:e]==q && !(c[e+1] in K1WRat) ]) |> sort! - newQ = [ vcat(q, [kv]) for kv in K1WRat ] - - if !isempty(newQ) - RFq = computeRM(V, dimV, Q=newQ, C=C) - R = vcat(R, RFq) +function computeRM( + V::Ideal{T} where T <: QQMPolyRingElem; # input ideal + Q::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # base points with rational coefficients + C::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # query points with rational coefficients + v::Int=0, # verbosity level + checks::Bool=false # perform checks (dimension, regularity, etc.) + ) + # Some preprocessing + V.dim == -1 && dimension(V) + println(Q) + isempty(Q) && push!(Q,[]) + # Get data + A = parent(V) + varias, nvarias = gens(A), nvars(A) + e = length(first(Q)) + fixvarias = varias[1:e] + + RM = Vector{Ideal{QQMPolyRingElem}}(undef,0) + for q in Q + ## Fq ## + if e > 0 + hFq = change_ringvar([evaluate(h, fixvarias, q) for h in V.gens], A.S[e+1:end]) + Fq = Ideal(hFq) + else + Fq = V + end + # Genericity assumption (can be checked) + Fq.dim = V.dim - e + + if V.dim - e <= 1 + curve = change_ringvar(Fq.gens, A.S) + push!(RM, Ideal(vcat(curve, [fixvarias[j] - q[j] for j in 1:e]))) + else + ## sing(Fq) ## + if checks + v>0 && println("Compute first the singular points") + singFq = computepolar(0, Fq, v=max(v-1,0)) + @assert(isempty(real_solutions(singFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads())), "Non-emtpy real sing locus!") + end + + ## K(pi_1,Fq) ## + v>0 && println("First critical points") + K1Fq = computepolar(1, Fq, v=max(v-1,0)) + K1Fq = real_solutions(K1Fq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) + + ## K(pi_2, Fq) ## + v>0 && println("Second critical points") + K2Fq = computepolar(2, Fq, v=max(v-1,0)) + if checks + @assert(isone(dimension(K2Fq)), "Non-generic polar variety") + end + K2Fq.dim = 1 + polar = change_ringvar(K2Fq.gens, A.S) + push!(RM, Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) + + ## Points with vertical tg in K(pi_2, Fq) ## + v>0 && println("Vertical tg points") + K1WmFq = computepolar(2, K2Fq, dimproj=0, v=max(v-1,0)) + K1WmFq = real_solutions(K1WmFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) + + ## New base points ## + K1W = vcat(K1Fq, K1WmFq) + K1WRat = MidRationalPoints(getindex(K1W, 1)) + # Heuristic to be proven + #K1WRat = K1WRat[2:end-1] + ########## + append!(K1WRat, [ c[e+1] for c in C if c[1:e]==q && !(c[e+1] in K1WRat) ]) |> sort! + newQ = [ vcat(q, [kv]) for kv in K1WRat ] + + if !isempty(newQ) + RMFq = computeRM(V, Q=newQ, C=C) + append!(RM, RMFq) + end end - end - end + end - return R + return RM end #= @@ -81,7 +95,7 @@ R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) #h = x1^2+x2^2+x3^2+x4^2-1 h = (x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2) h = evaluate(h,[x1,x2,x3],[x1+rand(-10:10)*x2+rand(-10:10)*x3+rand(-10:10)*x4,x2+rand(-10:10)*x3+rand(-10:10)*x4,x3+rand(-10:10)*x4]) -V = AlgebraicSolving.Ideal([h]) +V = Ideal([h]) carte = (computeRM(V, 3, [Vector{QQFieldElem}(undef,0)])) #println(carte) From 7f0c5614e40be5760791d989a8fbcb2ff9832425 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Fri, 18 Apr 2025 18:25:17 +0200 Subject: [PATCH 104/180] remove query points --- src/connectivity/computeRM.jl | 17 ++++++++++++----- 1 file changed, 12 insertions(+), 5 deletions(-) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 418a4fb..1d8d9f8 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -17,13 +17,19 @@ function computeRM( v::Int=0, # verbosity level checks::Bool=false # perform checks (dimension, regularity, etc.) ) + # Some base cases + A = parent(V) + varias = gens(A) + if length(varias)<=2 + return [V] + end # Some preprocessing V.dim == -1 && dimension(V) println(Q) + println(C) + println() isempty(Q) && push!(Q,[]) - # Get data - A = parent(V) - varias, nvarias = gens(A), nvars(A) + # Base points e = length(first(Q)) fixvarias = varias[1:e] @@ -76,11 +82,12 @@ function computeRM( # Heuristic to be proven #K1WRat = K1WRat[2:end-1] ########## - append!(K1WRat, [ c[e+1] for c in C if c[1:e]==q && !(c[e+1] in K1WRat) ]) |> sort! + Cq = [c for c in C if c[1:e]==q] + append!(K1WRat, getindex.(Cq, e+1)) |> sort! newQ = [ vcat(q, [kv]) for kv in K1WRat ] if !isempty(newQ) - RMFq = computeRM(V, Q=newQ, C=C) + RMFq = computeRM(V, Q=newQ, C=Cq) append!(RM, RMFq) end end From 9477d47954c0b1a1cf5f219325cd5c3c3c6ebb82 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Tue, 22 Apr 2025 20:18:42 +0200 Subject: [PATCH 105/180] remove custom small_mid_point + debut canny param --- src/connectivity/Cannytools.jl | 30 +-------- src/connectivity/computeRM.jl | 113 ++++++++++++++++++--------------- 2 files changed, 64 insertions(+), 79 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 16c274a..49dd3c6 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -77,32 +77,6 @@ function detmpoly(A::Matrix{T} where T<:MPolyRingElem, R) return detA end -function modfQQ(x::QQFieldElem) - ipart, fpart = [ f(numerator(x), denominator(x)) for f in [div, rem]] - return QQFieldElem(fpart, denominator(x)), ipart -end - -function small_mid_point(a::QQFieldElem,b::QQFieldElem) - a == b && return a - if b < a - a, b = b, a - end - x = (a+b)/ QQFieldElem(2) - fpart, ipart = modfQQ(x) - println("\n",fpart," , ", ipart) - q1, q2 = QQFieldElem(1//0), QQFieldElem(ipart,1) - while true - #println("(",q1," ; ",q2,")") - if numerator(fpart) == 0 || (q2 > a && q2 < b) - return q2 - end - x = inv(fpart) - fpart, ipart = modfQQ(x) - println(fpart," , ", ipart) - q1, q2 = q2, QQFieldElem(numerator(q1) + ipart*numerator(q2), denominator(q1) + ipart*denominator(q2)) - end -end - function MidRationalPoints(S::Vector{Vector{QQFieldElem}}) # S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] # such that the [l_i, r_i] are rational and disjoint open intervals. @@ -118,8 +92,8 @@ function MidRationalPoints(S::Vector{Vector{QQFieldElem}}) for i in 1:(n- 1) ri, li1 = S1[i][2], S1[i+1][1] @assert ri < li1 "The intervals are not disjoint." - #ratioP[i] = small_mid_point(ri, li1) - ratioP[i] = simplest_between(ri, li1) + eps = (li1-ri)//1000 + ratioP[i] = simplest_between(ri + eps, li1 - eps) end return ratioP end diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 1d8d9f8..9257763 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,13 +4,22 @@ #using AlgebraicSolving #using Nemo -export computeRM, computepolarproj, computepolarphi, computepolar +export roadmap, computepolarproj, computepolarphi, computepolar # DEBUG -export compute_minors, detmpoly, change_ringvar_mod, MPolyBuild - +export compute_minors, detmpoly, change_ringvar_mod, MPolyBuild, small_mid_point include("Cannytools.jl") -function computeRM( +function roadmap( + V::Ideal{P}; # input ideal + Q::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # base points with rational coefficients + C::Vector{Vector{P}}=Vector{Vector{P}}(), # query points with rational coefficients + v::Int=0, # verbosity level + checks::Bool=false # perform checks (dimension, regularity, etc.) +) where (P <: QQMPolyRingElem) + CQ = real_solutions(C, info_level=max(v-1,0), nr_thrds=Threads.nthreads()) +end + +function roadmap( V::Ideal{T} where T <: QQMPolyRingElem; # input ideal Q::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # base points with rational coefficients C::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # query points with rational coefficients @@ -36,60 +45,62 @@ function computeRM( RM = Vector{Ideal{QQMPolyRingElem}}(undef,0) for q in Q ## Fq ## - if e > 0 - hFq = change_ringvar([evaluate(h, fixvarias, q) for h in V.gens], A.S[e+1:end]) - Fq = Ideal(hFq) + Fq = e > 0 ? Ideal(change_ringvar([evaluate(h, fixvarias, q) for h in V.gens], A.S[e+1:end])) : V + # Genericity assumption (can be checked) + if checks + @assert(dimension(Fq) == V.dim - e, "Non-generic polar variety") else - Fq = V + Fq.dim = V.dim - e end - # Genericity assumption (can be checked) - Fq.dim = V.dim - e - if V.dim - e <= 1 + # Terminal case (dim <=1) + if Fq.dim <= 1 curve = change_ringvar(Fq.gens, A.S) push!(RM, Ideal(vcat(curve, [fixvarias[j] - q[j] for j in 1:e]))) + continue + end + + ## sing(Fq) ## + if checks + v>0 && println("Compute first the singular points") + singFq = computepolar(0, Fq, v=max(v-1,0)) + @assert(isempty(real_solutions(singFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads())), "Non-emtpy real sing locus!") + end + + ## K(pi_1,Fq) ## + v>0 && println("First critical points") + K1Fq = computepolar(1, Fq, v=max(v-1,0)) + K1Fq = real_solutions(K1Fq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) + + ## K(pi_2, Fq) ## + v>0 && println("Second critical points") + K2Fq = computepolar(2, Fq, v=max(v-1,0)) + if checks + @assert(isone(dimension(K2Fq)), "Non-generic polar variety") else - ## sing(Fq) ## - if checks - v>0 && println("Compute first the singular points") - singFq = computepolar(0, Fq, v=max(v-1,0)) - @assert(isempty(real_solutions(singFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads())), "Non-emtpy real sing locus!") - end - - ## K(pi_1,Fq) ## - v>0 && println("First critical points") - K1Fq = computepolar(1, Fq, v=max(v-1,0)) - K1Fq = real_solutions(K1Fq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) - - ## K(pi_2, Fq) ## - v>0 && println("Second critical points") - K2Fq = computepolar(2, Fq, v=max(v-1,0)) - if checks - @assert(isone(dimension(K2Fq)), "Non-generic polar variety") - end K2Fq.dim = 1 - polar = change_ringvar(K2Fq.gens, A.S) - push!(RM, Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) - - ## Points with vertical tg in K(pi_2, Fq) ## - v>0 && println("Vertical tg points") - K1WmFq = computepolar(2, K2Fq, dimproj=0, v=max(v-1,0)) - K1WmFq = real_solutions(K1WmFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) - - ## New base points ## - K1W = vcat(K1Fq, K1WmFq) - K1WRat = MidRationalPoints(getindex(K1W, 1)) - # Heuristic to be proven - #K1WRat = K1WRat[2:end-1] - ########## - Cq = [c for c in C if c[1:e]==q] - append!(K1WRat, getindex.(Cq, e+1)) |> sort! - newQ = [ vcat(q, [kv]) for kv in K1WRat ] - - if !isempty(newQ) - RMFq = computeRM(V, Q=newQ, C=Cq) - append!(RM, RMFq) - end + end + polar = change_ringvar(K2Fq.gens, A.S) + push!(RM, Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) + + ## Points with vertical tg in K(pi_2, Fq) ## + v>0 && println("Vertical tg points") + K1WmFq = computepolar(2, K2Fq, dimproj=0, v=max(v-1,0)) + K1WmFq = real_solutions(K1WmFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) + + ## New base points ## + K1W = vcat(K1Fq, K1WmFq) + K1WRat = MidRationalPoints(getindex(K1W, 1)) + # Heuristic to be proven + #K1WRat = K1WRat[2:end-1] + ########## + Cq = [c for c in C if c[1:e]==q] + append!(K1WRat, getindex.(Cq, e+1)) |> sort! + newQ = [ vcat(q, [kv]) for kv in K1WRat ] + + if !isempty(newQ) + RMFq = roadmap(V, Q=newQ, C=Cq) + append!(RM, RMFq) end end From 0d811458d37af7b337415f7c8b6217f37d404f6e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 23 Apr 2025 18:33:23 +0200 Subject: [PATCH 106/180] roadmap query ideal --- src/algorithms/paramcurve.jl | 2 +- src/connectivity/computeRM.jl | 24 +++++++++++++----------- 2 files changed, 14 insertions(+), 12 deletions(-) diff --git a/src/algorithms/paramcurve.jl b/src/algorithms/paramcurve.jl index 7868ff5..f74a061 100644 --- a/src/algorithms/paramcurve.jl +++ b/src/algorithms/paramcurve.jl @@ -1,4 +1,4 @@ -export rational_curve_parametrization +export rational_curve_parametrization, add_genvars @doc Markdown.doc""" rational_curve_parametrization(I::Ideal{T} where T <: MPolyRingElem, ) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 9257763..1979775 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -9,16 +9,6 @@ export roadmap, computepolarproj, computepolarphi, computepolar export compute_minors, detmpoly, change_ringvar_mod, MPolyBuild, small_mid_point include("Cannytools.jl") -function roadmap( - V::Ideal{P}; # input ideal - Q::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # base points with rational coefficients - C::Vector{Vector{P}}=Vector{Vector{P}}(), # query points with rational coefficients - v::Int=0, # verbosity level - checks::Bool=false # perform checks (dimension, regularity, etc.) -) where (P <: QQMPolyRingElem) - CQ = real_solutions(C, info_level=max(v-1,0), nr_thrds=Threads.nthreads()) -end - function roadmap( V::Ideal{T} where T <: QQMPolyRingElem; # input ideal Q::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # base points with rational coefficients @@ -95,7 +85,7 @@ function roadmap( #K1WRat = K1WRat[2:end-1] ########## Cq = [c for c in C if c[1:e]==q] - append!(K1WRat, getindex.(Cq, e+1)) |> sort! + append!(K1WRat, unique(getindex.(Cq, e+1))) |> sort! newQ = [ vcat(q, [kv]) for kv in K1WRat ] if !isempty(newQ) @@ -107,6 +97,18 @@ function roadmap( return RM end +function roadmap( + V::Ideal{P}, # input ideal + C::Ideal{P}; # query points as an ideal + v::Int=0, # verbosity level + checks::Bool=false # perform checks (dimension, regularity, etc.) +) where (P <: QQMPolyRingElem) + println("plop") + @assert(parent(V)==parent(C), "Equations for variety and query points must be in the same ring") + CQ = real_solutions(C, info_level=max(v-1,0), nr_thrds=Threads.nthreads()) + return roadmap(V, C=CQ, v=v, checks=checks) +end + #= ## Test ## R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) From c65a16932851ba2deea860872f78fbb56efb3a5c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 23 Apr 2025 19:51:46 +0200 Subject: [PATCH 107/180] MidRationalPoints: improve + add query points --- src/connectivity/Cannytools.jl | 57 ++++++++++++++++++++++++++-------- src/connectivity/computeRM.jl | 4 +-- 2 files changed, 45 insertions(+), 16 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 49dd3c6..6a7f90f 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -77,24 +77,55 @@ function detmpoly(A::Matrix{T} where T<:MPolyRingElem, R) return detA end -function MidRationalPoints(S::Vector{Vector{QQFieldElem}}) - # S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] +function MidRationalPoints(S::Vector{Vector{T}}, Q::Vector{T} = T[]) where {T <: QQFieldElem} + # * S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] # such that the [l_i, r_i] are rational and disjoint open intervals. + # * Q is a list of rationals that intersects no [l_i,r_i] # - # It orders the [l_i,r_i], removes repetitions and computes the simplest - # rational points between these intervals. - if isempty(S) - return QQFieldElem[] + # It orders the [l_i,r_i], and compute a list ratioP such that + # strictly between each of these intervals there is: + # - either at least one element of Q + # - or the simplest rational number + isempty(S) && return Q + + S1, Q1 = sort(S, lt=(x, y) -> x[2] <= y[1]), sort(Q) + ratioP = T[] + qidx = 1 + qlen = length(Q1) + + # Handle left gap before first interval + while qidx <= qlen && Q1[qidx] < S1[1][1] + push!(ratioP, Q1[qidx]) + qidx += 1 end - S1 = sort(S, lt=(x, y) -> x[2] <= y[1]) - n = unique!(S1) |> length - ratioP = Vector{QQFieldElem}(undef, n-1) - for i in 1:(n- 1) + + # Loop through gaps between sorted disjoint intervals + for i in 1:(length(S1) - 1) ri, li1 = S1[i][2], S1[i+1][1] - @assert ri < li1 "The intervals are not disjoint." - eps = (li1-ri)//1000 - ratioP[i] = simplest_between(ri + eps, li1 - eps) + @assert ri < li1 "Intervals are not disjoint." + inserted = false + while qidx <= qlen && Q1[qidx] < li1 + push!(ratioP, Q1[qidx]) + inserted = true + qidx += 1 + end + if !inserted + eps = (li1 - ri)//1000 # for open interval + # We choose the simplest in absolute value + if -ri > li1 # this means ri is negative and the largest in absolute value + push!(ratioP, -simplest_between(-ri - eps, -li1 + eps)) + else + push!(ratioP, simplest_between(ri + eps, li1 - eps)) + end + end + end + + # Append remaining right-side Q points + while qidx <= qlen + push!(ratioP, Q1[qidx]) + qidx += 1 end + return ratioP end diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 1979775..de7a387 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,9 +4,7 @@ #using AlgebraicSolving #using Nemo -export roadmap, computepolarproj, computepolarphi, computepolar -# DEBUG -export compute_minors, detmpoly, change_ringvar_mod, MPolyBuild, small_mid_point +export roadmap, computepolar include("Cannytools.jl") function roadmap( From 9b2691aaa21d63ff6dca9dd866da3ae91ae7352d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 23 Apr 2025 21:18:22 +0200 Subject: [PATCH 108/180] avoid intermediate fibers when already intermediate query points + big bug --- src/algorithms/paramcurve.jl | 2 +- src/algorithms/solvers.jl | 2 +- src/connectivity/Cannytools.jl | 1 + src/connectivity/computeRM.jl | 41 ++++++++++++++++------------------ 4 files changed, 22 insertions(+), 24 deletions(-) diff --git a/src/algorithms/paramcurve.jl b/src/algorithms/paramcurve.jl index f74a061..a4e7640 100644 --- a/src/algorithms/paramcurve.jl +++ b/src/algorithms/paramcurve.jl @@ -1,4 +1,4 @@ -export rational_curve_parametrization, add_genvars +export rational_curve_parametrization, add_genvars, change_ringvar @doc Markdown.doc""" rational_curve_parametrization(I::Ideal{T} where T <: MPolyRingElem, ) diff --git a/src/algorithms/solvers.jl b/src/algorithms/solvers.jl index ebf4539..af5a162 100644 --- a/src/algorithms/solvers.jl +++ b/src/algorithms/solvers.jl @@ -272,7 +272,7 @@ end rational_solutions(I::Ideal{T} where T <: MPolyRingElem, ) Given an ideal `I` with a finite solution set over the complex numbers, return -the rational roots of the ideal. +the rational roots of the ideal. # Arguments - `I::Ideal{T} where T <: MPolyRingElem`: input generators. diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 6a7f90f..2cf35df 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -105,6 +105,7 @@ function MidRationalPoints(S::Vector{Vector{T}}, Q::Vector{T} = T[]) where {T <: @assert ri < li1 "Intervals are not disjoint." inserted = false while qidx <= qlen && Q1[qidx] < li1 + @assert(Q1[qidx] > ri, "A query point is singular") push!(ratioP, Q1[qidx]) inserted = true qidx += 1 diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index de7a387..c508184 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,7 +4,7 @@ #using AlgebraicSolving #using Nemo -export roadmap, computepolar +export roadmap, computepolar, MidRationalPoints include("Cannytools.jl") function roadmap( @@ -22,9 +22,6 @@ function roadmap( end # Some preprocessing V.dim == -1 && dimension(V) - println(Q) - println(C) - println() isempty(Q) && push!(Q,[]) # Base points e = length(first(Q)) @@ -50,18 +47,19 @@ function roadmap( ## sing(Fq) ## if checks - v>0 && println("Compute first the singular points") + v>0 && println("Check real quasi-smoothness") singFq = computepolar(0, Fq, v=max(v-1,0)) - @assert(isempty(real_solutions(singFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads())), "Non-emtpy real sing locus!") + @assert(isempty(real_solutions(singFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads())), + "Non-empty real sing locus!") end ## K(pi_1,Fq) ## - v>0 && println("First critical points") + v>0 && println("V-critical points") K1Fq = computepolar(1, Fq, v=max(v-1,0)) K1Fq = real_solutions(K1Fq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) ## K(pi_2, Fq) ## - v>0 && println("Second critical points") + v>0 && println("Polar variety") K2Fq = computepolar(2, Fq, v=max(v-1,0)) if checks @assert(isone(dimension(K2Fq)), "Non-generic polar variety") @@ -72,20 +70,20 @@ function roadmap( push!(RM, Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) ## Points with vertical tg in K(pi_2, Fq) ## - v>0 && println("Vertical tg points") + v>0 && println("W-critical points with vertical tangent") K1WmFq = computepolar(2, K2Fq, dimproj=0, v=max(v-1,0)) K1WmFq = real_solutions(K1WmFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) - ## New base points ## + ## New base and query points ## + Cq = isempty(q) ? C : [ c[2:end] for c in C if c[1] == q[e]] K1W = vcat(K1Fq, K1WmFq) - K1WRat = MidRationalPoints(getindex(K1W, 1)) - # Heuristic to be proven - #K1WRat = K1WRat[2:end-1] + # Heuristic to be proven (Reeb's th) + #K1W = K1W[2:end-1] ########## - Cq = [c for c in C if c[1:e]==q] - append!(K1WRat, unique(getindex.(Cq, e+1))) |> sort! - newQ = [ vcat(q, [kv]) for kv in K1WRat ] + K1WRat = MidRationalPoints(first.(K1W), unique(first.(Cq))) + newQ = vcat.(Ref(q), K1WRat) + # Recursively compute roadmap of possible fibers if !isempty(newQ) RMFq = roadmap(V, Q=newQ, C=Cq) append!(RM, RMFq) @@ -96,13 +94,12 @@ function roadmap( end function roadmap( - V::Ideal{P}, # input ideal - C::Ideal{P}; # query points as an ideal - v::Int=0, # verbosity level - checks::Bool=false # perform checks (dimension, regularity, etc.) + V::Ideal{P}, # input ideal + C::Ideal{P}; # ideal defining query points + v::Int=0, # verbosity level + checks::Bool=false # perform checks (dimension, regularity, etc.) ) where (P <: QQMPolyRingElem) - println("plop") - @assert(parent(V)==parent(C), "Equations for variety and query points must be in the same ring") + @assert(parent(V)==parent(C), "Equations for variety and query points must live the same ring") CQ = real_solutions(C, info_level=max(v-1,0), nr_thrds=Threads.nthreads()) return roadmap(V, C=CQ, v=v, checks=checks) end From 8c96896a4aadd205c8d59e3989d83d7c1a214c46 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 23 Apr 2025 22:23:37 +0200 Subject: [PATCH 109/180] no evaluation during recursive steps of roadmap --- src/connectivity/Cannytools.jl | 5 +++-- src/connectivity/computeRM.jl | 27 +++++++++++++++------------ 2 files changed, 18 insertions(+), 14 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 2cf35df..57f1af9 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -3,13 +3,14 @@ function computepolar( j::Int, # j-th first coordinate images of phi V::Ideal{P}; # input ideal phi::Vector{P} = P[], # polynomial map in consideration (completed by sufficiently many projections) + dim = -1, # specify dimension of V dimproj = j-1, # maximum dimension of tangent space of phi v=0, # verbosity level ) where (P <: MPolyRingElem) - V.dim == -1 && dimension(V) + dim == -1 && V.dim == -1 && dimension(V) R = parent(V) n = nvars(R) - c = n - V.dim + c = n - max(dim, V.dim) nphi = length(phi) JW = transpose([ derivative(f, k) for k=max(j+1-nphi,0):n, f in vcat(V.gens, phi[1:min(j,nphi)])]) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index c508184..e15943b 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -25,13 +25,12 @@ function roadmap( isempty(Q) && push!(Q,[]) # Base points e = length(first(Q)) - fixvarias = varias[1:e] RM = Vector{Ideal{QQMPolyRingElem}}(undef,0) for q in Q ## Fq ## - Fq = e > 0 ? Ideal(change_ringvar([evaluate(h, fixvarias, q) for h in V.gens], A.S[e+1:end])) : V # Genericity assumption (can be checked) + Fq = fbr(V, q) if checks @assert(dimension(Fq) == V.dim - e, "Non-generic polar variety") else @@ -40,47 +39,46 @@ function roadmap( # Terminal case (dim <=1) if Fq.dim <= 1 - curve = change_ringvar(Fq.gens, A.S) - push!(RM, Ideal(vcat(curve, [fixvarias[j] - q[j] for j in 1:e]))) + push!(RM, Fq) continue end ## sing(Fq) ## if checks v>0 && println("Check real quasi-smoothness") - singFq = computepolar(0, Fq, v=max(v-1,0)) + singFq = fbr(computepolar(e, V, v=max(v-1,0)), q) @assert(isempty(real_solutions(singFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads())), "Non-empty real sing locus!") end ## K(pi_1,Fq) ## v>0 && println("V-critical points") - K1Fq = computepolar(1, Fq, v=max(v-1,0)) + K1Fq = fbr(computepolar(e+1, V, v=max(v-1,0)), q) K1Fq = real_solutions(K1Fq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) ## K(pi_2, Fq) ## v>0 && println("Polar variety") - K2Fq = computepolar(2, Fq, v=max(v-1,0)) + K2Fqmins = computepolar(e+2, V, v=max(v-1,0)) + K2Fq = fbr(K2Fqmins, q) if checks @assert(isone(dimension(K2Fq)), "Non-generic polar variety") else K2Fq.dim = 1 end - polar = change_ringvar(K2Fq.gens, A.S) - push!(RM, Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) + push!(RM, K2Fq) ## Points with vertical tg in K(pi_2, Fq) ## v>0 && println("W-critical points with vertical tangent") - K1WmFq = computepolar(2, K2Fq, dimproj=0, v=max(v-1,0)) + K1WmFq = fbr(computepolar(e+2, K2Fqmins, dim=e+1, dimproj=e+0, v=max(v-1,0)), q) K1WmFq = real_solutions(K1WmFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) ## New base and query points ## - Cq = isempty(q) ? C : [ c[2:end] for c in C if c[1] == q[e]] + Cq = isempty(q) ? C : [ c for c in C if c[e] == q[e]] K1W = vcat(K1Fq, K1WmFq) # Heuristic to be proven (Reeb's th) #K1W = K1W[2:end-1] ########## - K1WRat = MidRationalPoints(first.(K1W), unique(first.(Cq))) + K1WRat = MidRationalPoints(getindex.(K1W,e+1), unique(getindex.(Cq, e+1))) newQ = vcat.(Ref(q), K1WRat) # Recursively compute roadmap of possible fibers @@ -104,6 +102,11 @@ function roadmap( return roadmap(V, C=CQ, v=v, checks=checks) end +function fbr(I::Ideal{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) + vars = gens(parent(I)) + return Ideal(vcat(I.gens, [vars[i] - Q[i] for i in 1:min(length(vars),length(Q))])) +end + #= ## Test ## R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) From 5de7bd0758b4bba33e027cd4d90e74c83183b344 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Thu, 24 Apr 2025 19:58:33 +0200 Subject: [PATCH 110/180] correct bug, improve output --- src/connectivity/Cannytools.jl | 12 ++- src/connectivity/computeRM.jl | 140 +++++++++++++++++---------------- 2 files changed, 80 insertions(+), 72 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 57f1af9..456a324 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -3,21 +3,25 @@ function computepolar( j::Int, # j-th first coordinate images of phi V::Ideal{P}; # input ideal phi::Vector{P} = P[], # polynomial map in consideration (completed by sufficiently many projections) - dim = -1, # specify dimension of V dimproj = j-1, # maximum dimension of tangent space of phi v=0, # verbosity level + only_mins = false # return only minors without eqns of V ) where (P <: MPolyRingElem) - dim == -1 && V.dim == -1 && dimension(V) + V.dim == -1 && dimension(V) R = parent(V) n = nvars(R) - c = n - max(dim, V.dim) + c = n - V.dim nphi = length(phi) JW = transpose([ derivative(f, k) for k=max(j+1-nphi,0):n, f in vcat(V.gens, phi[1:min(j,nphi)])]) sizeminors = c + min(nphi,j) + min(dimproj,j-1) - (j-1) minors = compute_minors(sizeminors, JW, R) - return Ideal(vcat(V.gens, minors)) + if only_mins + return minors + else + return vcat(V.gens, minors) + end end function compute_minors(p, A, R) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index e15943b..f26f65d 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,86 +4,82 @@ #using AlgebraicSolving #using Nemo -export roadmap, computepolar, MidRationalPoints +export roadmap, computepolar, MidRationalPoints, fbr include("Cannytools.jl") function roadmap( - V::Ideal{T} where T <: QQMPolyRingElem; # input ideal - Q::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # base points with rational coefficients - C::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # query points with rational coefficients - v::Int=0, # verbosity level - checks::Bool=false # perform checks (dimension, regularity, etc.) - ) + V::Ideal{T} where T <: QQMPolyRingElem; # input ideal + q::Vector{QQFieldElem}=QQFieldElem[], # single base point with rational coefficients + C::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # query points with rational coefficients + v::Int=0, # verbosity level + checks::Bool=false # perform checks (dimension, regularity, etc.) +) # Some base cases A = parent(V) varias = gens(A) if length(varias)<=2 - return [V] + return [V.gens] end # Some preprocessing V.dim == -1 && dimension(V) - isempty(Q) && push!(Q,[]) # Base points - e = length(first(Q)) - - RM = Vector{Ideal{QQMPolyRingElem}}(undef,0) - for q in Q - ## Fq ## - # Genericity assumption (can be checked) - Fq = fbr(V, q) - if checks - @assert(dimension(Fq) == V.dim - e, "Non-generic polar variety") - else - Fq.dim = V.dim - e - end + e = length(q) - # Terminal case (dim <=1) - if Fq.dim <= 1 - push!(RM, Fq) - continue - end + RM = Vector{Tuple{Vector{QQMPolyRingElem}, Vector{QQFieldElem}}}(undef, 0) + ## Fq ## + # Genericity assumption (can be checked) + if checks + @assert(dimension(fbr(V,q)) == V.dim - e, "Non-generic coordinates") + end - ## sing(Fq) ## - if checks - v>0 && println("Check real quasi-smoothness") - singFq = fbr(computepolar(e, V, v=max(v-1,0)), q) - @assert(isempty(real_solutions(singFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads())), - "Non-empty real sing locus!") - end + # Terminal case (dim <=1) + if V.dim - e <= 1 + push!(RM, ([], q)) + return RM + end - ## K(pi_1,Fq) ## - v>0 && println("V-critical points") - K1Fq = fbr(computepolar(e+1, V, v=max(v-1,0)), q) - K1Fq = real_solutions(K1Fq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) - - ## K(pi_2, Fq) ## - v>0 && println("Polar variety") - K2Fqmins = computepolar(e+2, V, v=max(v-1,0)) - K2Fq = fbr(K2Fqmins, q) - if checks - @assert(isone(dimension(K2Fq)), "Non-generic polar variety") - else - K2Fq.dim = 1 - end - push!(RM, K2Fq) - - ## Points with vertical tg in K(pi_2, Fq) ## - v>0 && println("W-critical points with vertical tangent") - K1WmFq = fbr(computepolar(e+2, K2Fqmins, dim=e+1, dimproj=e+0, v=max(v-1,0)), q) - K1WmFq = real_solutions(K1WmFq, info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) - - ## New base and query points ## - Cq = isempty(q) ? C : [ c for c in C if c[e] == q[e]] - K1W = vcat(K1Fq, K1WmFq) - # Heuristic to be proven (Reeb's th) - #K1W = K1W[2:end-1] - ########## - K1WRat = MidRationalPoints(getindex.(K1W,e+1), unique(getindex.(Cq, e+1))) - newQ = vcat.(Ref(q), K1WRat) - - # Recursively compute roadmap of possible fibers - if !isempty(newQ) - RMFq = roadmap(V, Q=newQ, C=Cq) + ## sing(Fq) ## + if checks + v>0 && println("Check real quasi-smoothness") + singFq = computepolar(e, V, v=max(v-1,0)) |> Ideal + @assert(isempty(real_solutions(fbr(singFq, q), info_level=max(v-1,0), nr_thrds=Threads.nthreads())), + "Non-empty real sing locus!") + end + + ## K(pi_1,Fq) ## + v>0 && println("V-critical points") + K1Fq = computepolar(e+1, V, v=max(v-1,0)) |> Ideal + K1Fq = real_solutions(fbr(K1Fq,q), info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) + + ## K(pi_2, Fq) ## + v>0 && println("Polar variety") + K2Fqmins = computepolar(e+2, V, v=max(v-1,0), only_mins=true) + K2Fq = vcat(V.gens, K2Fqmins) |> Ideal + if checks + @assert(fbr(K2Fq, q) |> dimension == 1, "Non-generic polar variety") + else + K2Fq.dim = e + 1 + end + push!(RM, (K2Fqmins, q)) + + ## Points with vertical tg in K(pi_2, Fq) ## + v>0 && println("W-critical points with vertical tangent") + K1WmFq = computepolar(e+2, K2Fq, dimproj=e, v=max(v-1,0)) |> Ideal + K1WmFq = real_solutions(fbr(K1WmFq,q), info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) + + ## New base and query points ## + Cq = isempty(q) ? C : [ c for c in C if c[e] == q[e]] + K1W = vcat(K1Fq, K1WmFq) + # Heuristic to be proven (Reeb's th) + #K1W = K1W[2:end-1] + ########## + K1WRat = MidRationalPoints(getindex.(K1W,e+1), unique(getindex.(Cq, e+1))) + newQ = vcat.(Ref(q), K1WRat) + + # Recursively compute roadmap of possible fibers + if !isempty(newQ) + for newq in newQ + RMFq = roadmap(V, q=newq, C=Cq) append!(RM, RMFq) end end @@ -91,6 +87,8 @@ function roadmap( return RM end + + function roadmap( V::Ideal{P}, # input ideal C::Ideal{P}; # ideal defining query points @@ -102,9 +100,15 @@ function roadmap( return roadmap(V, C=CQ, v=v, checks=checks) end + +function fbr(F::Vector{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) + @assert(!isempty(F), "Empty polynomial vector") + vars = gens(parent(first(F))) + return Ideal(vcat(F, [vars[i] - Q[i] for i in 1:min(length(vars),length(Q))])) +end + function fbr(I::Ideal{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) - vars = gens(parent(I)) - return Ideal(vcat(I.gens, [vars[i] - Q[i] for i in 1:min(length(vars),length(Q))])) + return fbr(I.gens, Q) end #= From 4366ed4326d2e67474a911eac96c7ba8507d7e7d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Thu, 24 Apr 2025 20:52:15 +0200 Subject: [PATCH 111/180] start Roadmap structure --- Project.toml | 1 + src/connectivity/computeRM.jl | 66 ++++++++++++++++++++++++++++++----- src/types.jl | 4 ++- 3 files changed, 61 insertions(+), 10 deletions(-) diff --git a/Project.toml b/Project.toml index e01efb9..e8efddd 100644 --- a/Project.toml +++ b/Project.toml @@ -4,6 +4,7 @@ authors = ["ederc ", "Mohab Safey El Din 0 && println("W-critical points with vertical tangent") @@ -80,15 +78,17 @@ function roadmap( if !isempty(newQ) for newq in newQ RMFq = roadmap(V, q=newq, C=Cq) - append!(RM, RMFq) + push!(RM.children, RMFq) end end - return RM + if e == 0 + return Roadmap(V, RM) + else + return RM + end end - - function roadmap( V::Ideal{P}, # input ideal C::Ideal{P}; # ideal defining query points @@ -111,6 +111,54 @@ function fbr(I::Ideal{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) return fbr(I.gens, Q) end +mutable struct RMnode + polar_eqs::Vector{QQMPolyRingElem} + base_pt::Vector{QQFieldElem} + children::Vector{RMnode} +end + +mutable struct Roadmap + initial_ideal::Ideal{QQMPolyRingElem} + root::RMnode +end + +function all_eqs(RM::Roadmap) + function all_eqs_rec(RMn::RMnode) + eqs = [fbr(vcat(RM.initial_ideal.gens, RMn.polar_eqs), RMn.base_pt)] + for child in RMn.children + append!(eqs, all_eqs_rec(child)) + end + return eqs + end + return all_eqs_rec(RM.root) +end + +function all_base_pts(RM::Roadmap) + function all_base_pts_rec(RMn::RMnode) + eqs = [RMn.base_pt] + for child in RMn.children + append!(eqs, all_base_pts_rec(child)) + end + return eqs + end + return all_base_pts_rec(RM.root) +end + +function nb_nodes(RM::Roadmap) + function nb_nodes_rec(RMn::RMnode) + nb = 1 + for child in RMn.children + nb += nb_nodes_rec(child) + end + return nb + end + return nb_nodes_rec(RM.root) +end + +Base.show(io::IO, RM::Roadmap) = print(io, all_base_pts(RM)) +Base.getindex(RM::Roadmap, idx::Union{Int, UnitRange}) = all_eqs(RM)[idx] +Base.lastindex(RM::Roadmap) = nb_nodes(RM) + #= ## Test ## R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) diff --git a/src/types.jl b/src/types.jl index a041ef9..381dc63 100644 --- a/src/types.jl +++ b/src/types.jl @@ -75,4 +75,6 @@ Base.parent(I::Ideal) = Nemo.parent(I.gens[1]) Base.show(io::IO, I::Ideal) = print(io, I.gens) -Base.getindex(I::Ideal, idx::Int) = I.gens[idx] +Base.getindex(I::Ideal, idx::Union{Int, UnitRange}) = I.gens[idx] + +Base.lastindex(I::Ideal) = lastindex(I.gens) From 4a9f502e31cd21f8c2f300065e476f1baa9bef70 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Mon, 28 Apr 2025 14:46:39 +0200 Subject: [PATCH 112/180] remove abstract trees --- Project.toml | 1 - 1 file changed, 1 deletion(-) diff --git a/Project.toml b/Project.toml index e8efddd..e01efb9 100644 --- a/Project.toml +++ b/Project.toml @@ -4,7 +4,6 @@ authors = ["ederc ", "Mohab Safey El Din Date: Sat, 28 Jun 2025 23:09:59 +0200 Subject: [PATCH 113/180] maj dim nothing --- src/connectivity/computeRM.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 67192fa..8c63ea4 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -21,7 +21,7 @@ function roadmap( return [V.gens] end # Some preprocessing - V.dim == -1 && dimension(V) + isnothing(V.dim) && dimension(V) # Base points e = length(q) From ee70bc5009b7670287ec91c01e9ff384176f8f0d Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 13 Oct 2025 10:22:54 +0200 Subject: [PATCH 114/180] move RM struct to types.jl + improve internal functions --- src/connectivity/computeRM.jl | 50 +---------------------------------- src/types.jl | 37 ++++++++++++++++++++++++++ 2 files changed, 38 insertions(+), 49 deletions(-) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 8c63ea4..358012f 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,7 +4,7 @@ #using AlgebraicSolving #using Nemo -export roadmap, computepolar, MidRationalPoints, fbr, all_eqs, all_base_pts +export roadmap, computepolar, MidRationalPoints, fbr, all_eqs, all_base_pts, nb_nodes include("Cannytools.jl") function roadmap( @@ -111,54 +111,6 @@ function fbr(I::Ideal{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) return fbr(I.gens, Q) end -mutable struct RMnode - polar_eqs::Vector{QQMPolyRingElem} - base_pt::Vector{QQFieldElem} - children::Vector{RMnode} -end - -mutable struct Roadmap - initial_ideal::Ideal{QQMPolyRingElem} - root::RMnode -end - -function all_eqs(RM::Roadmap) - function all_eqs_rec(RMn::RMnode) - eqs = [fbr(vcat(RM.initial_ideal.gens, RMn.polar_eqs), RMn.base_pt)] - for child in RMn.children - append!(eqs, all_eqs_rec(child)) - end - return eqs - end - return all_eqs_rec(RM.root) -end - -function all_base_pts(RM::Roadmap) - function all_base_pts_rec(RMn::RMnode) - eqs = [RMn.base_pt] - for child in RMn.children - append!(eqs, all_base_pts_rec(child)) - end - return eqs - end - return all_base_pts_rec(RM.root) -end - -function nb_nodes(RM::Roadmap) - function nb_nodes_rec(RMn::RMnode) - nb = 1 - for child in RMn.children - nb += nb_nodes_rec(child) - end - return nb - end - return nb_nodes_rec(RM.root) -end - -Base.show(io::IO, RM::Roadmap) = print(io, all_base_pts(RM)) -Base.getindex(RM::Roadmap, idx::Union{Int, UnitRange}) = all_eqs(RM)[idx] -Base.lastindex(RM::Roadmap) = nb_nodes(RM) - #= ## Test ## R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) diff --git a/src/types.jl b/src/types.jl index e51750e..6ef5453 100644 --- a/src/types.jl +++ b/src/types.jl @@ -77,3 +77,40 @@ Base.show(io::IO, I::Ideal) = print(io, I.gens) Base.getindex(I::Ideal, idx::Union{Int, UnitRange}) = I.gens[idx] Base.lastindex(I::Ideal) = lastindex(I.gens) + +mutable struct RMnode + polar_eqs::Vector{QQMPolyRingElem} + base_pt::Vector{QQFieldElem} + children::Vector{RMnode} +end + +mutable struct Roadmap + initial_ideal::Ideal{QQMPolyRingElem} + root::RMnode +end + +function _collect_roadmap(RMn::RMnode, F) + data = [F(RMn)] + for child in RMn.children + append!(data, _collect_roadmap(child, F)) + end + return data +end + +function all_eqs(RM::Roadmap) + func(s) = fbr(vcat(RM.initial_ideal.gens, s.polar_eqs), s.base_pt) + return _collect_roadmap(RM.root, func) +end + +function all_base_pts(RM::Roadmap) + return _collect_roadmap(RM.root, s->s.base_pt) +end + +function nb_nodes(RM::Roadmap) + return length(_collect_roadmap(RM.root, s -> true)) +end + +Base.show(io::IO, RM::Roadmap) = print(io, all_base_pts(RM)) +Base.getindex(RM::Roadmap, idx::Union{Int, UnitRange}) = all_eqs(RM)[idx] +Base.lastindex(RM::Roadmap) = nb_nodes(RM) +Base.length(RM::Roadmap) = nb_nodes(RM) \ No newline at end of file From 4a9393611e4584ed9f20ba2510dcb42240d189dc Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Wed, 15 Oct 2025 00:13:01 +0200 Subject: [PATCH 115/180] start doc + some renamings --- src/connectivity/Cannytools.jl | 7 ++- src/connectivity/computeRM.jl | 112 ++++++++++++++++++++++++--------- 2 files changed, 85 insertions(+), 34 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 456a324..2327ff1 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -4,16 +4,16 @@ function computepolar( V::Ideal{P}; # input ideal phi::Vector{P} = P[], # polynomial map in consideration (completed by sufficiently many projections) dimproj = j-1, # maximum dimension of tangent space of phi - v=0, # verbosity level only_mins = false # return only minors without eqns of V ) where (P <: MPolyRingElem) - V.dim == -1 && dimension(V) + isnothing(V.dim) && dimension(V) R = parent(V) n = nvars(R) c = n - V.dim nphi = length(phi) - JW = transpose([ derivative(f, k) for k=max(j+1-nphi,0):n, f in vcat(V.gens, phi[1:min(j,nphi)])]) + psi = vcat(phi, V.gens[nphi+1:end]) + JW = transpose([ derivative(f, k) for k=max(j+1-nphi,0):n, f in psi]) sizeminors = c + min(nphi,j) + min(dimproj,j-1) - (j-1) minors = compute_minors(sizeminors, JW, R) @@ -24,6 +24,7 @@ function computepolar( end end + function compute_minors(p, A, R) #Computes the p-minors of a matrix A n, m = size(A) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 358012f..3719727 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,55 +4,105 @@ #using AlgebraicSolving #using Nemo -export roadmap, computepolar, MidRationalPoints, fbr, all_eqs, all_base_pts, nb_nodes +export roadmap, computepolar, MidRationalPoints, fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis include("Cannytools.jl") +@doc Markdown.doc""" + roadmap(I::Ideal{T} where T <: MPolyRingElem, ) + +Given a **radical** ideal `I` with solution set X, that is smooth and +whose real trace XR is bounded, return a roadmap of XR + +The output is given as a Roadmap structure, encoding the recursive structure +of roadmaps. It is encoded as a chained list, whose root is containing the equations defining X +and each node representing a curve component, that is defined by additional polar equation and base point< +Moreover it is linked to fibers, that share the same base point. + +# Arguments +- `I::Ideal{T} where T <: QQMPolyRingElem`: input generators. +- `q::Vector{QQFieldElem}=QQFieldElem[]`: single base point with rational coefficients +- `C::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[]`: query points with rational coefficients +- `info_level::Int=0`: verbosity level +- `checks::Bool=false`: whether perform checks (dimension, regularity, etc.) +- 'generic_change=false": whether it performs a prior random linear change of variables (TODO) +) + +# Examples +```jldoctest +julia> using AlgebraicSolving + +julia> R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) +(Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x1, x2, x3, x4]) + +julia> I = Ideal([x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2)]) +QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64] + +julia> RM = roadmap(I) +Vector{QQFieldElem}[[], [-3], [-3, -2], [-1], [-1, -2], [-1, -1], [-1, 2], [3], [3, 2]] + +julia> nb_nodes(RM) +9 + +julia> all_eqs(RM) +9-element Vector{Ideal{QQMPolyRingElem}}: + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, 4*x1^2*x3 + 4*x2^2*x3 + 4*x3^3 + 4*x3*x4^2 - 40*x3, 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4, x1 + 3] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 + 3, x2 + 2] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4, x1 + 1] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 + 1, x2 + 2] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 + 1, x2 + 1] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 + 1, x2 - 2] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4, x1 - 3] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 - 3, x2 - 2] + +julia> roadmap(V, generic_change=true) +..... +``` +""" function roadmap( - V::Ideal{T} where T <: QQMPolyRingElem; # input ideal + I::Ideal{T} where T <: QQMPolyRingElem; # input ideal q::Vector{QQFieldElem}=QQFieldElem[], # single base point with rational coefficients C::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # query points with rational coefficients - v::Int=0, # verbosity level + info_level::Int=0, # verbosity level checks::Bool=false # perform checks (dimension, regularity, etc.) ) # Some base cases - A = parent(V) - varias = gens(A) - if length(varias)<=2 - return [V.gens] + if nvars(parent(I))<=2 + return [I.gens] end # Some preprocessing - isnothing(V.dim) && dimension(V) + isnothing(I.dim) && dimension(I) # Base points e = length(q) ## Fq ## # Genericity assumption (can be checked) if checks - @assert(dimension(fbr(V,q)) == V.dim - e, "Non-generic coordinates") + @assert(dimension(fbr(I,q)) == I.dim - e, "Non-generic coordinates") end # Terminal case (dim <=1) - if V.dim - e <= 1 + if I.dim - e <= 1 return RMnode([], q, RMnode[]) end ## sing(Fq) ## if checks - v>0 && println("Check real quasi-smoothness") - singFq = computepolar(e, V, v=max(v-1,0)) |> Ideal - @assert(isempty(real_solutions(fbr(singFq, q), info_level=max(v-1,0), nr_thrds=Threads.nthreads())), + info_level>0 && println("Check real quasi-smoothness") + singFq = computepolar(e, I) |> Ideal + @assert(isempty(real_solutions(fbr(singFq, q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads())), "Non-empty real sing locus!") end ## K(pi_1,Fq) ## - v>0 && println("V-critical points") - K1Fq = computepolar(e+1, V, v=max(v-1,0)) |> Ideal - K1Fq = real_solutions(fbr(K1Fq,q), info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) + info_level>0 && println("I-critical points") + K1Fq = computepolar(e+1, I) |> Ideal + K1Fq = real_solutions(fbr(K1Fq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) ## K(pi_2, Fq) ## - v>0 && println("Polar variety") - K2Fqmins = computepolar(e+2, V, v=max(v-1,0), only_mins=true) - K2Fq = vcat(V.gens, K2Fqmins) |> Ideal + info_level>0 && println("Polar variety") + K2Fqmins = computepolar(e+2, I, only_mins=true) + K2Fq = vcat(I.gens, K2Fqmins) |> Ideal if checks @assert(fbr(K2Fq, q) |> dimension == 1, "Non-generic polar variety") else @@ -61,9 +111,9 @@ function roadmap( RM = RMnode(K2Fqmins, q, RMnode[]) ## Points with vertical tg in K(pi_2, Fq) ## - v>0 && println("W-critical points with vertical tangent") - K1WmFq = computepolar(e+2, K2Fq, dimproj=e, v=max(v-1,0)) |> Ideal - K1WmFq = real_solutions(fbr(K1WmFq,q), info_level=max(v-1,0), nr_thrds=Threads.nthreads(), interval=true) + info_level>0 && println("W-critical points with vertical tangent") + K1WmFq = computepolar(e+2, K2Fq, dimproj=e) |> Ideal + K1WmFq = real_solutions(fbr(K1WmFq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) ## New base and query points ## Cq = isempty(q) ? C : [ c for c in C if c[e] == q[e]] @@ -77,27 +127,27 @@ function roadmap( # Recursively compute roadmap of possible fibers if !isempty(newQ) for newq in newQ - RMFq = roadmap(V, q=newq, C=Cq) + RMFq = roadmap(I, q=newq, C=Cq) push!(RM.children, RMFq) end end if e == 0 - return Roadmap(V, RM) + return Roadmap(I, RM) else return RM end end function roadmap( - V::Ideal{P}, # input ideal + I::Ideal{P}, # input ideal C::Ideal{P}; # ideal defining query points - v::Int=0, # verbosity level + info_level::Int=0, # verbosity level checks::Bool=false # perform checks (dimension, regularity, etc.) ) where (P <: QQMPolyRingElem) - @assert(parent(V)==parent(C), "Equations for variety and query points must live the same ring") - CQ = real_solutions(C, info_level=max(v-1,0), nr_thrds=Threads.nthreads()) - return roadmap(V, C=CQ, v=v, checks=checks) + @assert(parent(I)==parent(C), "Equations for variety and query points must live the same ring") + CQ = real_solutions(C, info_level=max(info_level-1,0), nr_thrds=Threads.nthreads()) + return roadmap(I, C=CQ, info_level=info_level, checks=checks) end @@ -117,9 +167,9 @@ R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) #h = x1^2+x2^2+x3^2+x4^2-1 h = (x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2) h = evaluate(h,[x1,x2,x3],[x1+rand(-10:10)*x2+rand(-10:10)*x3+rand(-10:10)*x4,x2+rand(-10:10)*x3+rand(-10:10)*x4,x3+rand(-10:10)*x4]) -V = Ideal([h]) +I = Ideal([h]) -carte = (computeRM(V, 3, [Vector{QQFieldElem}(undef,0)])) +carte = (computeRM(I, 3, [Vector{QQFieldElem}(undef,0)])) #println(carte) =# From da73da700be98c4fad8f0fbe48d4eb6ff2083fe6 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Wed, 15 Oct 2025 19:44:56 +0200 Subject: [PATCH 116/180] add index list for compute polar --- src/connectivity/Cannytools.jl | 35 ++++++++++++++++++++++------------ src/connectivity/computeRM.jl | 10 +++++----- 2 files changed, 28 insertions(+), 17 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 2327ff1..8969f00 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -1,20 +1,32 @@ -# Compute the set of points x where phi_j(T_x(V)) has dimension < dimproj +# Compute the set of points x where, if psi in the map whose elts are the ones in [phi_1,..,phi_p, x_{p+1},...x_n] indexed in J, +# then psi(T_x(V)) has dimension < dimproj function computepolar( - j::Int, # j-th first coordinate images of phi - V::Ideal{P}; # input ideal - phi::Vector{P} = P[], # polynomial map in consideration (completed by sufficiently many projections) - dimproj = j-1, # maximum dimension of tangent space of phi - only_mins = false # return only minors without eqns of V + J::Union{Vector{Int},UnitRange{Int}}, # coordinate images of [phi,proj] (as above) + V::Ideal{P}; # input ideal + phi::Vector{P} = P[], # polynomial map in consideration (completed by sufficiently many projections) + dimproj = length(J)-1, # maximum dimension of tangent space of phi + only_mins = false # return only minors without eqns of V ) where (P <: MPolyRingElem) - isnothing(V.dim) && dimension(V) + R = parent(V) n = nvars(R) - c = n - V.dim nphi = length(phi) + @assert all([1<=j<=n for j in J]) - psi = vcat(phi, V.gens[nphi+1:end]) - JW = transpose([ derivative(f, k) for k=max(j+1-nphi,0):n, f in psi]) - sizeminors = c + min(nphi,j) + min(dimproj,j-1) - (j-1) + isnothing(V.dim) && dimension(V) + c = n - V.dim + + ## Is it correct AND useful? + sort!(J) + ## + Jphi = [ j for j in J if j <= nphi ] + Jproj = setdiff(J, Jphi) + + # Construct the truncated Jacobian matrix + psi = vcat(V.gens, phi[Jphi]) + JW = transpose([ derivative(f, k) for k in setdiff(1:n, Jproj), f in psi]) + # Compute the minors + sizeminors = c + length(Jphi) + min(dimproj, length(J)-1) - (length(J)-1) minors = compute_minors(sizeminors, JW, R) if only_mins @@ -24,7 +36,6 @@ function computepolar( end end - function compute_minors(p, A, R) #Computes the p-minors of a matrix A n, m = size(A) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 3719727..08ca373 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,7 +4,7 @@ #using AlgebraicSolving #using Nemo -export roadmap, computepolar, MidRationalPoints, fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis +export roadmap, computepolar, MidRationalPoints, fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis, computepolarL include("Cannytools.jl") @doc Markdown.doc""" @@ -89,19 +89,19 @@ function roadmap( ## sing(Fq) ## if checks info_level>0 && println("Check real quasi-smoothness") - singFq = computepolar(e, I) |> Ideal + singFq = computepolar(1:e, I) |> Ideal @assert(isempty(real_solutions(fbr(singFq, q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads())), "Non-empty real sing locus!") end ## K(pi_1,Fq) ## info_level>0 && println("I-critical points") - K1Fq = computepolar(e+1, I) |> Ideal + K1Fq = computepolar(1:e+1, I) |> Ideal K1Fq = real_solutions(fbr(K1Fq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) ## K(pi_2, Fq) ## info_level>0 && println("Polar variety") - K2Fqmins = computepolar(e+2, I, only_mins=true) + K2Fqmins = computepolar(1:e+2, I, only_mins=true) K2Fq = vcat(I.gens, K2Fqmins) |> Ideal if checks @assert(fbr(K2Fq, q) |> dimension == 1, "Non-generic polar variety") @@ -112,7 +112,7 @@ function roadmap( ## Points with vertical tg in K(pi_2, Fq) ## info_level>0 && println("W-critical points with vertical tangent") - K1WmFq = computepolar(e+2, K2Fq, dimproj=e) |> Ideal + K1WmFq = computepolar(1:e+2, K2Fq, dimproj=e) |> Ideal K1WmFq = real_solutions(fbr(K1WmFq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) ## New base and query points ## From 7e67eeb7a8882eb858ee0f357af407406660a901 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Wed, 15 Oct 2025 23:01:04 +0200 Subject: [PATCH 117/180] doc --- src/connectivity/Cannytools.jl | 62 ++++++++++++++++++++++++++++++++-- src/connectivity/computeRM.jl | 3 -- 2 files changed, 60 insertions(+), 5 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 8969f00..8ceb3ce 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -1,5 +1,63 @@ -# Compute the set of points x where, if psi in the map whose elts are the ones in [phi_1,..,phi_p, x_{p+1},...x_n] indexed in J, -# then psi(T_x(V)) has dimension < dimproj +@doc Markdown.doc""" + computepolar( + J::Union{Vector{Int},UnitRange{Int}}, + V::Ideal{P}; + phi::Vector{P}=P[], + dimproj::Int=length(J)-1, + only_mins::Bool=false + ) where {P <: MPolyRingElem} + +Compute the **polar variety** associated with the map whose components are +`[phi_1, …, phi_p, x_{p+1}, …, x_n]` indexed by `J`, for an algebraic variety defined +by the ideal `V`. + +More precisely, this function computes the set of points `x` in `V` such that, +if `psi` denotes the above map, then the image of the tangent space `Tₓ(V)` under +the differential `psi` has dimension strictly less than `dimproj`. + +This is a key geometric construction in the computation of polar varieties, +used in the roadmap algorithm and critical point methods. + +# Arguments +- `J::Union{Vector{Int},UnitRange{Int}}`: + Indices of the selected coordinate functions +- `V::Ideal{P} where P <: MPolyRingElem`: + Input ideal defining the variety V on which critical loci is computed +- `phi::Vector{P}=P[]`: + Polynomial map possibly completed by projection coordinates to have a map of total length `n`. +- `dimproj::Int=length(J)-1`: + Expected maximal dimension of the image of the tangent space. + Typically equals the number of projection coordinates minus one. +- `only_mins::Bool=false`: + If `true`, only the computed minors of the Jacobian are returned; + otherwise, the output includes both the generators of `V` and those minors. + +# Returns +- If `only_mins=false` (default): + A `Vector{P}` containing the union of the generators of `V` and the computed minors. + This defines the ideal of the polar variety. +- If `only_mins=true`: + A `Vector{P}` containing only the minors (without the original equations of `V`). + +# Example +```jldoctest +julia> using AlgebraicSolving + +julia> R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) +(Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x1, x2, x3, x4]) + +julia> I = Ideal([(x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2)]) +QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64] + +julia> computepolar(1:3, I, dimproj=1, phi=[x1^2+x2^2+x3^2+x4^2]) +5-element Vector{QQMPolyRingElem}: + x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64 + 4*x1^3 + 4*x1*x2^2 + 4*x1*x3^2 + 4*x1*x4^2 - 40*x1 + 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4 + 2*x1 + 2*x4 +``` +""" function computepolar( J::Union{Vector{Int},UnitRange{Int}}, # coordinate images of [phi,proj] (as above) V::Ideal{P}; # input ideal diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 08ca373..c33b907 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -54,9 +54,6 @@ julia> all_eqs(RM) QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 + 1, x2 - 2] QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4, x1 - 3] QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 - 3, x2 - 2] - -julia> roadmap(V, generic_change=true) -..... ``` """ function roadmap( From bafd3ce2264f083dad43ab213d8c66afd13b6e45 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sat, 18 Oct 2025 13:33:37 +0200 Subject: [PATCH 118/180] improve genericity checks + choice for determinant function (after some tests) --- src/connectivity/Cannytools.jl | 25 +++++++-- src/connectivity/computeRM.jl | 93 ++++++++++++++++++++++------------ 2 files changed, 83 insertions(+), 35 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index 8ceb3ce..a730125 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -82,7 +82,7 @@ function computepolar( # Construct the truncated Jacobian matrix psi = vcat(V.gens, phi[Jphi]) - JW = transpose([ derivative(f, k) for k in setdiff(1:n, Jproj), f in psi]) + JW = matrix(R, QQMPolyRingElem[ derivative(f, k) for f in psi, k in setdiff(1:n, Jproj)]) # Compute the minors sizeminors = c + length(Jphi) + min(dimproj, length(J)-1) - (length(J)-1) minors = compute_minors(sizeminors, JW, R) @@ -101,9 +101,24 @@ function compute_minors(p, A, R) colsmins = collect(combinations(1:m, p)) mins = Vector{eltype(A)}(undef, length(rowsmins) * length(colsmins)) k = 1 + # for performance tweaks, check if there are non-linear polynomials or if all are linear or constant + degmax = 0 + for a in A + degmax = min(2, max(degmax, total_degree(a))) + if degmax > 1 + break + end + end + # TODO: use algos from FLINT (in particular berkowitz) + # Naive function performs better for high degree or small matrices + if (degmax == 0 && p <= 2) || (degmax == 1 && p <= 6) || (degmax == 2) + detfct = s->detmpoly(s, R) + else # else use fraction-free LU from AbstractAlgebra.jl + detfct = det + end for rowsmin in rowsmins for colsmin in colsmins - mins[k] = detmpoly(A[rowsmin, colsmin], R) + mins[k] = detfct(A[rowsmin, colsmin]) k += 1 end end @@ -129,7 +144,7 @@ function combinations(a, n) return _combinations(a, n, 1, Vector{Int}([])) end -function detmpoly(A::Matrix{T} where T<:MPolyRingElem, R) +function detmpoly(A, R) # Get the size of the matrix n = size(A, 1) if n != size(A, 2) @@ -140,6 +155,10 @@ function detmpoly(A::Matrix{T} where T<:MPolyRingElem, R) return A[1, 1] end + if n == 2 + return A[1, 1] * A[2, 2] - A[1,2] * A[2, 1] + end + # Initialize the determinant polynomial detA = zero(R) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index c33b907..3278497 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,7 +4,7 @@ #using AlgebraicSolving #using Nemo -export roadmap, computepolar, MidRationalPoints, fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis, computepolarL +export roadmap, computepolar, MidRationalPoints, fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis, computepolarL, detmpoly include("Cannytools.jl") @doc Markdown.doc""" @@ -67,15 +67,23 @@ function roadmap( if nvars(parent(I))<=2 return [I.gens] end - # Some preprocessing - isnothing(I.dim) && dimension(I) - # Base points + + # Some preprocessng + if isnothing(I.dim) + lucky_prime = _generate_lucky_primes(I.gens, one(ZZ)<<30, one(ZZ)<<31-1, 1) |> first + local INEW = Ideal(change_base_ring.(Ref(GF(lucky_prime)), I.gens)) + dimension(INEW) + I.dim = INEW.dim + end e = length(q) ## Fq ## # Genericity assumption (can be checked) if checks - @assert(dimension(fbr(I,q)) == I.dim - e, "Non-generic coordinates") + local Fnew = fbr(I,q).gens + new_lucky_prime = _generate_lucky_primes(Fnew, one(ZZ)<<30, one(ZZ)<<31-1, 1) |> first + local INEW = Ideal(change_base_ring.(Ref(GF(new_lucky_prime)), Fnew)) + @assert(dimension(INEW) == I.dim - e, "Non-generic coordinates") end # Terminal case (dim <=1) @@ -85,30 +93,34 @@ function roadmap( ## sing(Fq) ## if checks - info_level>0 && println("Check real quasi-smoothness") - singFq = computepolar(1:e, I) |> Ideal - @assert(isempty(real_solutions(fbr(singFq, q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads())), - "Non-empty real sing locus!") + info_level>0 && println("Check smoothness") + local FNEW = fbr(computepolar(1:e, I)|> Ideal, q).gens + new_lucky_prime = _generate_lucky_primes(FNEW, one(ZZ)<<30, one(ZZ)<<31-1, 1) |> first + local INEW = Ideal(change_base_ring.(Ref(GF(new_lucky_prime)), FNEW)) + @assert(dimension(INEW) == -1, "Non-empty sing locus!") end ## K(pi_1,Fq) ## - info_level>0 && println("I-critical points") + info_level>0 && println("Compute x1-critical points: K1") K1Fq = computepolar(1:e+1, I) |> Ideal K1Fq = real_solutions(fbr(K1Fq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) ## K(pi_2, Fq) ## - info_level>0 && println("Polar variety") + info_level>0 && println("Compute (x1,x2)-polar variety: W") K2Fqmins = computepolar(1:e+2, I, only_mins=true) K2Fq = vcat(I.gens, K2Fqmins) |> Ideal if checks - @assert(fbr(K2Fq, q) |> dimension == 1, "Non-generic polar variety") + local FNEW = fbr(K2Fq, q).gens + new_lucky_prime = _generate_lucky_primes(FNEW, one(ZZ)<<30, one(ZZ)<<31-1, 1) |> first + local INEW = Ideal(change_base_ring.(Ref(GF(new_lucky_prime)), FNEW)) + @assert(dimension(INEW) == 1, "Non-generic polar variety") else K2Fq.dim = e + 1 end RM = RMnode(K2Fqmins, q, RMnode[]) ## Points with vertical tg in K(pi_2, Fq) ## - info_level>0 && println("W-critical points with vertical tangent") + info_level>0 && println("Compute W-critical points with vertical tangent: K1W") K1WmFq = computepolar(1:e+2, K2Fq, dimproj=e) |> Ideal K1WmFq = real_solutions(fbr(K1WmFq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) @@ -148,26 +160,43 @@ function roadmap( end -function fbr(F::Vector{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) - @assert(!isempty(F), "Empty polynomial vector") - vars = gens(parent(first(F))) - return Ideal(vcat(F, [vars[i] - Q[i] for i in 1:min(length(vars),length(Q))])) -end - function fbr(I::Ideal{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) - return fbr(I.gens, Q) + @assert(!isempty(I.gens), "Empty polynomial vector") + vars = gens(parent(first(I.gens))) + return Ideal(vcat(I.gens, [vars[i] - Q[i] for i in 1:min(length(vars),length(Q))])) end -#= -## Test ## -R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) -#h = x1^2+x2^2+x3^2+x4^2-1 -h = (x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2) -h = evaluate(h,[x1,x2,x3],[x1+rand(-10:10)*x2+rand(-10:10)*x3+rand(-10:10)*x4,x2+rand(-10:10)*x3+rand(-10:10)*x4,x3+rand(-10:10)*x4]) -I = Ideal([h]) - -carte = (computeRM(I, 3, [Vector{QQFieldElem}(undef,0)])) -#println(carte) -=# - +# Generate N primes > start that do not divide any numerator/denominator +# of any coefficient in polynomials from LP +function _generate_lucky_primes( + LF::Vector{P} where P<:MPolyRingElem, + low::ZZRingElem, + up::ZZRingElem, + N::Int64 + ) + # Avoid repetitive enumeration and redundant divisibility check + CF = ZZRingElem[] + for f in LF, c in coefficients(f), part in (numerator(c), denominator(c)) + if !isone(part) + push!(CF, part) + end + end + sort!(CF, rev=true) + unique!(CF) + + # Test primes + Lprim = ZZRingElem[] + while length(Lprim) < N + cur_prim = next_prime(rand(low:up)) + is_lucky = !(cur_prim in Lprim) + i = firstindex(CF) + # Exploit decreasing order of CF + while is_lucky && i <= lastindex(CF) && CF[i] > cur_prim + is_lucky = !is_divisible_by(CF[i], cur_prim) + i += 1 + end + is_lucky && push!(Lprim, cur_prim) + end + return Lprim +end From 8486af01bc22c44e50398a53d1ba2185357d70a5 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sat, 18 Oct 2025 13:39:57 +0200 Subject: [PATCH 119/180] internalize functions that must be --- src/connectivity/Cannytools.jl | 34 ++++++++--------- src/connectivity/computeRM.jl | 69 ++++++++++++++++++++++++++++++---- 2 files changed, 76 insertions(+), 27 deletions(-) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl index a730125..897925f 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/Cannytools.jl @@ -85,7 +85,7 @@ function computepolar( JW = matrix(R, QQMPolyRingElem[ derivative(f, k) for f in psi, k in setdiff(1:n, Jproj)]) # Compute the minors sizeminors = c + length(Jphi) + min(dimproj, length(J)-1) - (length(J)-1) - minors = compute_minors(sizeminors, JW, R) + minors = _compute_minors(sizeminors, JW, R) if only_mins return minors @@ -94,11 +94,11 @@ function computepolar( end end -function compute_minors(p, A, R) +function _compute_minors(p, A, R) #Computes the p-minors of a matrix A n, m = size(A) - rowsmins = collect(combinations(1:n, p)) - colsmins = collect(combinations(1:m, p)) + rowsmins = collect(_combinations(1:n, p, 1, Vector{Int}([]))) + colsmins = collect(_combinations(1:m, p, 1, Vector{Int}([]))) mins = Vector{eltype(A)}(undef, length(rowsmins) * length(colsmins)) k = 1 # for performance tweaks, check if there are non-linear polynomials or if all are linear or constant @@ -126,22 +126,18 @@ function compute_minors(p, A, R) return mins end -function combinations(a, n) - # Helper function to recursively generate combinations - function _combinations(a, n, start, chosen) - if length(chosen) == n - return [chosen] - elseif start > length(a) - return Vector{Int}([]) - else - # Include the current element and recurse - include_current = _combinations(a, n, start + 1, [chosen; a[start]]) - # Exclude the current element and recurse - exclude_current = _combinations(a, n, start + 1, chosen) - return vcat(include_current, exclude_current) - end +function _combinations(a, n, start, chosen) + if length(chosen) == n + return [chosen] + elseif start > length(a) + return Vector{Int}([]) + else + # Include the current element and recurse + include_current = _combinations(a, n, start + 1, [chosen; a[start]]) + # Exclude the current element and recurse + exclude_current = _combinations(a, n, start + 1, chosen) + return vcat(include_current, exclude_current) end - return _combinations(a, n, 1, Vector{Int}([])) end function detmpoly(A, R) diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl index 3278497..2031b36 100644 --- a/src/connectivity/computeRM.jl +++ b/src/connectivity/computeRM.jl @@ -4,7 +4,7 @@ #using AlgebraicSolving #using Nemo -export roadmap, computepolar, MidRationalPoints, fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis, computepolarL, detmpoly +export roadmap, computepolar, _mid_rational_points, _fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis, computepolarL, detmpoly include("Cannytools.jl") @doc Markdown.doc""" @@ -80,7 +80,7 @@ function roadmap( ## Fq ## # Genericity assumption (can be checked) if checks - local Fnew = fbr(I,q).gens + local Fnew = _fbr(I,q).gens new_lucky_prime = _generate_lucky_primes(Fnew, one(ZZ)<<30, one(ZZ)<<31-1, 1) |> first local INEW = Ideal(change_base_ring.(Ref(GF(new_lucky_prime)), Fnew)) @assert(dimension(INEW) == I.dim - e, "Non-generic coordinates") @@ -94,7 +94,7 @@ function roadmap( ## sing(Fq) ## if checks info_level>0 && println("Check smoothness") - local FNEW = fbr(computepolar(1:e, I)|> Ideal, q).gens + local FNEW = _fbr(computepolar(1:e, I)|> Ideal, q).gens new_lucky_prime = _generate_lucky_primes(FNEW, one(ZZ)<<30, one(ZZ)<<31-1, 1) |> first local INEW = Ideal(change_base_ring.(Ref(GF(new_lucky_prime)), FNEW)) @assert(dimension(INEW) == -1, "Non-empty sing locus!") @@ -103,14 +103,14 @@ function roadmap( ## K(pi_1,Fq) ## info_level>0 && println("Compute x1-critical points: K1") K1Fq = computepolar(1:e+1, I) |> Ideal - K1Fq = real_solutions(fbr(K1Fq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) + K1Fq = real_solutions(_fbr(K1Fq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) ## K(pi_2, Fq) ## info_level>0 && println("Compute (x1,x2)-polar variety: W") K2Fqmins = computepolar(1:e+2, I, only_mins=true) K2Fq = vcat(I.gens, K2Fqmins) |> Ideal if checks - local FNEW = fbr(K2Fq, q).gens + local FNEW = _fbr(K2Fq, q).gens new_lucky_prime = _generate_lucky_primes(FNEW, one(ZZ)<<30, one(ZZ)<<31-1, 1) |> first local INEW = Ideal(change_base_ring.(Ref(GF(new_lucky_prime)), FNEW)) @assert(dimension(INEW) == 1, "Non-generic polar variety") @@ -122,7 +122,7 @@ function roadmap( ## Points with vertical tg in K(pi_2, Fq) ## info_level>0 && println("Compute W-critical points with vertical tangent: K1W") K1WmFq = computepolar(1:e+2, K2Fq, dimproj=e) |> Ideal - K1WmFq = real_solutions(fbr(K1WmFq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) + K1WmFq = real_solutions(_fbr(K1WmFq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) ## New base and query points ## Cq = isempty(q) ? C : [ c for c in C if c[e] == q[e]] @@ -130,7 +130,7 @@ function roadmap( # Heuristic to be proven (Reeb's th) #K1W = K1W[2:end-1] ########## - K1WRat = MidRationalPoints(getindex.(K1W,e+1), unique(getindex.(Cq, e+1))) + K1WRat = _mid_rational_points(getindex.(K1W,e+1), unique(getindex.(Cq, e+1))) newQ = vcat.(Ref(q), K1WRat) # Recursively compute roadmap of possible fibers @@ -160,12 +160,65 @@ function roadmap( end -function fbr(I::Ideal{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) +function _fbr(I::Ideal{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) @assert(!isempty(I.gens), "Empty polynomial vector") vars = gens(parent(first(I.gens))) return Ideal(vcat(I.gens, [vars[i] - Q[i] for i in 1:min(length(vars),length(Q))])) end +function _mid_rational_points(S::Vector{Vector{T}}, Q::Vector{T} = T[]) where {T <: QQFieldElem} + # * S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] + # such that the [l_i, r_i] are rational and disjoint open intervals. + # * Q is a list of rationals that intersects no [l_i,r_i] + # + # It orders the [l_i,r_i], and compute a list ratioP such that + # strictly between each of these intervals there is: + # - either at least one element of Q + # - or the simplest rational number + isempty(S) && return Q + + S1, Q1 = sort(S, lt=(x, y) -> x[2] <= y[1]), sort(Q) + ratioP = T[] + qidx = 1 + qlen = length(Q1) + + # Handle left gap before first interval + while qidx <= qlen && Q1[qidx] < S1[1][1] + push!(ratioP, Q1[qidx]) + qidx += 1 + end + + # Loop through gaps between sorted disjoint intervals + for i in 1:(length(S1) - 1) + ri, li1 = S1[i][2], S1[i+1][1] + @assert ri < li1 "Intervals are not disjoint." + inserted = false + while qidx <= qlen && Q1[qidx] < li1 + @assert(Q1[qidx] > ri, "A query point is singular") + push!(ratioP, Q1[qidx]) + inserted = true + qidx += 1 + end + if !inserted + eps = (li1 - ri)//1000 # for open interval + # We choose the simplest in absolute value + if -ri > li1 # this means ri is negative and the largest in absolute value + push!(ratioP, -simplest_between(-ri - eps, -li1 + eps)) + else + push!(ratioP, simplest_between(ri + eps, li1 - eps)) + end + end + end + + # Append remaining right-side Q points + while qidx <= qlen + push!(ratioP, Q1[qidx]) + qidx += 1 + end + + return ratioP +end + # Generate N primes > start that do not divide any numerator/denominator # of any coefficient in polynomials from LP From 731b7d4ec4e5c5e157071a8f25c0dc7273004d01 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sat, 18 Oct 2025 13:42:05 +0200 Subject: [PATCH 120/180] rename files --- src/connectivity/{Cannytools.jl => polar.jl} | 57 +------------------ src/connectivity/{computeRM.jl => roadmap.jl} | 0 2 files changed, 3 insertions(+), 54 deletions(-) rename src/connectivity/{Cannytools.jl => polar.jl} (75%) rename src/connectivity/{computeRM.jl => roadmap.jl} (100%) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/polar.jl similarity index 75% rename from src/connectivity/Cannytools.jl rename to src/connectivity/polar.jl index 897925f..2937a22 100644 --- a/src/connectivity/Cannytools.jl +++ b/src/connectivity/polar.jl @@ -112,7 +112,7 @@ function _compute_minors(p, A, R) # TODO: use algos from FLINT (in particular berkowitz) # Naive function performs better for high degree or small matrices if (degmax == 0 && p <= 2) || (degmax == 1 && p <= 6) || (degmax == 2) - detfct = s->detmpoly(s, R) + detfct = s->_detmpoly(s, R) else # else use fraction-free LU from AbstractAlgebra.jl detfct = det end @@ -140,7 +140,7 @@ function _combinations(a, n, start, chosen) end end -function detmpoly(A, R) +function _detmpoly(A, R) # Get the size of the matrix n = size(A, 1) if n != size(A, 2) @@ -161,62 +161,11 @@ function detmpoly(A, R) # Compute the determinant polynomial for j = 1:n submatrix = A[2:end, [i for i = 1:n if i != j]] - detA += (-1)^(1+j)*A[1, j] * detmpoly(submatrix, R) + detA += (-1)^(1+j)*A[1, j] * _detmpoly(submatrix, R) end return detA end -function MidRationalPoints(S::Vector{Vector{T}}, Q::Vector{T} = T[]) where {T <: QQFieldElem} - # * S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] - # such that the [l_i, r_i] are rational and disjoint open intervals. - # * Q is a list of rationals that intersects no [l_i,r_i] - # - # It orders the [l_i,r_i], and compute a list ratioP such that - # strictly between each of these intervals there is: - # - either at least one element of Q - # - or the simplest rational number - isempty(S) && return Q - - S1, Q1 = sort(S, lt=(x, y) -> x[2] <= y[1]), sort(Q) - ratioP = T[] - qidx = 1 - qlen = length(Q1) - - # Handle left gap before first interval - while qidx <= qlen && Q1[qidx] < S1[1][1] - push!(ratioP, Q1[qidx]) - qidx += 1 - end - - # Loop through gaps between sorted disjoint intervals - for i in 1:(length(S1) - 1) - ri, li1 = S1[i][2], S1[i+1][1] - @assert ri < li1 "Intervals are not disjoint." - inserted = false - while qidx <= qlen && Q1[qidx] < li1 - @assert(Q1[qidx] > ri, "A query point is singular") - push!(ratioP, Q1[qidx]) - inserted = true - qidx += 1 - end - if !inserted - eps = (li1 - ri)//1000 # for open interval - # We choose the simplest in absolute value - if -ri > li1 # this means ri is negative and the largest in absolute value - push!(ratioP, -simplest_between(-ri - eps, -li1 + eps)) - else - push!(ratioP, simplest_between(ri + eps, li1 - eps)) - end - end - end - - # Append remaining right-side Q points - while qidx <= qlen - push!(ratioP, Q1[qidx]) - qidx += 1 - end - return ratioP -end diff --git a/src/connectivity/computeRM.jl b/src/connectivity/roadmap.jl similarity index 100% rename from src/connectivity/computeRM.jl rename to src/connectivity/roadmap.jl From 6dd94b8beb21ce95b847cceb21554c1df613d18c Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sat, 18 Oct 2025 14:11:57 +0200 Subject: [PATCH 121/180] change name of roadmap fct + remove code duplication --- src/AlgebraicSolving.jl | 2 +- src/connectivity/roadmap.jl | 76 ++++++++++++------------------------- 2 files changed, 26 insertions(+), 52 deletions(-) diff --git a/src/AlgebraicSolving.jl b/src/AlgebraicSolving.jl index 612d3b1..e3fa4ff 100644 --- a/src/AlgebraicSolving.jl +++ b/src/AlgebraicSolving.jl @@ -19,7 +19,7 @@ include("algorithms/hilbert.jl") #= siggb =# include("siggb/siggb.jl") #= connectivity =# -include("connectivity/computeRM.jl") +include("connectivity/roadmap.jl") #= examples =# include("examples/katsura.jl") include("examples/cyclic.jl") diff --git a/src/connectivity/roadmap.jl b/src/connectivity/roadmap.jl index 2031b36..98d2f94 100644 --- a/src/connectivity/roadmap.jl +++ b/src/connectivity/roadmap.jl @@ -5,7 +5,7 @@ #using Nemo export roadmap, computepolar, _mid_rational_points, _fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis, computepolarL, detmpoly -include("Cannytools.jl") +include("polar.jl") @doc Markdown.doc""" roadmap(I::Ideal{T} where T <: MPolyRingElem, ) @@ -20,7 +20,6 @@ Moreover it is linked to fibers, that share the same base point. # Arguments - `I::Ideal{T} where T <: QQMPolyRingElem`: input generators. -- `q::Vector{QQFieldElem}=QQFieldElem[]`: single base point with rational coefficients - `C::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[]`: query points with rational coefficients - `info_level::Int=0`: verbosity level - `checks::Bool=false`: whether perform checks (dimension, regularity, etc.) @@ -57,11 +56,31 @@ julia> all_eqs(RM) ``` """ function roadmap( - I::Ideal{T} where T <: QQMPolyRingElem; # input ideal - q::Vector{QQFieldElem}=QQFieldElem[], # single base point with rational coefficients + I::Ideal{P}; # input ideal C::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # query points with rational coefficients - info_level::Int=0, # verbosity level + info_level::Int=0, # verbosity level checks::Bool=false # perform checks (dimension, regularity, etc.) +) where (P <: QQMPolyRingElem) + return _roadmap_rec(I, QQFieldElem[], C, info_level, checks) +end + +function roadmap( + I::Ideal{P}, # input ideal + C::Ideal{P}; # ideal defining query points + info_level::Int=0, # verbosity level + checks::Bool=false # perform checks (dimension, regularity, etc.) +) where (P <: QQMPolyRingElem) + @assert(parent(I)==parent(C), "Equations for variety and query points must live the same ring") + CI = real_solutions(C, info_level=max(info_level-1,0), nr_thrds=Threads.nthreads()) + return _roadmap_rec(I, QFieldElem[], CI, info_level, checks) +end + +function _roadmap_rec( + I::Ideal{T} where T <: QQMPolyRingElem, # input ideal + q::Vector{QQFieldElem}, # single base point with rational coefficients + C::Vector{Vector{QQFieldElem}}, # query points with rational coefficients + info_level::Int, # verbosity level + checks::Bool # perform checks (dimension, regularity, etc.) ) # Some base cases if nvars(parent(I))<=2 @@ -136,7 +155,7 @@ function roadmap( # Recursively compute roadmap of possible fibers if !isempty(newQ) for newq in newQ - RMFq = roadmap(I, q=newq, C=Cq) + RMFq = _roadmap_rec(I, newq, Cq, info_level, checks) push!(RM.children, RMFq) end end @@ -148,18 +167,6 @@ function roadmap( end end -function roadmap( - I::Ideal{P}, # input ideal - C::Ideal{P}; # ideal defining query points - info_level::Int=0, # verbosity level - checks::Bool=false # perform checks (dimension, regularity, etc.) -) where (P <: QQMPolyRingElem) - @assert(parent(I)==parent(C), "Equations for variety and query points must live the same ring") - CQ = real_solutions(C, info_level=max(info_level-1,0), nr_thrds=Threads.nthreads()) - return roadmap(I, C=CQ, info_level=info_level, checks=checks) -end - - function _fbr(I::Ideal{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) @assert(!isempty(I.gens), "Empty polynomial vector") vars = gens(parent(first(I.gens))) @@ -220,36 +227,3 @@ function _mid_rational_points(S::Vector{Vector{T}}, Q::Vector{T} = T[]) where {T end -# Generate N primes > start that do not divide any numerator/denominator -# of any coefficient in polynomials from LP -function _generate_lucky_primes( - LF::Vector{P} where P<:MPolyRingElem, - low::ZZRingElem, - up::ZZRingElem, - N::Int64 - ) - # Avoid repetitive enumeration and redundant divisibility check - CF = ZZRingElem[] - for f in LF, c in coefficients(f), part in (numerator(c), denominator(c)) - if !isone(part) - push!(CF, part) - end - end - sort!(CF, rev=true) - unique!(CF) - - # Test primes - Lprim = ZZRingElem[] - while length(Lprim) < N - cur_prim = next_prime(rand(low:up)) - is_lucky = !(cur_prim in Lprim) - i = firstindex(CF) - # Exploit decreasing order of CF - while is_lucky && i <= lastindex(CF) && CF[i] > cur_prim - is_lucky = !is_divisible_by(CF[i], cur_prim) - i += 1 - end - is_lucky && push!(Lprim, cur_prim) - end - return Lprim -end From d2646af9ca6cc882eba877a24ca28bda97bf8fd8 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Sat, 18 Oct 2025 15:01:44 +0200 Subject: [PATCH 122/180] new function for interval query points --- src/connectivity/roadmap.jl | 64 ++++++++++++++++++++++++++++++++++++- 1 file changed, 63 insertions(+), 1 deletion(-) diff --git a/src/connectivity/roadmap.jl b/src/connectivity/roadmap.jl index 98d2f94..82d72f8 100644 --- a/src/connectivity/roadmap.jl +++ b/src/connectivity/roadmap.jl @@ -4,7 +4,7 @@ #using AlgebraicSolving #using Nemo -export roadmap, computepolar, _mid_rational_points, _fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis, computepolarL, detmpoly +export roadmap, computepolar, _mid_rational_points, _mid_rational_points_inter, _fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis, computepolarL, detmpoly include("polar.jl") @doc Markdown.doc""" @@ -226,4 +226,66 @@ function _mid_rational_points(S::Vector{Vector{T}}, Q::Vector{T} = T[]) where {T return ratioP end +function _mid_rational_points_inter(S::Vector{Vector{T}}, Q::Vector{Vector{T}} = Vector{T}[]) where {T <: QQFieldElem} + # * S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] + # such that the [l_i, r_i] are rational and disjoint open intervals. + # * Same assumptions on Q + # * Intervals in S and Q do not intersect as well + # + # It orders the [l_i,r_i], and compute a list ratioP such that + # strictly between each of these intervals there is: + # - either at least one element inside an interval of Q + # - or the simplest rational number + # TODO: + isempty(S) && return Q + + S1, Q1 = sort(S, lt=(x, y) -> x[2] <= y[1]), sort(Q, lt=(x, y) -> x[2] <= y[1]) + ratioP = T[] + qidx = 1 + qlen = length(Q1) + + # Handle left gap before first interval + while qidx <= qlen && Q1[qidx][2] < S1[1][1] + ql, qr = Q1[qidx] + push!(ratioP, _open_simplest_between(ql, qr, abs(qr - ql)//1000)) + qidx += 1 + end + + # Loop through gaps between sorted disjoint intervals + for i in 1:(length(S1) - 1) + ri, li1 = S1[i][2], S1[i+1][1] + @assert ri < li1 "Intervals are not disjoint." + inserted = false + while qidx <= qlen && Q1[qidx][2] < li1 + ql, qr = Q1[qidx] + @assert(ql > ri, "A query point might be singular") + push!(ratioP, _open_simplest_between(ql, qr, abs(qr - ql)//1000)) + inserted = true + qidx += 1 + end + @assert qidx > qlen || Q1[qidx][1] > S1[i+1][2] "A query point might be singular" + # If there's already rational betwee no need to add new + !inserted && push!(ratioP, _open_simplest_between(ri, li1, abs(li1 - ri)//1000)) + end + + # Append remaining right-side Q points + while qidx <= qlen + ql, qr = Q1[qidx] + push!(ratioP, _open_simplest_between(ql, qr, abs(qr - ql)//1000)) + qidx += 1 + end + + return ratioP +end + + +function _open_simplest_between(a::QQFieldElem, b::QQFieldElem, eps::QQFieldElem) + # We choose the simplest in absolute value + if -a > b # this means a is negative and the largest in absolute value + return -simplest_between(-a - eps, -b + eps) + else + return simplest_between( a + eps, b - eps) + end +end + From e8381ead2def3432c5a59e9173928e0efbcbed8b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Tue, 21 Oct 2025 19:09:45 +0200 Subject: [PATCH 123/180] improve and simplify minor computations --- src/connectivity/polar.jl | 93 ++++++++----------------------------- src/connectivity/roadmap.jl | 2 +- 2 files changed, 21 insertions(+), 74 deletions(-) diff --git a/src/connectivity/polar.jl b/src/connectivity/polar.jl index 2937a22..8913967 100644 --- a/src/connectivity/polar.jl +++ b/src/connectivity/polar.jl @@ -74,8 +74,6 @@ function computepolar( isnothing(V.dim) && dimension(V) c = n - V.dim - ## Is it correct AND useful? - sort!(J) ## Jphi = [ j for j in J if j <= nphi ] Jproj = setdiff(J, Jphi) @@ -85,7 +83,7 @@ function computepolar( JW = matrix(R, QQMPolyRingElem[ derivative(f, k) for f in psi, k in setdiff(1:n, Jproj)]) # Compute the minors sizeminors = c + length(Jphi) + min(dimproj, length(J)-1) - (length(J)-1) - minors = _compute_minors(sizeminors, JW, R) + minors = _compute_minors(sizeminors, JW) if only_mins return minors @@ -94,78 +92,27 @@ function computepolar( end end -function _compute_minors(p, A, R) - #Computes the p-minors of a matrix A - n, m = size(A) - rowsmins = collect(_combinations(1:n, p, 1, Vector{Int}([]))) - colsmins = collect(_combinations(1:m, p, 1, Vector{Int}([]))) - mins = Vector{eltype(A)}(undef, length(rowsmins) * length(colsmins)) - k = 1 - # for performance tweaks, check if there are non-linear polynomials or if all are linear or constant - degmax = 0 - for a in A - degmax = min(2, max(degmax, total_degree(a))) - if degmax > 1 - break - end - end - # TODO: use algos from FLINT (in particular berkowitz) - # Naive function performs better for high degree or small matrices - if (degmax == 0 && p <= 2) || (degmax == 1 && p <= 6) || (degmax == 2) - detfct = s->_detmpoly(s, R) - else # else use fraction-free LU from AbstractAlgebra.jl - detfct = det - end - for rowsmin in rowsmins - for colsmin in colsmins - mins[k] = detfct(A[rowsmin, colsmin]) - k += 1 - end - end - - return mins +function _compute_minors(p, A) + # Computes the p-minors of a matrix A + rowsmins = _combinations(1:nrows(A), p) + colsmins = _combinations(1:ncols(A), p) + # We use charpoly for a division-free determinant method + return [ coeff(charpoly(A[rows, cols]), 0) for rows in rowsmins for cols in colsmins ] end -function _combinations(a, n, start, chosen) - if length(chosen) == n - return [chosen] - elseif start > length(a) - return Vector{Int}([]) - else - # Include the current element and recurse - include_current = _combinations(a, n, start + 1, [chosen; a[start]]) - # Exclude the current element and recurse - exclude_current = _combinations(a, n, start + 1, chosen) - return vcat(include_current, exclude_current) - end +function _combinations(v::UnitRange{Int}, k::Int) + # Compute the k-subsets of v + n = length(v) + ans = Vector{Int}[] + k > n && return ans + _combinations_dfs!(ans, Vector{Int}(undef, k), v, n, k) + return ans end -function _detmpoly(A, R) - # Get the size of the matrix - n = size(A, 1) - if n != size(A, 2) - throw(ArgumentError("Matrix must be square")) - end - - if n == 1 - return A[1, 1] - end - - if n == 2 - return A[1, 1] * A[2, 2] - A[1,2] * A[2, 1] +function _combinations_dfs!(ans::Vector{Vector{Int}}, comb::Vector{Int}, v::UnitRange{Int}, n::Int, k::Int) + k < 1 && (pushfirst!(ans, comb[:]); return) + for m in n:-1:k + comb[k] = v[m] + _combinations_dfs!(ans, comb, v, m - 1, k - 1) end - - # Initialize the determinant polynomial - detA = zero(R) - - # Compute the determinant polynomial - for j = 1:n - submatrix = A[2:end, [i for i = 1:n if i != j]] - detA += (-1)^(1+j)*A[1, j] * _detmpoly(submatrix, R) - end - - return detA -end - - - +end \ No newline at end of file diff --git a/src/connectivity/roadmap.jl b/src/connectivity/roadmap.jl index 82d72f8..21be64e 100644 --- a/src/connectivity/roadmap.jl +++ b/src/connectivity/roadmap.jl @@ -4,7 +4,7 @@ #using AlgebraicSolving #using Nemo -export roadmap, computepolar, _mid_rational_points, _mid_rational_points_inter, _fbr, all_eqs, all_base_pts, nb_nodes, compute_minors, compute_minors_bis, computepolarL, detmpoly +export roadmap, computepolar, _mid_rational_points, _mid_rational_points_inter, _fbr, all_eqs, all_base_pts, nb_nodes, computepolar include("polar.jl") @doc Markdown.doc""" From ef3487822632751931475dc34e2826424c221abb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 22 Oct 2025 15:34:46 +0200 Subject: [PATCH 124/180] complete the doc --- docs/make.jl | 6 +- docs/src/connectivity.md | 48 ++++++++++++++++ docs/src/types.md | 14 ++--- src/algorithms/solvers.jl | 2 +- src/connectivity/polar.jl | 24 +++----- src/connectivity/roadmap.jl | 108 +++++++++--------------------------- src/types.jl | 8 ++- 7 files changed, 104 insertions(+), 106 deletions(-) create mode 100644 docs/src/connectivity.md diff --git a/docs/make.jl b/docs/make.jl index 9c761f2..8a25b1b 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -1,6 +1,9 @@ +using Pkg +Pkg.activate("../../AlgebraicSolving.jl") using AlgebraicSolving using Documenter + push!(LOAD_PATH, "../src") DocMeta.setdocmeta!(AlgebraicSolving, :DocTestSetup, :(using AlgebraicSolving); recursive=true) @@ -24,7 +27,8 @@ makedocs( "hilbert.md", "dimension.md", "solvers.md", - "decomposition.md"], + "decomposition.md", + "connectivity.md"], "Examples" => "katsura.md" ] ) diff --git a/docs/src/connectivity.md b/docs/src/connectivity.md new file mode 100644 index 0000000..a932210 --- /dev/null +++ b/docs/src/connectivity.md @@ -0,0 +1,48 @@ +```@meta +CurrentModule = AlgebraicSolving +DocTestSetup = quote + using AlgebraicSolving +end +``` + +```@setup algebraicsolving +using AlgebraicSolving +``` + +```@contents +Pages = ["connectivity.md"] +``` + +# Algorithms for connectivity queries on smooth bounded algebraic sets + +## Introduction + +AlgebraicSolving allows to compute a roadmap for the real trace of the zero-set +of the ideal spanned by given input generators over the rationals. + +It assumes that the underlying algebraic set is **smooth**, and its real trace is **bounded**. + +The underlying engine is provided by msolve. + +## Functionality + +```@docs + roadmap( + I::Ideal{P} where P <: QQMPolyRingElem; + C::Vector{Vector{Vector{QQFieldElem}}}=Vector{Vector{QQFieldElem}}[], + info_level::Int=0, + checks::Bool=false + ) +``` + +In addition, AlgebraicSolving can compute equations definition critical loci of polynomial maps over the given algebraic set. + +```@docs + computepolar( + J::Union{Vector{Int},UnitRange{Int}}, + V::Ideal{P}; + phi::Vector{P} = P[], + dimproj = length(J)-1, + only_mins = false + ) where (P <: MPolyRingElem) +``` \ No newline at end of file diff --git a/docs/src/types.md b/docs/src/types.md index b60edce..bc4a2a0 100644 --- a/docs/src/types.md +++ b/docs/src/types.md @@ -17,21 +17,21 @@ Pages = ["types.md"] ## Introduction -AlgebraicSolving handles ideals in multivariate polynomial rings over a prime +AlgebraicSolving handles ideals in multivariate polynomial rings over a prime field of characteristic $0$ or $p$ where $p$ is a prime number $<2^{31}$. ## Polynomial Rings -We use [Nemo](https://www.nemocas.org/)'s multivariate polynomial +We use [Nemo](https://www.nemocas.org/)'s multivariate polynomial ring structures: ```@repl using AlgebraicSolving R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"], internal_ordering=:degrevlex) ``` -The above example defines a multivariate polynomial ring in three variables `x`, -`y`, and `z` over the rationals using the dgree reverse lexicographical ordering -for printing polynomials in the following. One can also define polynomial rings +The above example defines a multivariate polynomial ring in three variables `x`, +`y`, and `z` over the rationals using the dgree reverse lexicographical ordering +for printing polynomials in the following. One can also define polynomial rings over finite fields: ```@repl @@ -41,8 +41,8 @@ R, (x,y,z) = polynomial_ring(GF(101), ["x", "y", "z"], internal_ordering=:degrev ## Ideals -Ideals can be constructed by giving an array of generators. Ideals cache varies -data structures connected to ideals in order to make computational algebra more +Ideals can be constructed by giving an array of generators. Ideals cache varies +data structures connected to ideals in order to make computational algebra more effective: ```@repl diff --git a/src/algorithms/solvers.jl b/src/algorithms/solvers.jl index 52c9445..234e84e 100644 --- a/src/algorithms/solvers.jl +++ b/src/algorithms/solvers.jl @@ -295,8 +295,8 @@ QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x julia> rat_sols = rational_solutions(I) 2-element Vector{Vector{QQFieldElem}}: - [1, 0, 0] [1//3, 0, 1//3] + [1, 0, 0] julia> map(r->map(p->evaluate(p, r), I.gens), rat_sols) 2-element Vector{Vector{QQFieldElem}}: diff --git a/src/connectivity/polar.jl b/src/connectivity/polar.jl index 8913967..ad0805c 100644 --- a/src/connectivity/polar.jl +++ b/src/connectivity/polar.jl @@ -1,11 +1,5 @@ @doc Markdown.doc""" - computepolar( - J::Union{Vector{Int},UnitRange{Int}}, - V::Ideal{P}; - phi::Vector{P}=P[], - dimproj::Int=length(J)-1, - only_mins::Bool=false - ) where {P <: MPolyRingElem} + computepolar(J::Union{Vector{Int},UnitRange{Int}}, V::Ideal{P} where P <: MPolyRingElem; ) Compute the **polar variety** associated with the map whose components are `[phi_1, …, phi_p, x_{p+1}, …, x_n]` indexed by `J`, for an algebraic variety defined @@ -46,16 +40,16 @@ julia> using AlgebraicSolving julia> R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) (Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x1, x2, x3, x4]) -julia> I = Ideal([(x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2)]) -QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64] +julia> I = Ideal([(x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2) + 1]) +QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65] julia> computepolar(1:3, I, dimproj=1, phi=[x1^2+x2^2+x3^2+x4^2]) 5-element Vector{QQMPolyRingElem}: - x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64 - 4*x1^3 + 4*x1*x2^2 + 4*x1*x3^2 + 4*x1*x4^2 - 40*x1 - 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4 - 2*x1 - 2*x4 + x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65 + -4*x1^3 - 4*x1*x2^2 - 4*x1*x3^2 - 4*x1*x4^2 + 40*x1 + -4*x1^2*x4 - 4*x2^2*x4 - 4*x3^2*x4 - 4*x4^3 - 32*x4 + -2*x1 + -2*x4 ``` """ function computepolar( @@ -100,7 +94,7 @@ function _compute_minors(p, A) return [ coeff(charpoly(A[rows, cols]), 0) for rows in rowsmins for cols in colsmins ] end -function _combinations(v::UnitRange{Int}, k::Int) +function _combinations(v::UnitRange{Int}, k::Int) # Compute the k-subsets of v n = length(v) ans = Vector{Int}[] diff --git a/src/connectivity/roadmap.jl b/src/connectivity/roadmap.jl index 21be64e..a49e079 100644 --- a/src/connectivity/roadmap.jl +++ b/src/connectivity/roadmap.jl @@ -31,39 +31,43 @@ Moreover it is linked to fibers, that share the same base point. julia> using AlgebraicSolving julia> R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) -(Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x1, x2, x3, x4]) +(Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x1, x2, x3, x4]) -julia> I = Ideal([x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2)]) -QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64] +julia> I = Ideal([(x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2) + 1]) +QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65] -julia> RM = roadmap(I) -Vector{QQFieldElem}[[], [-3], [-3, -2], [-1], [-1, -2], [-1, -1], [-1, 2], [3], [3, 2]] +julia> RM = roadmap(I, checks=true) +Vector{QQFieldElem}[[], [-3], [-3, -2], [-2], [-2, -1], [-2, 0], [-2, 1], [3], [3, 2]] julia> nb_nodes(RM) 9 julia> all_eqs(RM) 9-element Vector{Ideal{QQMPolyRingElem}}: - QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, 4*x1^2*x3 + 4*x2^2*x3 + 4*x3^3 + 4*x3*x4^2 - 40*x3, 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4] - QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4, x1 + 3] - QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 + 3, x2 + 2] - QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4, x1 + 1] - QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 + 1, x2 + 2] - QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 + 1, x2 + 1] - QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 + 1, x2 - 2] - QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, 4*x1^2*x4 + 4*x2^2*x4 + 4*x3^2*x4 + 4*x4^3 + 32*x4, x1 - 3] - QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 64, x1 - 3, x2 - 2] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65, -4*x1^2*x3 - 4*x2^2*x3 - 4*x3^3 - 4*x3*x4^2 + 40*x3, -4*x1^2*x4 - 4*x2^2*x4 - 4*x3^2*x4 - 4*x4^3 - 32*x4] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65, -4*x1^2*x4 - 4*x2^2*x4 - 4*x3^2*x4 - 4*x4^3 - 32*x4, x1 + 3] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65, x1 + 3, x2 + 2] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65, -4*x1^2*x4 - 4*x2^2*x4 - 4*x3^2*x4 - 4*x4^3 - 32*x4, x1 + 2] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65, x1 + 2, x2 + 1] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65, x1 + 2, x2] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65, x1 + 2, x2 - 1] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65, -4*x1^2*x4 - 4*x2^2*x4 - 4*x3^2*x4 - 4*x4^3 - 32*x4, x1 - 3] + QQMPolyRingElem[x1^4 + 2*x1^2*x2^2 + 2*x1^2*x3^2 + 2*x1^2*x4^2 - 20*x1^2 + x2^4 + 2*x2^2*x3^2 + 2*x2^2*x4^2 - 20*x2^2 + x3^4 + 2*x3^2*x4^2 - 20*x3^2 + x4^4 + 16*x4^2 + 65, x1 - 3, x2 - 2] ``` """ function roadmap( - I::Ideal{P}; # input ideal - C::Vector{Vector{QQFieldElem}}=Vector{QQFieldElem}[], # query points with rational coefficients - info_level::Int=0, # verbosity level - checks::Bool=false # perform checks (dimension, regularity, etc.) + I::Ideal{P}; # input ideal + C::Vector{Vector{Vector{QQFieldElem}}}=Vector{Vector{QQFieldElem}}[], # query points: interval with rational coefficients + info_level::Int=0, # verbosity level + checks::Bool=false # perform checks (dimension, regularity, etc.) ) where (P <: QQMPolyRingElem) return _roadmap_rec(I, QQFieldElem[], C, info_level, checks) end +@doc Markdown.doc""" + roadmap(I::Ideal{T} where T <: MPolyRingElem, I::Ideal{P}, C::Ideal{P}; info_level::Int=0, checks::Bool=false) +``` +""" function roadmap( I::Ideal{P}, # input ideal C::Ideal{P}; # ideal defining query points @@ -78,7 +82,7 @@ end function _roadmap_rec( I::Ideal{T} where T <: QQMPolyRingElem, # input ideal q::Vector{QQFieldElem}, # single base point with rational coefficients - C::Vector{Vector{QQFieldElem}}, # query points with rational coefficients + C::Vector{Vector{Vector{QQFieldElem}}}, # query points with rational coefficients info_level::Int, # verbosity level checks::Bool # perform checks (dimension, regularity, etc.) ) @@ -144,12 +148,12 @@ function _roadmap_rec( K1WmFq = real_solutions(_fbr(K1WmFq,q), info_level=max(info_level-1,0), nr_thrds=Threads.nthreads(), interval=true) ## New base and query points ## - Cq = isempty(q) ? C : [ c for c in C if c[e] == q[e]] + Cq = isempty(q) ? C : [ c for c in C if q[e] in c[e]] K1W = vcat(K1Fq, K1WmFq) # Heuristic to be proven (Reeb's th) #K1W = K1W[2:end-1] ########## - K1WRat = _mid_rational_points(getindex.(K1W,e+1), unique(getindex.(Cq, e+1))) + K1WRat = _mid_rational_points_inter(getindex.(K1W,e+1), unique(getindex.(Cq, e+1))) newQ = vcat.(Ref(q), K1WRat) # Recursively compute roadmap of possible fibers @@ -167,72 +171,14 @@ function _roadmap_rec( end end -function _fbr(I::Ideal{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) - @assert(!isempty(I.gens), "Empty polynomial vector") - vars = gens(parent(first(I.gens))) - return Ideal(vcat(I.gens, [vars[i] - Q[i] for i in 1:min(length(vars),length(Q))])) -end - -function _mid_rational_points(S::Vector{Vector{T}}, Q::Vector{T} = T[]) where {T <: QQFieldElem} - # * S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] - # such that the [l_i, r_i] are rational and disjoint open intervals. - # * Q is a list of rationals that intersects no [l_i,r_i] - # - # It orders the [l_i,r_i], and compute a list ratioP such that - # strictly between each of these intervals there is: - # - either at least one element of Q - # - or the simplest rational number - isempty(S) && return Q - - S1, Q1 = sort(S, lt=(x, y) -> x[2] <= y[1]), sort(Q) - ratioP = T[] - qidx = 1 - qlen = length(Q1) - - # Handle left gap before first interval - while qidx <= qlen && Q1[qidx] < S1[1][1] - push!(ratioP, Q1[qidx]) - qidx += 1 - end - - # Loop through gaps between sorted disjoint intervals - for i in 1:(length(S1) - 1) - ri, li1 = S1[i][2], S1[i+1][1] - @assert ri < li1 "Intervals are not disjoint." - inserted = false - while qidx <= qlen && Q1[qidx] < li1 - @assert(Q1[qidx] > ri, "A query point is singular") - push!(ratioP, Q1[qidx]) - inserted = true - qidx += 1 - end - if !inserted - eps = (li1 - ri)//1000 # for open interval - # We choose the simplest in absolute value - if -ri > li1 # this means ri is negative and the largest in absolute value - push!(ratioP, -simplest_between(-ri - eps, -li1 + eps)) - else - push!(ratioP, simplest_between(ri + eps, li1 - eps)) - end - end - end - - # Append remaining right-side Q points - while qidx <= qlen - push!(ratioP, Q1[qidx]) - qidx += 1 - end - - return ratioP -end - function _mid_rational_points_inter(S::Vector{Vector{T}}, Q::Vector{Vector{T}} = Vector{T}[]) where {T <: QQFieldElem} # * S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] # such that the [l_i, r_i] are rational and disjoint open intervals. # * Same assumptions on Q # * Intervals in S and Q do not intersect as well # - # It orders the [l_i,r_i], and compute a list ratioP such that + # It orders the [l_i,r_i], and compute a list ratioP + # intersecting all intervals of Q and such that # strictly between each of these intervals there is: # - either at least one element inside an interval of Q # - or the simplest rational number diff --git a/src/types.jl b/src/types.jl index 6ef5453..bd4b7f8 100644 --- a/src/types.jl +++ b/src/types.jl @@ -97,8 +97,14 @@ function _collect_roadmap(RMn::RMnode, F) return data end +function _fbr(I::Ideal{P} where P <: QQMPolyRingElem, Q::Vector{QQFieldElem}) + @assert(!isempty(I.gens), "Empty polynomial vector") + vars = gens(parent(first(I.gens))) + return Ideal(vcat(I.gens, [vars[i] - Q[i] for i in 1:min(length(vars),length(Q))])) +end + function all_eqs(RM::Roadmap) - func(s) = fbr(vcat(RM.initial_ideal.gens, s.polar_eqs), s.base_pt) + func(s) = _fbr(vcat(RM.initial_ideal.gens, s.polar_eqs) |> Ideal, s.base_pt) return _collect_roadmap(RM.root, func) end From 8881239e145ec4a0ac484caf505c8b9f551c9565 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 22 Oct 2025 15:35:30 +0200 Subject: [PATCH 125/180] revert a change --- docs/make.jl | 2 -- 1 file changed, 2 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 8a25b1b..722d8f2 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -1,5 +1,3 @@ -using Pkg -Pkg.activate("../../AlgebraicSolving.jl") using AlgebraicSolving using Documenter From 872c7154eb13743233d20503ee38ae67e10ad36f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Tue, 4 Nov 2025 17:35:34 +0100 Subject: [PATCH 126/180] start documenting ratparams and roadmaps --- docs/src/types.md | 122 +++++++++++++++++++++++++++++++++- src/algorithms/param-curve.jl | 3 +- 2 files changed, 121 insertions(+), 4 deletions(-) diff --git a/docs/src/types.md b/docs/src/types.md index bc4a2a0..fa440d9 100644 --- a/docs/src/types.md +++ b/docs/src/types.md @@ -41,9 +41,7 @@ R, (x,y,z) = polynomial_ring(GF(101), ["x", "y", "z"], internal_ordering=:degrev ## Ideals -Ideals can be constructed by giving an array of generators. Ideals cache varies -data structures connected to ideals in order to make computational algebra more -effective: +Ideals can be constructed by giving an array of generators: ```@repl using AlgebraicSolving @@ -51,3 +49,121 @@ R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"], internal_ordering=:degrevlex) I = Ideal([x+y+1, y*z^2-13*y^2]) ``` +Ideals cache various data structures connected to ideals in order to make +computational algebra more effective. Assume that `T <: MPolyRingElem`, then + * `gens::Vector{T}`: generators of the Ideal provded by the user; + * `deg::Int`: degree of the ideal (`Nothing` if unknown); + * `dim::Int`: Krull dimension of the Ideal (`Nothing` if unknown); + * `gb::Dict{Int, Vector{T}}`: Gröbner bases of the Ideal where the key correspond to the number of variables eliminated (starting with the first); + * `inter_sols::Vector{Vector{Vector{QQFieldElem}}}`: intervals with rational endpoints, containing the real solutions of the system (if `dim=0`); + * `real_sols::Vector{Vector{QQFieldElem}}`: midpoints of the above intervals; + * `rat_sols::Vector{Vector{QQFieldElem}}`: rational solutions of the system (if `dim=0`). + * `rat_param::Union{RationalParametrization, RationalCurveParametrization}`: rational parametrization encoding the complex solution set of the Ideal (see below). +## Rational Parametrizations + +Rational Parametrizations are special data structure for representing equidimensionnal +algebraic sets of dimension 0 and 1. They are typical outputs of algorithm for solving +polynomial systems encoding such algebraic sets thanks to their nice behaviour with +subsequent computations. + +### Zero-dimensionnal parametrizations: finite set of points (see also [there](https://msolve.lip6.fr/downloads/msolve-tutorial.pdf#section.6)) + +A *zero-dimensional parametrization* $\mathscr{P}$ with +coefficients in a field $\mathbb{Q}$ consists of: +* polynomials $(w, w', v_1, \ldots, v_n)$ in $\mathbb{K}[t]$ where $t$ is + a new variable and such that + * $w$ is a monic square-free polynomial; + * $w'=1$ when $\mathbb{K}$ is a prime field, $w'=\frac{dw}{dt}$ else; + * $\deg(v_i) < \deg(w)$. +* a linear form $l$ in the variables $x_1,\dotsc, x_n$, +such that +$$ +l(\rho_1,\dotsc,\rho_n) = t \mod w. +$$ + +Such a data-structure encodes the following finite set of points +$$ +\left\{\left (\frac{\rho_1(\vartheta)}{w'(\vartheta)}, +\ldots, \frac{\rho_n(\vartheta)}{w'(\vartheta)} \right) \middle|\, w(\vartheta) = 0\right\}. +$$ +According to this definition, the roots of $w$ are exactly the +values taken by $l$ on this set. + +The type `RationalParametrization` therefore caches the following attributes: + * `vars::Vector{Symbol}`: variables used for the parametrization the last one playing the role of the above $t$ + (hence, maybe with one more variable than the ones given as input); + * `cfs_lf::Vector{ZZRingElem}`: coefficients on the linear form $l$ (when variables are added); + * `elim::QQPolyRingElem`: elimination polynomial $w$ ; + * `denom::QQPolyRingElem`: denominator polynomial (usually $w'$); + * `param::Vector{QQPolyRingElem}`: numerators $\rho_i$'s. + +See the documentation of the [rational_parametrization](@ref) function for further details. + +### One-dimensionnal parametrizations: algebraic curves + +A *one-dimensional parametrization* $\mathscr{C}$ with +coefficients in a field $\mathbb{C}$ consists of: +* polynomials $(w, w', v_1, \ldots, v_n)$ in $\mathbb{K}[t,s]$ where $t,s$ are + new variables and such that + * $w$ is a monic square-free polynomial and $w'=\frac{\partial w}{\partial t}$; + * $\deg(v_i) < \deg(w)$. +* two linear forms $(l,l')$ in the variables $x_1,\dotsc, x_n$, +such that +$$ +l(\rho_1,\dotsc,\rho_n) = t\, w'\mod w \quad \text{and} \quad +l'(\rho_1,\dotsc,\rho_n) = s\,w' \mod w +$$ + +Such a data-structure encodes the curve defined as the Zariski closure of the following set +$$ +\left\{\left (\frac{\rho_1(\vartheta,\eta)}{w'(\vartheta,\eta)}, +\ldots, \frac{\rho_n(\vartheta,\eta)}{w'(\vartheta,\eta)} \right) +\middle|\, w(\vartheta,\eta) = 0,\, w'(\vartheta, \eta) \neq 0\right\}. +$$ +According to this definition, the roots of $w$ are exactly the +values taken by $l$ on this set. + +The type `RationalCurveParametrization` therefore caches the following attributes: + * `vars::Vector{Symbol}`: variables used for the parametrization the last two ones playing the role of the above $(t,s)$ + (hence, maybe with up to two more variable than the ones given as input);; + * `cfs_lfs::Vector{Vector{ZZRingElem}}`: coefficients on the linear form $l$ (when variables are added); + * `elim::QQMPolyRingElem`: elimination polynomial $w$ ; + * `denom::QQMPolyRingElem`: denominator polynomial (usually $w'$); + * `param::Vector{QQMPolyRingElem}`: numerators $\rho_i$'s. + +See the documentation of the [rational_curve_parametrization](@ref) function for further details. + +## Roadmaps + +Roadmaps are algebraic curves capturing the connectivity properties of an algebraic +set containing it. They are computed as union of several curves, organized in a tree +due to the recursive nature of the roadmap algorithms. + +```julia +mutable struct Roadmap + initial_ideal::Ideal{QQMPolyRingElem} + root::RMnode +end +``` + +Hence, it is composed of a main node, containing the equations of the initial algebraic set and a reference to the root node of the tree. + +```julia +mutable struct RMnode + polar_eqs::Vector{QQMPolyRingElem} + base_pt::Vector{QQFieldElem} + children::Vector{RMnode} +end +``` + +Each roadmap node (including the root) correspond to a curve component of the roadmap. These are defined in fibers of the initial variety, and are arranged w.r.t. to the specialized variables they share. In particular, all child nodes (referenced in `children`) of a node will have the same specialized variable, plus a new distinct one. + +Each of these components is defined as the polar variety (whose equations are in `polar_eqs`) over a fiber of the initial algebraic set, which are defined by specializing the first variables to the `base_pt` of its parents, and of itsef (in this order). + + +See the documentation of the [roadmap](@ref) function for further details. + + +``` +TODO : un dessin ? les fonctions all_eqs, all_base_pts et nb_nodes (utiliser la doc du code?) +``` \ No newline at end of file diff --git a/src/algorithms/param-curve.jl b/src/algorithms/param-curve.jl index 1e553f2..e1757b4 100644 --- a/src/algorithms/param-curve.jl +++ b/src/algorithms/param-curve.jl @@ -232,7 +232,8 @@ function _evalvar( return LFeval end -# Generate N primes > start that do not divide any numerator/denominator +# Generate N random primes between low and up +# that do not divide any numerator/denominator # of any coefficient in polynomials from LP function _generate_lucky_primes( LF::Vector{P} where P<:MPolyRingElem, From def0143992793cb53e408520d873cd545699b5b9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 5 Nov 2025 15:57:10 +0100 Subject: [PATCH 127/180] doc for roadmap --- docs/src/types.md | 77 +++++++++++++++++++++++++++++++++-------------- src/types.jl | 2 +- 2 files changed, 56 insertions(+), 23 deletions(-) diff --git a/docs/src/types.md b/docs/src/types.md index fa440d9..216eb88 100644 --- a/docs/src/types.md +++ b/docs/src/types.md @@ -54,13 +54,19 @@ computational algebra more effective. Assume that `T <: MPolyRingElem`, then * `gens::Vector{T}`: generators of the Ideal provded by the user; * `deg::Int`: degree of the ideal (`Nothing` if unknown); * `dim::Int`: Krull dimension of the Ideal (`Nothing` if unknown); - * `gb::Dict{Int, Vector{T}}`: Gröbner bases of the Ideal where the key correspond to the number of variables eliminated (starting with the first); - * `inter_sols::Vector{Vector{Vector{QQFieldElem}}}`: intervals with rational endpoints, containing the real solutions of the system (if `dim=0`); + * `gb::Dict{Int, Vector{T}}`: Gröbner bases of the Ideal where the key + correspond to the number of variables eliminated (starting with the first); + * `inter_sols::Vector{Vector{Vector{QQFieldElem}}}`: intervals with rational + endpoints, containing the real solutions of the system (if `dim=0`); * `real_sols::Vector{Vector{QQFieldElem}}`: midpoints of the above intervals; - * `rat_sols::Vector{Vector{QQFieldElem}}`: rational solutions of the system (if `dim=0`). - * `rat_param::Union{RationalParametrization, RationalCurveParametrization}`: rational parametrization encoding the complex solution set of the Ideal (see below). -## Rational Parametrizations + * `rat_sols::Vector{Vector{QQFieldElem}}`: rational solutions of the system + (if `dim=0`). + * `rat_param::Union{RationalParametrization, RationalCurveParametrization}`: + rational parametrization encoding the complex solution set of the Ideal (see + below). + +## Rational Parametrizations Rational Parametrizations are special data structure for representing equidimensionnal algebraic sets of dimension 0 and 1. They are typical outputs of algorithm for solving polynomial systems encoding such algebraic sets thanks to their nice behaviour with @@ -123,21 +129,39 @@ $$ According to this definition, the roots of $w$ are exactly the values taken by $l$ on this set. -The type `RationalCurveParametrization` therefore caches the following attributes: - * `vars::Vector{Symbol}`: variables used for the parametrization the last two ones playing the role of the above $(t,s)$ - (hence, maybe with up to two more variable than the ones given as input);; - * `cfs_lfs::Vector{Vector{ZZRingElem}}`: coefficients on the linear form $l$ (when variables are added); +The type `RationalCurveParametrization` therefore caches the following +attributes: + * `vars::Vector{Symbol}`: variables used for the parametrization the last two + ones playing the role of the above $(t,s)$ (hence, maybe with up to two more + variable than the ones given as input);; + * `cfs_lfs::Vector{Vector{ZZRingElem}}`: coefficients on the linear form $l$ + (when variables are added); * `elim::QQMPolyRingElem`: elimination polynomial $w$ ; * `denom::QQMPolyRingElem`: denominator polynomial (usually $w'$); * `param::Vector{QQMPolyRingElem}`: numerators $\rho_i$'s. -See the documentation of the [rational_curve_parametrization](@ref) function for further details. +See the documentation of the [rational_curve_parametrization](@ref) function for +further details. ## Roadmaps -Roadmaps are algebraic curves capturing the connectivity properties of an algebraic -set containing it. They are computed as union of several curves, organized in a tree -due to the recursive nature of the roadmap algorithms. +Consider an algebraic set $V\subset \mathbb{C}^n$ and a finite set of query +points $\mathcal{P} \subset V$, both defined by polynomials with coefficients in +$\mathbb{Q}$. A *roadmap* $\mathcal{R}$ associated to $(V,\mathcal{P})$ is an +algebraic curve such that + * $\mathcal{P} \subset \mathcal{R} \subset V$; + * $C \cap \mathcal{R}$ is non-empty and connected, for each connected + component $C$ of $V\cap \mathbb{R}^n$. + +Roadmaps are algebraic curves capturing the connectivity properties of an +algebraic set containing it so that points in $\mathcal{P}$ are equivalently +connected both on $\mathcal{R}$ and $V\cap \mathbb{R}^n$. + +The effective construction of roadmaps relies on connectivity statements which +allow one to construct real algebraic subsets of $V\cap \mathbb{R}^n$, of +smaller dimension, having a connected intersection with the connected components +of $V\cap \mathbb{R}^n$ Therefore, the output is union of several curves, +organized in a tree due to the recursive nature of the roadmap algorithms. ```julia mutable struct Roadmap @@ -146,24 +170,33 @@ mutable struct Roadmap end ``` -Hence, it is composed of a main node, containing the equations of the initial algebraic set and a reference to the root node of the tree. +Hence, it is composed of a main node, containing the equations of the initial +algebraic set $V$ and a reference to the root node of the tree. ```julia mutable struct RMnode - polar_eqs::Vector{QQMPolyRingElem} base_pt::Vector{QQFieldElem} + polar_eqs::Vector{QQMPolyRingElem} children::Vector{RMnode} end ``` -Each roadmap node (including the root) correspond to a curve component of the roadmap. These are defined in fibers of the initial variety, and are arranged w.r.t. to the specialized variables they share. In particular, all child nodes (referenced in `children`) of a node will have the same specialized variable, plus a new distinct one. +Each roadmap node (including the root) correspond to a curve component of the +roadmap. More precisely, they are defined by as an algebraic subset $W$ (called +polar variety) of a fiber $F$ of the initial variety $V$ such that: + * if `base_pt` contains $\mathbf{q}=(q_1,\dotsc,q_e) \in \mathbb{Q}^e$ then $$ + F = V \cap \left\{x_1=q_1,\,\dotsc,\, x_e=q_e\right\}; $$ + * if `polar_eqs` contains the polynomials $g_1,\dotsc,g_s \in + \mathbb{Q}[x_1,\dotsc,x_n]$ then $$ W = F \cap \{g_1=0,\, \ldots,\, g_s = 0\}. + $$ -Each of these components is defined as the polar variety (whose equations are in `polar_eqs`) over a fiber of the initial algebraic set, which are defined by specializing the first variables to the `base_pt` of its parents, and of itsef (in this order). +Moreover, `children` rassembles all the tree nodes that contains curves +component for which their attribute `base_pt` contains a point $\mathbf{q}'$ +that shares the same first $e$ coordinates with $\mathbf{q}$. +The reason of this tree arrangement is mainly because of the following property: +*two roadmap components intersects if, and only if, one's node is a descendant +of the other's*. In many cases, one can even replace "descendant" by "parent". -See the documentation of the [roadmap](@ref) function for further details. - -``` -TODO : un dessin ? les fonctions all_eqs, all_base_pts et nb_nodes (utiliser la doc du code?) -``` \ No newline at end of file +See the documentation of the [roadmap](@ref) function for further details. \ No newline at end of file diff --git a/src/types.jl b/src/types.jl index bd4b7f8..56f1c08 100644 --- a/src/types.jl +++ b/src/types.jl @@ -79,8 +79,8 @@ Base.getindex(I::Ideal, idx::Union{Int, UnitRange}) = I.gens[idx] Base.lastindex(I::Ideal) = lastindex(I.gens) mutable struct RMnode - polar_eqs::Vector{QQMPolyRingElem} base_pt::Vector{QQFieldElem} + polar_eqs::Vector{QQMPolyRingElem} children::Vector{RMnode} end From 81183244f65a855d45f78e8b04a88e30ab881813 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 10 Dec 2025 18:44:31 +0100 Subject: [PATCH 128/180] fix args RMnode --- src/connectivity/roadmap.jl | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/src/connectivity/roadmap.jl b/src/connectivity/roadmap.jl index a49e079..e0c9a96 100644 --- a/src/connectivity/roadmap.jl +++ b/src/connectivity/roadmap.jl @@ -82,7 +82,7 @@ end function _roadmap_rec( I::Ideal{T} where T <: QQMPolyRingElem, # input ideal q::Vector{QQFieldElem}, # single base point with rational coefficients - C::Vector{Vector{Vector{QQFieldElem}}}, # query points with rational coefficients + C::Vector{Vector{Vector{QQFieldElem}}}, # query points with rational coefficients info_level::Int, # verbosity level checks::Bool # perform checks (dimension, regularity, etc.) ) @@ -111,7 +111,7 @@ function _roadmap_rec( # Terminal case (dim <=1) if I.dim - e <= 1 - return RMnode([], q, RMnode[]) + return RMnode(q, [], RMnode[]) end ## sing(Fq) ## @@ -140,7 +140,7 @@ function _roadmap_rec( else K2Fq.dim = e + 1 end - RM = RMnode(K2Fqmins, q, RMnode[]) + RM = RMnode(q, K2Fqmins, RMnode[]) ## Points with vertical tg in K(pi_2, Fq) ## info_level>0 && println("Compute W-critical points with vertical tangent: K1W") From fd72a6d76dcaf1e68d4a9855202c4e4de043578b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Fri, 27 Feb 2026 16:59:00 +0100 Subject: [PATCH 129/180] typo --- src/connectivity/roadmap.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/roadmap.jl b/src/connectivity/roadmap.jl index e0c9a96..318501f 100644 --- a/src/connectivity/roadmap.jl +++ b/src/connectivity/roadmap.jl @@ -210,7 +210,7 @@ function _mid_rational_points_inter(S::Vector{Vector{T}}, Q::Vector{Vector{T}} = qidx += 1 end @assert qidx > qlen || Q1[qidx][1] > S1[i+1][2] "A query point might be singular" - # If there's already rational betwee no need to add new + # If there's already rational between no need to add new !inserted && push!(ratioP, _open_simplest_between(ri, li1, abs(li1 - ri)//1000)) end From 2bc7a32a4d589b8719d65facc3b8d12b032036f1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Tue, 3 Mar 2026 12:14:42 +0100 Subject: [PATCH 130/180] fix roadmap doc --- docs/make.jl | 2 ++ docs/src/types.md | 49 ++++++++++++++----------------------- src/connectivity/roadmap.jl | 2 +- 3 files changed, 21 insertions(+), 32 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 722d8f2..563d01f 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -1,3 +1,5 @@ +#using Pkg +#Pkg.activate("../../AlgebraicSolving.jl/") using AlgebraicSolving using Documenter diff --git a/docs/src/types.md b/docs/src/types.md index 216eb88..1a18966 100644 --- a/docs/src/types.md +++ b/docs/src/types.md @@ -78,20 +78,15 @@ A *zero-dimensional parametrization* $\mathscr{P}$ with coefficients in a field $\mathbb{Q}$ consists of: * polynomials $(w, w', v_1, \ldots, v_n)$ in $\mathbb{K}[t]$ where $t$ is a new variable and such that - * $w$ is a monic square-free polynomial; - * $w'=1$ when $\mathbb{K}$ is a prime field, $w'=\frac{dw}{dt}$ else; - * $\deg(v_i) < \deg(w)$. -* a linear form $l$ in the variables $x_1,\dotsc, x_n$, + * $w$ is a monic square-free polynomial; + * $w'=1$ when $\mathbb{K}$ is a prime field, $w'=\frac{dw}{dt}$ else; + * $\deg(v_i) < \deg(w)$. +* a linear form $l$ in the variables $x_1,\dotsc, x_n$, such that -$$ -l(\rho_1,\dotsc,\rho_n) = t \mod w. -$$ +$l(\rho_1,\dotsc,\rho_n) = t \mod w$. Such a data-structure encodes the following finite set of points -$$ -\left\{\left (\frac{\rho_1(\vartheta)}{w'(\vartheta)}, -\ldots, \frac{\rho_n(\vartheta)}{w'(\vartheta)} \right) \middle|\, w(\vartheta) = 0\right\}. -$$ +* $\left\{\left(\frac{\rho_1(\vartheta)}{w'(\vartheta)}, \ldots, \frac{\rho_n(\vartheta)}{w'(\vartheta)} \right) \middle|\, w(\vartheta) = 0\right\}$. According to this definition, the roots of $w$ are exactly the values taken by $l$ on this set. @@ -103,7 +98,7 @@ The type `RationalParametrization` therefore caches the following attributes: * `denom::QQPolyRingElem`: denominator polynomial (usually $w'$); * `param::Vector{QQPolyRingElem}`: numerators $\rho_i$'s. -See the documentation of the [rational_parametrization](@ref) function for further details. +See the documentation of the [`rational_parametrization`](@ref) function for further details. ### One-dimensionnal parametrizations: algebraic curves @@ -111,21 +106,14 @@ A *one-dimensional parametrization* $\mathscr{C}$ with coefficients in a field $\mathbb{C}$ consists of: * polynomials $(w, w', v_1, \ldots, v_n)$ in $\mathbb{K}[t,s]$ where $t,s$ are new variables and such that - * $w$ is a monic square-free polynomial and $w'=\frac{\partial w}{\partial t}$; - * $\deg(v_i) < \deg(w)$. + * $w$ is a monic square-free polynomial and $w'=\frac{\partial w}{\partial t}$; + * $\deg(v_i) < \deg(w)$. * two linear forms $(l,l')$ in the variables $x_1,\dotsc, x_n$, such that -$$ -l(\rho_1,\dotsc,\rho_n) = t\, w'\mod w \quad \text{and} \quad -l'(\rho_1,\dotsc,\rho_n) = s\,w' \mod w -$$ +$l(\rho_1,\dotsc,\rho_n) = t\, w'\mod w \quad \text{and} \quad l'(\rho_1,\dotsc,\rho_n) = s\,w' \mod w$ Such a data-structure encodes the curve defined as the Zariski closure of the following set -$$ -\left\{\left (\frac{\rho_1(\vartheta,\eta)}{w'(\vartheta,\eta)}, -\ldots, \frac{\rho_n(\vartheta,\eta)}{w'(\vartheta,\eta)} \right) -\middle|\, w(\vartheta,\eta) = 0,\, w'(\vartheta, \eta) \neq 0\right\}. -$$ +* $\left\{\left(\frac{\rho_1(\vartheta,\eta)}{w'(\vartheta,\eta)}, \ldots, \frac{\rho_n(\vartheta,\eta)}{w'(\vartheta,\eta)} \right) \middle|\, w(\vartheta,\eta) = 0,\, w'(\vartheta, \eta) \neq 0\right\}$. According to this definition, the roots of $w$ are exactly the values taken by $l$ on this set. @@ -140,7 +128,7 @@ attributes: * `denom::QQMPolyRingElem`: denominator polynomial (usually $w'$); * `param::Vector{QQMPolyRingElem}`: numerators $\rho_i$'s. -See the documentation of the [rational_curve_parametrization](@ref) function for +See the documentation of the [`rational_curve_parametrization`](@ref) function for further details. ## Roadmaps @@ -149,8 +137,8 @@ Consider an algebraic set $V\subset \mathbb{C}^n$ and a finite set of query points $\mathcal{P} \subset V$, both defined by polynomials with coefficients in $\mathbb{Q}$. A *roadmap* $\mathcal{R}$ associated to $(V,\mathcal{P})$ is an algebraic curve such that - * $\mathcal{P} \subset \mathcal{R} \subset V$; - * $C \cap \mathcal{R}$ is non-empty and connected, for each connected + * $\mathcal{P} \subset \mathcal{R} \subset V$; + * $C \cap \mathcal{R}$ is non-empty and connected, for each connected component $C$ of $V\cap \mathbb{R}^n$. Roadmaps are algebraic curves capturing the connectivity properties of an @@ -184,11 +172,10 @@ end Each roadmap node (including the root) correspond to a curve component of the roadmap. More precisely, they are defined by as an algebraic subset $W$ (called polar variety) of a fiber $F$ of the initial variety $V$ such that: - * if `base_pt` contains $\mathbf{q}=(q_1,\dotsc,q_e) \in \mathbb{Q}^e$ then $$ - F = V \cap \left\{x_1=q_1,\,\dotsc,\, x_e=q_e\right\}; $$ - * if `polar_eqs` contains the polynomials $g_1,\dotsc,g_s \in - \mathbb{Q}[x_1,\dotsc,x_n]$ then $$ W = F \cap \{g_1=0,\, \ldots,\, g_s = 0\}. - $$ + * if `base_pt` contains $\mathbf{q}=(q_1,\dotsc,q_e) \in \mathbb{Q}^e$ then + * $F = V \cap \left\{x_1=q_1,\,\dotsc,\, x_e=q_e\right\}$; + * if `polar_eqs` contains the polynomials $g_1,\dotsc,g_s \in \mathbb{Q}[x_1,\dotsc,x_n]$ then + * $W = F \cap \{g_1=0,\, \ldots,\, g_s = 0\}$. Moreover, `children` rassembles all the tree nodes that contains curves component for which their attribute `base_pt` contains a point $\mathbf{q}'$ diff --git a/src/connectivity/roadmap.jl b/src/connectivity/roadmap.jl index 318501f..0f1e6e8 100644 --- a/src/connectivity/roadmap.jl +++ b/src/connectivity/roadmap.jl @@ -179,7 +179,7 @@ function _mid_rational_points_inter(S::Vector{Vector{T}}, Q::Vector{Vector{T}} = # # It orders the [l_i,r_i], and compute a list ratioP # intersecting all intervals of Q and such that - # strictly between each of these intervals there is: + # strictly between each of the [l_i,r_i] there is: # - either at least one element inside an interval of Q # - or the simplest rational number # TODO: From 8d4abfebc519a518ef6331cc9778a62e39ca1bcb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Tue, 3 Mar 2026 14:17:51 +0100 Subject: [PATCH 131/180] exported functions --- src/connectivity/roadmap.jl | 13 +------------ src/exports.jl | 3 ++- 2 files changed, 3 insertions(+), 13 deletions(-) diff --git a/src/connectivity/roadmap.jl b/src/connectivity/roadmap.jl index 0f1e6e8..ae3da33 100644 --- a/src/connectivity/roadmap.jl +++ b/src/connectivity/roadmap.jl @@ -1,12 +1,3 @@ -#using Pkg -#Pkg.activate("AlgebraicSolving.jl") -#using Revise -#using AlgebraicSolving -#using Nemo - -export roadmap, computepolar, _mid_rational_points, _mid_rational_points_inter, _fbr, all_eqs, all_base_pts, nb_nodes, computepolar -include("polar.jl") - @doc Markdown.doc""" roadmap(I::Ideal{T} where T <: MPolyRingElem, ) @@ -179,10 +170,9 @@ function _mid_rational_points_inter(S::Vector{Vector{T}}, Q::Vector{Vector{T}} = # # It orders the [l_i,r_i], and compute a list ratioP # intersecting all intervals of Q and such that - # strictly between each of the [l_i,r_i] there is: + # *strictly* between each of the [l_i,r_i] there is: # - either at least one element inside an interval of Q # - or the simplest rational number - # TODO: isempty(S) && return Q S1, Q1 = sort(S, lt=(x, y) -> x[2] <= y[1]), sort(Q, lt=(x, y) -> x[2] <= y[1]) @@ -224,7 +214,6 @@ function _mid_rational_points_inter(S::Vector{Vector{T}}, Q::Vector{Vector{T}} = return ratioP end - function _open_simplest_between(a::QQFieldElem, b::QQFieldElem, eps::QQFieldElem) # We choose the simplest in absolute value if -a > b # this means a is negative and the largest in absolute value diff --git a/src/exports.jl b/src/exports.jl index 5e3d57e..ce4142a 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -5,4 +5,5 @@ export polynomial_ring, MPolyRing, GFElem, MPolyRingElem, prime_field, sig_groebner_basis, cyclic, leading_coefficient, equidimensional_decomposition, homogenize, dimension, FqMPolyRingElem, hilbert_series, hilbert_dimension, hilbert_degree, hilbert_polynomial, - rational_curve_parametrization + rational_curve_parametrization, roadmap, computepolar, all_eqs, + all_base_pts, nb_nodes From a1222c28650c55011babbface050b3092266aaa0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Sun, 22 Mar 2026 16:47:51 +0100 Subject: [PATCH 132/180] merge --- Manifest.toml | 799 ++++++++++++++++-------------- Project.toml | 17 +- src/algorithms/param-curve.jl | 7 +- src/connectivity/Cannytools.jl | 309 ------------ src/connectivity/buildpoly.jl | 140 ++++++ src/connectivity/computeRM.jl | 90 ---- src/connectivity/connectcurves.jl | 5 +- src/connectivity/isolate.jl | 4 +- src/connectivity/paramcurve.jl | 219 -------- 9 files changed, 578 insertions(+), 1012 deletions(-) delete mode 100644 src/connectivity/Cannytools.jl create mode 100644 src/connectivity/buildpoly.jl delete mode 100644 src/connectivity/computeRM.jl delete mode 100644 src/connectivity/paramcurve.jl diff --git a/Manifest.toml b/Manifest.toml index 7faf1d8..b99aa50 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -1,24 +1,42 @@ # This file is machine-generated - editing it directly is not advised -julia_version = "1.10.1" +julia_version = "1.12.5" manifest_format = "2.0" -project_hash = "11eb6a443ca7f27cf646ae7e6a1882d5932bc885" +project_hash = "2c4a2b32eac43961eadb14cefb3546541a48cf2b" [[deps.AbstractAlgebra]] -deps = ["InteractiveUtils", "LinearAlgebra", "MacroTools", "Preferences", "Random", "RandomExtensions", "SparseArrays", "Test"] -git-tree-sha1 = "709a09fbc20ae499657a9cd2e832c9946809ece8" +deps = ["LinearAlgebra", "MacroTools", "PrecompileTools", "Preferences", "Random", "RandomExtensions", "SparseArrays"] +git-tree-sha1 = "14745b9234c1e4ea56fb13f89dd7e798ffbfd399" uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d" -version = "0.43.6" +version = "0.48.4" +weakdeps = ["Test"] + + [deps.AbstractAlgebra.extensions] + TestExt = "Test" + +[[deps.AlgebraicSolving]] +deps = ["Colors", "LinearAlgebra", "Logging", "Markdown", "Nemo", "Primes", "Printf", "Random", "StaticArrays", "msolve_jll"] +path = "." +uuid = "66b61cbe-0446-4d5d-9090-1ff510639f9d" +version = "0.10.4" + +[[deps.AliasTables]] +deps = ["PtrArrays", "Random"] +git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff" +uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8" +version = "1.1.3" [[deps.ArgTools]] uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" -version = "1.1.1" +version = "1.1.2" [[deps.Artifacts]] uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" +version = "1.11.0" [[deps.Base64]] uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" +version = "1.11.0" [[deps.BitFlags]] git-tree-sha1 = "0691e34b3bb8be9307330f88d1a3c3f25466c24d" @@ -26,40 +44,44 @@ uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35" version = "0.1.9" [[deps.Bzip2_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "1b96ea4a01afe0ea4090c5c8039690672dd13f2e" uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" -version = "1.0.8+1" +version = "1.0.9+0" [[deps.Cairo_jll]] deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] -git-tree-sha1 = "009060c9a6168704143100f36ab08f06c2af4642" +git-tree-sha1 = "a21c5464519504e41e0cbc91f0188e8ca23d7440" uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" -version = "1.18.2+1" +version = "1.18.5+1" [[deps.CodecZlib]] deps = ["TranscodingStreams", "Zlib_jll"] -git-tree-sha1 = "bce6804e5e6044c6daab27bb533d1295e4a2e759" +git-tree-sha1 = "962834c22b66e32aa10f7611c08c8ca4e20749a9" uuid = "944b1d66-785c-5afd-91f1-9de20f533193" -version = "0.7.6" +version = "0.7.8" [[deps.ColorSchemes]] deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"] -git-tree-sha1 = "b5278586822443594ff615963b0c09755771b3e0" +git-tree-sha1 = "b0fd3f56fa442f81e0a47815c92245acfaaa4e34" uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4" -version = "3.26.0" +version = "3.31.0" [[deps.ColorTypes]] deps = ["FixedPointNumbers", "Random"] -git-tree-sha1 = "b10d0b65641d57b8b4d5e234446582de5047050d" +git-tree-sha1 = "67e11ee83a43eb71ddc950302c53bf33f0690dfe" uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f" -version = "0.11.5" +version = "0.12.1" +weakdeps = ["StyledStrings"] + + [deps.ColorTypes.extensions] + StyledStringsExt = "StyledStrings" [[deps.ColorVectorSpace]] deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"] -git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249" +git-tree-sha1 = "8b3b6f87ce8f65a2b4f857528fd8d70086cd72b1" uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4" -version = "0.10.0" +version = "0.11.0" [deps.ColorVectorSpace.extensions] SpecialFunctionsExt = "SpecialFunctions" @@ -69,30 +91,20 @@ version = "0.10.0" [[deps.Colors]] deps = ["ColorTypes", "FixedPointNumbers", "Reexport"] -git-tree-sha1 = "362a287c3aa50601b0bc359053d5c2468f0e7ce0" +git-tree-sha1 = "37ea44092930b1811e666c3bc38065d7d87fcc74" uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" -version = "0.12.11" - -[[deps.Compat]] -deps = ["TOML", "UUIDs"] -git-tree-sha1 = "8ae8d32e09f0dcf42a36b90d4e17f5dd2e4c4215" -uuid = "34da2185-b29b-5c13-b0c7-acf172513d20" -version = "4.16.0" -weakdeps = ["Dates", "LinearAlgebra"] - - [deps.Compat.extensions] - CompatLinearAlgebraExt = "LinearAlgebra" +version = "0.13.1" [[deps.CompilerSupportLibraries_jll]] deps = ["Artifacts", "Libdl"] uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" -version = "1.1.0+0" +version = "1.3.0+1" [[deps.ConcurrentUtilities]] deps = ["Serialization", "Sockets"] -git-tree-sha1 = "ea32b83ca4fefa1768dc84e504cc0a94fb1ab8d1" +git-tree-sha1 = "21d088c496ea22914fe80906eb5bce65755e5ec8" uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb" -version = "2.4.2" +version = "2.5.1" [[deps.Contour]] git-tree-sha1 = "439e35b0b36e2e5881738abc8857bd92ad6ff9a8" @@ -105,20 +117,21 @@ uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a" version = "1.16.0" [[deps.DataStructures]] -deps = ["Compat", "InteractiveUtils", "OrderedCollections"] -git-tree-sha1 = "1d0a14036acb104d9e89698bd408f63ab58cdc82" +deps = ["OrderedCollections"] +git-tree-sha1 = "e357641bb3e0638d353c4b29ea0e40ea644066a6" uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8" -version = "0.18.20" +version = "0.19.3" [[deps.Dates]] deps = ["Printf"] uuid = "ade2ca70-3891-5945-98fb-dc099432e06a" +version = "1.11.0" [[deps.Dbus_jll]] deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl"] -git-tree-sha1 = "fc173b380865f70627d7dd1190dc2fce6cc105af" +git-tree-sha1 = "473e9afc9cf30814eb67ffa5f2db7df82c3ad9fd" uuid = "ee1fde0b-3d02-5ea6-8484-8dfef6360eab" -version = "1.14.10+0" +version = "1.16.2+0" [[deps.DelimitedFiles]] deps = ["Mmap"] @@ -127,54 +140,54 @@ uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" version = "1.9.1" [[deps.DocStringExtensions]] -deps = ["LibGit2"] -git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d" +git-tree-sha1 = "7442a5dfe1ebb773c29cc2962a8980f47221d76c" uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" -version = "0.9.3" +version = "0.9.5" 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deps = ["FFMPEG_jll"] -git-tree-sha1 = "53ebe7511fa11d33bec688a9178fac4e49eeee00" +git-tree-sha1 = "95ecf07c2eea562b5adbd0696af6db62c0f52560" uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a" -version = "0.4.2" +version = "0.4.5" [[deps.FFMPEG_jll]] deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"] -git-tree-sha1 = "466d45dc38e15794ec7d5d63ec03d776a9aff36e" +git-tree-sha1 = "01ba9d15e9eae375dc1eb9589df76b3572acd3f2" uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5" -version = "4.4.4+1" +version = "8.0.1+0" [[deps.FLINT_jll]] deps = ["Artifacts", "GMP_jll", "JLLWrappers", "Libdl", "MPFR_jll", "OpenBLAS32_jll"] -git-tree-sha1 = "4bde447e7bc6de73de36870fc942df02f4dd44b5" +git-tree-sha1 = "b730e276143ad63360611f64243117d00276b632" uuid = "e134572f-a0d5-539d-bddf-3cad8db41a82" -version = "300.100.300+0" +version = "301.400.1+0" [[deps.FileWatching]] uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee" +version = "1.11.0" [[deps.FixedPointNumbers]] deps = ["Statistics"] @@ -184,9 +197,9 @@ version = "0.8.5" [[deps.Fontconfig_jll]] deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Zlib_jll"] -git-tree-sha1 = "db16beca600632c95fc8aca29890d83788dd8b23" +git-tree-sha1 = "f85dac9a96a01087df6e3a749840015a0ca3817d" uuid = "a3f928ae-7b40-5064-980b-68af3947d34b" -version = "2.13.96+0" +version = "2.17.1+0" [[deps.Format]] git-tree-sha1 = "9c68794ef81b08086aeb32eeaf33531668d5f5fc" @@ -195,56 +208,68 @@ version = "1.3.7" [[deps.FreeType2_jll]] deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"] -git-tree-sha1 = "5c1d8ae0efc6c2e7b1fc502cbe25def8f661b7bc" +git-tree-sha1 = "2c5512e11c791d1baed2049c5652441b28fc6a31" uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7" -version = "2.13.2+0" +version = "2.13.4+0" [[deps.FriBidi_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "1ed150b39aebcc805c26b93a8d0122c940f64ce2" +git-tree-sha1 = "7a214fdac5ed5f59a22c2d9a885a16da1c74bbc7" uuid = "559328eb-81f9-559d-9380-de523a88c83c" -version = "1.0.14+0" +version = "1.0.17+0" [[deps.GLFW_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll", "libdecor_jll", "xkbcommon_jll"] -git-tree-sha1 = "532f9126ad901533af1d4f5c198867227a7bb077" +git-tree-sha1 = "b7bfd56fa66616138dfe5237da4dc13bbd83c67f" uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89" -version = "3.4.0+1" +version = "3.4.1+0" [[deps.GMP_jll]] deps = ["Artifacts", "Libdl"] uuid = "781609d7-10c4-51f6-84f2-b8444358ff6d" -version = "6.2.1+6" +version = "6.3.0+2" [[deps.GR]] deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"] -git-tree-sha1 = "ee28ddcd5517d54e417182fec3886e7412d3926f" +git-tree-sha1 = "ee0585b62671ce88e48d3409733230b401c9775c" uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71" -version = "0.73.8" +version = "0.73.22" + + [deps.GR.extensions] + IJuliaExt = "IJulia" + + [deps.GR.weakdeps] + IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a" [[deps.GR_jll]] deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"] -git-tree-sha1 = "f31929b9e67066bee48eec8b03c0df47d31a74b3" +git-tree-sha1 = "7dd7173f7129a1b6f84e0f03e0890cd1189b0659" uuid = "d2c73de3-f751-5644-a686-071e5b155ba9" -version = "0.73.8+0" +version = "0.73.22+0" + +[[deps.GettextRuntime_jll]] +deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll"] +git-tree-sha1 = 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"24f6def62397474a297bfcec22384101609142ed" uuid = "7746bdde-850d-59dc-9ae8-88ece973131d" -version = "2.80.5+0" +version = "2.86.3+0" [[deps.Graphite2_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "8a6dbda1fd736d60cc477d99f2e7a042acfa46e8" uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472" -version = "1.3.14+0" +version = "1.3.15+0" [[deps.Grisu]] git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2" @@ -252,78 +277,90 @@ uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe" version = "1.0.2" [[deps.HTTP]] -deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"] -git-tree-sha1 = "d1d712be3164d61d1fb98e7ce9bcbc6cc06b45ed" +deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "PrecompileTools", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"] +git-tree-sha1 = "5e6fe50ae7f23d171f44e311c2960294aaa0beb5" uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3" -version = "1.10.8" +version = "1.10.19" [[deps.HarfBuzz_jll]] deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll"] -git-tree-sha1 = "401e4f3f30f43af2c8478fc008da50096ea5240f" +git-tree-sha1 = "f923f9a774fcf3f5cb761bfa43aeadd689714813" uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566" -version = "8.3.1+0" +version = "8.5.1+0" [[deps.IntegerMathUtils]] -git-tree-sha1 = "b8ffb903da9f7b8cf695a8bead8e01814aa24b30" +git-tree-sha1 = "4c1acff2dc6b6967e7e750633c50bc3b8d83e617" uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235" -version = "0.1.2" +version = "0.1.3" [[deps.InteractiveUtils]] deps = ["Markdown"] uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240" +version = "1.11.0" [[deps.IrrationalConstants]] -git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2" +git-tree-sha1 = "b2d91fe939cae05960e760110b328288867b5758" uuid = "92d709cd-6900-40b7-9082-c6be49f344b6" -version = "0.2.2" +version = "0.2.6" [[deps.JLFzf]] -deps = ["Pipe", "REPL", "Random", "fzf_jll"] -git-tree-sha1 = "39d64b09147620f5ffbf6b2d3255be3c901bec63" +deps = ["REPL", "Random", "fzf_jll"] +git-tree-sha1 = "82f7acdc599b65e0f8ccd270ffa1467c21cb647b" uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c" -version = "0.1.8" +version = "0.1.11" [[deps.JLLWrappers]] deps = ["Artifacts", "Preferences"] -git-tree-sha1 = "be3dc50a92e5a386872a493a10050136d4703f9b" +git-tree-sha1 = "0533e564aae234aff59ab625543145446d8b6ec2" uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210" -version = "1.6.1" +version = "1.7.1" [[deps.JSON]] -deps = ["Dates", "Mmap", "Parsers", "Unicode"] -git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a" +deps = ["Dates", "Logging", "Parsers", "PrecompileTools", "StructUtils", "UUIDs", "Unicode"] +git-tree-sha1 = "b3ad4a0255688dcb895a52fafbaae3023b588a90" uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6" -version = "0.21.4" +version = "1.4.0" + + [deps.JSON.extensions] + JSONArrowExt = ["ArrowTypes"] + + [deps.JSON.weakdeps] + ArrowTypes = "31f734f8-188a-4ce0-8406-c8a06bd891cd" [[deps.JpegTurbo_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "25ee0be4d43d0269027024d75a24c24d6c6e590c" +git-tree-sha1 = "b6893345fd6658c8e475d40155789f4860ac3b21" uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8" -version = "3.0.4+0" +version = "3.1.4+0" + +[[deps.JuliaSyntaxHighlighting]] +deps = ["StyledStrings"] +uuid = "ac6e5ff7-fb65-4e79-a425-ec3bc9c03011" +version = "1.12.0" [[deps.LAME_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "170b660facf5df5de098d866564877e119141cbd" +git-tree-sha1 = "059aabebaa7c82ccb853dd4a0ee9d17796f7e1bc" uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d" -version = "3.100.2+0" +version = "3.100.3+0" [[deps.LERC_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "36bdbc52f13a7d1dcb0f3cd694e01677a515655b" +git-tree-sha1 = "aaafe88dccbd957a8d82f7d05be9b69172e0cee3" uuid = "88015f11-f218-50d7-93a8-a6af411a945d" -version = "4.0.0+0" +version = "4.0.1+0" [[deps.LLVMOpenMP_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "78211fb6cbc872f77cad3fc0b6cf647d923f4929" +git-tree-sha1 = "eb62a3deb62fc6d8822c0c4bef73e4412419c5d8" uuid = "1d63c593-3942-5779-bab2-d838dc0a180e" -version = "18.1.7+0" +version = "18.1.8+0" [[deps.LZO_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "854a9c268c43b77b0a27f22d7fab8d33cdb3a731" +git-tree-sha1 = "1c602b1127f4751facb671441ca72715cc95938a" uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac" -version = "2.10.2+1" +version = "2.10.3+0" [[deps.LaTeXStrings]] git-tree-sha1 = "dda21b8cbd6a6c40d9d02a73230f9d70fed6918c" @@ -331,20 +368,22 @@ uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" version = "1.4.0" [[deps.Latexify]] -deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"] -git-tree-sha1 = "ce5f5621cac23a86011836badfedf664a612cee4" +deps = ["Format", "Ghostscript_jll", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"] +git-tree-sha1 = "44f93c47f9cd6c7e431f2f2091fcba8f01cd7e8f" uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316" -version = "0.16.5" +version = "0.16.10" [deps.Latexify.extensions] DataFramesExt = "DataFrames" SparseArraysExt = "SparseArrays" SymEngineExt = "SymEngine" + TectonicExt = "tectonic_jll" [deps.Latexify.weakdeps] DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8" + tectonic_jll = "d7dd28d6-a5e6-559c-9131-7eb760cdacc5" [[deps.LibCURL]] deps = ["LibCURL_jll", "MozillaCACerts_jll"] @@ -352,84 +391,75 @@ uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21" version = "0.6.4" [[deps.LibCURL_jll]] -deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"] +deps = ["Artifacts", "LibSSH2_jll", "Libdl", "OpenSSL_jll", "Zlib_jll", "nghttp2_jll"] uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0" -version = "8.4.0+0" +version = "8.15.0+0" [[deps.LibGit2]] -deps = ["Base64", "LibGit2_jll", "NetworkOptions", "Printf", "SHA"] +deps = ["LibGit2_jll", "NetworkOptions", "Printf", "SHA"] uuid = "76f85450-5226-5b5a-8eaa-529ad045b433" +version = "1.11.0" [[deps.LibGit2_jll]] -deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll"] +deps = ["Artifacts", "LibSSH2_jll", "Libdl", "OpenSSL_jll"] uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5" -version = "1.6.4+0" +version = "1.9.0+0" [[deps.LibSSH2_jll]] -deps = ["Artifacts", "Libdl", "MbedTLS_jll"] +deps = ["Artifacts", "Libdl", "OpenSSL_jll"] uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8" -version = "1.11.0+1" +version = "1.11.3+1" [[deps.Libdl]] uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb" +version = "1.11.0" [[deps.Libffi_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "c8da7e6a91781c41a863611c7e966098d783c57a" uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490" -version = "3.2.2+1" - -[[deps.Libgcrypt_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll"] -git-tree-sha1 = "9fd170c4bbfd8b935fdc5f8b7aa33532c991a673" -uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4" -version = "1.8.11+0" +version = "3.4.7+0" [[deps.Libglvnd_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"] -git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733" +deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll", "Xorg_libXext_jll"] +git-tree-sha1 = "d36c21b9e7c172a44a10484125024495e2625ac0" uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29" -version = "1.6.0+0" - -[[deps.Libgpg_error_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "fbb1f2bef882392312feb1ede3615ddc1e9b99ed" -uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8" -version = "1.49.0+0" +version = "1.7.1+1" [[deps.Libiconv_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "f9557a255370125b405568f9767d6d195822a175" +git-tree-sha1 = "be484f5c92fad0bd8acfef35fe017900b0b73809" uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531" -version = "1.17.0+0" +version = "1.18.0+0" [[deps.Libmount_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "0c4f9c4f1a50d8f35048fa0532dabbadf702f81e" +git-tree-sha1 = "97bbca976196f2a1eb9607131cb108c69ec3f8a6" uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9" -version = "2.40.1+0" +version = "2.41.3+0" [[deps.Libtiff_jll]] deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"] -git-tree-sha1 = "b404131d06f7886402758c9ce2214b636eb4d54a" +git-tree-sha1 = "f04133fe05eff1667d2054c53d59f9122383fe05" uuid = "89763e89-9b03-5906-acba-b20f662cd828" -version = "4.7.0+0" +version = "4.7.2+0" [[deps.Libuuid_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "5ee6203157c120d79034c748a2acba45b82b8807" +git-tree-sha1 = "d0205286d9eceadc518742860bf23f703779a3d6" uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700" -version = "2.40.1+0" +version = "2.41.3+0" [[deps.LinearAlgebra]] deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"] uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +version = "1.12.0" [[deps.LogExpFunctions]] deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"] -git-tree-sha1 = "a2d09619db4e765091ee5c6ffe8872849de0feea" +git-tree-sha1 = "13ca9e2586b89836fd20cccf56e57e2b9ae7f38f" uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688" -version = "0.3.28" +version = "0.3.29" [deps.LogExpFunctions.extensions] LogExpFunctionsChainRulesCoreExt = "ChainRulesCore" @@ -443,43 +473,45 @@ version = "0.3.28" [[deps.Logging]] uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" +version = "1.11.0" [[deps.LoggingExtras]] deps = ["Dates", "Logging"] -git-tree-sha1 = "c1dd6d7978c12545b4179fb6153b9250c96b0075" +git-tree-sha1 = "f00544d95982ea270145636c181ceda21c4e2575" uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36" -version = "1.0.3" +version = "1.2.0" [[deps.MPFR_jll]] deps = ["Artifacts", "GMP_jll", "Libdl"] uuid = "3a97d323-0669-5f0c-9066-3539efd106a3" -version = "4.2.0+1" +version = "4.2.2+0" [[deps.MacroTools]] -deps = ["Markdown", "Random"] -git-tree-sha1 = "2fa9ee3e63fd3a4f7a9a4f4744a52f4856de82df" +git-tree-sha1 = "1e0228a030642014fe5cfe68c2c0a818f9e3f522" uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" -version = "0.5.13" +version = "0.5.16" [[deps.Markdown]] -deps = ["Base64"] +deps = ["Base64", "JuliaSyntaxHighlighting", "StyledStrings"] uuid = "d6f4376e-aef5-505a-96c1-9c027394607a" +version = "1.11.0" [[deps.MbedTLS]] deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"] -git-tree-sha1 = "c067a280ddc25f196b5e7df3877c6b226d390aaf" +git-tree-sha1 = "8785729fa736197687541f7053f6d8ab7fc44f92" uuid = "739be429-bea8-5141-9913-cc70e7f3736d" -version = "1.1.9" +version = "1.1.10" [[deps.MbedTLS_jll]] -deps = ["Artifacts", "Libdl"] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "ff69a2b1330bcb730b9ac1ab7dd680176f5896b8" uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1" -version = "2.28.2+1" +version = "2.28.1010+0" [[deps.Measures]] -git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102" +git-tree-sha1 = "b513cedd20d9c914783d8ad83d08120702bf2c77" uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e" -version = "0.3.2" +version = "0.3.3" [[deps.Missings]] deps = ["DataAPI"] @@ -489,122 +521,121 @@ version = "1.2.0" [[deps.Mmap]] uuid = "a63ad114-7e13-5084-954f-fe012c677804" +version = "1.11.0" [[deps.MozillaCACerts_jll]] uuid = "14a3606d-f60d-562e-9121-12d972cd8159" -version = "2023.1.10" +version = "2025.11.4" [[deps.NaNMath]] deps = ["OpenLibm_jll"] -git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4" +git-tree-sha1 = "9b8215b1ee9e78a293f99797cd31375471b2bcae" uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3" -version = "1.0.2" +version = "1.1.3" [[deps.Nemo]] -deps = ["AbstractAlgebra", "FLINT_jll", "Libdl", "LinearAlgebra", "Pkg", "Random", "RandomExtensions", "SHA"] -git-tree-sha1 = "b02de63b9379b37f75488c299f2f1f49da666d84" +deps = ["AbstractAlgebra", "FLINT_jll", "LinearAlgebra", "Random", "RandomExtensions", "SHA"] +git-tree-sha1 = "dc1998cf33825b8e2550309acf72adf462cd57c8" uuid = "2edaba10-b0f1-5616-af89-8c11ac63239a" -version = "0.47.2" +version = "0.54.1" [[deps.NetworkOptions]] uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" -version = "1.2.0" +version = "1.3.0" [[deps.Ogg_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "b6aa4566bb7ae78498a5e68943863fa8b5231b59" uuid = 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"1d1aaa7d449b58415f97d2839c318b70ffb525a0" uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c" -version = "1.4.3" +version = "1.6.1" [[deps.OpenSSL_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "7493f61f55a6cce7325f197443aa80d32554ba10" +deps = ["Artifacts", "Libdl"] uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95" -version = "3.0.15+1" +version = "3.5.4+0" [[deps.Opus_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "6703a85cb3781bd5909d48730a67205f3f31a575" +git-tree-sha1 = "e2bb57a313a74b8104064b7efd01406c0a50d2ff" uuid = "91d4177d-7536-5919-b921-800302f37372" -version = "1.3.3+0" +version = "1.6.1+0" [[deps.OrderedCollections]] -git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5" +git-tree-sha1 = "05868e21324cede2207c6f0f466b4bfef6d5e7ee" uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d" -version = "1.6.3" +version = "1.8.1" [[deps.PCRE2_jll]] deps = ["Artifacts", "Libdl"] uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15" -version = "10.42.0+1" 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"Printf", "Random", "Reexport", "StableRNGs", "Statistics"] -git-tree-sha1 = "650a022b2ce86c7dcfbdecf00f78afeeb20e5655" +git-tree-sha1 = "26ca162858917496748aad52bb5d3be4d26a228a" uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043" -version = "1.4.2" +version = "1.4.4" [[deps.Plots]] deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "TOML", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"] -git-tree-sha1 = "45470145863035bb124ca51b320ed35d071cc6c2" +git-tree-sha1 = "fd2476993d84cedaaf6a03cf1a291d9acc18f70e" uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" -version = "1.40.8" +version = "1.41.0" [deps.Plots.extensions] FileIOExt = "FileIO" @@ -622,57 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+version = "1.4.0" [[deps.Qt6Base_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Vulkan_Loader_jll", "Xorg_libSM_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_cursor_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "libinput_jll", "xkbcommon_jll"] -git-tree-sha1 = "492601870742dcd38f233b23c3ec629628c1d724" +git-tree-sha1 = "34f7e5d2861083ec7596af8b8c092531facf2192" uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56" -version = "6.7.1+1" +version = "6.8.2+2" [[deps.Qt6Declarative_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll", "Qt6ShaderTools_jll"] -git-tree-sha1 = "e5dd466bf2569fe08c91a2cc29c1003f4797ac3b" +git-tree-sha1 = "da7adf145cce0d44e892626e647f9dcbe9cb3e10" uuid = "629bc702-f1f5-5709-abd5-49b8460ea067" -version = "6.7.1+2" +version = "6.8.2+1" [[deps.Qt6ShaderTools_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll"] -git-tree-sha1 = "1a180aeced866700d4bebc3120ea1451201f16bc" +git-tree-sha1 = "9eca9fc3fe515d619ce004c83c31ffd3f85c7ccf" uuid = "ce943373-25bb-56aa-8eca-768745ed7b5a" -version = "6.7.1+1" +version = "6.8.2+1" [[deps.Qt6Wayland_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll", "Qt6Declarative_jll"] -git-tree-sha1 = "729927532d48cf79f49070341e1d918a65aba6b0" +git-tree-sha1 = "8f528b0851b5b7025032818eb5abbeb8a736f853" uuid = "e99dba38-086e-5de3-a5b1-6e4c66e897c3" -version = "6.7.1+1" +version = "6.8.2+2" [[deps.REPL]] -deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"] +deps = ["InteractiveUtils", "JuliaSyntaxHighlighting", "Markdown", "Sockets", "StyledStrings", "Unicode"] uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" +version = "1.11.0" [[deps.Random]] deps = ["SHA"] uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +version = "1.11.0" [[deps.RandomExtensions]] deps = ["Random", "SparseArrays"] @@ -705,9 +744,9 @@ version = "1.0.1" [[deps.Requires]] deps = ["UUIDs"] -git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7" +git-tree-sha1 = "62389eeff14780bfe55195b7204c0d8738436d64" uuid = "ae029012-a4dd-5104-9daa-d747884805df" -version = "1.3.0" +version = "1.3.1" [[deps.SHA]] uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" @@ -715,12 +754,13 @@ version = "0.7.0" [[deps.Scratch]] deps = ["Dates"] -git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386" +git-tree-sha1 = "9b81b8393e50b7d4e6d0a9f14e192294d3b7c109" uuid = "6c6a2e73-6563-6170-7368-637461726353" -version = "1.2.1" +version = "1.3.0" [[deps.Serialization]] uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" +version = "1.11.0" [[deps.Showoff]] deps = ["Dates", "Grisu"] @@ -735,29 +775,30 @@ version = "1.2.0" [[deps.Sockets]] uuid = "6462fe0b-24de-5631-8697-dd941f90decc" +version = "1.11.0" [[deps.SortingAlgorithms]] deps = ["DataStructures"] -git-tree-sha1 = "66e0a8e672a0bdfca2c3f5937efb8538b9ddc085" +git-tree-sha1 = "64d974c2e6fdf07f8155b5b2ca2ffa9069b608d9" uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c" -version = "1.2.1" +version = "1.2.2" [[deps.SparseArrays]] deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"] uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" -version = "1.10.0" +version = "1.12.0" [[deps.StableRNGs]] deps = ["Random"] -git-tree-sha1 = "83e6cce8324d49dfaf9ef059227f91ed4441a8e5" +git-tree-sha1 = "4f96c596b8c8258cc7d3b19797854d368f243ddc" uuid = "860ef19b-820b-49d6-a774-d7a799459cd3" -version = "1.0.2" +version = "1.0.4" [[deps.StaticArrays]] deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"] -git-tree-sha1 = "eeafab08ae20c62c44c8399ccb9354a04b80db50" +git-tree-sha1 = "0f529006004a8be48f1be25f3451186579392d47" uuid = "90137ffa-7385-5640-81b9-e52037218182" -version = "1.9.7" +version = "1.9.17" [deps.StaticArrays.extensions] StaticArraysChainRulesCoreExt = "ChainRulesCore" @@ -768,31 +809,54 @@ version = "1.9.7" Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" [[deps.StaticArraysCore]] -git-tree-sha1 = "192954ef1208c7019899fbf8049e717f92959682" +git-tree-sha1 = "6ab403037779dae8c514bad259f32a447262455a" uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c" -version = "1.4.3" +version = "1.4.4" [[deps.Statistics]] -deps = ["LinearAlgebra", "SparseArrays"] +deps = ["LinearAlgebra"] +git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0" uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" -version = "1.10.0" +version = "1.11.1" +weakdeps = ["SparseArrays"] + + [deps.Statistics.extensions] + SparseArraysExt = ["SparseArrays"] [[deps.StatsAPI]] deps = ["LinearAlgebra"] -git-tree-sha1 = "1ff449ad350c9c4cbc756624d6f8a8c3ef56d3ed" +git-tree-sha1 = "178ed29fd5b2a2cfc3bd31c13375ae925623ff36" uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0" -version = "1.7.0" +version = "1.8.0" [[deps.StatsBase]] -deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"] -git-tree-sha1 = "5cf7606d6cef84b543b483848d4ae08ad9832b21" +deps = ["AliasTables", "DataAPI", "DataStructures", "IrrationalConstants", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"] +git-tree-sha1 = "aceda6f4e598d331548e04cc6b2124a6148138e3" uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" -version = "0.34.3" +version = "0.34.10" + +[[deps.StructUtils]] +deps = ["Dates", "UUIDs"] +git-tree-sha1 = "28145feabf717c5d65c1d5e09747ee7b1ff3ed13" +uuid = "ec057cc2-7a8d-4b58-b3b3-92acb9f63b42" +version = "2.6.3" + + [deps.StructUtils.extensions] + StructUtilsMeasurementsExt = ["Measurements"] + StructUtilsTablesExt = ["Tables"] + + [deps.StructUtils.weakdeps] + Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7" + Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c" + +[[deps.StyledStrings]] +uuid = "f489334b-da3d-4c2e-b8f0-e476e12c162b" +version = "1.11.0" [[deps.SuiteSparse_jll]] deps = ["Artifacts", "Libdl", "libblastrampoline_jll"] uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c" -version = "7.2.1+1" +version = "7.8.3+2" [[deps.TOML]] deps = ["Dates"] @@ -813,6 +877,7 @@ version = "0.1.1" [[deps.Test]] deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" +version = "1.11.0" [[deps.TranscodingStreams]] git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742" @@ -820,16 +885,18 @@ uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa" version = "0.11.3" [[deps.URIs]] -git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b" +git-tree-sha1 = "bef26fb046d031353ef97a82e3fdb6afe7f21b1a" uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4" -version = "1.5.1" +version = "1.6.1" [[deps.UUIDs]] deps = ["Random", "SHA"] uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" +version = "1.11.0" [[deps.Unicode]] uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" +version = "1.11.0" [[deps.UnicodeFun]] deps = ["REPL"] @@ -839,23 +906,27 @@ version = "0.4.1" [[deps.Unitful]] deps = ["Dates", "LinearAlgebra", "Random"] -git-tree-sha1 = "d95fe458f26209c66a187b1114df96fd70839efd" +git-tree-sha1 = "6258d453843c466d84c17a58732dda5deeb8d3af" uuid = "1986cc42-f94f-5a68-af5c-568840ba703d" -version = "1.21.0" +version = "1.24.0" [deps.Unitful.extensions] ConstructionBaseUnitfulExt = "ConstructionBase" + ForwardDiffExt = "ForwardDiff" InverseFunctionsUnitfulExt = "InverseFunctions" + PrintfExt = "Printf" [deps.Unitful.weakdeps] ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9" + ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112" + Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" [[deps.UnitfulLatexify]] deps = ["LaTeXStrings", "Latexify", "Unitful"] -git-tree-sha1 = "975c354fcd5f7e1ddcc1f1a23e6e091d99e99bc8" +git-tree-sha1 = "af305cc62419f9bd61b6644d19170a4d258c7967" uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728" -version = "1.6.4" 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"Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"] @@ -1095,71 +1136,71 @@ uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f" version = "0.2.2+0" [[deps.libevdev_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "56d643b57b188d30cccc25e331d416d3d358e557" uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc" -version = "1.11.0+0" +version = "1.13.4+0" [[deps.libfdk_aac_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "8a22cf860a7d27e4f3498a0fe0811a7957badb38" +git-tree-sha1 = "646634dd19587a56ee2f1199563ec056c5f228df" uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" -version = "2.0.3+0" +version = "2.0.4+0" [[deps.libinput_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"] -git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce" +deps = ["Artifacts", "JLLWrappers", "Libdl", "eudev_jll", "libevdev_jll", "mtdev_jll"] +git-tree-sha1 = "91d05d7f4a9f67205bd6cf395e488009fe85b499" uuid = "36db933b-70db-51c0-b978-0f229ee0e533" -version = "1.18.0+0" +version = "1.28.1+0" [[deps.libpng_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"] -git-tree-sha1 = "b70c870239dc3d7bc094eb2d6be9b73d27bef280" +git-tree-sha1 = "e015f211ebb898c8180887012b938f3851e719ac" uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" -version = "1.6.44+0" +version = "1.6.55+0" [[deps.libvorbis_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] -git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3" +deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll"] +git-tree-sha1 = "11e1772e7f3cc987e9d3de991dd4f6b2602663a5" uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" -version = "1.3.7+2" +version = "1.3.8+0" [[deps.msolve_jll]] -deps = ["Artifacts", "CompilerSupportLibraries_jll", "FLINT_jll", "GMP_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl", "MPFR_jll"] -git-tree-sha1 = "31d4b30cc109d1e49293ce94d468a73932093aac" +deps = ["Artifacts", "CompilerSupportLibraries_jll", "FLINT_jll", "GMP_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl", "MPFR_jll", "OpenBLAS32_jll"] +git-tree-sha1 = "acd1dc4f0213298fa267501e0ff5906952df2678" uuid = "6d01cc9a-e8f6-580e-8c54-544227e08205" -version = "0.700.300+0" +version = "0.900.400+0" [[deps.mtdev_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "b4d631fd51f2e9cdd93724ae25b2efc198b059b1" uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e" -version = "1.1.6+0" +version = "1.1.7+0" [[deps.nghttp2_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" -version = "1.52.0+1" +version = "1.64.0+1" [[deps.p7zip_jll]] -deps = ["Artifacts", "Libdl"] +deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"] uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" -version = "17.4.0+2" +version = "17.7.0+0" [[deps.x264_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "14cc7083fc6dff3cc44f2bc435ee96d06ed79aa7" uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" -version = "2021.5.5+0" +version = "10164.0.1+0" [[deps.x265_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "e7b67590c14d487e734dcb925924c5dc43ec85f3" uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" -version = "3.5.0+0" +version = "4.1.0+0" [[deps.xkbcommon_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] -git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37" +deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] +git-tree-sha1 = "a1fc6507a40bf504527d0d4067d718f8e179b2b8" uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" -version = "1.4.1+1" +version = "1.13.0+0" diff --git a/Project.toml b/Project.toml index 5daa79a..9f7e4dd 100644 --- a/Project.toml +++ b/Project.toml @@ -1,35 +1,36 @@ name = "AlgebraicSolving" uuid = "66b61cbe-0446-4d5d-9090-1ff510639f9d" -authors = ["ederc ", "Mohab Safey El Din ", "RĂ©mi Prebet "] version = "0.10.4" +authors = ["ederc ", "Mohab Safey El Din ", "RĂ©mi Prebet "] [deps] +Colors = "5ae59095-9a9b-59fe-a467-6f913c188581" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" -Colors = "5ae59095-9a9b-59fe-a467-6f913c188581" Primes = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae" Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" msolve_jll = "6d01cc9a-e8f6-580e-8c54-544227e08205" -[extras] -Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" - -[targets] -test = ["Test"] - [compat] LinearAlgebra = "1.6" Logging = "1.6" Markdown = "1.6" Nemo = "0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.50, 0.51, 0.52, 0.53, 0.54" +Plots = "1.41.0" Printf = "1.6" Random = "1.6" StaticArrays = "1" Test = "1.6" julia = "1.10" msolve_jll = "0.900.300" + +[extras] +Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" + +[targets] +test = ["Test"] diff --git a/src/algorithms/param-curve.jl b/src/algorithms/param-curve.jl index e1757b4..13a5878 100644 --- a/src/algorithms/param-curve.jl +++ b/src/algorithms/param-curve.jl @@ -103,12 +103,13 @@ function rational_curve_parametrization( # Compute parametrization of each evaluation Lr = Vector{RationalParametrization}(undef, length(free_ind)) for j in 1:length(free_ind) - info_level>0 && print("Evaluated parametrizations: $(j+DEG+2-length(free_ind))/$(DEG+2)", "\r") + info_level>0 && print("Evaluated parametrizations: $(j)/$(length(free_ind))", "\r") Lr[j] = rational_parametrization(LFeval[j], nr_thrds=nr_thrds) end info_level>0 && println() for j in 1:length(free_ind) # Specialization checks: same vars order, generic degree + @show Lr[j].vars if Lr[j].vars == [symbols(R)[1:N-2]; symbols(R)[N]] && degree(Lr[j].elim) == DEG if isnothing(lc) lc = leading_coefficient(Lr[j].elim) @@ -118,8 +119,8 @@ function rational_curve_parametrization( fact = lc / leading_coefficient(Lr[j].elim) rr = [ p*fact for p in vcat(Lr[j].elim, Lr[j].denom, Lr[j].param) ] end - PARAM[j] = rr - _values[j] = curr_values[j] + PARAM[free_ind[j]] = rr + _values[free_ind[j]] = curr_values[j] used_ind[j] = true else info_level>0 && println("bad specialization: ", i+j-1) diff --git a/src/connectivity/Cannytools.jl b/src/connectivity/Cannytools.jl deleted file mode 100644 index 27b970b..0000000 --- a/src/connectivity/Cannytools.jl +++ /dev/null @@ -1,309 +0,0 @@ -# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables -function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} - R = parent(first(F)) - # Locate variables of R in newvarias - to_varias = Vector{Int}(undef,0) - for v in newvarias_S - ind = findfirst(x->x==v, R.S) - push!(to_varias, typeof(ind)==Nothing ? length(R.S)+1 : ind) - end - - ind_novarias = setdiff(eachindex(R.S), to_varias) - newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) - - res = typeof(first(F))[] - ctx = MPolyBuildCtx(newR) - - for f in F - for (e, c) in zip(exponent_vectors(f), coefficients(f)) - @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") - push!(e, 0) - push_term!(ctx, c, [e[i] for i in to_varias ]) - end - push!(res, finish(ctx)) - end - - return res -end - -function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: PolyRingElem} - R = parent(first(F)) - to_varias = [ v==R.S ? 1 : 2 for v in newvarias_S] - newR, = polynomial_ring(base_ring(R), newvarias_S) - - res = typeof(zero(newR))[] - ctx = MPolyBuildCtx(newR) - - LcF = [ filter!(t->t[2]!=0, collect(enumerate(coefficients(f)))) for f in F ] - for f in LcF - for (ef, c) in f - e = [ef-1, 0] - push_term!(ctx, c, [e[i] for i in to_varias ]) - end - push!(res, finish(ctx)) - end - - return res -end - -function change_ringvar(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) - return first(change_ringvar([f], newvarias_S)) -end - -function change_ringvar(F::Vector{P}, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {P <: MPolyRingElem, I <: Int64} - R = parent(first(F)) - return change_ringvar(F, [R.S[i] for i in ind_newvarias]) -end - -function change_ringvar(f::MPolyRingElem, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {I <: Int64} - R = parent(f) - return first(change_ringvar([f], [R.S[i] for i in ind_newvarias])) -end - -# Return the polynomials in F, but injected in the polynomial ring with the variables occuring in F -function change_ringvar(F::Vector{P}) where {P <: MPolyRingElem} - union_varias = Set{Symbol}() - for f in F - union!(union_varias, map(Symbol, vars(f)) ) - end - return change_ringvar(F, collect(union_varias)) -end - -function change_ringvar(f::MPolyRingElem) - return first(change_ringvar([f])) -end - -# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables -function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} - R = parent(first(F)) - # Locate variables of R in newvarias - to_varias = Vector{Int}(undef,0) - for v in newvarias_S - ind = findfirst(x->x==v, oldvarias_S) - push!(to_varias, typeof(ind)==Nothing ? length(oldvarias_S)+1 : ind) - end - - ind_novarias = setdiff(eachindex(oldvarias_S), to_varias) - newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) - - res = typeof(first(F))[] - ctx = MPolyBuildCtx(newR) - - for f in F - for (e, c) in zip(exponent_vectors(f), coefficients(f)) - @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") - push!(e, 0) - push_term!(ctx, c, [e[i] for i in to_varias ]) - end - push!(res, finish(ctx)) - end - - return res -end - -function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: PolyRingElem} - R = parent(first(F)) - A, (x,) = polynomial_ring(base_ring(R), oldvarias_S) - return change_ringvar_mod([ evaluate(f, x) for f in F ], newvarias_S, oldvarias_S) -end - -function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) - return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) -end - -#function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) -# return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) -#end - -function MPolyBuild(F::Vector{Vector{P}}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} - A = parent(first(first(F))) - R, = polynomial_ring(A, newvarias_S) - to_varias = [ i==idx ? 1 : 2 for i in eachindex(newvarias_S) ] - - res = typeof(zero(R))[] - ctx = MPolyBuildCtx(R) - - LcF = [ filter!(t->t[2]!=0, collect(enumerate(f))) for f in F ] - for f in LcF - for (ef, c) in f - e = [ef-1, 0] - push_term!(ctx, c, [e[i] for i in to_varias ]) - end - push!(res, finish(ctx)) - end - - return res -end - -function MPolyBuild(f::Vector{P}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} - return first(MPolyBuild([f], newvarias_S, idx)) -end - -function computepolarproj(j::Int, V::AlgebraicSolving.Ideal, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) - #println("$j $V $dimV") - # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj - @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" - R = parent(V) - n, hV = R.nvars, V.gens - c = n - dimV - - JW = transpose([ derivative(f, k) for k=j+1:n, f in hV ]) - sizeminors = c + dimproj - (j-1) - hW = vcat(hV, compute_minors(sizeminors, JW, R)) - filter!(!iszero, hW) - output_functions = Dict( - "minors" => x -> x, - "groebner" => x -> groebner_basis(x, info_level=verb,nr_thrds=nr_thrds), - "real" => x -> real_solutions(x, info_level=verb,nr_thrds=nr_thrds), - "interval" => x -> real_solutions(x, interval=true, info_level=verb,nr_thrds=nr_thrds), - "parametric" => x -> rational_parametrization(x, info_level=verb,nr_thrds=nr_thrds) - ) - - return output_functions[output](AlgebraicSolving.Ideal(hW)) -end - -function computepolarphi(j::Int, V::AlgebraicSolving.Ideal, phi::Vector{T} where T<:MPolyRingElem, dimV::Int, varbs; dimproj=j-1, characteristic=0, output="minors", verb=0, nr_thrds=1) - # Compute the set of points x where pi_j(T_x(V)) has dimension < dimproj - @assert output in ["minors", "groebner", "real", "parametric", "interval"] "Wrong output parameter" - R = parent(V) - n, hV = nvars(R), V.gens - c = n - dimV - - if j==0 - JW = transpose([ derivative(f, k) for k=1:n, f in hV ]) - sizeminors = c - else - JW = transpose([ derivative(f, k) for k=1:n, f in vcat(hV,phi) ]) - sizeminors = c + j + dimproj - (j-1) - end - hW = vcat(hV, compute_minors(sizeminors, JW, R)) - output_functions = Dict( - "minors" => x -> x, - "groebner" => x -> groebner_basis(x, info_level=verb,nr_thrds=nr_thrds), - "real" => x -> real_solutions(x, info_level=verb,nr_thrds=nr_thrds), - "interval" => x -> real_solutions(x, interval=true, info_level=verb,nr_thrds=nr_thrds), - "parametric" => x -> rational_parametrization(x, info_level=verb,nr_thrds=nr_thrds) - ) - - return output_functions[output](AlgebraicSolving.Ideal(hW)) -end - -function compute_minors(p, A, R) - #Computes the p-minors of a matrix A - n, m = size(A) - rowsmins = collect(combinations(1:n, p)) - colsmins = collect(combinations(1:m, p)) - mins = Vector{eltype(A)}(undef, length(rowsmins) * length(colsmins)) - k = 1 - for rowsmin in rowsmins - for colsmin in colsmins - mins[k] = detmpoly(A[rowsmin, colsmin], R) - k += 1 - end - end - - return mins -end - -function combinations(a, n) - # Helper function to recursively generate combinations - function _combinations(a, n, start, chosen) - if length(chosen) == n - return [chosen] - elseif start > length(a) - return Vector{Int}([]) - else - # Include the current element and recurse - include_current = _combinations(a, n, start + 1, [chosen; a[start]]) - # Exclude the current element and recurse - exclude_current = _combinations(a, n, start + 1, chosen) - return vcat(include_current, exclude_current) - end - end - return _combinations(a, n, 1, Vector{Int}([])) -end - -function detmpoly(A::Matrix{T} where T<:MPolyRingElem, R) - # Get the size of the matrix - n = size(A, 1) - if n != size(A, 2) - throw(ArgumentError("Matrix must be square")) - end - - if n == 1 - return A[1, 1] - end - - # Initialize the determinant polynomial - detA = zero(R) - - # Compute the determinant polynomial - for j = 1:n - submatrix = A[2:end, [i for i = 1:n if i != j]] - detA += (-1)^(1+j)*A[1, j] * detmpoly(submatrix, R) - end - - return detA -end - -function contfrac_convergents(x::Rational{Int}) - q = Rational{Int}[] - fpart, ipart = modf(x) - push!(q, ipart) - na, da, nb, db = Int(1), Int(0), Int(ipart), Int(1) - while true - fpart == 0 && return q - x = inv(fpart) - fpart, ipart = modf(x) - na, da, nb, db = nb, db, na+ipart*nb, da+ipart*db - push!(q, nb//db) - end -end - -function modfQQ(x::QQFieldElem) - ipart, fpart = [ f(numerator(x), denominator(x)) for f in [div, rem]] - return QQFieldElem(fpart, denominator(x)), ipart -end - -function small_mid_point(a::QQFieldElem,b::QQFieldElem) - a == b && return a - if b < a - a, b = b, a - end - x = (a+b)/ QQFieldElem(2) - fpart, ipart = modfQQ(x) - println("\n",fpart," , ", ipart) - q1, q2 = QQFieldElem(1//0), QQFieldElem(ipart,1) - while true - #println("(",q1," ; ",q2,")") - if numerator(fpart) == 0 || (q2 > a && q2 < b) - return q2 - end - x = inv(fpart) - fpart, ipart = modfQQ(x) - println(fpart," , ", ipart) - q1, q2 = q2, QQFieldElem(numerator(q1) + ipart*numerator(q2), denominator(q1) + ipart*denominator(q2)) - end -end - -function MidRationalPoints(S::Vector{Vector{QQFieldElem}}) - # S is a list of [ [l_1,r_1], ..., [l_n, r_n] ] - # such that the [l_i, r_i] are rational and disjoint open intervals. - # - # It orders the [l_i,r_i], removes repetitions and computes the simplest - # rational points between these intervals. - if isempty(S) - return QQFieldElem[] - end - S1 = sort(S, lt=(x, y) -> x[2] <= y[1]) - n = unique!(S1) |> length - ratioP = Vector{QQFieldElem}(undef, n-1) - for i in 1:(n- 1) - ri, li1 = S1[i][2], S1[i+1][1] - @assert ri < li1 "The intervals are not disjoint." - #ratioP[i] = small_mid_point(ri, li1) - ratioP[i] = simplest_between(ri, li1) - end - return ratioP -end - diff --git a/src/connectivity/buildpoly.jl b/src/connectivity/buildpoly.jl new file mode 100644 index 0000000..ae668c6 --- /dev/null +++ b/src/connectivity/buildpoly.jl @@ -0,0 +1,140 @@ +# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables +function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} + R = parent(first(F)) + # Locate variables of R in newvarias + to_varias = Vector{Int}(undef,0) + for v in newvarias_S + ind = findfirst(x->x==v, R.S) + push!(to_varias, typeof(ind)==Nothing ? length(R.S)+1 : ind) + end + + ind_novarias = setdiff(eachindex(R.S), to_varias) + newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) + + res = typeof(first(F))[] + ctx = MPolyBuildCtx(newR) + + for f in F + for (e, c) in zip(exponent_vectors(f), coefficients(f)) + @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") + push!(e, 0) + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res +end + +function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: PolyRingElem} + R = parent(first(F)) + to_varias = [ v==R.S ? 1 : 2 for v in newvarias_S] + newR, = polynomial_ring(base_ring(R), newvarias_S) + + res = typeof(zero(newR))[] + ctx = MPolyBuildCtx(newR) + + LcF = [ filter!(t->t[2]!=0, collect(enumerate(coefficients(f)))) for f in F ] + for f in LcF + for (ef, c) in f + e = [ef-1, 0] + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res +end + +function change_ringvar(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) + return first(change_ringvar([f], newvarias_S)) +end + +function change_ringvar(F::Vector{P}, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {P <: MPolyRingElem, I <: Int64} + R = parent(first(F)) + return change_ringvar(F, [R.S[i] for i in ind_newvarias]) +end + +function change_ringvar(f::MPolyRingElem, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {I <: Int64} + R = parent(f) + return first(change_ringvar([f], [R.S[i] for i in ind_newvarias])) +end + +# Return the polynomials in F, but injected in the polynomial ring with the variables occuring in F +function change_ringvar(F::Vector{P}) where {P <: MPolyRingElem} + union_varias = Set{Symbol}() + for f in F + union!(union_varias, map(Symbol, vars(f)) ) + end + return change_ringvar(F, collect(union_varias)) +end + +function change_ringvar(f::MPolyRingElem) + return first(change_ringvar([f])) +end + +# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables +function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} + R = parent(first(F)) + # Locate variables of R in newvarias + to_varias = Vector{Int}(undef,0) + for v in newvarias_S + ind = findfirst(x->x==v, oldvarias_S) + push!(to_varias, typeof(ind)==Nothing ? length(oldvarias_S)+1 : ind) + end + + ind_novarias = setdiff(eachindex(oldvarias_S), to_varias) + newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) + + res = typeof(first(F))[] + ctx = MPolyBuildCtx(newR) + + for f in F + for (e, c) in zip(exponent_vectors(f), coefficients(f)) + @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") + push!(e, 0) + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res +end + +function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: PolyRingElem} + R = parent(first(F)) + A, (x,) = polynomial_ring(base_ring(R), oldvarias_S) + return change_ringvar_mod([ evaluate(f, x) for f in F ], newvarias_S, oldvarias_S) +end + +function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) + return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) +end + +#function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) +# return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) +#end + +function MPolyBuild(F::Vector{Vector{P}}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} + A = parent(first(first(F))) + R, = polynomial_ring(A, newvarias_S) + to_varias = [ i==idx ? 1 : 2 for i in eachindex(newvarias_S) ] + + res = typeof(zero(R))[] + ctx = MPolyBuildCtx(R) + + LcF = [ filter!(t->t[2]!=0, collect(enumerate(f))) for f in F ] + for f in LcF + for (ef, c) in f + e = [ef-1, 0] + push_term!(ctx, c, [e[i] for i in to_varias ]) + end + push!(res, finish(ctx)) + end + + return res +end + +function MPolyBuild(f::Vector{P}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} + return first(MPolyBuild([f], newvarias_S, idx)) +end \ No newline at end of file diff --git a/src/connectivity/computeRM.jl b/src/connectivity/computeRM.jl deleted file mode 100644 index 504fc95..0000000 --- a/src/connectivity/computeRM.jl +++ /dev/null @@ -1,90 +0,0 @@ -#using Pkg -#Pkg.activate("AlgebraicSolving.jl") -#using Revise -#using AlgebraicSolving -#using Nemo - -export computeRM, computepolarproj, computepolarphi -# DEBUG -export change_ringvar, compute_minors, detmpoly, change_ringvar_mod, MPolyBuild - -include("Cannytools.jl") - -function computeRM(V::Ideal{T} where T <: QQMPolyRingElem, dimV::Int; Q=Vector{Vector{QQFieldElem}}([[]]), C=Vector{Vector{QQFieldElem}}([]), v=0) - # V is a variety of dimension dimV - # Q are base points with rational coefficients - # C are query points with rational coefficients - println(Q) - A = parent(V) - varias, nvarias = gens(A), nvars(A) - hV = V.gens - #println(Q) - e = length(first(Q)) - fixvarias, newvarias = varias[1:e], varias[e+1:nvarias] - - R = Vector{AlgebraicSolving.Ideal{QQMPolyRingElem}}(undef,0) - - for q in Q - ## Fq ## - if e > 0 - hFq = change_ringvar([evaluate(h, fixvarias, q) for h in V.gens], e+1:nvarias) - Fq = AlgebraicSolving.Ideal(hFq) - else - Fq = V - end - - if dimV - e <= 1 - curve = change_ringvar(Fq.gens, A.S) - push!(R, AlgebraicSolving.Ideal(vcat(curve, [fixvarias[j] - q[j] for j in 1:e]))) - else - ## sing(Fq) ## - v>0 && println("Compute first the singular points") - singFq = computepolarproj(0, Fq, dimV-e, newvarias, output="real", verb=max(v-1,0), nr_thrds=Threads.nthreads()) - @assert(length(singFq)==0, "Non-emtpy real sing locus!") - - ## K(pi_1,Fq) ## - v>0 && println("First critical points") - K1Fq = computepolarproj(1, Fq, dimV-e, newvarias, output="interval", verb=max(v-1,0), nr_thrds=Threads.nthreads()) - - ## K(pi_2, Fq) ## - v>0 && println("Second critical points") - K2Fq = computepolarproj(2, Fq, dimV-e, newvarias, output="minors", verb=max(v-1,0), nr_thrds=Threads.nthreads()) - polar = change_ringvar(K2Fq.gens, A.S) - push!(R, AlgebraicSolving.Ideal(vcat(polar, [fixvarias[j] - q[j] for j in 1:e]))) - - ## Points with vertical tg in K(pi_2, Fq) ## - v>0 && println("Vertical tg points") - K1WmFq = computepolarproj(2, K2Fq, 1, newvarias, output="interval", dimproj=0, verb=max(v-1,0), nr_thrds=Threads.nthreads()) - - ## New base points ## - K1W = vcat(K1Fq, K1WmFq) - K1WRat = MidRationalPoints(getindex(K1W, 1)) - # Heuristic to be proven - #K1WRat = K1WRat[2:end-1] - ########## - append!(K1WRat, [ c[e+1] for c in C if c[1:e]==q && !(c[e+1] in K1WRat) ]) |> sort! - newQ = [ vcat(q, [kv]) for kv in K1WRat ] - - if !isempty(newQ) - RFq = computeRM(V, dimV, Q=newQ, C=C) - R = vcat(R, RFq) - end - end - end - - return R -end - -#= -## Test ## -R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) -#h = x1^2+x2^2+x3^2+x4^2-1 -h = (x1^2+x2^2+x3^2+x4^2+9-1)^2-4*9*(x1^2+x2^2+x3^2) -h = evaluate(h,[x1,x2,x3],[x1+rand(-10:10)*x2+rand(-10:10)*x3+rand(-10:10)*x4,x2+rand(-10:10)*x3+rand(-10:10)*x4,x3+rand(-10:10)*x4]) -V = AlgebraicSolving.Ideal([h]) - -carte = (computeRM(V, 3, [Vector{QQFieldElem}(undef,0)])) -#println(carte) -=# - - diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 9dce70d..7458953 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -4,7 +4,7 @@ #pythonplot() export compute_graph, connected_components, number_connected_components, group_by_component, merge_graphs, - plot_graph, plot_graphs, plot_graph_comp, compute_param, Bresultant, param_crit_split + plot_graph, plot_graphs, plot_graph_comp, Bresultant, param_crit_split # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, @@ -19,6 +19,7 @@ include("graph.jl") include("plots.jl") include("arbtools.jl") include("src/resultant/bresultant.jl") +include("buildpoly.jl") function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) R = parent(f) @@ -49,7 +50,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen # TODO : check that no overlap between different isolations v > 0 && println("\nIsolating critical values with precision ", precx,"..") @iftime (v > 0) begin - xcrit = Dict(p[1]=> reduce(vcat, [isolate(pp, prec=precx) for pp in p[2][1]]) for p in params) + xcrit = Dict(p[1]=> reduce(vcat, [isolate(pp, prec=precx, software="msolve") for pp in p[2][1]]) for p in params) # Enlarge exact isolating root intervals for i in eachindex(xcrit) for j in eachindex(xcrit[i]) diff --git a/src/connectivity/isolate.jl b/src/connectivity/isolate.jl index 4c3eb00..73f151b 100644 --- a/src/connectivity/isolate.jl +++ b/src/connectivity/isolate.jl @@ -1,6 +1,6 @@ include("src/usolve/usolve.jl") -function isolate(f; prec = 32, software="usolve") +function isolate(f; prec = 32, software="msolve") #println(f) # Univariate isolation using usolve if total_degree(f) == 0 @@ -15,7 +15,7 @@ function isolate(f; prec = 32, software="usolve") end end -function isolate_eval(f, ivar, val; prec=64, software="usolve") +function isolate_eval(f, ivar, val; prec=64, software="msolve") #print(val) # univariate isolation of roots of a bivariate polynomial f # whose ivar-th variable is evaluated at val diff --git a/src/connectivity/paramcurve.jl b/src/connectivity/paramcurve.jl deleted file mode 100644 index 3ad2cbe..0000000 --- a/src/connectivity/paramcurve.jl +++ /dev/null @@ -1,219 +0,0 @@ -#println("Loading libraries and data..") -#using Pkg -#using Revise -#Pkg.activate("AlgebraicSolving.jl-official") -#using AlgebraicSolving -#import Nemo: coefficients, exponent_vectors, coeff, interpolate, MPolyBuildCtx, push_term!, finish, gens - -export compute_param, param_newvars - -function rem_var(f, i) - # Remove the occurence of the ith variable - R = parent(f) - A, Avars = polynomial_ring(base_ring(R), rem_ind(R.S, i)) - CE = [collect(coefficients(f)), collect(exponent_vectors(f))] - CE[2] = [ rem_ind(e, i) for e in CE[2]] - - # Reconstruct the polynomial in the ring A - C = MPolyBuildCtx(A) - R = base_ring(A) - for i in eachindex(CE[1]) - push_term!(C, R(CE[1][i]), CE[2][i]); - end - return finish(C) -end - -function rem_var(f, i, S) - # Remove the occurence of the ith variable - R = parent(f) - A, Avars = polynomial_ring(base_ring(R), rem_ind(S, i)) - CE = [collect(coefficients(f)), collect(exponent_vectors(f))] - CE[2] = [ rem_ind(e, i) for e in CE[2]] - - # Reconstruct the polynomial in the ring A - C = MPolyBuildCtx(A) - R = base_ring(A) - for i in eachindex(CE[1]) - push_term!(C, R(CE[1][i]), CE[2][i]); - end - return finish(C) -end - -function rem_ind(L,i::Int) - # remove element at index i - return [ L[1:i-1]; L[i+1:end] ] -end - -function deg_Alg(F, dim) - if dim <= 0 - r = rational_parametrization(Ideal(F)) - else - varias = gens(parent(first(F))) - planes = [ sum([ rand(-100:100)*v for v in vcat(varias,1) ]) for _ in 1:dim] - r = rational_parametrization(Ideal(vcat(F,planes))) - end - return degree(r.elim) -end - -function compute_param(I::Ideal{P} where P<:MPolyRingElem; use_lfs = false, lfs = []) - return compute_param(I.gens, use_lfs = use_lfs, lfs = lfs) -end - -function compute_param(F::Vector{P} where P<:MPolyRingElem; use_lfs = false, lfs = [], v=0) - R = parent(first(F)) - varias, N = gens(R), nvars(R) - DEG = deg_Alg(F,1) - - if !use_lfs && length(lfs)==0 - # Identification of two generic variables for the parametrization") - ivarias_gen = Vector{Int}(undef,0) - ind = N - while true - NEW_DEG = deg_Alg(vcat(F, varias[ind]-rand(-100:100)), 0) - if NEW_DEG == DEG - push!(ivarias_gen, ind) - end - (length(ivarias_gen) < 2 && ind > 1) || break - ind -= 1 - end - reverse!(ivarias_gen) - nb_lf = 2-length(ivarias_gen) - - if ivarias_gen != [N-1,N] - # Add new generic variables at the end if necessary - newvarias_S = [R.S[i] for i in vcat(setdiff(1:N, ivarias_gen), ivarias_gen)] - append!(newvarias_S, [:A,:B][nb_lf:-1:1] ) - - # We change the polynomial ring and add linear form(s) if necessary - Rold, Nold = R, N - R, varias = polynomial_ring(base_ring(Rold), newvarias_S) - N = length(varias) - - index_permut = Dict((v, i) for (i, v) in enumerate(newvarias_S)) - permut_varias = [ index_permut[v] for v in Rold.S ] - # TODO: permut exponents and use polynomial constructor - F = [ evaluate(f, [ varias[permut_varias[i]] for i in 1:Nold ]) for f in F ] - - if nb_lf > 0 - lf_cfs = [ rand(ZZ(-100):ZZ(100), N) for _ in 1:nb_lf] - append!(F, [ transpose(lf)*varias for lf in lf_cfs ]) - else - lf_cfs = Vector{Vector{ZZRingElem}}(undef,0) - end - else - lf_cfs = Vector{Vector{ZZRingElem}}(undef,0) - end - else - # Add new generic variables at the end if necessary - newvarias_S = vcat(R.S, [:B,:A]) - - # We change the polynomial ring and add linear form(s) if necessary - Rold, Nold = R, N - R, varias = polynomial_ring(base_ring(Rold), newvarias_S) - N = length(varias) - - F = [ evaluate(f, [ varias[i] for i in 1:Nold ]) for f in F ] - lf_cfs = vcat(lfs, [ rand(ZZ(-100):ZZ(100), N) for _ in 1:2-length(lfs)]) - append!(F, [ transpose(lf)*varias for lf in lf_cfs ]) - end - println(varias) - # Compute DEG+1 evaluations of the param (whose deg is bounded by DEG) - v > 0 && println("Parametrization step...") - #@iftime v>0 begin - PARAM = Vector{Vector{AlgebraicSolving.QQPolyRingElem}}(undef,DEG+2) - _values = Vector{QQFieldElem}(undef,DEG+2) - i = 1 - free_ind = collect(1:DEG+2) - used_ind = zeros(Bool, DEG+2) - while length(free_ind) > 0 - #println("$(DEG+2-length(free_ind))/ $(DEG+2)") - if i > 2*(DEG+2) - error("Too many bad specializations") - end - LFeval = Vector{AlgebraicSolving.Ideal}(undef, length(free_ind)) - Threads.@threads for j in 1:length(free_ind) - LFeval[i+j-1] = Ideal([ rem_var(evaluate(f, [N-1], [QQ(i+j-1)]), N-1) for f in F ]) - end - Lr = Vector{AlgebraicSolving.RationalParametrization}(undef, length(free_ind)) - for j in 1:length(free_ind) - #println("$(i+j-1)/$(DEG+2)") - Lr[i+j-1] = rational_parametrization(LFeval[i+j-1], nr_thrds=Threads.nthreads()) - end - for j in 1:length(free_ind) - # For lifting: the same variable must be chosen for the param - if Lr[j].vars == rem_ind(R.S, N-1) - lc = leading_coefficient(Lr[j].elim) - # TODO: why dividing by lc ? To get a unique representative? - rr = [ p/lc for p in vcat(Lr[j].elim, Lr[j].denom, Lr[j].param) ] - PARAM[j] = rr - _values[j] = QQ(i+j-1) - used_ind[j] = true - #println("Good specialization: ",i+j-1) - else - #println(r.vars, rem_ind(R.S, N-1)) - v>1 && println("bad specialization: ", i+j-1) - end - end - - i += length(free_ind) - free_ind = [ free_ind[j] for j in eachindex(free_ind) if !used_ind[j] ] - used_ind = zeros(Bool, length(free_ind)) - end - #end - - # Interpolate each coefficient of each poly in the param - v > 0 && println("Interpolation step...") - #@iftime v>0 begin - POLY_PARAM = Vector{QQMPolyRingElem}(undef,N) - T, (x,y) = polynomial_ring(QQ, [:x,:y]) - A, u = polynomial_ring(QQ, :u) - Threads.@threads for count in 1:N - #println("$count/$N") - COEFFS = Vector{QQPolyRingElem}(undef, DEG+1) - Threads.@threads for deg in 0:DEG - #println("$deg/$DEG") - _evals = [coeff(PARAM[i][count], deg) for i in 1:length(PARAM)] - COEFFS[deg+1] = interpolate(A, _values, _evals) - end - - C = [ collect(coefficients(c)) for c in COEFFS ] - POL_term = [C[i][j]*y^(i-1)*x^(j-1) for i in 1:length(C) for j in 1:length(C[i])] - POL = length(POL_term) > 0 ? sum(POL_term) : T(0) - - POLY_PARAM[count] = POL - end - #end - - return [R.S, lf_cfs, POLY_PARAM[1], POLY_PARAM[2], POLY_PARAM[3:end]] -end - -function param_newvars(F::Vector{P} where P <: MPolyRingElem, Svars::Vector{Symbol}, cfs_lf::Vector{Vector{I}} where I<:Union{ZZRingElem, QQFieldElem}) - Svarsbis = vcat(Svars[1:end-2], reverse!(Svars[end-1:end])) - eq = change_ringvar(F, Svarsbis) - newvarias = gens(parent(first(eq))) - newvariasbis = vcat(newvarias[1:end-2], reverse!(newvarias[end-1:end])) - neweq = vcat(eq, [ transpose(lf)*newvariasbis for lf in cfs_lf ]) - - C = rational_parametrization(Ideal(neweq)) - return change_ringvar([C.elim, C.elim == -1 ? C.elim : C.param[end], C.denom], [:x,:y]) -end - - -#= -# Tests -R, (a,b,c) = polynomial_ring(QQ, [:a,:b,:c]) -F = [-62*a^2-24*a*b+83*a*c-46*b^2-45*b*c+16*c^2+13*a-65*b-84*c-19, -92*a^2-a*b+39*a*c-16*b^2+61*b*c+78*c^2+17*a+49*b-97*c-56 -] - -R, (x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"]) -F = [ -x1^4 - 12*x1^3*x2 - 40*x1^3*x3 + 12*x1^3*x4 + 56*x1^2*x2^2 + 320*x1^2*x2*x3 - 148*x1^2*x2*x4 + 802*x1^2*x3^2 + 56*x1^2*x3*x4 + 288*x1^2*x4^2 - 20*x1^2 - 120*x1*x2^3 - 880*x1*x2^2*x3 + 576*x1*x2^2*x4 - 4012*x1*x2*x3^2 + 224*x1*x2*x3*x4 - 1968*x1*x2*x4^2 + 120*x1*x2 - 8040*x1*x3^3 - 3508*x1*x3^2*x4 - 3264*x1*x3*x4^2 + 400*x1*x3 + 1512*x1*x4^3 - 120*x1*x4 + 100*x2^4 + 800*x2^3*x3 - 760*x2^3*x4 + 5620*x2^2*x3^2 - 80*x2^2*x3*x4 + 3964*x2^2*x4^2 - 200*x2^2 + 16080*x2*x3^3 - 3436*x2*x3^2*x4 - 1168*x2*x3*x4^2 - 800*x2*x3 - 9576*x2*x4^3 + 760*x2*x4 + 40401*x3^4 + 59496*x3^3*x4 + 72556*x3^2*x4^2 - 4020*x3^2 + 37296*x3*x4^3 - 2960*x3*x4 + 15876*x4^4 - 2484*x4^2 + 64, - -40*x1^3 + 320*x1^2*x2 + 1604*x1^2*x3 + 56*x1^2*x4 - 880*x1*x2^2 - 8024*x1*x2*x3 + 224*x1*x2*x4 - 24120*x1*x3^2 - 7016*x1*x3*x4 - 3264*x1*x4^2 + 400*x1 + 800*x2^3 + 11240*x2^2*x3 - 80*x2^2*x4 + 48240*x2*x3^2 - 6872*x2*x3*x4 - 1168*x2*x4^2 - 800*x2 + 161604*x3^3 + 178488*x3^2*x4 + 145112*x3*x4^2 - 8040*x3 + 37296*x4^3 - 2960*x4, - 12*x1^3 - 148*x1^2*x2 + 56*x1^2*x3 + 576*x1^2*x4 + 576*x1*x2^2 + 224*x1*x2*x3 - 3936*x1*x2*x4 - 3508*x1*x3^2 - 6528*x1*x3*x4 + 4536*x1*x4^2 - 120*x1 - 760*x2^3 - 80*x2^2*x3 + 7928*x2^2*x4 - 3436*x2*x3^2 - 2336*x2*x3*x4 - 28728*x2*x4^2 + 760*x2 + 59496*x3^3 + 145112*x3^2*x4 + 111888*x3*x4^2 - 2960*x3 + 63504*x4^3 - 4968*x4 - ] - - @time begin - compute_param(F) - end -=# From 87c1f69ebee8700ebfb678594cc73c09099b4a88 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Mon, 23 Mar 2026 15:09:37 +0100 Subject: [PATCH 133/180] correction bug in arb conversion --- src/algorithms/param-curve.jl | 1 - src/connectivity/arbtools.jl | 91 ++++++++++++++++++++++--------- src/connectivity/connectcurves.jl | 26 ++++----- 3 files changed, 78 insertions(+), 40 deletions(-) diff --git a/src/algorithms/param-curve.jl b/src/algorithms/param-curve.jl index 13a5878..55512e6 100644 --- a/src/algorithms/param-curve.jl +++ b/src/algorithms/param-curve.jl @@ -109,7 +109,6 @@ function rational_curve_parametrization( info_level>0 && println() for j in 1:length(free_ind) # Specialization checks: same vars order, generic degree - @show Lr[j].vars if Lr[j].vars == [symbols(R)[1:N-2]; symbols(R)[N]] && degree(Lr[j].elim) == DEG if isnothing(lc) lc = leading_coefficient(Lr[j].elim) diff --git a/src/connectivity/arbtools.jl b/src/connectivity/arbtools.jl index cafa221..9f176cf 100644 --- a/src/connectivity/arbtools.jl +++ b/src/connectivity/arbtools.jl @@ -1,34 +1,75 @@ -function Arb_to_rat(x) - r = radius(x) - return map(simplest_rational_inside, [x-r, x+r]) +""" + arb_to_rat(x::ArbFieldElem) -> Tuple{Rational, Rational} + +Return a rational interval enclosing the Arb ball. +""" +function arb_to_rat(x::ArbFieldElem) + r = radius(x) + lo = x - 2r + hi = x + 2r + return (simplest_rational_inside(lo), simplest_rational_inside(hi)) end -function rat_to_Arb(x, prec) - x1,x2 = x - xm, xd = ArbField(prec)((x1+x2)/2), ArbField(prec)(x2-x1) - return ball(xm,xd) + +""" + rat_to_arb(interval::Tuple, field::ArbField) -> ArbFieldElem + +Convert rational interval (x1, x2) to Arb ball. +""" +function rat_to_arb(interval, field::ArbField) + x1, x2 = interval + @assert x1 <= x2 "Invalid interval: x1 > x2" + + mid = field((x1 + x2) / 2) + rad = field((x2 - x1) / 2) + + return ball(mid, rad) end -function evaluate_Arb(f, x::ArbFieldElem) - if is_zero(f) - return zero(parent(x)) - else - cf = coefficients_of_univariate(f) - return evalpoly(x, cf) - end + +""" + evaluate_arb(f, x::ArbFieldElem) + +Evaluate polynomial f at x using Arb arithmetic. +""" +function evaluate_arb(f, x::ArbFieldElem) + is_zero(f) && return zero(parent(x)) + cf = coefficients_of_univariate(f) + return evalpoly(x, cf) end -function evaluate_Arb(f, g, x::ArbFieldElem) - @assert !is_zero(g) "Denominator must be non-zero" - if is_zero(f) - return zero(parent(x)) - else - cf, cg = coefficients_of_univariate.([f, g]) - return evalpoly(x, cf) / evalpoly(x, cg) - end + +""" + evaluate_arb(f, g, x::ArbFieldElem) + +Evaluate rational function f/g at x. +""" +function evaluate_arb(f, g, x::ArbFieldElem) + @assert !is_zero(g) "Denominator must be non-zero" + + is_zero(f) && return zero(parent(x)) + + cf = coefficients_of_univariate(f) + cg = coefficients_of_univariate(g) + + num = evalpoly(x, cf) + den = evalpoly(x, cg) + + return num / den end -function Arb_eval(f, B, prec) - BA = [ rat_to_Arb(b, prec) for b in B ] - return evaluate(change_base_ring(ArbField(prec), f), BA) + +""" + arb_eval(f, B::Vector{Tuple}, prec::Int) + +Evaluate polynomial f over interval box B. +""" +function arb_eval(f, B::Vector{Tuple}, field::ArbField) + BA = Vector{ArbFieldElem}(undef, length(B)) + for i in eachindex(B) + BA[i] = rat_to_arb(B[i], field) + end + + f_arb = change_base_ring(field, f) + return evaluate(f_arb, BA) end \ No newline at end of file diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 7458953..dff5030 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -1,14 +1,10 @@ -#println("\nLoading libraries and data..") -#using Nemo -#using Plots, Colors -#pythonplot() export compute_graph, connected_components, number_connected_components, group_by_component, merge_graphs, plot_graph, plot_graphs, plot_graph_comp, Bresultant, param_crit_split # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, - rat_to_Arb, evaluate_Arb, evaluate_Arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, + rat_to_arb, evaluate_arb, evaluate_arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit include("tools.jl") @@ -32,8 +28,8 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen v > 1 && println(f) v > 0 && println("Compute parametrization of critical pts...") - @iftime (v > 0) params = param_crit_split(f,g,v=v-1, detect_app=true) - #@iftime (v > 0) params = mmod_param_crit(f, g,v=v-1, detect_app=false) + @iftime (v > 0) params = param_crit_split(f,g,v=v-1, detect_app=false) + #@iftime (v > 0) params = mmod_param_crit(f, g,v=v-1, detect_app=true) #=params = Bresultant(f, derivative(f,2), bspath="AlgebraicSolving.jl/src/connectivity/src/resultant/bresultant",v=2); params = change_ringvar.(params, Ref([:x,:y])) params = [ [[p[1]], p[3], p[2]] for p in params] @@ -62,11 +58,11 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen xcritpermut = order_permut2d(xcrit); end - v > 0 && println("\nComputing isolating critical boxes using Arb with precision ",max(precx,150),"..") + v > 0 && println("\nComputing isolating critical boxes using Arb with precision ",precx,"..") @iftime (v > 0) begin - precArb = precx - Pcrit = Dict( i => [[xc, evaluate_Arb(params[i][2], params[i][3], rat_to_Arb(xc, precArb))] for xc in xcrit[i]] for i in eachindex(xcrit)) - LBcrit =Dict( i=> [[ map(QQ, pc[1]), map(QQ, Arb_to_rat(pc[2])) ] for pc in pcrit] for (i, pcrit) in Pcrit) + arbField = ArbField(precx) + Pcrit = Dict( i => [[xc, evaluate_arb(params[i][2], params[i][3], rat_to_arb(xc, arbField))] for xc in xcrit[i]] for i in eachindex(xcrit)) + LBcrit =Dict( i=> [[ map(QQ, pc[1]), map(QQ, arb_to_rat(pc[2])) ] for pc in pcrit] for (i, pcrit) in Pcrit) # Enlarge exact isolating box vertical side (horizontal lines) for i in eachindex(LBcrit) for j in eachindex(LBcrit[i]) @@ -84,6 +80,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen break end end + # TODO: compteur pertinent ? if compt >= 5 error("Problem in isolating critical boxes") end @@ -91,7 +88,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen v > 0 && println("\nCompute critical boxes with msolve with precision ", precx,"..") @iftime (v > 0) begin # TODO: parameter -I - LBcrit = Dict(p[1]=>reduce(vcat,[ sort(real_solutions(AlgebraicSolving.Ideal([pp, p[2][3]*y-p[2][2]]), precision=precx,interval=true),by=t->t[1]) for pp in p[2][1] ]) for p in params) + LBcrit = Dict(p[1]=>reduce(vcat,[ sort(real_solutions(Ideal([pp, p[2][3]*y-p[2][2]]), precision=precx,interval=true),by=t->t[1]) for pp in p[2][1] ]) for p in params) # Enlarge each exact isolating box side for i in eachindex(LBcrit) for j in eachindex(LBcrit[i]) @@ -113,6 +110,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen ######################################################## # For each mult of sing pts (keys) give the corresponding factors of the resultant (values) ######################################################### + arbField = ArbField(precx) Lfyk = diff_list(f, 2, max(maximum(eachindex(LBcrit)),2)) for ind in eachindex(LBcrit) ind>1 || ind==0 || continue # extreme and control pts @@ -120,7 +118,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen while true flag = false for j in eachindex(LBcrit[ind]) - pcrit = [ rat_to_Arb(c, precx) for c in LBcrit[ind][j] ] + pcrit = [ rat_to_arb(c, arbField) for c in LBcrit[ind][j] ] # Check if the the mult(pcrit)-th derivative of f vanishes on pcrit if contains_zero(evaluate(Lfyk[m+1], pcrit)) (v > 0) && println("Refine singular boxes of multiplicity ", m) @@ -176,7 +174,7 @@ end end end LnPCside = Dict(i => [[length(indI) for (L, indI) in PB] for PB in LPCside[i]] for i in eachindex(LPCside)) - + #return LnPCside # Update extreme boxes if haskey(LBcrit, 1) for j in eachindex(LBcrit[1]) From b8227929161d0ea1a3ff3c047e59d2ee6bdab16d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Tue, 24 Mar 2026 09:38:48 +0100 Subject: [PATCH 134/180] du nettoyage --- src/connectivity/connectcurves.jl | 130 +- src/connectivity/isolate.jl | 18 +- src/connectivity/src/resultant/Makefile | 18 - .../__pycache__/bresultant.cpython-310.pyc | Bin 3376 -> 0 bytes src/connectivity/src/resultant/bresultant | Bin 3412328 -> 0 bytes src/connectivity/src/resultant/bresultant.jl | 113 -- .../src/resultant/bresultant.sage | 85 - src/connectivity/src/resultant/data.c | 387 ---- src/connectivity/src/resultant/data.h | 150 -- .../src/resultant/flint_euclide.c | 355 ---- .../src/resultant/flint_resultant.c | 1285 -------------- src/connectivity/src/resultant/io.c | 562 ------ src/connectivity/src/resultant/main.c | 1550 ----------------- src/connectivity/src/resultant/out.txt | 1 - .../src/resultant/ratreconstruct.c | 176 -- src/connectivity/src/usolve/usolve | Bin 2969640 -> 0 bytes src/connectivity/src/usolve/usolve.jl | 63 - src/connectivity/tools.jl | 2 +- 18 files changed, 51 insertions(+), 4844 deletions(-) delete mode 100644 src/connectivity/src/resultant/Makefile delete mode 100644 src/connectivity/src/resultant/__pycache__/bresultant.cpython-310.pyc delete mode 100755 src/connectivity/src/resultant/bresultant delete mode 100644 src/connectivity/src/resultant/bresultant.jl delete mode 100644 src/connectivity/src/resultant/bresultant.sage delete mode 100644 src/connectivity/src/resultant/data.c delete mode 100644 src/connectivity/src/resultant/data.h delete mode 100644 src/connectivity/src/resultant/flint_euclide.c delete mode 100644 src/connectivity/src/resultant/flint_resultant.c delete mode 100644 src/connectivity/src/resultant/io.c delete mode 100644 src/connectivity/src/resultant/main.c delete mode 100644 src/connectivity/src/resultant/out.txt delete mode 100644 src/connectivity/src/resultant/ratreconstruct.c delete mode 100755 src/connectivity/src/usolve/usolve delete mode 100644 src/connectivity/src/usolve/usolve.jl diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index dff5030..6d943d9 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -14,7 +14,6 @@ include("boxes.jl") include("graph.jl") include("plots.jl") include("arbtools.jl") -include("src/resultant/bresultant.jl") include("buildpoly.jl") function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) @@ -28,82 +27,58 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen v > 1 && println(f) v > 0 && println("Compute parametrization of critical pts...") - @iftime (v > 0) params = param_crit_split(f,g,v=v-1, detect_app=false) + @iftime (v > 0) params = param_crit_split(f,g,v=v-1, detect_app=true) #@iftime (v > 0) params = mmod_param_crit(f, g,v=v-1, detect_app=true) - #=params = Bresultant(f, derivative(f,2), bspath="AlgebraicSolving.jl/src/connectivity/src/resultant/bresultant",v=2); - params = change_ringvar.(params, Ref([:x,:y])) - params = [ [[p[1]], p[3], p[2]] for p in params] - params = Dict(1=>params[1], -1=>params[2])=# for i in 1:length(C) params[-i] = [ [C[i][1] |> intC], C[i][2], C[i][3] ] end - #println(keys(params)) - if arb - compt = 0 - while compt < 5 - try - # TODO : check that no overlap between different isolations - v > 0 && println("\nIsolating critical values with precision ", precx,"..") - @iftime (v > 0) begin - xcrit = Dict(p[1]=> reduce(vcat, [isolate(pp, prec=precx, software="msolve") for pp in p[2][1]]) for p in params) - # Enlarge exact isolating root intervals - for i in eachindex(xcrit) - for j in eachindex(xcrit[i]) - if xcrit[i][j][1]==xcrit[i][j][2] - xcrit[i][j] = [xcrit[i][j][1]-1//ZZ(1)< 0 && println("\nComputing isolating critical boxes using Arb with precision ",precx,"..") - @iftime (v > 0) begin - arbField = ArbField(precx) - Pcrit = Dict( i => [[xc, evaluate_arb(params[i][2], params[i][3], rat_to_arb(xc, arbField))] for xc in xcrit[i]] for i in eachindex(xcrit)) - LBcrit =Dict( i=> [[ map(QQ, pc[1]), map(QQ, arb_to_rat(pc[2])) ] for pc in pcrit] for (i, pcrit) in Pcrit) - # Enlarge exact isolating box vertical side (horizontal lines) - for i in eachindex(LBcrit) - for j in eachindex(LBcrit[i]) - if LBcrit[i][j][2][1]==LBcrit[i][j][2][2] - LBcrit[i][j][2] = [LBcrit[i][j][2][1]-1//ZZ(2)< 0 && println("\nIsolating critical values with precision ", precx,"..") + @iftime (v > 0) begin + xcrit = Dict(p[1]=> reduce(vcat, [isolate(pp, prec=precx) for pp in p[2][1]]) for p in params) + # Enlarge exact isolating root intervals + for i in eachindex(xcrit) + for j in eachindex(xcrit[i]) + if xcrit[i][j][1]==xcrit[i][j][2] + xcrit[i][j] = [xcrit[i][j][1]-1//ZZ(1)< 0 && println("\nRefine x-precision to $precx") - compt += 1 - else - break - end - end - # TODO: compteur pertinent ? - if compt >= 5 - error("Problem in isolating critical boxes") + xcritpermut = order_permut2d(xcrit); end - else - v > 0 && println("\nCompute critical boxes with msolve with precision ", precx,"..") - @iftime (v > 0) begin - # TODO: parameter -I - LBcrit = Dict(p[1]=>reduce(vcat,[ sort(real_solutions(Ideal([pp, p[2][3]*y-p[2][2]]), precision=precx,interval=true),by=t->t[1]) for pp in p[2][1] ]) for p in params) - # Enlarge each exact isolating box side - for i in eachindex(LBcrit) - for j in eachindex(LBcrit[i]) - for k in eachindex(LBcrit[i][j]) - if LBcrit[i][j][k][1]==LBcrit[i][j][k][2] - LBcrit[i][j][k] = [LBcrit[i][j][k][1]-1//ZZ(2-k)< 0 && println("\nComputing isolating critical boxes using Arb with precision ",precx,"..") + @iftime (v > 0) begin + arbField = ArbField(precx) + Pcrit = Dict( i => [[xc, evaluate_arb(params[i][2], params[i][3], rat_to_arb(xc, arbField))] for xc in xcrit[i]] for i in eachindex(xcrit)) + LBcrit = Dict( i=> [[ map(QQ, pc[1]), map(QQ, arb_to_rat(pc[2])) ] for pc in pcrit] for (i, pcrit) in Pcrit) + # Enlarge exact isolating box vertical side (horizontal lines) + for i in eachindex(LBcrit) + for j in eachindex(LBcrit[i]) + if LBcrit[i][j][2][1]==LBcrit[i][j][2][2] + LBcrit[i][j][2] = [LBcrit[i][j][2][1]-1//ZZ(2)<[ B[1] for B in lbcrit[2] ] for lbcrit in LBcrit) - xcritpermut = order_permut2d(xcrit); + catch + precx *= 2 + v > 0 && println("\nRefine x-precision to $precx") + compt += 1 + else + break + end end + # TODO: limite du compteur pertinent ? + if compt >= 5 + error("Problem in isolating critical boxes") end - #println(xcrit) v > 0 && println("\nTest for identifying singular boxes") @iftime (v > 0) begin @@ -113,7 +88,7 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen arbField = ArbField(precx) Lfyk = diff_list(f, 2, max(maximum(eachindex(LBcrit)),2)) for ind in eachindex(LBcrit) - ind>1 || ind==0 || continue # extreme and control pts + (ind < 0 && ind == 1) && continue # extreme and control pts m = ind==0 ? 2 : ind # nodes have mult 2 while true flag = false @@ -134,11 +109,7 @@ end v > 0 && println("\nCompute intersections with critical boxes..") @iftime (v > 0) begin - # Could be improved by handling nodes (or even any ordinary sing) as extreme boxes: - # when npcside = [2,2,0,0] just take nearest below and above - # intersections b with the curves on the vertical sides - # and change into npcside = [0,0,2,2] - ## TODO : Refine only the intervals that need to be refined + ## TODO : Refine only the intervals that need to be refined? LPCside = Dict{Int,Any}() ndig = maximum([ndigits(length(LBcrit[i])) for i in eachindex(LBcrit)]) for i in eachindex(LBcrit) @@ -174,7 +145,7 @@ end end end LnPCside = Dict(i => [[length(indI) for (L, indI) in PB] for PB in LPCside[i]] for i in eachindex(LPCside)) - #return LnPCside + # Update extreme boxes if haskey(LBcrit, 1) for j in eachindex(LBcrit[1]) @@ -216,19 +187,17 @@ end end end - #return LnPCside - - #println("\nGraph computation") - # Would be nice to have only one intermediate fiber (take the average of abscissa and ordinates) for plot - # And even remove this fiber for the graph + # Graph computation fct, typeout = outf ? (Float64, Float64) : (identity, QQFieldElem) + # List of vertex: at index i is the tuple of the coordinates of the i-th vertex Vert = Vector{Tuple{typeout, typeout}}() + # List of edges: a tuple (i,j) is an edge between the i-th and j-th vertices Edg = Vector{Tuple{Int, Int}}() Corr = Dict( m => [[[], [[], [], []], []] for j in xcrit[m] ] for m in eachindex(xcrit)) - Viso = [] Vcon = [ [] for _ in 1:length(C) ] + # Keep track of processed isolated & apparent singularities Lapp = [[],[]] for ind in eachindex(xcritpermut) @@ -239,10 +208,10 @@ end end if ind < length(xcritpermut) i2, j2 = xcritpermut[ind + 1] - I2L, nI2L = LPCside[i2][j2][3] + I2L, = LPCside[i2][j2][3] end - PCside, nPCside = LPCside[i][j], LnPCside[i][j] + PCside = LPCside[i][j] I = [ l[1] for l in PCside[3:end] ] nI = [ l[2] for l in PCside[3:end] ] @@ -278,9 +247,6 @@ end end ########################### # Below the critical point - #println() - #println(map(length,I)) - #println(nI[1],", ", nI[2], ", ", [length(I[1])+1]) for k in 1:ymincrit-1 push!(Vert, (xcmid, sum(I[1][k] + I[2][k])// 4) .|> fct) push!(Corr[i][j][2][1], length(Vert)) @@ -293,12 +259,6 @@ end # If we are dealing with a isolated node if i in [0,2] && isempty(nI[1]) && isempty(nI[2]) push!(Lapp[1], (i,j)) - #pass - # We can add the isolated vertex - # push!(Vert, [xcmid, ycmid]) - # push!(Corr[i][j][2][1], length(Vert)) - # We will subsequently add the vertex in the graph - # push!(Viso, length(Vert)) # If we are dealing with an apparent singularity elseif i == 0 # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 diff --git a/src/connectivity/isolate.jl b/src/connectivity/isolate.jl index 73f151b..f292456 100644 --- a/src/connectivity/isolate.jl +++ b/src/connectivity/isolate.jl @@ -1,31 +1,23 @@ -include("src/usolve/usolve.jl") - -function isolate(f; prec = 32, software="msolve") +function isolate(f; prec = 32) #println(f) # Univariate isolation using usolve if total_degree(f) == 0 return [] end @assert is_univariate(f) "Not univariate polynomial" - if software == "usolve" - return usolve(f, precision = prec, uspath="AlgebraicSolving.jl/src/connectivity/src/usolve/usolve", output="inter", v=2) - else - sols = real_solutions(Ideal([change_ringvar(f)]), precision=prec, interval=true, info_level=0) - return getindex.(sols, 1) - end + sols = real_solutions(Ideal([change_ringvar(f)]), precision=prec, interval=true, info_level=0) + return getindex.(sols, 1) end -function isolate_eval(f, ivar, val; prec=64, software="msolve") - #print(val) +function isolate_eval(f, ivar, val; prec=64) # univariate isolation of roots of a bivariate polynomial f # whose ivar-th variable is evaluated at val # uses msolve - #println(ivar,"\n", val,"\n", f) fev = change_ringvar(evaluate(f, [ivar], [val])) CD = lcm(map(denominator, collect(coefficients(fev)))) fev *= CD - tmp = isolate(fev, prec=prec, software=software) + tmp = isolate(fev, prec=prec) return tmp end \ No newline at end of file diff --git a/src/connectivity/src/resultant/Makefile b/src/connectivity/src/resultant/Makefile deleted file mode 100644 index 4711740..0000000 --- a/src/connectivity/src/resultant/Makefile +++ /dev/null @@ -1,18 +0,0 @@ -CC = gcc - -CPP = g++ - -GMP_INC_DIR=. -GMP_LIB_DIR=. - -LIB_PATHS = -L/usr/local/lib/ -L/opt/OpenBLAS/lib -INC_PATHS = -I/usr/local/include -I/opt/OpenBLAS/include - -CFLAGS = -std=c99 -O3 -msse -mavx -Wall -pedantic -funroll-loops --param max-unroll-times=2 -fomit-frame-pointer -fexpensive-optimizations - -LDFLAGS = $(DEBUG) $(LIB_PATHS) -static-libgcc -fopenmp -lgmp -lmpfr -lflint -lm -lopenblas -lpthread -LDFLAGS0 = -Wall $(DEBUG) $(LIB_PATHS) -lgmp -lmpfr -lflint -lm - -flint: - $(CC) -O3 -static main.c -o bresultant $(LDFLAGS) /usr/lib/x86_64-linux-gnu/libmpfr.a /usr/lib/x86_64-linux-gnu/libgmp.a /usr/lib/x86_64-linux-gnu/libflint.a - diff --git a/src/connectivity/src/resultant/__pycache__/bresultant.cpython-310.pyc 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""), "],\n["), Ref(",\n")) - Lcs = [ parse_poly.(ls) for ls in Ls ] - #println(Lcs) - return [ A.(ls) for ls in Lcs ] -end - -function Bresultant(f, g; fname1="/tmp/in.bs", fname2="/tmp/out.bs", bspath="./bresultant", v=0) - @time ToBresultant(f, g, fname1) - #err = Pipe() - @time process = run(pipeline(`$bspath -f $fname1 -o $fname2`)) - - #= - #close(err.in) - if v > 0 - c=0 - while c <100 - out = @async String(read(err)) - println(out) - c +=1 - end - end - #if v == 1 - # println(split(stderr(out), '\n')[end - 1] |> x -> split(x, ": ")[end] * "s") - #elseif v == 2 - # println(stderr(out)) - #end - wait(process) - =# - - return @time FromBresultant(fname2) -end - -#using Nemo -#R, (x,y) = Nemo.polynomial_ring(Nemo.ZZ, [:x,:y]) -#f = x^2+4*x+x*y-y^2+3*y-4 -#g = derivative(f,y) diff --git a/src/connectivity/src/resultant/bresultant.sage b/src/connectivity/src/resultant/bresultant.sage deleted file mode 100644 index 697a10d..0000000 --- a/src/connectivity/src/resultant/bresultant.sage +++ /dev/null @@ -1,85 +0,0 @@ -""" -25/02/2023 -""" - -import os -import subprocess - -def PolyToBRstring(f): - fc, fe = f.coefficients(), f.exponents() - s = "{} 2\n".format(len(fc)) - M = [ "{} {} {}".format(fc[i], fe[i][1], fe[i][0]) for i in range(len(fc)) ] - s += "\n".join(M) - return s - -def BRstringToPoly(s): - Ls = s.split("\n") - Ls = [ ls.split(" ") for ls in Ls] - Ls = [ [int(l) for l in ls] for ls in Ls ] - - A. = ZZ[] - F, i = [], 0 - while i = ZZ[] - f = open(foutput,'r') - s = f.read() - s = s.replace("\n","").replace(":","").replace(";","") - L = sage_eval(s, locals={'x': x, 'y': y}) - return L - -def Bresultant(f, g, fname1="/tmp/in.bs", fname2="/tmp/out.bs", bspath="./bresultant", v=0): - ToBresultant(f, g, fname1) - out = subprocess.run([bspath, "-f", fname1, "-o", fname2], capture_output=True,text=True) - if v==1: - print((out.stderr).split('\n')[-2].split(': ')[-1]+'s') - if v==2: - print(out.stderr) - return FromBresultant(fname2) - -#A. = ZZ[] -#f=A.random_element() -#g=diff(f,y) -#Bresultant(f,g,v=2) -#FromBresultant("p") diff --git a/src/connectivity/src/resultant/data.c b/src/connectivity/src/resultant/data.c deleted file mode 100644 index 2cd5744..0000000 --- a/src/connectivity/src/resultant/data.c +++ /dev/null @@ -1,387 +0,0 @@ -#include "data.h" - -//alloue ce qu'il faut, connaissant le degree deg de la param. -static fmpz_param_t *allocate_degree_sepelem_fmpz_param(ulong deg, - mp_ptr sepelem, - int nvars){ - fmpz_param_t *param = malloc(sizeof(fmpz_param_t)); - - param->recons = 0; - param->nvars = nvars; - param->degree = deg; - param->sepelem = sepelem; - param->coords = malloc(sizeof(fmpz_poly_t) * param->nvars); - param->coords_num = malloc(sizeof(fmpz_poly_t) * param->nvars); - param->coords_den = malloc(sizeof(fmpz_poly_t) * param->nvars); - param->coords_lcm = malloc(sizeof(fmpz_t) * param->nvars); - for(ulong i = 0; i < param->nvars; i++){ - fmpz_poly_init2(param->coords[i], deg); - fmpz_poly_init2(param->coords_num[i], deg); - fmpz_poly_init2(param->coords_den[i], deg); - fmpz_init(param->coords_lcm[i]); - fmpz_one(param->coords_lcm[i]); - for(ulong j = 0; j < deg; j++){ - fmpz_poly_set_coeff_ui(param->coords[i], j, 1); - fmpz_poly_set_coeff_ui(param->coords_num[i], j, 1); - fmpz_poly_set_coeff_ui(param->coords_den[i], j, 1); - } - } - - fmpz_poly_init2(param->denom, deg + 1); - fmpz_poly_init2(param->elim, deg + 1); - - fmpz_poly_init2(param->elim_num, deg + 1); - fmpz_poly_init2(param->denom_num, deg + 1); - - fmpz_poly_init2(param->elim_den, deg + 1); - fmpz_poly_init2(param->denom_den, deg + 1); - - fmpz_init(param->elim_lcm); - fmpz_init(param->denom_lcm); - - fmpz_one(param->elim_lcm); - fmpz_one(param->denom_lcm); - - for(ulong j = 0; j <= deg; j++){ - fmpz_poly_set_coeff_ui(param->denom, j, 1); - fmpz_poly_set_coeff_ui(param->elim, j, 1); - - fmpz_poly_set_coeff_ui(param->denom_num, j, 1); - fmpz_poly_set_coeff_ui(param->elim_num, j, 1); - - fmpz_poly_set_coeff_ui(param->denom_den, j, 1); - fmpz_poly_set_coeff_ui(param->elim_den, j, 1); - } - param->rec_elim = 0; - param->rec_denom = 0; - param->rec_coords = malloc(sizeof(ulong)*nvars); - for(int i = 0; i < nvars; i++){ - param->rec_coords[i] = 0; - } - return param; -} - - -static void allocate_degrees_sepelem_fmpz_all_params(fmpz_all_params_t * fmpz_all_params, - data_heap_t *heap, - mp_ptr sepelem, - int nb_params, int nvars){ - - fmpz_all_params->nparams = nb_params; - fmpz_all_params->params = malloc(sizeof(fmpz_param_t *) * fmpz_all_params->nparams); - for(int i = 0; i < fmpz_all_params->nparams; i++){ - fmpz_all_params->params[i] = - allocate_degree_sepelem_fmpz_param((heap->sqf_part->p + i)->length - 1, sepelem, nvars); - } - -} - - -static nmod_param_t *allocate_nmod_param(int nvars, mp_limb_t prime){ - nmod_param_t *param = malloc(sizeof(nmod_param_t)); - param->nvars = nvars; - param->degree = 0; - param->sepelem = NULL; - param->coords = malloc(sizeof(nmod_poly_t) * param->nvars); - for(int i = 0; i < param->nvars; i++){ - nmod_poly_init(param->coords[i], prime); - } - nmod_poly_init(param->denom, prime); - nmod_poly_init(param->elim, prime); - - return param; -} - -static nmod_param_t *allocate_degree_sepelem_nmod_param(ulong deg, mp_ptr sepelem, - int nvars, mp_limb_t prime){ - nmod_param_t *param = malloc(sizeof(nmod_param_t)); - param->nvars = nvars; - param->degree = deg; - param->sepelem = sepelem; - param->coords = malloc(sizeof(nmod_poly_t) * param->nvars); - for(int i = 0; i < param->nvars; i++){ - nmod_poly_init2(param->coords[i], prime, deg); - } - nmod_poly_init2(param->denom, prime, deg); - nmod_poly_init2(param->elim, prime, deg + 1); - - return param; -} - - -static nmod_all_params_t *allocate_nmod_all_params(int nb_params, int nvars, - mp_limb_t prime){ - nmod_all_params_t *nmod_all_params = malloc(sizeof(nmod_all_params_t)); - nmod_all_params->nparams = nb_params; - nmod_all_params->params = malloc(sizeof(nmod_param_t *) * nmod_all_params->nparams); - for(int i = 0; i < nmod_all_params->nparams; i++){ - nmod_all_params->params[i] = allocate_nmod_param(nvars, prime); - } - return nmod_all_params; -} - -static nmod_all_params_t *allocate_degrees_sepelem_nmod_all_params(data_heap_t *heap, - mp_ptr sepelem, - int nb_params, int nvars, - mp_limb_t prime){ - nmod_all_params_t *nmod_all_params = malloc(sizeof(nmod_all_params_t)); - nmod_all_params->nparams = nb_params; - nmod_all_params->params = malloc(sizeof(nmod_param_t *) * nmod_all_params->nparams); - for(int i = 0; i < nmod_all_params->nparams; i++){ - nmod_all_params->params[i] = - allocate_degree_sepelem_nmod_param((heap->sqf_part->p+i)->length - 1, - sepelem, - nvars, prime); - } - return nmod_all_params; -} - -static void free_bsolve_fmpz_param(bsolve_fmpz_param_t *param){ - fmpz_poly_clear(param->elim); - fmpz_poly_clear(param->denom); - for(int i = 0; i < param->nvars; i++){ - fmpz_poly_clear(param->coords[i]); - fmpz_clear(param->cfs[i]); - } - free(param->sepelem); - free(param->coords); - free(param->cfs); - free(param); -} - -static void free_bsolve_fmpz_all_params(bsolve_fmpz_all_params_t *allpars){ - for(int i = 0; i < allpars->nparams; i++ ){ - free_bsolve_fmpz_param(allpars->params[i]); - } - free(allpars); -} - -static void free_nmod_param(nmod_param_t *param){ - for(int i = 0; i < param->nvars; i++){ - nmod_poly_clear(param->coords[i]); - } - nmod_poly_clear(param->denom); - nmod_poly_clear(param->elim); - - free(param); -} - -static void free_nmod_all_params(nmod_all_params_t *nmod_all_params){ - for(int i = 0; i < nmod_all_params->nparams; i++){ - free_nmod_param(nmod_all_params->params[i]); - } - free(nmod_all_params); -} - -static void free_fmpz_param(fmpz_param_t *param){ - for(int i = 0; i < param->nvars; i++){ - fmpz_poly_clear(param->coords[i]); - } - fmpz_poly_clear(param->denom); - fmpz_poly_clear(param->elim); - free(param->rec_coords); - free(param); -} - -static void free_fmpz_all_params(fmpz_all_params_t *fmpz_all_params){ - for(int i = 0; i < fmpz_all_params->nparams; i++){ - free_fmpz_param(fmpz_all_params->params[i]); - } - free(fmpz_all_params); -} - -/* - - tdeg = total degree - mdeg = main degree - sdeg = degree in the other variable - -*/ -static data_heap_t *allocate_data_heap(slong tdegA, slong tdegB, - slong mdegA, slong mdegB, - slong sdegA, slong sdegB, - int size_mod_array){ - if(mdegA < mdegB){ - fprintf(stderr, "Bad call to allocator (error in degrees)\n"); - exit(1); - } - - data_heap_t * heap_bsolve = (data_heap_t *)(malloc(sizeof(data_heap_t))); - heap_bsolve->size_mod_array = size_mod_array; - heap_bsolve->nmod_coeffs_array = _nmod_vec_init(3 * (mdegA + 1)); - - heap_bsolve->npts = MIN(tdegA * tdegB + 1, mdegB * sdegA + mdegA * sdegB + 1); - - heap_bsolve->primes_array = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_mod_array)); - - mp_limb_t prime = n_nextprime(1152921504606847009, 0); - heap_bsolve->a_mod_eval_all = malloc(sizeof(mp_ptr) * (mdegA + 1)); - for(ulong i = 0; i<=mdegA; i++){ - heap_bsolve->a_mod_eval_all[i] = malloc(sizeof(mp_limb_t) * heap_bsolve->npts); - } - - heap_bsolve->b_mod_eval_all = malloc(sizeof(mp_ptr) * (mdegB + 1)); - for(ulong i = 0; i<=mdegB; i++){ - heap_bsolve->b_mod_eval_all[i] = malloc(sizeof(mp_limb_t) * heap_bsolve->npts); - } - - - nmod_poly_init2(heap_bsolve->a_mod_eval, prime, mdegA + 1); - heap_bsolve->a_mod_eval->length = mdegA + 1; - nmod_poly_init2(heap_bsolve->b_mod_eval, prime, mdegB + 1); - heap_bsolve->b_mod_eval->length = mdegB + 1; - - heap_bsolve->res_mod_eval = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * 2 * heap_bsolve->npts)); - heap_bsolve->ev_pts = heap_bsolve->res_mod_eval + heap_bsolve->npts; - - heap_bsolve->par_h_mod_eval = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * 2 * heap_bsolve->npts)); - heap_bsolve->par_t_mod_eval = heap_bsolve->par_h_mod_eval + heap_bsolve->npts; - - heap_bsolve->tree = _nmod_poly_tree_alloc(heap_bsolve->npts); - - heap_bsolve->a_mod = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * (mdegA + 1 + mdegB + 1))); - heap_bsolve->b_mod = heap_bsolve->a_mod + mdegA + 1; - - for(ulong i = 0; i <= mdegA; i++){ - nmod_poly_init(heap_bsolve->a_mod[i], prime); - } - for(ulong i = 0; i <= mdegB; i++){ - nmod_poly_init(heap_bsolve->b_mod[i], prime); - } - heap_bsolve->res_mod_array = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * ( 1 + size_mod_array ))); - for(ulong i = 0; i <= size_mod_array; i++){ - nmod_poly_init(heap_bsolve->res_mod_array[i], prime); - } - heap_bsolve->res_mod = heap_bsolve->res_mod_array + size_mod_array; - - heap_bsolve->res_mod_prime_array = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * ( size_mod_array ))); - for(ulong i = 0; i < size_mod_array; i++){ - nmod_poly_init(heap_bsolve->res_mod_prime_array[i], prime); - } - - heap_bsolve->par_h_mod_array = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * ( size_mod_array ))); - for(ulong i = 0; i < size_mod_array; i++){ - nmod_poly_init(heap_bsolve->par_h_mod_array[i], prime); - } - - heap_bsolve->par_t_mod_array = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * ( size_mod_array ))); - for(ulong i = 0; i < size_mod_array; i++){ - nmod_poly_init(heap_bsolve->par_t_mod_array[i], prime); - } - - heap_bsolve->GCDINV = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * ( size_mod_array ))); - for(ulong i = 0; i < size_mod_array; i++){ - nmod_poly_init(heap_bsolve->GCDINV[i], prime); - } - - heap_bsolve->prod_primes = (fmpz_t *)(malloc(sizeof(fmpz_t)*(size_mod_array + 1))); - - for(int i = 0; i <= size_mod_array; i++){ - fmpz_init(heap_bsolve->prod_primes[i]); - fmpz_one(heap_bsolve->prod_primes[i]); - } - - nmod_poly_factor_init(heap_bsolve->sqf_part); - - heap_bsolve->nmod_lparams_array = malloc(sizeof(nmod_all_params_t *) * size_mod_array); - for(int i = 0; i < size_mod_array; i++){ - heap_bsolve->nmod_lparams_array[i] = allocate_nmod_all_params(1, 2, prime); - } - - heap_bsolve->coef = malloc(sizeof(mpz_rat_t)); - fmpz_init(heap_bsolve->coef->numer); - fmpz_init(heap_bsolve->coef->denom); - - fmpz_init(heap_bsolve->h_prod); - - fmpz_init(heap_bsolve->lcm); - fmpz_one(heap_bsolve->lcm); - - heap_bsolve->prod_mod = malloc(sizeof(fmpz_t)); - fmpz_init(heap_bsolve->prod_mod[0]); - //allocation si besoin dans la fonction de calcul de parametrisation - //square-free (quand le resultant ne l'est pas) - return heap_bsolve; -} - - -static void free_data_heap(slong mdegA, slong mdegB, - int size_mod_array, data_heap_t *heap_bsolve){ - - _nmod_vec_clear(heap_bsolve->nmod_coeffs_array); - nmod_poly_factor_clear(heap_bsolve->sqf_part); - _nmod_poly_tree_free(heap_bsolve->tree, heap_bsolve->npts); - - free(heap_bsolve->primes_array); - - for(ulong i = 0; i<=mdegA; i++){ - free(heap_bsolve->a_mod_eval_all[i]); - } - free(heap_bsolve->a_mod_eval_all); - - for(ulong i = 0; i<=mdegB; i++){ - free(heap_bsolve->b_mod_eval_all[i]); - } - free(heap_bsolve->b_mod_eval_all); - - nmod_poly_clear(heap_bsolve->a_mod_eval); - nmod_poly_clear(heap_bsolve->b_mod_eval); - - free(heap_bsolve->res_mod_eval); - free(heap_bsolve->par_h_mod_eval); - - for(ulong i = 0; i <= mdegA; i++){ - nmod_poly_clear(heap_bsolve->a_mod[i]); - } - for(ulong i = 0; i <= mdegB; i++){ - nmod_poly_clear(heap_bsolve->b_mod[i]); - } - free(heap_bsolve->a_mod); - - for(ulong i = 0; i <= size_mod_array; i++){ - nmod_poly_clear(heap_bsolve->res_mod_array[i]); - } - free(heap_bsolve->res_mod_array); - - for(ulong i = 0; i < size_mod_array; i++){ - nmod_poly_clear(heap_bsolve->res_mod_prime_array[i]); - } - free(heap_bsolve->res_mod_prime_array); - - for(ulong i = 0; i < size_mod_array; i++){ - nmod_poly_clear(heap_bsolve->par_h_mod_array[i]); - } - free(heap_bsolve->par_h_mod_array); - - for(ulong i = 0; i < size_mod_array; i++){ - nmod_poly_clear(heap_bsolve->par_t_mod_array[i]); - } - free(heap_bsolve->par_t_mod_array); - - for(ulong i = 0; i < size_mod_array; i++){ - nmod_poly_clear(heap_bsolve->GCDINV[i]); - } - free(heap_bsolve->GCDINV); - - for(int i = 0; i <= size_mod_array; i++){ - fmpz_clear(heap_bsolve->prod_primes[i]); - } - - fmpz_clear(heap_bsolve->coef->numer); - fmpz_clear(heap_bsolve->coef->denom); - free(heap_bsolve->coef); - - fmpz_clear(heap_bsolve->h_prod); - fmpz_clear(heap_bsolve->lcm); - fmpz_clear(heap_bsolve->prod_mod[0]); - free(heap_bsolve->prod_mod); - - //attention : ecrire une fonction speciale pour desallouer ces zones car elles - //ne sont allouees que quand c'est necessaire (resultant non square-free et - //calcul de parametrisation) - - /* for(int i = 0; i < size_mod_array; i++){ */ - /* free_nmod_all_params(heap_bsolve->nmod_lparams_array[i]); */ - /* } */ - free(heap_bsolve->nmod_lparams_array); -} diff --git a/src/connectivity/src/resultant/data.h b/src/connectivity/src/resultant/data.h deleted file mode 100644 index 70fba5a..0000000 --- a/src/connectivity/src/resultant/data.h +++ /dev/null @@ -1,150 +0,0 @@ -typedef struct{ - fmpz_t numer; - fmpz_t denom; -} mpz_rat_t; - - -typedef struct{ - int nvars; - mp_ptr sepelem; - fmpz_poly_t * coords; - fmpz_poly_t denom; - fmpz_poly_t elim; - fmpz_t *cfs; -} bsolve_fmpz_param_t; - - -typedef struct{ - int nparams; - bsolve_fmpz_param_t **params; -} bsolve_fmpz_all_params_t; - -typedef struct{ - int recons; - int nvars; - int degree; - mp_ptr sepelem; - fmpz_poly_t * coords; // numerateurs des parametrisations - fmpz_poly_t denom; //denominateur - fmpz_poly_t elim; //polynome eliminant - fmpz_poly_t * coords_num; // numerateurs des parametrisations - fmpz_poly_t denom_num; //denominateur - fmpz_poly_t elim_num; //polynome eliminant - fmpz_poly_t * coords_den; // numerateurs des parametrisations - fmpz_poly_t denom_den; //denominateur - fmpz_poly_t elim_den; //polynome eliminant - fmpz_t * coords_lcm; // numerateurs des parametrisations - fmpz_t denom_lcm; //denominateur - fmpz_t elim_lcm; //polynome eliminant - ulong *rec_coords; - ulong rec_denom; - ulong rec_elim; -} fmpz_param_t; - - -typedef struct{ - int nvars; //nvars est le nbre de variables initiales. - ulong degree; // degre de la parametrisation - mp_ptr sepelem; - nmod_poly_t * coords; // numerateurs des parametrisations - //on en a autant que de coordonnees initiales - nmod_poly_t denom; // polynome denomninateur - nmod_poly_t elim; // polynome eliminant -} nmod_param_t; -// donc au total on a exactement nvars + 1 polynomes - - -typedef struct{ - int nparams; // nombre de parametrisations - fmpz_param_t **params; // tableau de parametrisations -} fmpz_all_params_t; - - -typedef struct{ - int nparams; - nmod_param_t **params; -} nmod_all_params_t; - - -typedef struct{ - int verb ; - int task ; // 0 -> parametrisation - // 1 -> square-free resultant - // 2 -> resultant - int binary ; // 1 -> output file in binary format - char *input_file ; - char *output_file ; -} bsolve_flags; - -/* - - Zone memoire pour donnees intermediaires. - - Le but est de calculer le resultant de A et B qui sont des polynomes bivaries. - (ou bien de calculer une parametrisation rationnelle des solutions) - -*/ -typedef struct -{ - ulong size_mod_array; - mp_ptr nmod_coeffs_array; // tableau pour suite des restes euclidiens - ulong npts; // nbre de points pour l'evaluation interpolation - - mp_ptr primes_array; // tableau de premiers utilises pour les calculs - // multi-modulaires - mp_ptr ev_pts; // tableau contenant les points d'evaluation utilises pour - // l'interpolation - mp_ptr *tree; // arbre pour l'evaluation rapide multi-point - mp_ptr *a_mod_eval_all; // tableau qui recevra les coeffs de A mod prime - // dont on a specialise une variable aux entrees - // de ev_pts - mp_ptr *b_mod_eval_all; // tableau qui recevra les coeffs de B mod prime - // dont on a specialise une variable aux entrees - // de ev_pts - nmod_poly_t a_mod_eval; // evaluation de a_mod - nmod_poly_t b_mod_eval; // evaluation de b_mod - - nmod_poly_t * a_mod; // image modulare de A - nmod_poly_t * b_mod; // image modulaire de B - - - mp_ptr res_mod_eval; // tableau recevant les specialisations du resultant de - // A mod prime et B mod prime - - nmod_poly_t * res_mod_array; // tableau contenant les images modulaires du resultant - nmod_poly_t * res_mod_prime_array; // tableau contenant les images modulaires - // de la derivee du resultant - nmod_poly_t * res_mod; // tableau contenant une image modulaire du resultant ; - // sera utilise pour verifier qu'on a fini le calcul - - // la longueur de ces tableaux est la meme que celle de res_mod_eval - mp_ptr par_h_mod_eval; // tableau recevant les coeffs dominants de - // sous-resultants (univaries) de degre 1 - // ici on a evalue une variable - mp_ptr par_t_mod_eval; // tableau recevant les coeffs constants de - // sous-resultants (univaries) de degre 1 - // ici on a evalue une variable - - nmod_poly_t * par_h_mod_array; // tableau contenant les images modulaires du - // coeff dominant du sous-resultant de degre 1 - nmod_poly_t * par_t_mod_array; // tableau contenant les images modulaires du - // coeff constant du sous-resultant de degre 1 - - nmod_poly_t * GCDINV; // quand le GCD du coeff de dom. du - // sous-resultant de degre 1 avec le resultant est = 1 on inverse le coeff - // dominant modulo le resultant - - nmod_all_params_t **nmod_lparams_array; //tableau contenant des images - //modulaires des parametrisations - - fmpz_t *prod_primes; // contiendra des produits de nbre premiers - nmod_poly_factor_t sqf_part; // contiendra la partie square-free - - //data pour les reconstructions. - fmpz_t *prod_mod; - mpz_rat_t *coef; - fmpz_t h_prod; - fmpz_t lcm; - fmpz_t *coef_num_array; - fmpz_t *coef_den_array; -} data_heap_t; diff --git a/src/connectivity/src/resultant/flint_euclide.c b/src/connectivity/src/resultant/flint_euclide.c deleted file mode 100644 index df86f74..0000000 --- a/src/connectivity/src/resultant/flint_euclide.c +++ /dev/null @@ -1,355 +0,0 @@ -/* - Functions below are very slight modifications of FLINT file - resultant_euclidean.c which is part of FLINT. - - Copyright (C) 2007, 2008 William Hart - Copyright (C) 2011 Sebastian Pancratz - FLINT is free software: you can redistribute it and/or modify it under - the terms of the GNU Lesser General Public License (LGPL) as published - by the Free Software Foundation; either version 2.1 of the License, or - (at your option) any later version. See . -*/ - -//taken from FLINT -#define MYMPN_NORM(a, an) \ - do { \ - while ((an) != 0 && (a)[(an) - 1] == 0) \ - (an)--; \ - } while (0) - -static void _my_nmod_vec_scalar_mul_nmod_large(mp_ptr res, mp_srcptr vec, - slong len, mp_limb_t c, nmod_t mod){ - for (slong i = 0; i < len; i++) - { - mp_limb_t hi, lo; - umul_ppmm(hi, lo, vec[i], c); - NMOD_RED2(res[i], hi, lo, mod); /* hi already reduced mod n */ - } -} - - -static void _my_nmod_poly_rem_q1(mp_ptr R, - mp_srcptr A, slong lenA, mp_srcptr B, slong lenB, - nmod_t mod) -{ - const mp_limb_t invL = (B[lenB-1] == 1) ? 1 : n_invmod(B[lenB-1], mod.n); - - if (lenB > 1) - { - mp_limb_t t, q0, q1; - - q1 = n_mulmod2_preinv(A[lenA-1], invL, mod.n, mod.ninv); - t = n_mulmod2_preinv(q1, B[lenB-2], mod.n, mod.ninv); - t = n_submod(A[lenA-2], t, mod.n); - q0 = n_mulmod2_preinv(t, invL, mod.n, mod.ninv); - - if (FLINT_BITS + 2 <= 2 * mod.norm) - { - mpn_mul_1(R, B, lenB - 1, q0); - if (lenB > 2) - mpn_addmul_1(R + 1, B, lenB - 2, q1); - _nmod_vec_reduce(R, R, lenB - 1, mod); - } - else - { - _my_nmod_vec_scalar_mul_nmod_large(R, B, lenB - 1, q0, mod); - if (lenB > 2) - _nmod_vec_scalar_addmul_nmod(R + 1, B, lenB - 2, q1, mod); - } - - _nmod_vec_sub(R, A, R, lenB - 1, mod); - } -} - -static void _my_nmod_poly_rem(mp_ptr R, mp_srcptr A, slong lenA, - mp_srcptr B, slong lenB, nmod_t mod) -{ - TMP_INIT; - - if (lenA - lenB == 1) - { - _my_nmod_poly_rem_q1(R, A, lenA, B, lenB, mod); - } - else if (lenA < FMPZ_POLY_SQRTREM_DIVCONQUER_CUTOFF) - { - mp_ptr W; - - TMP_START; - W = TMP_ALLOC(NMOD_DIVREM_BC_ITCH(lenA, lenB, mod)*sizeof(mp_limb_t)); - - _nmod_poly_rem_basecase(R, W, A, lenA, B, lenB, mod); - TMP_END; - } - else - { - mp_ptr Q = _nmod_vec_init(lenA - lenB + 1); - - _nmod_poly_divrem(Q, R, A, lenA, B, lenB, mod); - _nmod_vec_clear(Q); - } -} - -//Les coefficients sont ranges dans le tableau par degres croissants. -//dans param on se retrouvera avec les coefficients de la parametrisation -//attention si il n'y a pas de polynome de degre 1 dans la suite des sous-resultants -//le contenu de param reste inchange (c'est pour ca qu'il faut l'initialiser a 0) -static mp_limb_t -_nmod_poly_param_euclidean_allocated(mp_srcptr poly1, slong len1, - mp_srcptr poly2, slong len2, - nmod_t mod, mp_ptr w, - mp_ptr head, - mp_ptr tail) -{ - if(DEBUG>3){ - fprintf(stderr, "lengths = [%ld, %ld], prime = %ld\n", len1, len2, mod.n); - } - if (poly1 == poly2) - { - return 0; - } - else if (len2 == 1) - { - if (len1 == 1) - { - return 1; - } - else if (len1 == 2) - { - head[0] = poly1[1]; - tail[0] = poly1[0]; - return poly2[0]; - } - else - { - return n_powmod2_ui_preinv(poly2[0], len1 - 1, mod.n, mod.ninv); - } - } - else{ /* len1 >= len2 >= 2 */ - if(len2 == 2){ - head[0] = poly2[1]; - tail[0] = poly2[0]; - } - mp_limb_t res = 1; - - mp_ptr u, v, r, t; - slong l0, l1, l2; - mp_limb_t lc; - - u = w; - v = w + len1; - r = v + len1; - //u == poly1 - _nmod_vec_set(u, poly1, len1); - //v == poly2 - _nmod_vec_set(v, poly2, len2); - l1 = len1; - l2 = len2; - - if(DEBUG>5){ - fprintf(stderr, "Affichage de u\n"); - nmod_vec_print(stderr, u, len1); - fprintf(stderr, "Affichage de v\n"); - nmod_vec_print(stderr, v, len2); - } - - do - { - l0 = l1; - l1 = l2; - //coefficient dominant de v - lc = v[l1 - 1]; - - if(DEBUG>5){ - fprintf(stderr, "u = "); - nmod_vec_print(stderr, u, l0); - fprintf(stderr, "v = "); - nmod_vec_print(stderr, v, l1); - } - //u est de longueur l0, v est de longueur l1 - //r = remainder(u, v) - _my_nmod_poly_rem(r, u, l0, v, l1, mod); - // _nmod_poly_rem(r, u, l0, v, l1, mod); - l2 = l1 - 1; - //determine la longueur de r (decremente l2 tant que le top coeff == 0) - //r est de degre l2 - 1 - MYMPN_NORM(r, l2); - if(DEBUG>5){ - fprintf(stderr, "r = "); - nmod_vec_print(stderr, r, l2); - fprintf(stderr, "l0 = %ld\n", l0); - fprintf(stderr, "l1 = %ld\n", l1); - fprintf(stderr, "l2 = %ld\n", l2); - fprintf(stderr, "lc = %ld\n", lc); - fprintf(stderr, "res = %ld\n", res); - } - //mise a jour - { - t = u; - u = v; - v = r; - r = t; - } - if (l2 >= 1){ - lc = n_powmod2_preinv(lc, l0 - l2, mod.n, mod.ninv); - res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); - - if (((l0 | l1) & 1) == 0) - { - if(DEBUG>5){ - fprintf(stderr, "[%ld, %ld] ", l0, l1); - } - res = nmod_neg(res, mod); - } - if(l2==2){ /* degree of the remainder -- which is now stored in v -- is 1 */ - mp_limb_t hi, lo; //, c; - umul_ppmm(hi, lo, v[0], res); - NMOD_RED2(tail[0], hi, lo, mod); /* hi already reduced mod n */ - hi = 0; lo = 0; - umul_ppmm(hi, lo, v[1], res); - NMOD_RED2(head[0], hi, lo, mod); /* hi already reduced mod n */ - } - if(l2==1){/* degree of the remainder -- which is now stored in v -- is 0 */ - /* head[0] = u[1]; */ - /* tail[0] = u[0]; */ - /* fprintf(stderr, "--> head = %ld\n", head[0]); */ - /* fprintf(stderr, "--> tail = %ld\n", tail[0]); */ - } - } - else /* l2 == 0 */ - { - if (l1 == 1) - { - lc = n_powmod2_preinv(lc, l0 - 1, mod.n, mod.ninv); - res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); - /* head[0] = u[1]; */ - /* tail[0] = u[0]; */ - } - else - { - if(l1==2){ - fprintf(stderr, "l1 == 2 et lc = %ld\n", lc); - lc = n_powmod2_preinv(lc, l0 - 1, mod.n, mod.ninv); - fprintf(stderr, "et maintenant lc = %ld\n", lc); - res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); - fprintf(stderr, "et res = %ld\n", res); - head[0] = u[1]; - tail[0] = u[0]; - /* mp_limb_t hi, lo; //, c; */ - /* umul_ppmm(hi, lo, u[0], res); */ - /* NMOD_RED2(tail[0], hi, lo, mod); /\* hi already reduced mod n *\/ */ - /* hi = 0; lo = 0; */ - /* umul_ppmm(hi, lo, u[1], res); */ - /* NMOD_RED2(head[0], hi, lo, mod); /\* hi already reduced mod n *\/ */ - } - else{ - head[0] = 0; - tail[0] = 0; - } - res = 0; - } - } - } - while (l2 > 0); - - return res; - } -} - - -//Les coefficients sont ranges dans le tableau par degre croissant. -static mp_limb_t -_nmod_poly_resultant_euclidean_allocated(mp_srcptr poly1, slong len1, - mp_srcptr poly2, slong len2, nmod_t mod, mp_ptr w) -{ - if (poly1 == poly2) - { - return 0; - } - else if (len2 == 1) - { - if (len1 == 1) - { - return 1; - } - else if (len1 == 2) - { - return poly2[0]; - } - else - { - return n_powmod2_ui_preinv(poly2[0], len1 - 1, mod.n, mod.ninv); - } - } - else /* len1 >= len2 >= 2 */ - { - mp_limb_t res = 1; - - mp_ptr u, v, r, t; - slong l0, l1, l2; - mp_limb_t lc; - - u = w; - v = w + len1; - r = v + len1; - //u == poly1 - _nmod_vec_set(u, poly1, len1); - //v == poly2 - _nmod_vec_set(v, poly2, len2); - l1 = len1; - l2 = len2; - - do - { - l0 = l1; - l1 = l2; - //coefficient dominant de v - lc = v[l1 - 1]; - - //u est de longueur l0, v est de longueur l1 - //r = remainder(u, v) - _my_nmod_poly_rem(r, u, l0, v, l1, mod); - l2 = l1 - 1; - //determine la longueur de r (decremente l2 tant que le top coeff == 0) - //r est de degre l2 - 1 - MYMPN_NORM(r, l2); - //mise a jour - { - t = u; - u = v; - v = r; - r = t; - } - - if (l2 >= 1) - { - lc = n_powmod2_preinv(lc, l0 - l2, mod.n, mod.ninv); - res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); - - if (((l0 | l1) & 1) == 0) - { - res = nmod_neg(res, mod); - } - } - else - { - if (l1 == 1) - { - lc = n_powmod2_preinv(lc, l0 - 1, mod.n, mod.ninv); - res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); - } - else - { - res = 0; - } - } - } - while (l2 > 0); - - return res; - } -} - - -/* - END OF FLINT modified resultant_euclidean.c - */ diff --git a/src/connectivity/src/resultant/flint_resultant.c b/src/connectivity/src/resultant/flint_resultant.c deleted file mode 100644 index ba9535c..0000000 --- a/src/connectivity/src/resultant/flint_resultant.c +++ /dev/null @@ -1,1285 +0,0 @@ -/** -Author: Mohab Safey El Din - - - - **/ - -#include -#include -#include -#include -#include -#include -#include -#include -#include - -#include "flint/flint.h" -#include "flint/ulong_extras.h" -#include "flint/fmpz.h" -#include "flint/fmpz_poly.h" -#include "flint/nmod_poly.h" - -#define LOG2(X) ((unsigned) (8*sizeof (unsigned long long) - __builtin_clzll((X)) - 1)) - -#define MPN_NORM(a, an) \ - do { \ - while ((an) != 0 && (a)[(an) - 1] == 0) \ - (an)--; \ - } while (0) - - -void fmpz_poly_random_dense(fmpz_poly_t pol, slong deg, mp_bitcnt_t bits, flint_rand_t state){ - - fmpz_t coeff; - fmpz_init(coeff); - - // flint_randseed(state, (ulong) time(NULL), (ulong) clock()); - - long i; - flint_randseed(state, (ulong) clock(), (ulong)(10000*clock())); - - for(i=0;i<=deg;i++){ - fmpz_randbits(coeff, state, bits); - fmpz_poly_set_coeff_fmpz(pol, i, coeff); - flint_randseed(state, (ulong) (i), (ulong)(10000*clock()*(i+1))); - } - fmpz_clear(coeff); -} - -void fmpz_poly_random_dense_old(fmpz_poly_t pol, slong deg, mp_bitcnt_t bits){ - - fmpz_t coeff; - fmpz_init(coeff); - - flint_rand_t state; - flint_randinit(state); - // flint_randseed(state, (ulong) time(NULL), (ulong) clock()); - - long i; - - for(i=0;i<=deg;i++){ - fmpz_randbits(coeff, state, bits); - fmpz_poly_set_coeff_fmpz(pol, i, coeff); - // flint_randseed(state, (ulong) (i), (ulong)(10000*time(NULL)*(i+1))); - } - fmpz_clear(coeff); -} - -void make_mod_poly(nmod_poly_t a_mod, fmpz_poly_t A, mp_limb_t prime){ - for(unsigned long int i=0; ilength; i++){ - nmod_poly_set_coeff_ui(a_mod, i, fmpz_fdiv_ui(A->coeffs+i, prime)); - } -} - - -void run_res_flint(unsigned long int deg, flint_rand_t state){ - - unsigned long int newdeg = deg; - - puts("FLINT resultant functions (nbits = deg / 2)"); - - while(newdeg<=8090){ - unsigned long int deg1 = newdeg, deg2 = deg1; - unsigned int nbits = deg1 / 2; - - fmpz_poly_t A, B; - fmpz_poly_init2(A, deg1+1); - fmpz_poly_init2(B, deg2+1); - fmpz_poly_random_dense(A, deg1, nbits, state); - fmpz_poly_random_dense(B, deg2, nbits, state); - - fmpz_t res_normal; - fmpz_init(res_normal); - - double e_normal = 0, t; - t = omp_get_wtime(); - fmpz_poly_resultant(res_normal, A, B); - e_normal = omp_get_wtime() - t; - - fprintf(stdout, "Degree: %lu\n", newdeg); - fprintf(stdout, "Elapsed time (normal): %f\n\n", e_normal); - - if(fmpz_cmp_ui(res_normal, 0)==0){ - puts("Resultant was 0\n"); - } - newdeg = 2*newdeg; - - fmpz_poly_clear(A); - fmpz_poly_clear(B); - - } -} - -void myresultantold(fmpz_t res, fmpz_poly_t A, fmpz_poly_t B, int nthreads){ - - mp_limb_t myprime; - - unsigned long bound ; //= (deg1+deg2) * nbits + 2 * LOG2( (deg1 + deg2) ) ; - bound = (A->length + B->length - 1)*FLINT_BIT_COUNT((10*(A->length + B->length - 1) + 26)/27) + 3; - - mp_bitcnt_t bits1 = FLINT_ABS(_fmpz_vec_max_bits(A->coeffs, A->length)); - mp_bitcnt_t bits2 = FLINT_ABS(_fmpz_vec_max_bits(B->coeffs, B->length)); - - /* Upper bound Hadamard bound */ - bound += (A->length - 1)*bits1 + (B->length - 1)*bits2; - - unsigned int PRIMESIZE = 32; - - myprime = n_nextprime(1152921504606847009, 0); - // myprime = n_nextprime(4611686018427388039, 0); - fprintf(stdout,"LOG2(prime) = %d\n", LOG2(myprime)); - - unsigned int nbits_prime = 0; //LOG2(myprime); - long count = 1; - long count_primes = 0; - - double e_crt = 0, e_modular = 0, t = omp_get_wtime(); - long size_table = (bound / PRIMESIZE) + 2; - mp_limb_t * primes_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; - mp_limb_t * res_mod_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; - - while(nbits_prime < bound){ - myprime = n_nextprime(myprime, 0); - - if(fmpz_divisible_si(fmpz_poly_lead(A), myprime)==0 && - fmpz_divisible_si(fmpz_poly_lead(B), myprime)==0){ - nbits_prime += LOG2(myprime); - primes_table[count_primes] = myprime; - count_primes++; - } - else{ - fprintf(stdout, "! %ld\n", count); - } - count++; - } - fprintf(stdout, "count = %ld\n", count); - fflush(stdout); - - nmod_poly_t a, b; - nmod_poly_init2(a, myprime, A->length); - nmod_poly_init2(b, myprime, B->length); - - double t_in = 0, e_in = 0; - - omp_set_num_threads(nthreads); -#pragma omp parallel for num_threads(nthreads) - for(long i = 0; i < count_primes; i++){ - mp_limb_t res_mod; - mp_limb_t prime = primes_table[i]; - a->mod.n = prime; - a->mod.ninv = n_preinvert_limb(prime); - count_leading_zeros(a->mod.norm, prime); - - b->mod.n = myprime; - b->mod.ninv = n_preinvert_limb(prime); - count_leading_zeros(b->mod.norm, prime); - - make_mod_poly(a, A, prime); - make_mod_poly(b, B, prime); - t_in = omp_get_wtime(); - res_mod = _nmod_poly_resultant(a->coeffs, A->length, b->coeffs, B->length, a->mod); - e_in += omp_get_wtime() - t_in; - res_mod_table[i] = res_mod; - } - e_modular = omp_get_wtime() - t; - - //utilisation de fmpz_CRT pour recuperer le resultant - fmpz_t prod; - fmpz_init(prod); - fmpz_zero(res); - fmpz_one(prod); - - puts("CRT starts"); - t = omp_get_wtime() ; - for(long i = 0; i < count_primes; i++){ - fmpz_CRT_ui(res, res, prod, res_mod_table[i], primes_table[i], 1); - fmpz_mul_ui(prod, prod, primes_table[i]); - } - e_crt = omp_get_wtime() - t; - - - fprintf(stdout, "Elapsed time (multi-mod resultant): %f (%f + %f)\n", e_modular + e_crt, e_modular, e_crt); - fprintf(stdout, "Elapsed time MM in %f\n", e_in); - fprintf(stdout, "Elapsed time per mod comp. %f\n", e_in / count); - - if (fmpz_cmp_ui(res, 0)==0){ - puts("\nResultant was 0\n"); - } - fmpz_clear(prod); - - free(primes_table); - nmod_poly_clear(a); - nmod_poly_clear(b); - -} - - - -//ce resultant est parallelisable mais consomme trop de memoire (et ca nuit a ses performances) -void myresultant_mem_not_eff(fmpz_t res, fmpz_poly_t A, fmpz_poly_t B, int nthreads){ - - mp_limb_t myprime; - - unsigned long bound ; //= (deg1+deg2) * nbits + 2 * LOG2( (deg1 + deg2) ) ; - bound = (A->length + B->length - 1)*FLINT_BIT_COUNT((10*(A->length + B->length - 1) + 26)/27) + 3; - - mp_bitcnt_t bits1 = FLINT_ABS(_fmpz_vec_max_bits(A->coeffs, A->length)); - mp_bitcnt_t bits2 = FLINT_ABS(_fmpz_vec_max_bits(B->coeffs, B->length)); - - /* Upper bound Hadamard bound */ - bound += (A->length - 1)*bits1 + (B->length - 1)*bits2; - - unsigned int PRIMESIZE = 32; - - myprime = n_nextprime(1152921504606847009, 0); - // myprime = n_nextprime(4611686018427388039, 0); - fprintf(stdout,"LOG2(prime) = %d\n", LOG2(myprime)); - - unsigned int nbits_prime = 0; //LOG2(myprime); - long count = 1; - long count_primes = 0; - - double e_crt = 0, e_modular = 0, t = omp_get_wtime(); - long size_table = (bound / PRIMESIZE) + 2; - mp_limb_t * primes_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; - mp_limb_t * res_mod_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; - - fmpz * leadA = fmpz_poly_lead(A); - fmpz * leadB = fmpz_poly_lead(B); - while(nbits_prime < bound){ - myprime = n_nextprime(myprime, 0); - - if(fmpz_divisible_si(leadA, myprime)==0 && - fmpz_divisible_si(leadB, myprime)==0){ - nbits_prime += LOG2(myprime); - primes_table[count_primes] = myprime; - count_primes++; - } - else{ - fprintf(stdout, "! %ld\n", count); - } - count++; - } - fprintf(stdout, "count = %ld\n", count); - fflush(stdout); - - nmod_poly_t *amod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * count_primes)); - nmod_poly_t *bmod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * count_primes)); - - for(long i = 0 ; i < count_primes; i++){ - mp_limb_t prime = primes_table[i]; - nmod_poly_init2(amod_table[i], prime, A->length); - nmod_poly_init2(bmod_table[i], prime, A->length); - - make_mod_poly(amod_table[i], A, prime); - make_mod_poly(bmod_table[i], B, prime); - - } - double t_in = 0, e_in = 0; - - omp_set_num_threads(nthreads); -#pragma omp parallel for num_threads(nthreads) - for(long i =0 ; i < count_primes ; i++){ - - t_in = omp_get_wtime(); - mp_limb_t res_mod = _nmod_poly_resultant(amod_table[i]->coeffs, A->length, bmod_table[i]->coeffs, B->length, amod_table[i]->mod); - e_in += omp_get_wtime() - t_in; - res_mod_table[i] = res_mod; - - } - - e_modular = omp_get_wtime() - t; - - //utilisation de fmpz_CRT pour recuperer le resultant - fmpz_t prod; - fmpz_init(prod); - fmpz_zero(res); - fmpz_one(prod); - - t = omp_get_wtime() ; - for(long i = 0; i < count_primes; i++){ - fmpz_CRT_ui(res, res, prod, res_mod_table[i], primes_table[i], 1); - fmpz_mul_ui(prod, prod, primes_table[i]); - } - e_crt = omp_get_wtime() - t; - - - fprintf(stdout, "Elapsed time (multi-mod resultant): %f (%f + %f)\n", e_modular + e_crt, e_modular, e_crt); - fprintf(stdout, "Elapsed time MM in %f\n", e_in); - fprintf(stdout, "Elapsed time per mod comp. %f\n", e_in / count); - - if (fmpz_cmp_ui(res, 0)==0){ - puts("\nResultant was 0\n"); - } - fmpz_clear(prod); - - free(primes_table); - //nettoyage memoire a terminer - -} - -unsigned long int compute_bsize_norm(fmpz *l, unsigned long int s){ - fmpz_t sum, sq; - fmpz_init_set_ui(sum, 0); - fmpz_init(sq); - for(unsigned long int i = 0; i < s; i++){ - fmpz_pow_ui(sq, l+i, 2); - fmpz_add(sum, sum, sq); - } - return fmpz_bits(sum) / 2; -} - -//l1 et l2 sont 2 tableaux de coefficients de taille respectives l1 et l2 -unsigned long int compute_bsize_bound_resultant(fmpz *l1, fmpz *l2, unsigned long int s1, unsigned long int s2){ - unsigned long int b1 = compute_bsize_norm(l1, s1); - unsigned long int b2 = compute_bsize_norm(l2, s2); - return (unsigned long int) ( (s1-1) * b2 + (s2-1) * b1 ); -} - - - -static mp_limb_t -_nmod_poly_dth_resultant(mp_srcptr poly1, slong len1, - mp_srcptr poly2, slong len2, - nmod_t mod, - mp_ptr head, - slong sdeg - ) -{ - if (poly1 == poly2) - { - return 0; - } - else if (len2 == 1) - { - if (len1 == 1) - { - return 1; - } - else if (len1 == 2) - { - return poly2[0]; - } - else - { - return n_powmod2_ui_preinv(poly2[0], len1 - 1, mod.n, mod.ninv); - } - } - else /* len1 >= len2 >= 2 */ - { - mp_limb_t res = 1; - - mp_ptr u, v, r, t, w; - slong l0, l1, l2; - mp_limb_t lc; - w = _nmod_vec_init(3 * len1); - - u = w; - v = w + len1; - r = v + len1; - //u == poly1 - _nmod_vec_set(u, poly1, len1); - //v == poly2 - _nmod_vec_set(v, poly2, len2); - l1 = len1; - l2 = len2; - - do - { - l0 = l1; - l1 = l2; - //coefficient dominant de v - lc = v[l1 - 1]; - - /* if(DEBUG>3){ */ - /* fprintf(stderr, "Affichage de v\n"); */ - /* nmod_vec_print(stderr, v, l1); */ - /* } */ - - //u est de longueur l0, v est de longueur l1 - //r = remainder(u, v) - _nmod_poly_rem(r, u, l0, v, l1, mod); - l2 = l1 - 1; - //determine la longueur de r (decremente l2 tant que le top coeff == 0) - //r est de degre l2 - 1 - MPN_NORM(r, l2); - //mise a jour - { - t = u; - u = v; - v = r; - r = t; - } - - if (l2 >= 1) - { - lc = n_powmod2_preinv(lc, l0 - l2, mod.n, mod.ninv); - res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); - - if (((l0 | l1) & 1) == 0) - { - res = nmod_neg(res, mod); - } - if(l2==sdeg+1){ - mp_limb_t hi, lo; - // umul_ppmm(hi, lo, v[0], res); - // NMOD_RED2(tail[0], hi, lo, mod); /* hi already reduced mod n */ - umul_ppmm(hi, lo, v[sdeg], res); - NMOD_RED2(head[0], hi, lo, mod); /* hi already reduced mod n */ - _nmod_vec_clear(w); - return res; - } - } - else - { - if (l1 == 1) - { - lc = n_powmod2_preinv(lc, l0 - 1, mod.n, mod.ninv); - res = n_mulmod2_preinv(res, lc, mod.n, mod.ninv); - } - else - { - res = 0; - } - } - } - while (l2 > 0); - _nmod_vec_clear(w); - return res; - } -} - - - -//Calcul du resultant de A et B -//nthreads est le nombre de threads utilises -void my_dth_subresultant(fmpz_t res, fmpz_poly_t A, fmpz_poly_t B, - slong sdeg, int nthreads){ - if(A->lengthlength){ - fprintf(stderr, "Warning: polynomials have been given with increasing degree ; possible sign variation\n"); - my_dth_subresultant(res, B, A, sdeg, nthreads); - return; - } - - mp_limb_t myprime; - - unsigned long bound ; //= (deg1+deg2) * nbits + 2 * LOG2( (deg1 + deg2) ) ; - bound = (A->length + B->length - 1)*FLINT_BIT_COUNT((10*(A->length + B->length - 1) + 26)/27) + 3; - - mp_bitcnt_t bits1 = FLINT_ABS(_fmpz_vec_max_bits(A->coeffs, A->length)); - mp_bitcnt_t bits2 = FLINT_ABS(_fmpz_vec_max_bits(B->coeffs, B->length)); - - /* Upper bound Hadamard bound */ - bound += (A->length - 1)*bits1 + (B->length - 1)*bits2; - - // fprintf(stderr, "Old bound %lu\n", bound); - - bound = compute_bsize_bound_resultant(A->coeffs, B->coeffs, A->length, B->length); - - fprintf(stderr, "Output bit size bound %lu\n", bound); - - //4611686018427388039 - //1152921504606847009 - - myprime = n_nextprime(4611686018427388039, 0); - unsigned int PRIMESIZE = LOG2(myprime); - // myprime = n_nextprime(4611686018427388039, 0); - fprintf(stderr,"LOG2(prime) = %d\n", LOG2(myprime)); - - unsigned int nbits_prime = 0; //LOG2(myprime); - long count = 1; - long count_primes = 0; - - double e_end, e_start; - long size_table = (bound / PRIMESIZE) + 2; - mp_limb_t * primes_table_init = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; - mp_limb_t * primes_table = primes_table_init; - mp_limb_t * res_mod_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * nthreads)) ; - - fmpz * leadA = fmpz_poly_lead(A); - fmpz * leadB = fmpz_poly_lead(B); - e_start = omp_get_wtime(); - while(nbits_prime < bound){ - myprime = n_nextprime(myprime, 0); - if(fmpz_divisible_si(leadA, myprime)==0 && - fmpz_divisible_si(leadB, myprime)==0){ - nbits_prime += LOG2(myprime); - primes_table_init[count_primes] = myprime; - count_primes++; - } - else{ - fprintf(stderr, "! %ld\n", count); - } - count++; - } - fprintf(stderr, "count = %ld / count_primes = %ld\n", count, count_primes); - // fflush(stdout); - - nmod_poly_t *amod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * nthreads)); - nmod_poly_t *bmod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * nthreads)); - - //Il faut les initialiser - for(int i =0; i < nthreads; i++){ - mp_limb_t prime = primes_table[i]; - nmod_poly_init2(amod_table[i], prime, A->length); - nmod_poly_init2(bmod_table[i], prime, A->length); - } - mp_ptr head = malloc(sizeof(mp_limb_t)*size_table); - fprintf(stderr, "First initialization done\n\n"); - unsigned long int nblocks = count_primes / nthreads; - - // double t_in = 0, e_in = 0; - fmpz_t prod; - fmpz_init(prod); - fmpz_zero(res); - fmpz_one(prod); - int index = 0; - omp_set_num_threads(nthreads); - double e_in = 0; - - for(unsigned long int block = 0; block < nblocks; block++){ - // unsigned long int index = block*nthreads; -#pragma omp parallel for num_threads(nthreads) - for(int i =0; i < nthreads; i++){ - - mp_limb_t prime = primes_table[i]; - // fprintf(stderr, "prime = %lu\n", prime); - amod_table[i]->mod.n = prime; - amod_table[i]->mod.ninv = n_preinvert_limb(prime); - count_leading_zeros(amod_table[i]->mod.norm, prime); - - bmod_table[i]->mod.n = prime; - bmod_table[i]->mod.ninv = n_preinvert_limb(prime); - count_leading_zeros(bmod_table[i]->mod.norm, prime); - - make_mod_poly(amod_table[i], A, prime); - make_mod_poly(bmod_table[i], B, prime); - - double t_in = omp_get_wtime(); - _nmod_poly_dth_resultant(amod_table[i]->coeffs, - A->length, - bmod_table[i]->coeffs, - B->length, - amod_table[i]->mod, - head+i+index, - sdeg); - if(e_in==0){ - e_in = omp_get_wtime() - t_in; - fprintf(stderr, "\nRun time modp comp. = %f\n",e_in); - } - res_mod_table[i+index] = head[i+index]; - - } - - if(fmpz_fdiv_ui(res, primes_table[0])==res_mod_table[index]){ - // fprintf(stderr, "Probabilistic stop\n"); - break; - } - else{ - for(int i =0; i < nthreads; i++){ - // unsigned long int index = block*nthreads; - // fprintf(stderr, "Ici: %lu (%d)\n", primes_table[i+index], i); - fmpz_CRT_ui(res, res, prod, res_mod_table[i+index], primes_table[i+index], 1); - // fprintf(stderr, "La?\n"); - fmpz_mul_ui(prod, prod, primes_table[i+index]); - // fprintf(stderr, "On incremente\n"); - // fprintf(stderr, "%lu, %lu, %lu\n", primes_table_init[0], primes_table_init[1], primes_table_init[2]); - } - primes_table+=nthreads; - } - } - /* // fprintf(stderr, "after loops\n"); */ - /* // unsigned long int index = nblocks*nthreads; */ - /* for(unsigned long int i = 0; i < count_primes - index; i++){ */ - /* mp_limb_t prime = primes_table[0]; */ - - /* amod_table[i]->mod.n = prime; */ - /* amod_table[i]->mod.ninv = n_preinvert_limb(prime); */ - /* count_leading_zeros(amod_table[i]->mod.norm, prime); */ - - /* bmod_table[i]->mod.n = prime; */ - /* bmod_table[i]->mod.ninv = n_preinvert_limb(prime); */ - /* count_leading_zeros(bmod_table[i]->mod.norm, prime); */ - - /* make_mod_poly(amod_table[i], A, prime); */ - /* make_mod_poly(bmod_table[i], B, prime); */ - - - /* // t_in = omp_get_wtime(); */ - /* mp_limb_t res_mod = _nmod_poly_dth_resultant( */ - /* amod_table[i]->coeffs, */ - /* A->length, */ - /* bmod_table[i]->coeffs, */ - /* B->length, */ - /* amod_table[i]->mod, */ - /* head+i+index, */ - /* sdeg); */ - /* // e_in += omp_get_wtime() - t_in; */ - - /* res_mod_table[i+index] = head[i+index]; */ - - /* if(fmpz_fdiv_ui(res, primes_table[0])==res_mod_table[i+index]){ */ - /* break; */ - /* } */ - /* else{ */ - /* fmpz_CRT_ui(res, res, prod, res_mod_table[i+index], primes_table[i+index], 1); */ - /* fmpz_mul_ui(prod, prod, primes_table[i+index]); */ - /* primes_table++; */ - /* } */ - /* } */ - e_end = omp_get_wtime() - e_start; - - - //utilisation de fmpz_CRT pour recuperer le resultant - //Obsolete - - /* t = omp_get_wtime() ; */ - /* for(long i = 0; i < count_primes; i++){ */ - /* fmpz_CRT_ui(res, res, prod, res_mod_table[i], primes_table[i], 1); */ - /* fmpz_mul_ui(prod, prod, primes_table[i]); */ - /* } */ - /* e_crt = omp_get_wtime() - t; */ - fprintf(stderr, "Bit size of the result = %ld\n", fmpz_bits(res)); - fprintf(stderr, "Elapsed time (multi-mod resultant): %f\n", e_end); - // fprintf(stderr, "Elapsed time MM in %f\n", e_in); - // fprintf(stderr, "Elapsed time per mod comp. %f\n", e_in / count); - - if (fmpz_cmp_ui(res, 0)==0){ - fprintf(stderr,"\nResultant was 0\n"); - } - fmpz_clear(prod); - - free(primes_table_init); - - for(int i = 0; i < nthreads; i++){ - nmod_poly_clear(amod_table[i]); - nmod_poly_clear(bmod_table[i]); - } - - free(res_mod_table); - free(amod_table); - free(bmod_table); - - //nettoyage memoire a terminer - -} - - -//Calcul du resultant de A et B -//nthreads est le nombre de threads utilises -void myresultant(fmpz_t res, fmpz_poly_t A, fmpz_poly_t B, int nthreads){ - if(A->lengthlength){ - fprintf(stderr, "Warning: polynomials have been given with increasing degree ; possible sign variation\n"); - myresultant(res, B, A, nthreads); - return; - } - - mp_limb_t myprime; - - unsigned long bound ; //= (deg1+deg2) * nbits + 2 * LOG2( (deg1 + deg2) ) ; - bound = (A->length + B->length - 1)*FLINT_BIT_COUNT((10*(A->length + B->length - 1) + 26)/27) + 3; - - mp_bitcnt_t bits1 = FLINT_ABS(_fmpz_vec_max_bits(A->coeffs, A->length)); - mp_bitcnt_t bits2 = FLINT_ABS(_fmpz_vec_max_bits(B->coeffs, B->length)); - - /* Upper bound Hadamard bound */ - bound += (A->length - 1)*bits1 + (B->length - 1)*bits2; - - bound = compute_bsize_bound_resultant(A->coeffs, B->coeffs, A->length, B->length); - - fprintf(stderr, "Output bit size bound %lu\n", bound); - - //4611686018427388039 - myprime = n_nextprime(1152921504606847009, 0); - unsigned int PRIMESIZE = LOG2(myprime); - // myprime = n_nextprime(4611686018427388039, 0); - fprintf(stderr,"LOG2(prime) = %d\n", LOG2(myprime)); - - unsigned int nbits_prime = 0; //LOG2(myprime); - long count = 1; - long count_primes = 0; - - double e_end, e_start; //= omp_get_wtime(); - long size_table = (bound / PRIMESIZE) + 2; - mp_limb_t * primes_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; - mp_limb_t * res_mod_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * size_table)) ; - - fmpz * leadA = fmpz_poly_lead(A); - fmpz * leadB = fmpz_poly_lead(B); - e_start = omp_get_wtime(); - while(nbits_prime < bound){ - myprime = n_nextprime(myprime, 0); - if(fmpz_divisible_si(leadA, myprime)==0 && - fmpz_divisible_si(leadB, myprime)==0){ - nbits_prime += LOG2(myprime); - primes_table[count_primes] = myprime; - count_primes++; - } - else{ - fprintf(stderr, "! %ld\n", count); - } - count++; - } - fprintf(stderr, "count = %ld / count_primes = %ld\n", count, count_primes); - // fflush(stdout); - - nmod_poly_t *amod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * nthreads)); - nmod_poly_t *bmod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * nthreads)); - - //Il faut les initialiser - for(int i =0; i < nthreads; i++){ - mp_limb_t prime = primes_table[i]; - nmod_poly_init2(amod_table[i], prime, A->length); - nmod_poly_init2(bmod_table[i], prime, A->length); - } - fprintf(stderr, "First initialization done\n\n"); - unsigned long int nblocks = count_primes / nthreads; - - // double t_in = 0, e_in = 0; - fmpz_t prod; - fmpz_init(prod); - fmpz_zero(res); - fmpz_one(prod); - - omp_set_num_threads(nthreads); - for(unsigned long int block = 0; block < nblocks; block++){ - unsigned long int index = block*nthreads; -#pragma omp parallel for num_threads(nthreads) - for(int i =0; i < nthreads; i++){ - - mp_limb_t prime = primes_table[i+index]; - - amod_table[i]->mod.n = prime; - amod_table[i]->mod.ninv = n_preinvert_limb(prime); - count_leading_zeros(amod_table[i]->mod.norm, prime); - - bmod_table[i]->mod.n = prime; - bmod_table[i]->mod.ninv = n_preinvert_limb(prime); - count_leading_zeros(bmod_table[i]->mod.norm, prime); - - make_mod_poly(amod_table[i], A, prime); - make_mod_poly(bmod_table[i], B, prime); - - - // t_in = omp_get_wtime(); - mp_limb_t res_mod = _nmod_poly_resultant( - amod_table[i]->coeffs, - A->length, - bmod_table[i]->coeffs, - B->length, - amod_table[i]->mod); - // e_in += omp_get_wtime() - t_in; - - res_mod_table[i+index] = res_mod; - - } - if(fmpz_fdiv_ui(res, primes_table[index])==res_mod_table[index]){ - // fprintf(stderr, "Probabilistic stop\n"); - break; - } - else{ - for(int i =0; i < nthreads; i++){ - unsigned long int index = block*nthreads; - - // mp_limb_t prime = primes_table[i+index]; - fmpz_CRT_ui(res, res, prod, res_mod_table[i+index], primes_table[i+index], 1); - fmpz_mul_ui(prod, prod, primes_table[i+index]); - } - } - } - // fprintf(stderr, "after loops\n"); - unsigned long int index = nblocks*nthreads; - for(unsigned long int i = 0; i < count_primes - index; i++){ - mp_limb_t prime = primes_table[i+index]; - - amod_table[i]->mod.n = prime; - amod_table[i]->mod.ninv = n_preinvert_limb(prime); - count_leading_zeros(amod_table[i]->mod.norm, prime); - - bmod_table[i]->mod.n = prime; - bmod_table[i]->mod.ninv = n_preinvert_limb(prime); - count_leading_zeros(bmod_table[i]->mod.norm, prime); - - make_mod_poly(amod_table[i], A, prime); - make_mod_poly(bmod_table[i], B, prime); - - - // t_in = omp_get_wtime(); - mp_limb_t res_mod = _nmod_poly_resultant( - amod_table[i]->coeffs, - A->length, - bmod_table[i]->coeffs, - B->length, - amod_table[i]->mod); - // e_in += omp_get_wtime() - t_in; - - res_mod_table[i+index] = res_mod; - - if(fmpz_fdiv_ui(res, primes_table[i+index])==res_mod_table[i+index]){ - break; - } - else{ - fmpz_CRT_ui(res, res, prod, res_mod_table[i+index], primes_table[i+index], 1); - fmpz_mul_ui(prod, prod, primes_table[i+index]); - } - } - e_end = omp_get_wtime() - e_start; - - - //utilisation de fmpz_CRT pour recuperer le resultant - //Obsolete - - /* t = omp_get_wtime() ; */ - /* for(long i = 0; i < count_primes; i++){ */ - /* fmpz_CRT_ui(res, res, prod, res_mod_table[i], primes_table[i], 1); */ - /* fmpz_mul_ui(prod, prod, primes_table[i]); */ - /* } */ - /* e_crt = omp_get_wtime() - t; */ - fprintf(stderr, "Bit size of the result = %ld\n", fmpz_bits(res)); - fprintf(stderr, "Elapsed time (multi-mod resultant): %f \n", e_end); - // fprintf(stderr, "Elapsed time MM in %f\n", e_in); - // fprintf(stderr, "Elapsed time per mod comp. %f\n", e_in / count); - - if (fmpz_cmp_ui(res, 0)==0){ - fprintf(stderr,"\nResultant was 0\n"); - } - fmpz_clear(prod); - - free(primes_table); - for(int i = 0; i < nthreads; i++){ - nmod_poly_clear(amod_table[i]); - nmod_poly_clear(bmod_table[i]); - } - - free(res_mod_table); - free(amod_table); - free(bmod_table); - - //nettoyage memoire a terminer - -} - -//Compares FLINT resultant with a hand-made multi-mod resultant -//(still using FLINT basics) -void run_compare(unsigned long int deg, flint_rand_t state){ - - unsigned long int deg1 = deg, deg2 = deg1; - unsigned int nbits = deg1 ; - - fmpz_poly_t A, B; - fmpz_poly_init2(A, deg1+1); - fmpz_poly_init2(B, deg2+1); - fmpz_poly_random_dense(A, deg1, nbits, state); - fmpz_poly_random_dense(B, deg2, nbits, state); - - /* fmpz_poly_random_dense_old(A, deg1, nbits); */ - /* fmpz_poly_random_dense_old(B, deg2, nbits); */ - - fmpz_t res_normal, res; - fmpz_init(res_normal); - fmpz_init(res); - - double e_normal = 0, t; - t = omp_get_wtime(); - fmpz_poly_resultant(res_normal, A, B); - e_normal = omp_get_wtime() - t; - fprintf(stderr, "Elapsed time (FLINT resultant): %f\n\n", e_normal); - - t = omp_get_wtime(); - myresultant(res, A, B, 1); - e_normal = omp_get_wtime() - t; - fprintf(stderr, "Elapsed time (my resultant): %f\n", e_normal); - - if(fmpz_cmp(res, res_normal)!=0){ - puts("\n\t BUG BUG BUG\n"); - } - - puts(""); - - /* if(fmpz_cmp_ui(res, 0)==1){ */ - /* puts("Positive"); */ - /* } */ - /* else{ */ - /* puts("Negative"); */ - /* } */ - fmpz_clear(res); - fmpz_clear(res_normal); - -} - -//runs modular FLINT resultant modulo 32 bits prime -void run_modular16(flint_rand_t state, int ntimes){ - - unsigned long int deg = 64; - mp_limb_t myprime = 65537; - - puts("\nFLINT resultant modulo 16 bits prime\n"); - while(deg<=2*8192){ - - fmpz_poly_t A, B; - fmpz_poly_init2(A, deg+1); - fmpz_poly_init2(B, deg+1); - fmpz_poly_random_dense(A, deg, deg / 2, state); - fmpz_poly_random_dense(B, deg, deg / 2, state); - - nmod_poly_t a_mod,b_mod; - nmod_poly_init2(a_mod,myprime, deg+1); - nmod_poly_init2(b_mod,myprime, deg+1); - //attention a la gestion des coefficients negatifs - // nmod_poly_set_coeff_ui(x,3,9002); - // nmod_poly_set_coeff_ui(x,0,6); - - make_mod_poly(a_mod, A, myprime); - make_mod_poly(b_mod, B, myprime); - - fprintf(stdout,"Degree = %lu\n", deg); - - // nmod_poly_print(x);flint_printf("\n"); - // nmod_poly_print(y);flint_printf("\n"); - double e = 0, t = omp_get_wtime(); - int j; - for(int i = 1; i<=ntimes; i++){ - // res = nmod_poly_resultant_hgcd(a_mod, b_mod); - nmod_poly_resultant(a_mod, b_mod); //combine gcd et euclide en fonction du degre - j = j+i; - } - e = omp_get_wtime() - t; - // fprintf(stdout,"%lu \n", res); - fprintf(stdout, "Elapsed time Half gcd resultant = %f\n", e); - - double e2 = 0, t2 = omp_get_wtime(); - for(int i =1 ; i <=ntimes; i++){ - nmod_poly_resultant_euclidean(a_mod, b_mod); - j = j+i; - } - e2 = omp_get_wtime() - t2; - fprintf(stdout, "Elapsed time Euclidean resultant = %f\n", e2); - puts(""); - - nmod_poly_clear(a_mod); - nmod_poly_clear(b_mod); - - fmpz_poly_clear(A); - fmpz_poly_clear(B); - - deg = 2*deg; - } -} - -//runs modular FLINT resultant modulo 32 bits prime -void run_modular32(flint_rand_t state, int ntimes){ - - unsigned long int deg = 30; - mp_limb_t myprime = 4294967311; - - puts("\nFLINT resultant modulo 32 bits prime\n"); - while(deg<=2*8192){ - - fmpz_poly_t A, B; - fmpz_poly_init2(A, deg+1); - fmpz_poly_init2(B, deg+1); - fmpz_poly_random_dense(A, deg, deg / 2, state); - fmpz_poly_random_dense(B, deg, deg / 2, state); - - nmod_poly_t a_mod,b_mod; - nmod_poly_init2(a_mod,myprime, deg+1); - nmod_poly_init2(b_mod,myprime, deg+1); - //attention a la gestion des coefficients negatifs - // nmod_poly_set_coeff_ui(x,3,9002); - // nmod_poly_set_coeff_ui(x,0,6); - - make_mod_poly(a_mod, A, myprime); - make_mod_poly(b_mod, B, myprime); - - fprintf(stdout,"Degree = %lu\n", deg); - - double e = 0, t = omp_get_wtime(); - int j; - for(int i = 1; i<=ntimes; i++){ - // res = nmod_poly_resultant_hgcd(a_mod, b_mod); - nmod_poly_resultant_hgcd(a_mod, b_mod); //combine gcd et euclide en fonction du degre - j = j+i; - } - e = omp_get_wtime() - t; - fprintf(stdout, "Elapsed time Half gcd resultant = %f\n", e); - - double e2 = 0, t2 = omp_get_wtime(); - for(int i =1 ; i <=ntimes; i++){ - nmod_poly_resultant_euclidean(a_mod, b_mod); - j = j+i; - } - e2 = omp_get_wtime() - t2; - fprintf(stdout, "Elapsed time Euclidean resultant = %f\n", e2); - puts(""); - - nmod_poly_clear(a_mod); - nmod_poly_clear(b_mod); - - fmpz_poly_clear(A); - fmpz_poly_clear(B); - - deg = 2*deg; - } -} - -//runs modular FLINT resultant modulo 60 bits fftprime -void run_modular60fftprime(flint_rand_t state, int ntimes){ - - unsigned long int deg = 64; - mp_limb_t myprime = 1945555039024054273; - - puts("\nFLINT resultant modulo 60 bits FFT prime\n"); - while(deg<=8192){ - - fmpz_poly_t A, B; - fmpz_poly_init2(A, deg+1); - fmpz_poly_init2(B, deg+1); - fmpz_poly_random_dense(A, deg, deg / 2, state); - fmpz_poly_random_dense(B, deg, deg / 2, state); - - nmod_poly_t a_mod,b_mod; - nmod_poly_init2(a_mod,myprime, deg+1); - nmod_poly_init2(b_mod,myprime, deg+1); - //attention a la gestion des coefficients negatifs - // nmod_poly_set_coeff_ui(x,3,9002); - // nmod_poly_set_coeff_ui(x,0,6); - - make_mod_poly(a_mod, A, myprime); - make_mod_poly(b_mod, B, myprime); - - fprintf(stdout,"Degree = %lu\n", deg); - - double e = 0, t = omp_get_wtime(); - int j; - for(int i = 1; i<=ntimes; i++){ - // res = nmod_poly_resultant_hgcd(a_mod, b_mod); - nmod_poly_resultant(a_mod, b_mod); //combine gcd et euclide en fonction du degre - j = j+i; - } - e = omp_get_wtime() - t; - - fprintf(stdout, "Elapsed time Half gcd resultant = %f\n", e); - - double e2 = 0, t2 = omp_get_wtime(); - for(int i =1 ; i <=ntimes; i++){ - nmod_poly_resultant_euclidean(a_mod, b_mod); - j = j+i; - } - e2 = omp_get_wtime() - t2; - fprintf(stdout, "Elapsed time Euclidean resultant = %f\n", e2); - puts(""); - - nmod_poly_clear(a_mod); - nmod_poly_clear(b_mod); - - fmpz_poly_clear(A); - fmpz_poly_clear(B); - - deg = 2*deg; - } -} - -//runs modular FLINT resultant modulo 60 bits prime -void run_modular60prime(flint_rand_t state, int ntimes){ - - unsigned long int deg = 256; - mp_limb_t myprime = 1152921504606847009; - - puts("\nFLINT resultant modulo 60 bits prime\n"); - while(deg<=8192){ - - fmpz_poly_t A, B; - fmpz_poly_init2(A, deg+1); - fmpz_poly_init2(B, deg+1); - fmpz_poly_random_dense(A, deg, deg / 2, state); - fmpz_poly_random_dense(B, deg, deg / 2, state); - - nmod_poly_t a_mod,b_mod; - nmod_poly_init2(a_mod,myprime, deg+1); - nmod_poly_init2(b_mod,myprime, deg+1); - //attention a la gestion des coefficients negatifs - // nmod_poly_set_coeff_ui(x,3,9002); - // nmod_poly_set_coeff_ui(x,0,6); - - make_mod_poly(a_mod, A, myprime); - make_mod_poly(b_mod, B, myprime); - - fprintf(stdout,"Degree = %lu\n", deg); - - double e = 0, t = omp_get_wtime(); - int j; - for(int i = 1; i<=ntimes; i++){ - // res = nmod_poly_resultant_hgcd(a_mod, b_mod); - nmod_poly_resultant_hgcd(a_mod, b_mod); //combine gcd et euclide en fonction du degre - j = j+i; - } - e = omp_get_wtime() - t; - - fprintf(stdout, "Elapsed time Half gcd resultant = %f\n", e/ntimes); - - double e2 = 0, t2 = omp_get_wtime(); - for(int i =1 ; i <=ntimes; i++){ - nmod_poly_resultant_euclidean(a_mod, b_mod); - j = j+i; - } - e2 = omp_get_wtime() - t2; - fprintf(stdout, "Elapsed time Euclidean resultant = %f\n", e2/ntimes); - puts(""); - - nmod_poly_clear(a_mod); - nmod_poly_clear(b_mod); - - fmpz_poly_clear(A); - fmpz_poly_clear(B); - - deg = deg * 2; - } -} - -void display_help(){ - fprintf(stdout, "Basic Flint based C program for computing resultant and subresultant in Z[x]\n"); - fprintf(stdout, "Implemented by M. Safey El Din (Sorbonne Univ./CNRS/Inria), mohab.safey@lip6.fr\n"); - fprintf(stdout, "Provided without any guarantee for ** academic use only ** by students, teachers and researchers hosted in high-schools, universities or academic (non-industtrial) research institutes\n"); - fprintf(stdout, "Any kind of other use requires formal agreement from the author\n\n"); - - fprintf(stdout, "-h \t diplays this help\n"); - fprintf(stdout, "-r \t generates random dense polynomials of degree d and runs the resultant computation\n"); - fprintf(stdout, "-f \t reads polynomials in filename and computes the resultant of those polynomials\n"); - fprintf(stdout, "\n Format file: \nFiles provide 2 polynomials encoded as follows \ndegree\ncoef_0\n...\ncoef_degree\n"); - - fprintf(stdout, "\n\nTODO:\n"); - fprintf(stdout, "Main difference with FLINT functions are in memory management+multi-threading\n"); - fprintf(stdout, "Lifting is not that efficient - can be improved\n"); - fprintf(stdout, "Use of fast reductions still needs to be implemented\n"); -} - - - -static char *getoptions(int argc, char **argv, char ** input_file, - ulong *deg, slong *sdeg, int *nthreads){ - int optch, errflag = 0, fflag = 1; - extern int opterr; - - char options[] = "hf:r:d:t:"; - char *filename = NULL; - opterr = 1; - - while ((optch = getopt(argc, argv, options)) != -1) - switch (optch) { - case 'f': - fflag = 0; - *input_file = optarg; - optind--; - break; - case 'h': - display_help(); - exit(1); - case 'r': - *deg = strtol(optarg, NULL, 10); - optind--; - break; - case 'd': - *sdeg = strtol(optarg, NULL, 10); - optind--; - break; - case 't': - *nthreads = strtol(optarg, NULL, 10); - optind--; - break; - default: - errflag++; - break; - } - if(fflag==1){ - fprintf(stderr, "No given file\n"); - *input_file = NULL; - } - if(errflag){ - fprintf(stderr,"Invalid usage\n"); - fprintf(stderr,"%s -f file_name\n", argv[0]); - exit(1); - } - return filename; -} - -void get_input_polynomials(FILE *file, ulong *degA, ulong *degB, - fmpz_poly_t A, fmpz_poly_t B){ - fmpz_t c; - fmpz_init(c); - if(fscanf(file, "%lu", degA)){ - fprintf(stderr, "Degree %lu\n", *degA); - for(ulong i=0; i <= *degA; i++){ - fmpz_fread(file, c); - fmpz_poly_set_coeff_fmpz(A, i, c); - } - } - if(fscanf(file, "%lu", degB)){ - fprintf(stderr, "Degree %lu\n", *degB); - for(ulong i=0; i <= *degB; i++){ - fmpz_fread(file, c); - fmpz_poly_set_coeff_fmpz(B, i, c); - } - } - fmpz_clear(c); -} - -int main(int argc, char *argv[]){ - char **input_file = malloc(sizeof(char**)); - ulong deg = 0; - slong sdeg = -1; - int nthreads = 1; - getoptions(argc, argv, input_file, °, &sdeg, &nthreads); - - if(*input_file!=NULL){ - fprintf(stderr, "Reading file...\n"); - FILE *file = fopen(*input_file,"r"); - ulong degA = 0, degB = 0; - fmpz_poly_t A; - fmpz_poly_t B; - fmpz_poly_init(A); - fmpz_poly_init(B); - get_input_polynomials(file, °A, °B, A, B); - fprintf(stderr, "Done.\n\n"); - fmpz_t res; - fmpz_init(res); - if(sdeg>0){ - my_dth_subresultant(res, A, B, sdeg, nthreads); - } - else{ - myresultant(res, A, B, nthreads); - } - // fmpz_zero(res); - fmpz_fprint(stdout, res); - fmpz_poly_clear(A); - fmpz_poly_clear(B); - fmpz_clear(res); - free(input_file); - return 0; - } - - fprintf(stdout, "\nRunning resultant computations for random dense polynomials in Z[x]\n\n"); - // run_modular(); - flint_rand_t state; - flint_randinit(state); - run_compare(deg, state); - - //FLINT resultant sur les entiers - // run_res_flint(64, state); - - //FLINT resultant modulo premier 16 bits - // run_modular16(state, 100); - - //FLINT resultant modulo premier 32 bits - // run_modular32(state, 10000); - - //FLINT resultant modulo premier 60 bits - run_modular60prime(state, 400); - - //FLINT resultant modulo premier fft 60 bits - // run_modular60fftprime(state, 100); - - flint_randclear(state); - return 0; -} diff --git a/src/connectivity/src/resultant/io.c b/src/connectivity/src/resultant/io.c deleted file mode 100644 index c1ee6b3..0000000 --- a/src/connectivity/src/resultant/io.c +++ /dev/null @@ -1,562 +0,0 @@ -static void print_nmod_param(FILE * file, nmod_param_t *param){ - char str[2]={"x"}; - fprintf(file, "%d\n", param->nvars); - fprintf(file, "["); - - for(int i = 0; i < param->nvars; i++){ - nmod_poly_fprint_pretty(file, param->coords[i], str); - } - fprintf(file, "]\n"); - nmod_poly_fprint_pretty(file, param->denom, str); - fprintf(file, "\n"); - nmod_poly_fprint_pretty(file, param->elim, str); - fprintf(stderr, "\n"); -} - - -static inline void print_nmod_all_params_pretty(FILE *file, nmod_all_params_t *all_params){ - fprintf(file, "\n"); - for(int i = 0; i < all_params->nparams; i++){ - print_nmod_param(file, (all_params->params)[i]); - } -} - -static inline void fmpz_poly_fprint_bin(FILE *file, const fmpz_poly_t poly){ - slong len = poly->length; - fprintf(file, "%ld\n", len); - fprintf(stderr, "LENGTH = %ld\n", len); - for(slong i = 0; i < len; i++){ - fmpz_out_raw(file, poly->coeffs + i); - } -} - -static inline void print_fmpz_param_bin(FILE *file, fmpz_param_t *param){ - fprintf(file, "%d\n", param->nvars); - for(int i = 0; i < param->nvars-1; i++){ - fmpz_poly_fprint_bin(file, param->coords[i]); - } - fmpz_poly_fprint_bin(file, param->denom); - fmpz_poly_fprint_bin(file, param->elim); -} - -static inline void print_fmpz_param_pretty(FILE *file, fmpz_param_t *param){ - char stra[2] = {"x"}; - fprintf(file, "%d\n", param->nvars); - fprintf(file, "["); - - for(int i = 0; i < param->nvars; i++){ - fmpz_poly_fprint_pretty(file, param->coords[i], stra); - fprintf(file, ",\n"); - } - fmpz_poly_fprint_pretty(file, param->coords[param->nvars-1], stra); - fprintf(file, "]\n"); - fmpz_poly_fprint_pretty(file, param->denom, stra); - fprintf(file, "\n"); - fmpz_poly_fprint_pretty(file, param->elim, stra); - fprintf(stderr, "\n"); -} - -static inline void print_bs_fmpz_param_bin(FILE *file, bsolve_fmpz_param_t *param){ - fprintf(stderr, "ELIM -> "); - fmpz_poly_fprint_bin(file, param->elim); - fprintf(stderr, "DENOM -> "); - fmpz_poly_fprint_bin(file, param->denom); - int nv = param->nvars + 1; - fprintf(stderr, "NVARS = %d\n", nv); - fprintf(file, "%d\n", nv); - for(int i = 0; i < param->nvars; i++){ - fprintf(stderr, "COORD -> "); - fmpz_poly_fprint_bin(file, param->coords[i]); - fmpz_out_raw(file, param->cfs[i]); - } -} - -static inline void print_bs_fmpz_param_pretty(FILE *file, bsolve_fmpz_param_t *param){ - char stra[2] = {"x"}; - fprintf(file, "["); - fmpz_poly_fprint_pretty(file, param->elim, stra); - fprintf(file, ",\n"); - fmpz_poly_fprint_pretty(file, param->denom, stra); - fprintf(file, ",\n"); - for(int i = 0; i < param->nvars-1; i++){ - fmpz_poly_fprint_pretty(file, param->coords[i], stra); - fprintf(file, ",\n"); - } - fmpz_poly_fprint_pretty(file, param->coords[param->nvars-1], stra); - fprintf(file, "]"); -} - -static inline void print_fmpz_all_params_bin(FILE *file, fmpz_all_params_t *all_params){ - fprintf(file, "%d\n", all_params->nparams); - - for(int i = 0; i < all_params->nparams; i++){ - print_fmpz_param_bin(file, all_params->params[i]); - } -} - - -static inline void print_fmpz_all_params_pretty(FILE *file, fmpz_all_params_t *all_params){ - fprintf(file, "\n"); - for(int i = 0; i < all_params->nparams; i++){ - print_fmpz_param_pretty(file, all_params->params[i]); - } -} - -static inline void print_bs_fmpz_all_params_bin(FILE *file, - bsolve_fmpz_all_params_t *all_params){ - fprintf(file, "%d\n", all_params->nparams); - - for(int i = 0; i < all_params->nparams-1; i++){ - fprintf(stderr, "Display PARAM %d\n", i); - print_bs_fmpz_param_bin(file, all_params->params[i]); - fprintf(file, "\n"); - } - fprintf(stderr, "Display PARAM %d\n", all_params->nparams-1); - print_bs_fmpz_param_bin(file, all_params->params[all_params->nparams-1]); - fprintf(file, "\n"); -} - -static inline void print_bs_fmpz_all_params_pretty(FILE *file, - bsolve_fmpz_all_params_t *all_params){ - fprintf(file, "[\n"); - for(int i = 0; i < all_params->nparams-1; i++){ - print_bs_fmpz_param_pretty(file, all_params->params[i]); - fprintf(file, ",\n"); - } - print_bs_fmpz_param_pretty(file, all_params->params[all_params->nparams-1]); - fprintf(file, "\n];\n"); -} - -static void nmod_vec_print(FILE *file, mp_srcptr vec, slong len){ - if(len==1) { - fprintf(file, "%lu ; \n", vec[0]); - return; - } - fprintf(file, "%lu + ", vec[0]); - for(slong i = 1; i < len - 1; i++){ - fprintf(file, "%lu * x^%ld + ", vec[i], i); - } - fprintf(file, "%lu * x^%ld; \n", vec[len-1], len-1); -} - -/* - Input: -*/ - -static void fmpz_bpoly_fprint_pretty(FILE *file, fmpz_poly_t *A, ulong deg){ - char strx[1]={"x"}; - for(slong i=deg; i >=1 ; i--){ - fprintf(file, "("); - fmpz_poly_fprint_pretty(file, A[i], strx); - fprintf(file, ")*y^%lu+", i); - } - fprintf(file, "("); - fmpz_poly_fprint_pretty(file, A[0], strx); - fprintf(file, ");"); - fprintf(file, "\n"); -} - -static ulong nbits_bound_fmpz_bvar_poly(fmpz_poly_t *A, ulong deg){ - ulong nbits = 0; - fmpz_t sum, sumtmp, tmp; - fmpz_init(sum); - fmpz_init(sumtmp); - fmpz_init(tmp); - fmpz_zero(sum); - for(ulong i = 0; i <= deg; i++){ - fmpz_zero(sumtmp); - for(ulong j = 0; j < A[i]->length; j++){ - fmpz_abs(tmp, A[i]->coeffs+j); - fmpz_add(sumtmp, sumtmp, tmp); - } - fmpz_mul(sumtmp, sumtmp, sumtmp); - fmpz_add(sum, sum, sumtmp); - } - nbits = fmpz_bits(sum) + 1; - fmpz_clear(sumtmp); - fmpz_clear(sum); - fmpz_clear(tmp); - return nbits / 2; -} - -static void crt_lift_resultant(fmpz_poly_t res, nmod_poly_t *res_mod_table, mp_limb_t *primes_table, ulong size, fmpz_t *prod_mod){ - slong maxdegree = -1; - ulong i; - for(i = 0; i < size; i++){ - if(res_mod_table[i]->length - 1 > maxdegree){ - maxdegree = res_mod_table[i]->length - 1; - } - } - if(res->length-1!=maxdegree){ - res->coeffs = malloc(sizeof(fmpz_t) * (maxdegree + 1)); - for(i = 0; i <= maxdegree; i++){ - fmpz_poly_set_coeff_ui(res, i, 1); - } - } - - fmpz_t prod_primes; - fmpz_init(prod_primes); - fmpz_one(prod_primes); - - for(i = 0; i < size; i++){ - for(ulong j = 0; j <= maxdegree; j++){ - myfmpz_CRT_ui((res->coeffs)+j, (res->coeffs)+j, - prod_primes, (res_mod_table[i]->coeffs)[j], - primes_table[i], 1, - prod_mod); - } - fmpz_mul_ui(prod_primes, prod_primes, primes_table[i]); - } - fmpz_clear(prod_primes); -} - - - -static slong get_total_degree(fmpz_poly_t *A, slong degA){ - slong total_degree = -1; - - for(slong i = 0; i <= degA; i++){ - if(A[i]->length - 1 + i > total_degree){ - total_degree = A[i]->length - 1 + i; - } - } - return total_degree; -} - -static slong get_partial_degree(fmpz_poly_t *A, slong degA){ - slong degAx = -1; - for(slong i = 0; i <= degA ; i++){ - if(A[i]->length - 1 > degAx){ - degAx = A[i]->length -1; - } - } - return degAx; -} - - -static void get_exponent(FILE *file, ulong *exp, ulong nvars){ - for(ulong i = 0; i < nvars-1; i++){ - if(fscanf(file, "%lu ", exp+i)){ - } - } - if(fscanf(file, "%lu\n", exp+nvars-1)){ - } -} - -static void get_mpoly_from_file(FILE *file, fmpz_mpoly_t A, fmpz_mpoly_ctx_t ctx){ - ulong nterms, nvars; - if(fscanf(file, "%lu", &nterms)){ - } - else{ - fprintf(stderr, "Error when reading file\n"); - } - if(fscanf(file, "%lu", &nvars)){ - } - else{ - fprintf(stderr, "Error when reading file\n"); - } - if(nvars!=2){ - fprintf(stderr, "Bad number of variables\n"); - exit(1); - } - fmpz_mpoly_fit_length(A, nterms, ctx); - fmpz_t coeff; - fmpz_init(coeff); - ulong * exp = malloc(sizeof(ulong)*nvars); - for(ulong i=0; i < nterms; i++){ - fmpz_fread(file, coeff); - get_exponent(file, exp, nvars); - // _fmpz_mpoly_emplacebackterm_fmpz_ui(A, coeff, exp, ctx); - fmpz_mpoly_push_term_fmpz_ui(A, coeff, exp, ctx); - } - fmpz_mpoly_sort_terms(A, ctx); - fmpz_mpoly_combine_like_terms(A, ctx); - free(exp); - fmpz_clear(coeff); -} - - -/* - -Input: A et B dependent de deux variables (x1,x2) -L'ordre utilise est l'ordre lex x1 > x2 - -On renvoie un pointeur sur les coefficients de A suivis de -ceux de B vus comme un polynome de Z[x2][x1] - -main_degree_A et main_degree_B sont les degres en x1 de A et B - -*/ -static fmpz_poly_t *make_bpoly_from_mpoly2(fmpz_mpoly_t A, fmpz_mpoly_t B, fmpz_mpoly_ctx_t ctx, - slong *main_degree_A, slong *main_degree_B){ - - *main_degree_A = fmpz_mpoly_degree_si(A, 0, ctx); - *main_degree_B = fmpz_mpoly_degree_si(B, 0, ctx); - - fmpz_poly_t *A_univ = (fmpz_poly_t *)(malloc(sizeof(fmpz_poly_t) * - (*main_degree_A + 1 + *main_degree_B + 1))); - for(ulong i = 0; i <= (*main_degree_A) + (*main_degree_B) + 1; i++){ - fmpz_poly_init(A_univ[i]); - fmpz_poly_zero(A_univ[i]); - } - fmpz_mpoly_t Term; - fmpz_mpoly_init(Term, ctx); - slong deg_mainvar_term = 0, old_deg_mainvar_term = -1; - slong deg_var2; - fmpz_t c; - fmpz_init(c); - for(ulong i = 0; i < A->length; i++){ - fmpz_mpoly_get_term(Term, A, i, ctx); - fmpz_mpoly_get_term_coeff_fmpz(c, Term, 0, ctx); - - deg_mainvar_term = fmpz_mpoly_degree_si(Term, 0, ctx); - deg_var2 = fmpz_mpoly_degree_si(Term, 1, ctx); - if(old_deg_mainvar_term != deg_mainvar_term){ - fmpz_poly_fit_length(A_univ[deg_mainvar_term], deg_var2 + 1); - } - fmpz_poly_set_coeff_fmpz(A_univ[deg_mainvar_term], deg_var2, c); - old_deg_mainvar_term = deg_mainvar_term; - } - for(ulong i = 0; i < B->length; i++){ - fmpz_mpoly_get_term(Term, B, i, ctx); - fmpz_mpoly_get_term_coeff_fmpz(c, Term, 0, ctx); - - deg_mainvar_term = fmpz_mpoly_degree_si(Term, 0, ctx); - deg_var2 = fmpz_mpoly_degree_si(Term, 1, ctx); - if(old_deg_mainvar_term!=deg_mainvar_term){ - fmpz_poly_fit_length(A_univ[*main_degree_A + 1 + deg_mainvar_term], deg_var2 + 1); - } - fmpz_poly_set_coeff_fmpz(A_univ[*main_degree_A + 1 + deg_mainvar_term], deg_var2, c); - old_deg_mainvar_term = deg_mainvar_term; - } - - fmpz_mpoly_clear(Term, ctx); - fmpz_clear(c); - return A_univ; -} - -#ifdef TESTDENSE -static void test_dense(slong deg, ulong nbits, flint_rand_t state){ - fmpz_poly_t *A = (fmpz_poly_t *)(malloc(sizeof(fmpz_poly_t) * (deg + 1))); - fmpz_poly_t *B = (fmpz_poly_t *)(malloc(sizeof(fmpz_poly_t) * (deg + 1))); - for(ulong i = 0; i <= deg; i++){ - fmpz_poly_init(A[i]); - fmpz_poly_init(B[i]); - } - - fmpz_bpoly_random_dense(A, deg, nbits, state); - fmpz_bpoly_random_dense(B, deg, nbits, state); - - fmpz_poly_t res; - fmpz_poly_init(res); - fmpz_poly_t res2; - fmpz_poly_init(res2); - fmpz_poly_t res3; - fmpz_poly_init(res3); - - fmpz_bpoly_resultant_deterministic(res, A, deg, B, deg); - fprintf(stderr, "\n\nStarts probabilistic implem.\n\n"); - fmpz_bpoly_resultant_probabilistic(res2, A, deg, B, deg, 0); - // fmpz_bpoly_sqfree_resultant_probabilistic(res2, A, deg, B, deg, 0); - fprintf(stderr, "\n\nStarts SQRFREE probabilistic implem.\n\n"); - fmpz_bpoly_sqfree_resultant_probabilistic(res2, A, deg, B, deg); - - - /* fprintf(stdout,"R:=PolynomialRing(Rationals());\n"); */ - /* fprintf(stdout,"P:=PolynomialRing(R);\n"); */ - /* fprintf(stdout, "A := "); */ - /* fmpz_bpoly_fprint_pretty(A, deg); */ - /* fprintf(stdout, "\nB := "); */ - /* fmpz_bpoly_fprint_pretty(B, deg); */ - /* char str[1]={"x"}; */ - /* fprintf(stdout, "\nmyres := "); */ - /* fmpz_poly_fprint_pretty(stdout, res2, str); */ - /* fprintf(stdout, ";\n"); */ - /* fprintf(stdout, "\ntime res := Resultant(A, B);\n"); */ - /* fprintf(stdout, "res-myres;"); */ - /* fprintf(stdout, "\n"); */ - - for(ulong i = 0; i <= deg; i++){ - fmpz_poly_clear(A[i]); - fmpz_poly_clear(B[i]); - } - fmpz_poly_clear(res); - fmpz_poly_clear(res2); - fmpz_poly_clear(res3); - free(A); - free(B); -} -#endif - -static void display_help(char **argv){ - fprintf(stdout, "Basic usage\n\n%s -f file_in\n\n", argv[0]); - fprintf(stdout, "Whenever it is possible, by default, it returns\n"); - fprintf(stdout, "a finite sequence of zero-dimensional parametrizations\n"); - fprintf(stdout, "of the set of common complex solutions to the input polynomials\n\n"); - - fprintf(stdout, "Each parametrization corresponds to distinct multiplicities \n"); - fprintf(stdout, "of the resultant of the input polynomials w.r.t. the first variable\n\n"); - - fprintf(stdout, "Additional options: \n"); - fprintf(stdout, "-r \t Computes the resultant\n"); - fprintf(stdout, "-q \t Computes the square-free part of the resultant\n"); - fprintf(stdout, "-b \t Output file will be in binary format\n"); - fprintf(stdout, "-o \t output file \n"); - fprintf(stdout, "-h \t displays this help\n\n"); - - fprintf(stdout, "\n\n file_in must have the following format: \n"); - fprintf(stdout, "First line looks like\nnt n\nwhere nt is the number of terms and n the number of variables\n"); - fprintf(stdout, "Next lines look like \ncoeff e1 e2\n where coeff is an integer coefficient to the monomial x1^e1...xn^en\n"); - fprintf(stdout, "And a next polynomial should be given with the same format\n"); - fprintf(stdout, "\nThe variable which is eliminated is the first one (the one whose exponent comes at first)\n"); -} - - -static fmpz_poly_t *get_input_polynomials(FILE *file, slong *degA, slong *degB){ - fmpz_mpoly_ctx_t ctx; - ordering_t ord = ORD_LEX; - fmpz_mpoly_t A, B; - fmpz_mpoly_ctx_init(ctx, 2, ord); - fmpz_mpoly_init(A, ctx); - fmpz_mpoly_init(B, ctx); - - get_mpoly_from_file(file, A, ctx); - get_mpoly_from_file(file, B, ctx); - - fmpz_poly_t *bA = make_bpoly_from_mpoly2(A, B, ctx, degA, degB); - - fmpz_mpoly_clear(A, ctx); - fmpz_mpoly_clear(B, ctx); - fmpz_mpoly_ctx_clear(ctx); - return bA; -} - -static void display_fmpz_poly_to_usolve(FILE *file, fmpz_poly_t res){ - fprintf(file, "%ld\n", res->length-1); - fmpz_t c; - fmpz_init(c); - if(res->length==0){ - fprintf(file,"%d\n", 0); - return; - } - for(ulong i=0; i < res->length; i++){ - fmpz_poly_get_coeff_fmpz(c, res, i); - fmpz_fprint(file, c); - fprintf(file, "\n"); - } - fmpz_clear(c); -} - -static void display_fmpz_poly_binary_to_usolve(FILE *file, fmpz_poly_t res){ - return; - /* const long length = res->length; */ - /* if(res->length==0){ */ - /* mpz_t * tab = (mpz_t *)(malloc(sizeof(mpz_t) )); */ - /* mpz_init(tab[0]); */ - /* mpz_set_ui(tab[0], 0); */ - /* mpz_t p; */ - /* binary_write_INT(file, p);//cette fonction fait un mpz_clear(p) */ - /* binary_write(file, tab, length); */ - /* mpz_clear(tab[0]); */ - /* free(tab); */ - /* return; */ - /* } */ - /* mpz_t * tab = (mpz_t *)(malloc(sizeof(mpz_t) * length)); */ - /* for(long i=0; i < length; i++){ */ - /* mpz_init(tab[i]); */ - /* fmpz_get_mpz(tab[i], res->coeffs+i); */ - /* } */ - /* mpz_t p; */ - /* binary_write_INT(file, p);//cette fonction fait un mpz_clear(p) */ - /* binary_write(file, tab, length); */ - /* for(long i=0; i < length; i++){ */ - /* mpz_clear(tab[i]); */ - /* } */ - /* free(tab); */ -} - - -static char *getoptions(int argc, char **argv, bsolve_flags * flags){ - int optch, errflag = 0, fflag = 1; - extern int opterr; - - char options[] = "rqhbf:o:v:"; - char *filename = NULL; - opterr = 1; - - while ((optch = getopt(argc, argv, options)) != -1) - switch (optch) { - case 'b': - flags->binary = 1; - break; - case 'f': - fflag = 0; - flags->input_file = optarg; - optind--; - break; - case 'h': - display_help(argv); - exit(1); - case 'o': - flags->output_file = optarg; - optind--; - break; - case 'q': - flags->task = 2; - break; - case 'r': - flags->task = 1; - break; - case 'v': - flags->verb = strtol(optarg, NULL, 10); - optind--; - break; - default: - errflag++; - break; - } - if(fflag){ - fprintf(stderr,"No given file\n"); - fprintf(stderr,"%s -f file_name\n", argv[0]); - exit(1); - } - if(errflag){ - fprintf(stderr,"Invalid usage\n"); - fprintf(stderr,"%s -f file_name\n", argv[0]); - exit(1); - } - return filename; -} - -static bsolve_flags *allocate_initialize_flags(){ - bsolve_flags *flags = malloc(sizeof(bsolve_flags)); - flags->verb=0; - flags->task = 0; - flags->binary = 0; - flags->input_file = NULL; - flags->output_file = NULL; - - return flags; -} - -static void free_flags(bsolve_flags * flags){ - free(flags); -} - -static inline void display_resutant(fmpz_poly_t res, bsolve_flags *flags, - int binary_format){ - if(flags->output_file!=NULL){ - FILE *outputfile = fopen(flags->output_file,"w"); - if(binary_format==0){ - display_fmpz_poly_to_usolve(outputfile, res); - } - else{ - display_fmpz_poly_binary_to_usolve(outputfile, res); - } - fclose(outputfile); - } - else{ - display_fmpz_poly_to_usolve(stdout, res); - } -} - diff --git a/src/connectivity/src/resultant/main.c b/src/connectivity/src/resultant/main.c deleted file mode 100644 index 4f39f54..0000000 --- a/src/connectivity/src/resultant/main.c +++ /dev/null @@ -1,1550 +0,0 @@ -#include -#include -#include -#include -#include -#include -#include -#include -#include - -#include "flint/flint.h" -#include "flint/ulong_extras.h" -#include "flint/mpn_extras.h" -#include "flint/fmpz.h" -#include "flint/fmpz_poly.h" -#include "flint/nmod_vec.h" -#include "flint/nmod_poly.h" -#include "flint/fmpz_mpoly.h" - -#define nthreads 1 - -#define LOG2(X) ((unsigned) (8*sizeof (unsigned long long) - __builtin_clzll((X)) - 1)) -#define MIN(a,b) (((a)<(b))?(a):(b)) - -#define DEBUG 2 - -#include "data.c" -#include "ratreconstruct.c" -#include "io.c" -#include "flint_euclide.c" - -//taken from FLINT -typedef unsigned int UDItype __attribute__ ((mode(DI))); -#define umul_ppmm2(w1, w0, u, v) \ - __asm__ ("mul{q} %3" \ - : "=a" ((UDItype) (w0)), \ - "=d" ((UDItype) (w1)) \ - : "%0" ((UDItype) (u)), \ - "rm" ((UDItype) (v))) - -#define NMOD_DIVREM_DIVCONQUER_CUTOFF 300 - - -/* -Input: Les coeffs des polynomes sont stockes du plus petit au plus grand degre - -pol devient un polynome de degre deg, coeffs de taille bits aleatoires - -*/ -static void fmpz_poly_random_dense(fmpz_poly_t pol, slong deg, mp_bitcnt_t bits, flint_rand_t state){ - - fmpz_t coeff; - fmpz_init(coeff); - - // flint_randseed(state, (ulong) time(NULL), (ulong) clock()); - - long i; - flint_randseed(state, (ulong) clock(), (ulong)(10000*clock())); - - for(i=0;i<=deg;i++){ - fmpz_randbits(coeff, state, bits); - fmpz_poly_set_coeff_fmpz(pol, i, coeff); - flint_randseed(state, (ulong) (i), (ulong)(10000*clock()*(i+1))); - } - fmpz_clear(coeff); -} - -/* -bivarpol est un tableau de taille degmain + 1 et dont les elements sont -des pointeurs sur tableau de taille degvar + 1 - -Les coefficients sont donnes du plus petit au plus grand degre -*/ -static void fmpz_bpoly_random_dense(fmpz_poly_t *bivarpol, - slong degmain, - mp_bitcnt_t bits, flint_rand_t state){ - for(slong i = 0; i <= degmain; i++){ - fmpz_poly_random_dense(bivarpol[i], degmain - i, bits, state); - } -} - -/* - -A est un polynome a coefficients dans Z et prime est un nbre premier (qui tient sur un mot-machine) - -a_mod contiendra A mod prime - -*/ -static void make_nmod_poly(nmod_poly_t a_mod, fmpz_poly_t A, mp_limb_t prime){ - a_mod->mod.n = prime; - a_mod->mod.ninv = n_preinvert_limb(prime); - flint_clz(a_mod->mod.norm); - a_mod->length = 0; - for(unsigned long int i=0; ilength; i++){ - nmod_poly_set_coeff_ui(a_mod, i, fmpz_fdiv_ui(A->coeffs+i, prime)); - } -} - -//On calcule A mod prime qu'on met dans a (a est suppose deja alloue) -static void make_nmod_bpoly(nmod_poly_t *a, fmpz_poly_t *A, unsigned long int deg, mp_limb_t prime){ - for(unsigned long int i = 0; i <= deg; i++){ - make_nmod_poly(a[i], A[i], prime); - } -} - - -static void nmod_bpoly_fast_eval_nmod_2_pols(mp_ptr *a_s_ptr, mp_ptr *b_s_ptr, - nmod_poly_t *a, const slong degA, - nmod_poly_t *b, const slong degB, - const mp_ptr eval_points, const ulong n, - mp_ptr * tree){ - nmod_t mod = a[0]->mod; - _nmod_poly_tree_build(tree, eval_points, n, mod); - - for(ulong i = 0; i <= degA; i++){ - _nmod_poly_evaluate_nmod_vec_fast_precomp(a_s_ptr[i], a[i]->coeffs, a[i]->length, tree, n, mod); - } - for(ulong i = 0; i <= degB; i++){ - _nmod_poly_evaluate_nmod_vec_fast_precomp(b_s_ptr[i], b[i]->coeffs, b[i]->length, tree, n, mod); - } - -} - - -static void nmod_bpoly_eval_nmod(nmod_poly_t a_s, - nmod_poly_t *a, const slong degmain, - const mp_limb_t eval_point){ - for(ulong i = 0; i <=degmain; i++){ - a_s->coeffs[i] = nmod_poly_evaluate_nmod(a[i], eval_point); - } - a_s->length = degmain + 1; -} - - -/* -res contiendra le resultat -a et b sont des pointeurs sur tableaux de nmod_poly_t de longueur degmain+1 -(degmain = degre de la variable principale) - -Chaque nmod_poly_t est de degre degvar - -numpoints est le nombre de points d'interpolation dont on a besoin ; il doit etre precalcule - */ -static void nmod_bpoly_resultant(nmod_poly_t res, nmod_poly_t *a, const slong degA, nmod_poly_t *b, - const slong degB, const ulong numpoints, - nmod_poly_t *a_s_ptr, nmod_poly_t *b_s_ptr, - mp_ptr restable, mp_ptr eval_points){ - - ulong count_points = 0, i = 0; - while(count_points < numpoints){ - if(nmod_poly_evaluate_nmod(a[degA], i) != 0){ - eval_points[count_points] = i; - count_points++; - i++; - } - else{ - i++; - } - } - mp_limb_t prime = a[0]->mod.n; - - mp_limb_t ninv = n_preinvert_limb(prime); - - a_s_ptr[0]->mod.n = prime; - a_s_ptr[0]->mod.ninv = ninv; - flint_clz(a_s_ptr[0]->mod.norm); - a_s_ptr[0]->length = 0; - - b_s_ptr[0]->mod.n = prime; - b_s_ptr[0]->mod.ninv = ninv; - flint_clz(b_s_ptr[0]->mod.norm); - b_s_ptr[0]->length = 0; - - // nmod_poly_init2(a_s, prime, degA+1); - // nmod_poly_init2(b_s, prime, degB+1); - // mp_limb_t * restable = (mp_limb_t *)(malloc(sizeof(mp_limb_t)*numpoints)); - // nmod_poly_evaluate_nmod_vec(); - - for(i = 0; i < numpoints; i++){ - nmod_bpoly_eval_nmod(a_s_ptr[0], a, degA, eval_points[i]); - nmod_bpoly_eval_nmod(b_s_ptr[0], b, degB, eval_points[i]); - restable[i] = nmod_poly_resultant(a_s_ptr[0], b_s_ptr[0]); - } - - nmod_poly_interpolate_nmod_vec(res, eval_points, restable, numpoints); -#ifdef DEBUG - char str[1]= {"x"}; - nmod_poly_fprint_pretty(stderr, res, str);fprintf(stderr, "\n"); -#endif - return; -} - - -static inline void get_coeffs_from_eval(nmod_poly_t a_s, mp_ptr *a_s_ptr, ulong deg, slong n){ - for(ulong i=0; i <= deg; i++){ - a_s->coeffs[i] = a_s_ptr[i][n]; - } -} - - - -//calcul du resultant par evaluation interpolation. -//on suppose que le tableau des points d'evaluation ne contient pas que des 0 et est deja alloue -//les donnees necessaires au calcul sont deja allouees egalement. -static void nmod_bpoly_resultant_allocated_feval(data_heap_t *heap, - slong mdegA, slong mdegB, - int pos){ - //a ameliorer - ulong count_points = 0, i = 0; - while(count_points < heap->npts){ - if(nmod_poly_evaluate_nmod(heap->a_mod[mdegA], i) != 0 && nmod_poly_evaluate_nmod(heap->b_mod[mdegB], i) != 0){ - heap->ev_pts[count_points] = i; - count_points++; - i++; - } - else{ - i++; - } - } - - nmod_bpoly_fast_eval_nmod_2_pols(heap->a_mod_eval_all, heap->b_mod_eval_all, - heap->a_mod, mdegA, heap->b_mod, mdegB, - heap->ev_pts, heap->npts, heap->tree); - - for(ulong i = 0; i < heap->npts; i++){ - //On ne peut pas paralleliser a cause de w qui est partage. Il faudra modifier ca. - - get_coeffs_from_eval(heap->a_mod_eval, heap->a_mod_eval_all, mdegA, i); - get_coeffs_from_eval(heap->b_mod_eval, heap->b_mod_eval_all, mdegB, i); - heap->res_mod_eval[i] = _nmod_poly_resultant_euclidean_allocated(heap->a_mod_eval->coeffs, - heap->a_mod_eval->length, - heap->b_mod_eval->coeffs, - heap->b_mod_eval->length, - heap->a_mod_eval->mod, - heap->nmod_coeffs_array); - } - - nmod_poly_interpolate_nmod_vec(heap->res_mod_array[pos], heap->ev_pts, heap->res_mod_eval, heap->npts); - - return; -} - -//Fonction qui renvoie la partie square-free d'un polynome pol - -static void square_free_part_nmod_poly(nmod_poly_t pol, nmod_poly_factor_t sqf){ - - sqf->num = 0; - mp_limb_t lc = pol->coeffs[pol->length-1]; - - nmod_poly_factor_squarefree(sqf, pol); - nmod_poly_set(pol, sqf->p); - - for(ulong count = 1; count < sqf->num; count++){ - nmod_poly_mul(pol, pol, sqf->p+count); - } - - nmod_poly_scalar_mul_nmod(pol, pol, lc); - sqf->num = 0; -} - -static inline void nmod_poly_init_copy(nmod_poly_t *poly1, nmod_poly_t *poly2){ - (*poly1)->length = (*poly2)->length; - (*poly1)->alloc = (*poly2)->alloc; - (*poly1)->coeffs = (*poly2)->coeffs; -} - -static inline void nmod_poly_copy(nmod_poly_t poly1, nmod_poly_t poly2){ - (poly1)->length = (poly2)->length; - for(ulong i = 0; i < (poly1)->length; i++){ - (poly1)->coeffs[i] = (poly2)->coeffs[i]; - } -} - -//calcul d'une param rationnelle par evaluation interpolation. -//on suppose que le tableau des points d'evaluation ne contient pas que des 0 et est deja alloue -//les donnees necessaires au calcul sont deja allouees egalement. -//On renvoie 0 si il y a un probleme -//Notamment, on suppose que le resultant est square-free. -//Du coup, une seule parametrisation est construite dans nmod_all_params_table+pos -static int nmod_bpoly_param_allocated_feval_sqfree(data_heap_t *heap, - slong mdegA, slong mdegB, - int pos){ - - ulong count_points = 0, i = 0; - while(count_points < heap->npts){ - if(nmod_poly_evaluate_nmod(heap->a_mod[mdegA], i) != 0 && - nmod_poly_evaluate_nmod(heap->b_mod[mdegB], i) != 0){ - heap->ev_pts[count_points] = i; - count_points++; - i++; - } - else{ - i++; - } - } - - nmod_bpoly_fast_eval_nmod_2_pols(heap->a_mod_eval_all, - heap->b_mod_eval_all, - heap->a_mod, mdegA, - heap->b_mod, mdegB, - heap->ev_pts, - heap->npts, heap->tree); - for(ulong i = 0; i < heap->npts; i++){ - //On ne peut pas paralleliser a cause de w qui est partage. Il faudra modifier ca. - - get_coeffs_from_eval(heap->a_mod_eval, heap->a_mod_eval_all, mdegA, i); - get_coeffs_from_eval(heap->b_mod_eval, heap->b_mod_eval_all, mdegB, i); - - if(DEBUG > 3){ - fprintf(stderr, "ev_pt = %ld\n", heap->ev_pts[i]); - char str[1] = {"x"}; - nmod_poly_fprint_pretty(stderr, heap->a_mod_eval, str); - fprintf(stderr, "\n"); - nmod_poly_fprint_pretty(stderr, heap->b_mod_eval, str); - fprintf(stderr, "\n"); - } - heap->res_mod_eval[i] = - _nmod_poly_param_euclidean_allocated(heap->a_mod_eval->coeffs, - heap->a_mod_eval->length, - heap->b_mod_eval->coeffs, - heap->b_mod_eval->length, - heap->a_mod_eval->mod, - heap->nmod_coeffs_array, - heap->par_h_mod_eval + i, - heap->par_t_mod_eval + i); - if(DEBUG > 3){ - fprintf(stderr, "Computed resultant = %ld\n", - heap->res_mod_eval[i]); - fprintf(stderr, "head -> %ld\n", - heap->par_h_mod_eval[i]); - fprintf(stderr, "tail -> %ld\n", - heap->par_t_mod_eval[i]); - } - } - - nmod_poly_interpolate_nmod_vec(heap->nmod_lparams_array[pos]->params[0]->elim, - heap->ev_pts, heap->res_mod_eval, heap->npts); - - nmod_poly_interpolate_nmod_vec(heap->nmod_lparams_array[pos]->params[0]->denom, - heap->ev_pts, heap->par_h_mod_eval, heap->npts); - - nmod_poly_interpolate_nmod_vec(heap->nmod_lparams_array[pos]->params[0]->coords[0], - heap->ev_pts, heap->par_t_mod_eval, heap->npts); - //On suppose que le resultant est square-free. - - if(DEBUG > 3){ - for(ulong k = 0; k < heap->npts; k++){ - fprintf(stderr, "%lu ", heap->par_t_mod_eval[k]); - } - fprintf(stderr, "\n"); - for(ulong k = 0; k < heap->npts; k++){ - fprintf(stderr, "%lu ", heap->ev_pts[k]); - } - fprintf(stderr, "\n"); - char str[1] = {"x"}; - fprintf(stderr, "degree = %ld\n", heap->par_t_mod_array[pos]->length - 1); - nmod_poly_fprint_pretty(stderr, heap->par_t_mod_array[pos], str); - fprintf(stderr,"\n"); - fprintf(stderr, "degree = %ld\n", heap->par_h_mod_array[pos]->length - 1); - nmod_poly_fprint_pretty(stderr, heap->par_h_mod_array[pos], str); - fprintf(stderr,"\n\n"); - nmod_poly_fprint_pretty(stderr, heap->nmod_lparams_array[pos]->params[0]->coords[0], str); - fprintf(stderr,"\n"); - } - - if(DEBUG > 4){ - fprintf(stderr, "\nParametrization mod %ld\n", heap->primes_array[pos]); - print_nmod_param(stderr, heap->nmod_lparams_array[pos]->params[0]); - fprintf(stderr, "prime in param struct = \n%ld, \n%ld\n", - heap->nmod_lparams_array[pos]->params[0]->denom->mod.n, - heap->nmod_lparams_array[pos]->params[0]->coords[0]->mod.n); - } - - return 1; -} - - -//calcul d'une param rationnelle par evaluation interpolation. -//on suppose que le tableau des points d'evaluation ne contient pas que des 0 et est deja alloue -//les donnees necessaires au calcul sont deja allouees egalement. -//On renvoie 0 si il y a un probleme -//Ici, on suppose que le resultant n'est pas square-free. - -static int nmod_bpoly_param_allocated_feval_nonsqfree(data_heap_t *heap, - slong mdegA, slong mdegB, - int pos){ - - ulong count_points = 0, i = 0; - while(count_points < heap->npts){ - if(nmod_poly_evaluate_nmod(heap->a_mod[mdegA], i) != 0 && - nmod_poly_evaluate_nmod(heap->b_mod[mdegB], i) != 0){ - heap->ev_pts[count_points] = i; - count_points++; - i++; - } - else{ - i++; - } - } - - nmod_bpoly_fast_eval_nmod_2_pols(heap->a_mod_eval_all, heap->b_mod_eval_all, - heap->a_mod, mdegA, heap->b_mod, mdegB, - heap->ev_pts, heap->npts, heap->tree); - for(ulong i = 0; i < heap->npts; i++){ - //On ne peut pas paralleliser a cause de w qui est partage. Il faudra modifier ca. - - get_coeffs_from_eval(heap->a_mod_eval, heap->a_mod_eval_all, mdegA, i); - get_coeffs_from_eval(heap->b_mod_eval, heap->b_mod_eval_all, mdegB, i); - - heap->res_mod_eval[i] = - _nmod_poly_param_euclidean_allocated(heap->a_mod_eval->coeffs, - heap->a_mod_eval->length, - heap->b_mod_eval->coeffs, - heap->b_mod_eval->length, - heap->a_mod_eval->mod, - heap->nmod_coeffs_array, - heap->par_h_mod_eval + i, - heap->par_t_mod_eval + i); - - } - - nmod_poly_interpolate_nmod_vec(heap->res_mod_array[pos], heap->ev_pts, heap->res_mod_eval, heap->npts); - nmod_poly_interpolate_nmod_vec(heap->par_h_mod_array[pos], - heap->ev_pts, heap->par_h_mod_eval, heap->npts); - nmod_poly_interpolate_nmod_vec(heap->par_t_mod_array[pos], - heap->ev_pts, heap->par_t_mod_eval, heap->npts); - - heap->sqf_part->num = 0; - nmod_poly_factor_squarefree(heap->sqf_part, heap->res_mod_array[pos]); - - for(ulong i = 0; i < heap->sqf_part->num; i++){ - nmod_poly_copy(heap->nmod_lparams_array[pos]->params[i]->elim, - heap->sqf_part->p+i); - - if(nmod_poly_invmod(heap->GCDINV[pos], - heap->par_h_mod_array[pos], - heap->nmod_lparams_array[pos]->params[i]->elim)){ - - nmod_poly_derivative(heap->nmod_lparams_array[pos]->params[i]->denom, - heap->nmod_lparams_array[pos]->params[i]->elim); - - nmod_poly_mul(heap->nmod_lparams_array[pos]->params[i]->coords[0], - heap->par_t_mod_array[pos], - heap->GCDINV[pos]); - - nmod_poly_rem(heap->nmod_lparams_array[pos]->params[i]->coords[0], - heap->nmod_lparams_array[pos]->params[i]->coords[0], - heap->nmod_lparams_array[pos]->params[i]->elim); - nmod_poly_mul(heap->nmod_lparams_array[pos]->params[i]->coords[0], - heap->nmod_lparams_array[pos]->params[i]->coords[0], - heap->nmod_lparams_array[pos]->params[i]->denom - ); - - nmod_poly_rem(heap->nmod_lparams_array[pos]->params[i]->coords[0], - heap->nmod_lparams_array[pos]->params[i]->coords[0], - heap->nmod_lparams_array[pos]->params[i]->elim); - } - else{ - fprintf(stderr, "Pas d'inversion possible\n"); - return 0; - } - } - - if(DEBUG>2){ - fprintf(stderr, "Prime = %ld\n", heap->primes_array[pos]); - print_nmod_all_params_pretty(stderr, heap->nmod_lparams_array[pos]); - } - - return 1; -} - -static void fmpz_bpoly_resultant_deterministic(fmpz_poly_t res, - fmpz_poly_t *A, slong degA, - fmpz_poly_t *B, slong degB){ - slong totaldegA = get_total_degree(A, degA); - slong totaldegB = get_total_degree(B, degB); - - fprintf(stderr, "Total degrees : %ld %ld\n", totaldegA, totaldegB); - //maximum degree in the variable that is not eliminated - slong degAx = get_partial_degree(A, degA); - slong degBx = get_partial_degree(B, degB); - - ulong numpoints = MIN(totaldegA * totaldegB + 1, degB * degAx + degA * degBx + 1); - ulong nbitsA = nbits_bound_fmpz_bvar_poly(A, degA); - ulong nbitsB = nbits_bound_fmpz_bvar_poly(B, degB); - fprintf(stderr, "Max nbits : %lu %lu\n", nbitsA, nbitsB); - ulong i; - - //Hadamard-type bound (Goldstein-Graham) - ulong bound_nbits = nbitsA*(degB) + nbitsB*(degA); - fprintf(stderr, "Bound (nbits) = %lu\n", bound_nbits); - - mp_limb_t prime = 1073741827; - prime = n_nextprime(1152921504606847009, 0); - // prime = n_nextprime(prime, 0); - ulong nbits_prime = LOG2(prime); - - nmod_poly_t *a = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * (degA + 1))); - nmod_poly_t *b = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * (degB + 1))); - - for(i = 0; i <= degA; i++){ - nmod_poly_init(a[i], prime); - make_nmod_poly(a[i], A[i], prime); - } - for(i = 0; i <= degB; i++){ - nmod_poly_init(b[i], prime); - make_nmod_poly(b[i], B[i], prime); - } - - //data for calling nmod_bpoly_resultant - //a_s_ptr contiendra la specialisation des coefficients de a en un point. - nmod_poly_t *a_s_ptr = malloc(sizeof(nmod_poly_t)); - nmod_poly_init2(a_s_ptr[0], prime, degA+1); - - nmod_poly_t *b_s_ptr = malloc(sizeof(nmod_poly_t)); - nmod_poly_init2(b_s_ptr[0], prime, degB+1); - - //contiendra les valeurs des resultants modulo des premiers - mp_limb_t * restable = (mp_limb_t *)(malloc(sizeof(mp_limb_t)*numpoints)); - //contiendra les points d'evaluation - mp_limb_t * eval_points = (mp_limb_t *)(malloc(sizeof(mp_limb_t)*numpoints)); - ////////////////////////////////// - - ulong count_nprimes = 1; - - nmod_poly_t *res_mod_table = (nmod_poly_t *)(malloc(sizeof(nmod_poly_t) * (bound_nbits / nbits_prime + 1) )); - mp_limb_t *primes_table = (mp_limb_t *)(malloc(sizeof(mp_limb_t) * (bound_nbits / nbits_prime + 1))); - double e = omp_get_wtime(); - nbits_prime = 0; - - fmpz_t *prod_mod = malloc(sizeof(fmpz_t)); - fmpz_init(prod_mod[0]); - while(nbits_prime < bound_nbits){ - for(i = 0; i <= degA; i++){ - make_nmod_poly(a[i], A[i], prime); - } - for(i = 0; i <= degB; i++){ - make_nmod_poly(b[i], B[i], prime); - } - if(a[degA]->length>0 && b[degB]->length>0){ - nmod_poly_init(res_mod_table[count_nprimes-1], prime); - primes_table[count_nprimes-1] = prime; - nmod_bpoly_resultant(res_mod_table[count_nprimes-1], a, degA, b, degB, numpoints, - a_s_ptr, b_s_ptr, restable, eval_points); - prime = n_nextprime(prime, 0); - nbits_prime += LOG2(prime); - count_nprimes++; - } - else{ - prime = n_nextprime(prime, 0); - } - } - count_nprimes--; - fprintf(stderr, "Number of used primes = %lu\n", count_nprimes); - fprintf(stderr, "Elapsed time (mod comp.): %f\n", omp_get_wtime() - e); - - e=omp_get_wtime(); - crt_lift_resultant(res, res_mod_table, primes_table, count_nprimes, prod_mod); - fprintf(stderr, "Elapsed time (CRT comp.): %f\n", omp_get_wtime() - e); - fprintf(stderr, "Final size coeffs: %ld\n", FLINT_ABS(_fmpz_vec_max_bits(res->coeffs, res->length))); - fprintf(stderr, "Degree of the output: %ld\n", res->length-1); - - fmpz_clear(prod_mod[0]); - free(prod_mod); - nmod_poly_clear(a_s_ptr[0]); - nmod_poly_clear(b_s_ptr[0]); - free(a_s_ptr); - free(b_s_ptr); - free(eval_points); - - for(i = 0; i< count_nprimes; i++){ - nmod_poly_clear(res_mod_table[i]); - } - for(i = 0; i <= degA; i++){ - nmod_poly_clear(a[i]); - } - for(i = 0; i <= degB; i++){ - nmod_poly_clear(b[i]); - } - free(res_mod_table); - free(restable); - free(primes_table); - free(a); - free(b); - return; -} - -/* - Input: dans res_mod_table on a N = size_table images modulaires de resultant - (modulo les premiers de primes_table). - - On vĂ©rifie que res modulo ces premiers correspond aux elements de res_mod_table -*/ -/* static int check_modular_images_old(fmpz_poly_t res, nmod_poly_t res_mod, nmod_poly_t *res_mod_table, */ -/* mp_limb_t *primes_table, int size_table, slong *max_degree){ */ -/* for(int i = 0; i < size_table; i++){ */ -/* if(*max_degree < res_mod_table[i]->length - 1){ */ -/* *max_degree = res_mod_table[i]->length - 1; */ -/* } */ -/* } */ -/* for(int i = 0; i < size_table; i++){ */ -/* make_nmod_poly(res_mod, res, primes_table[i]); */ -/* if(!nmod_poly_equal(res_mod, res_mod_table[i])){ */ -/* return 0; */ -/* } */ -/* } */ -/* return 1; */ -/* } */ - -/* - Input: dans res_mod_table on a N = size_table images modulaires de resultant - (modulo les premiers de primes_table). - - On vĂ©rifie que res modulo ces premiers correspond aux elements de res_mod_table -*/ -static int check_modular_images(fmpz_poly_t res, - data_heap_t *heap, - int size_table, slong *max_degree){ - for(int i = 0; i < size_table; i++){ - if(*max_degree < heap->res_mod_array[i]->length - 1){ - *max_degree = heap->res_mod_array[i]->length - 1; - } - } - for(int i = 0; i < size_table; i++){ - make_nmod_poly(heap->res_mod[0], res, heap->primes_array[i]); - if(!nmod_poly_equal(heap->res_mod[0], heap->res_mod_array[i])){ - return 0; - } - } - return 1; -} - - -static void update_poly_tables_with_prime(data_heap_t *heap, - int pos, mp_limb_t prime){ - mp_limb_t p = n_preinvert_limb(prime); - heap->primes_array[pos] = prime; - - heap->GCDINV[pos]->mod.n = prime; - heap->GCDINV[pos]->mod.ninv = p; - flint_clz(heap->GCDINV[pos]->mod.norm); - - heap->res_mod_array[pos]->mod.n = prime; - heap->res_mod_array[pos]->mod.ninv = p; - flint_clz(heap->res_mod_array[pos]->mod.norm); - - heap->par_t_mod_array[pos]->mod.n = prime; - heap->par_t_mod_array[pos]->mod.ninv = p; - flint_clz(heap->par_t_mod_array[pos]->mod.norm); - - heap->par_h_mod_array[pos]->mod.n = prime; - heap->par_h_mod_array[pos]->mod.ninv = p; - flint_clz(heap->par_h_mod_array[pos]->mod.norm); - - heap->a_mod_eval->mod.n = prime; - heap->a_mod_eval->mod.ninv = p; - flint_clz(heap->a_mod_eval->mod.norm); - - heap->b_mod_eval->mod.n = prime; - heap->b_mod_eval->mod.ninv = p; - flint_clz(heap->b_mod_eval->mod.norm); - -} - -static void update_nmod_param_with_prime(nmod_all_params_t *lparams, - mp_limb_t prime){ - mp_limb_t p = n_preinvert_limb(prime); - - for(int i = 0; i nparams; i++){ - nmod_param_t *param = lparams->params[i]; - param->denom->mod.n = prime; - param->denom->mod.ninv = p; - flint_clz(param->denom->mod.norm); - - param->elim->mod.n = prime; - param->elim->mod.ninv = p; - flint_clz(param->elim->mod.norm); - - for(int j = 0; j < param->nvars; j++){ - param->coords[j]->mod.n = prime; - param->coords[j]->mod.ninv = p; - flint_clz(param->coords[j]->mod.norm); - } - } -} - - -//Fonction qui teste si pol est square-free -//renvoie 0 si pol est square-free, un entier >= 1 sinon -static slong is_non_square_free(nmod_poly_t pol, nmod_poly_factor_t sqf){ - nmod_poly_factor_squarefree(sqf, pol); - int nf = sqf->num ; - sqf->num = 0; - return nf - 1; -} - - -static void get_degrees_and_nbits(fmpz_poly_t *A, slong mdegA, - fmpz_poly_t *B, slong mdegB, - slong *tdegA, slong *tdegB, - slong *sdegA, slong *sdegB, - ulong *nbitsA, ulong *nbitsB){ - //total degrees - *tdegA = get_total_degree(A, mdegA); - *tdegB = get_total_degree(B, mdegB); - - //maximum degree in the variable that is not eliminated - *sdegA = get_partial_degree(A, mdegA); - *sdegB = get_partial_degree(B, mdegB); - - *nbitsA = nbits_bound_fmpz_bvar_poly(A, mdegA); - *nbitsB = nbits_bound_fmpz_bvar_poly(B, mdegB); -} - -//renvoie 0 si on a encore besoin de lifter les coefficients -static inline int check_param_modular_images(fmpz_param_t *param, - data_heap_t *heap, int size){ - for(ulong i = 0; i < size; i++){ - //on verifie le polynome eliminant - make_nmod_poly(heap->res_mod[0], param->elim, heap->primes_array[i]); - if(!nmod_poly_equal(heap->res_mod[0], - heap->nmod_lparams_array[i]->params[0]->elim)){ - return 0; - } - make_nmod_poly(heap->res_mod[0], param->denom, heap->primes_array[i]); - //on verifie le polynome denominateur - if(!nmod_poly_equal(heap->res_mod[0], - heap->nmod_lparams_array[i]->params[0]->denom)){ - return 0; - } - //on verifie les coordonnees - make_nmod_poly(heap->res_mod[0], param->coords[0], heap->primes_array[i]); - if(!nmod_poly_equal(heap->res_mod[0], - heap->nmod_lparams_array[i]->params[0]->coords[0])){ - return 0; - } - } - return 1; -} - - -//renvoie 0 si on a encore besoin de lifter les coefficients -static inline int check_all_params_modular_image(fmpz_all_params_t *all_params, - data_heap_t *heap, int size){ - int nparams = all_params->nparams; - for(int i = 0; i < nparams; i++){ - if(!check_param_modular_images(all_params->params[i], heap, size)){ - return 0; - } - } - return 1; -} - -static inline void integer_param_crt_lifting_all_params(fmpz_all_params_t *all_params, - data_heap_t *heap, int size){ - slong maxdegree = -1; - fmpz_param_t *param = all_params->params[0]; - for(ulong i = 0; i < size; i++){ - if(heap->nmod_lparams_array[0]->params[0]->elim->length - 1 > maxdegree){ - maxdegree = heap->nmod_lparams_array[0]->params[0]->elim->length - 1; - } - } - if((param)->elim->length-1!=maxdegree){ - fprintf(stderr, "Error with degree estimates in integer_param_crt_lifting\n"); - fprintf(stderr, "maxdegree = %ld\n", maxdegree); - fprintf(stderr, "First param of degree = %ld\n", (param)->elim->length-1); - exit(1); - } - - if(DEBUG>=5){ - for(int i = 0; i < size; i++){ - fprintf(stderr, "prime = %ld\n", heap->primes_array[i]); - print_nmod_param(stderr, (heap->nmod_lparams_array[i]->params[0])); - fprintf(stderr, "\n"); - } - } - - for(ulong j = 0; j <= maxdegree; j++){ - for(ulong i = 0; i < size; i++){ - - fmpz_CRT_ui(((param)->elim->coeffs)+j, ((param)->elim->coeffs)+j, - heap->prod_primes[i], - (heap->nmod_lparams_array[i]->params[0]->elim->coeffs)[j], - heap->primes_array[i], 1); - - fmpz_CRT_ui(((param)->denom->coeffs)+j, ((param)->denom->coeffs)+j, - heap->prod_primes[i], - (heap->nmod_lparams_array[i]->params[0]->denom->coeffs)[j], - heap->primes_array[i], 1); - - fmpz_CRT_ui(((param)->coords[0]->coeffs)+j, ((param)->coords[0]->coeffs)+j, - heap->prod_primes[i], - (heap->nmod_lparams_array[i]->params[0]->coords[0]->coeffs)[j], - heap->primes_array[i], 1); - - } - } - -} - -static inline int rational_param_lifting(fmpz_param_t *param, - data_heap_t *heap, - int size, int mul){ - int b = 1; - - ulong deg = heap->nmod_lparams_array[0]->params[mul]->elim->length - 1; - if(param->rec_elim < deg){ - for(ulong j = 0; j <= deg; j++){ - for(ulong i = 0; i < size; i++){ - fmpz_CRT_ui(((param)->elim->coeffs)+j, ((param)->elim->coeffs)+j, - heap->prod_primes[i], - (heap->nmod_lparams_array[i]->params[mul]->elim->coeffs)[j], - heap->primes_array[i], 1); - } - } - fprintf(stderr, "Lifting the elimination polynomial\n"); - if(rat_recon(param->elim, param->elim_num, param->elim_den, param->elim_lcm, - heap, deg, &(param->rec_elim)) == 0){ - b = 0; - } - } - - deg = (heap->nmod_lparams_array[0]->params[mul]->coords[0]->length) - 1; - if(param->rec_coords[0] < deg){ - for(ulong j = 0; j <= deg; j++){ - for(ulong i = 0; i < size; i++){ - fmpz_CRT_ui(((param)->coords[0]->coeffs)+j, ((param)->coords[0]->coeffs)+j, - heap->prod_primes[i], - (heap->nmod_lparams_array[i]->params[mul]->coords[0]->coeffs)[j], - heap->primes_array[i], 1); - } - } - if(b==0){ - return b; - } - fprintf(stderr, "Lifting of the parametrization\n"); - if(rat_recon(param->coords[0], param->coords_num[0], param->coords_den[0], - param->coords_lcm[0], - heap, deg, param->rec_coords) == 0){ - b = 0; - } - } - fprintf(stderr, "LCM = "); - fmpz_fprint(stderr, param->coords_lcm[0]); - fprintf(stderr, "\n"); - - return b; -} - -//attention : ici le denominateur sera de tout de maniere la derivee du polynome -//eliminant -static inline int rational_param_lifting_all_params(fmpz_all_params_t *all_params, - data_heap_t *heap, int size){ - int b = 1; - for(ulong i = 0; i < all_params->nparams; i++){ - fmpz_param_t *param = all_params->params[i]; - if(param->recons == 0){ - if(rational_param_lifting(param, heap, size, i)==0){ - b = 0; - } - else{ - param->recons = 1; - } - } - } - return b; -} - - -static inline void copy_coeffs_poly(fmpz_poly_t poly1, fmpz_poly_t poly2){ - - for(ulong i = 0; i < poly2->length; i++){ - fmpz_poly_set_coeff_fmpz(poly1, i, poly2->coeffs + i); - } -} - -static inline bsolve_fmpz_param_t *copy_to_final_parametrization(fmpz_param_t *param){ - bsolve_fmpz_param_t *bs_param = malloc(sizeof(bsolve_fmpz_param_t)); - bs_param->nvars = param->nvars; - bs_param->sepelem = malloc(sizeof(mp_limb_t) * 2); - bs_param->cfs = malloc(sizeof(fmpz_t) * param->nvars); - - for(int i = 0; i < 2; i++){ - bs_param->sepelem[i] = param->sepelem[i]; - } - fmpz_poly_init2(bs_param->elim, param->elim_num->length); - - copy_coeffs_poly(bs_param->elim, param->elim_num); - - bs_param->coords = malloc(sizeof(fmpz_poly_t) * param->nvars); - - for(int i = 0; i < param->nvars; i++){ - fmpz_poly_init2(bs_param->coords[i], param->coords_num[i]->length); - copy_coeffs_poly(bs_param->coords[i], param->coords_num[i]); - fmpz_init(bs_param->cfs[i]); - fmpz_set(bs_param->cfs[i], param->coords_lcm[i]); - fprintf(stderr, "Warning: changing cfs\n"); - fmpz_set_ui(bs_param->cfs[i], 1); - } - fmpz_poly_init2(bs_param->denom, param->elim_num->length - 1); - - for(ulong i = 0; i < param->elim_num->length - 1; i++){ - fmpz_poly_set_coeff_ui(bs_param->denom, i, 1); - fmpz_mul_ui(bs_param->denom->coeffs + i, bs_param->elim->coeffs + (i+1), i+1); - } - return bs_param; -} - -static inline void copy_to_final_all_params(bsolve_fmpz_all_params_t *bs_params, - fmpz_all_params_t *params){ - bs_params->nparams = params->nparams; - fprintf(stderr, "Number of parametrizations = %d\n", params->nparams); - bs_params->params = malloc(sizeof(bsolve_fmpz_param_t *) * params->nparams); - for(int i = 0; i < params->nparams; i++){ - bs_params->params[i] = copy_to_final_parametrization(params->params[i]); - } -} - -//retourne 1 si il y a une param. rat. des solutions -//sinon retourne 0 - -/* output parametrization will be stored in bs_param */ -static int _fmpz_bpoly_param_probabilistic(bsolve_fmpz_all_params_t *bs_param, - fmpz_poly_t *A, slong mdegA, - fmpz_poly_t *B, slong mdegB){ - slong tdegA, tdegB, sdegA, sdegB; - ulong nbitsA, nbitsB; - int size_table = 8; - /* - tdegA and degB will be the total degrees of A and B - - sdegA and sdegB will be the partial degrees of A and B - in the variable that is kept. - - nbitsA and nbitsB are the max bit size coeffs of A and B - */ - get_degrees_and_nbits(A, mdegA, - B, mdegB, - &tdegA, &tdegB, - &sdegA, &sdegB, - &nbitsA, &nbitsB); - - data_heap_t *heap = allocate_data_heap(tdegA, tdegB, - mdegA, mdegB, - sdegA, sdegB, - size_table); - - fprintf(stderr, "Total degrees : %ld %ld\n", tdegA, tdegB); - fprintf(stderr, "Main degrees : %ld %ld\n", mdegA, mdegB); - fprintf(stderr, "Bit sizes : %lu %lu\n", nbitsA, nbitsB); - fprintf(stderr, "numpoints = %lu\n", heap->npts); - - /*Hadamard-type (Goldstein-Graham) to obtain a bound on the - bit size of the resultant - */ - ulong bound_nbits = nbitsA*(mdegB) + nbitsB*(mdegA); - - fprintf(stderr, "Bound (nbits) = %lu\n", bound_nbits); - - mp_limb_t prime = 1073741827; - prime = n_nextprime(1152921504606847009, 0); - ulong nbits_prime = LOG2(prime); - - ulong count_nprimes = 1; - - double e = omp_get_wtime(); - nbits_prime = 0; - - - double e_mod = 0; - - //On teste si le resultant est square-free - make_nmod_bpoly(heap->a_mod, A, mdegA, prime); - make_nmod_bpoly(heap->b_mod, B, mdegB, prime); - - update_poly_tables_with_prime(heap, 0, prime); - nmod_bpoly_param_allocated_feval_sqfree(heap, - mdegA, mdegB, 0); - - fprintf(stderr, "Degree of the resultant is %ld\n", heap->nmod_lparams_array[0]->params[0]->elim->length - 1); - - /* resultant is a non-zero constant -> no solution */ - if(heap->nmod_lparams_array[0]->params[0]->elim->length == 1){ -#if(DEBUG > 3) - char str[1] = {"x"}; - fprintf(stderr, "elim = "); - nmod_poly_fprint_pretty(stderr, - heap->nmod_lparams_array[0]->params[0]->elim, - str); - fprintf(stderr, "\n"); - fprintf(stderr, "denom = "); - nmod_poly_fprint_pretty(stderr, - heap->nmod_lparams_array[0]->params[0]->denom, - str); - fprintf(stderr, "\n"); -#endif - bs_param->nparams = 1; - bs_param->params = malloc(sizeof(bsolve_fmpz_param_t *)); - bs_param->params[0] = malloc(sizeof(bsolve_fmpz_param_t)); - bs_param->params[0]->nvars = 1; - - bs_param->params[0]->sepelem = malloc(sizeof(mp_limb_t) * 2); - bs_param->params[0]->sepelem[0] = 0; - bs_param->params[0]->sepelem[1] = 1; - - bs_param->params[0]->coords = malloc(sizeof(fmpz_poly_t) ); - - fmpz_poly_init2(bs_param->params[0]->elim, 1); - fmpz_poly_set_ui(bs_param->params[0]->elim, 1); - fmpz_poly_init2(bs_param->params[0]->coords[0], 1); - fmpz_poly_set_ui(bs_param->params[0]->coords[0], 0); - return 1; - } - if(DEBUG>3){ - char str[1] = {"x"}; - nmod_poly_fprint_pretty(stderr, *heap->res_mod_array, str); - fprintf(stderr, "\n"); - fprintf(stderr, "RESULTANT = "); - nmod_poly_fprint_pretty(stderr, heap->nmod_lparams_array[0]->params[0]->elim, str); - fprintf(stderr, "\n"); - } - - heap->sqf_part->num = 0; - nmod_poly_factor_squarefree(heap->sqf_part, heap->nmod_lparams_array[0]->params[0]->elim); - - int nb_sqfree = heap->sqf_part->num; - int is_sqf = 0; - if(nb_sqfree==1 && (heap->sqf_part->p)->length == heap->nmod_lparams_array[0]->params[0]->elim->length) - { - fprintf(stderr, "Resultant is square-free\n"); - is_sqf = 1; - } - else{ - fprintf(stderr, "Resultant is not square-free\n"); - fprintf(stderr, "Array of degree/multiplicity is ["); - for(int i = 0; i < nb_sqfree-1; i++){ - fprintf(stderr, "[%lu, %lu], ", (heap->sqf_part->p+i)->length - 1, (heap->sqf_part->exp[i])); - } - fprintf(stderr, "[%lu, %lu]]\n", (heap->sqf_part->p+(nb_sqfree-1))->length - 1, (heap->sqf_part->exp[nb_sqfree-1])); - } - - if(nmod_poly_invmod(heap->GCDINV[0], - heap->nmod_lparams_array[0]->params[0]->denom, - heap->nmod_lparams_array[0]->params[0]->elim) - == 0){ - - fprintf(stderr, "The input system is not in generic position\n"); - - return 0; - } - mp_ptr sepelem = malloc(sizeof(mp_limb_t) * 2); - sepelem[0]=0; - sepelem[1]=1; - - for(int i = 0; i < size_table; i++){ - heap->nmod_lparams_array[i] = allocate_degrees_sepelem_nmod_all_params(heap, sepelem, - nb_sqfree, 1, - prime); - } - - fmpz_all_params_t *param = malloc(sizeof(fmpz_all_params_t)); - allocate_degrees_sepelem_fmpz_all_params(param, heap, sepelem, - nb_sqfree, 1); - fprintf(stderr, "Allocation done\n"); - fprintf(stderr, "First param of degree = %ld\n", param->params[0]->elim->length-1); - - prime = n_nextprime(prime, 0); - int boo = 1; - while(boo){ - int pos = 0; - - while(pos < size_table){ - - make_nmod_bpoly(heap->a_mod, A, mdegA, prime); - make_nmod_bpoly(heap->b_mod, B, mdegB, prime); - - if(heap->a_mod[mdegA]->length>0 && heap->b_mod[mdegB]->length>0){ - - double start_mod = omp_get_wtime(); - update_poly_tables_with_prime(heap, pos, prime); - //Ici on met a jour nmod_all_primes_table avec prime - update_nmod_param_with_prime(heap->nmod_lparams_array[pos], prime); - - if(is_sqf==1){ - nmod_bpoly_param_allocated_feval_sqfree(heap, - mdegA, mdegB, pos); - } - else{ - if(nmod_bpoly_param_allocated_feval_nonsqfree(heap, - mdegA, mdegB, pos)==0){ - return 0; - } - } - -#if(DEBUG>2) - char str[1] = {"x"}; - fprintf(stderr, "prime = %ld\n", prime); - fprintf(stderr, "RESULTANT = "); - nmod_poly_fprint_pretty(stderr, heap->nmod_lparams_array[pos]->params[0]->elim, str); - fprintf(stderr, "\n"); -#endif - e_mod += (omp_get_wtime() - start_mod); - pos++; - fmpz_mul_ui(heap->prod_primes[pos], heap->prod_primes[pos - 1], prime); - - nbits_prime += LOG2(prime); - prime = n_nextprime(prime, 0); - count_nprimes++; - } - else{ - prime = n_nextprime(prime, 0); - } - } - - if(nb_sqfree==1){ - if(check_all_params_modular_image(param, heap, size_table) == 0){ - //Il faut continuer la construction - integer_param_crt_lifting_all_params(param, heap, - size_table); - fmpz_set(heap->prod_primes[0], heap->prod_primes[size_table]); - if(DEBUG>1){ - if(check_all_params_modular_image(param, heap, size_table)==0){ - fprintf(stderr, "Error in lifting\n"); - exit(1); - } - } - } - else{ - boo = 0; - } - } - else{ - if(rational_param_lifting_all_params(param, heap, size_table) == 0){ - fmpz_set(heap->prod_primes[0], heap->prod_primes[size_table]); - } - else{ - boo = 0; - } - } - } - copy_to_final_all_params(bs_param, param); - count_nprimes--; - fprintf(stderr, "Number of used primes = %lu\n", count_nprimes); - fprintf(stderr, "Elapsed time (modp): %f\n", e_mod); - fprintf(stderr, "Elapsed time (total): %f\n", omp_get_wtime() - e); - - free(sepelem); -// free_fmpz_all_params(all_params); - free_data_heap(mdegA, mdegB, size_table, heap); - - return 1; -} - -static int fmpz_bpoly_param(bsolve_fmpz_all_params_t *bs_param, - fmpz_poly_t *A, slong mdegA, - fmpz_poly_t *B, slong mdegB){ - if(mdegA < mdegB){ - return _fmpz_bpoly_param_probabilistic(bs_param, - B, mdegB, - A, mdegA); - } - else{ - return _fmpz_bpoly_param_probabilistic(bs_param, - A, mdegA, - B, mdegB); - } -} - - - -static void _fmpz_bpoly_resultant_probabilistic(fmpz_poly_t res, - fmpz_poly_t *A, slong mdegA, - fmpz_poly_t *B, slong mdegB){ - slong tdegA, tdegB, sdegA, sdegB; - ulong nbitsA, nbitsB; - int size_table = 4; - fprintf(stderr, "ici on est la\n"); - get_degrees_and_nbits(A, mdegA, - B, mdegB, - &tdegA, &tdegB, - &sdegA, &sdegB, - &nbitsA, &nbitsB); - fprintf(stderr, "allocation starts\n"); - data_heap_t *heap = allocate_data_heap(tdegA, tdegB, - mdegA, mdegB, - sdegA, sdegB, - size_table); - fprintf(stderr, "allocation done\n"); - - fprintf(stderr, "Total degrees : %ld %ld\n", tdegA, tdegB); - fprintf(stderr, "numpoints = %lu\n", heap->npts); - - //Hadamard-type (Goldstein-Graham) - ulong bound_nbits = nbitsA*(mdegB) + nbitsB*(mdegA); - - fprintf(stderr, "Bound (nbits) = %lu\n", bound_nbits); - - mp_limb_t prime = 1073741827; - prime = n_nextprime(1152921504606847009, 0); - // prime = 4611686018427388039; // prime = n_nextprime(prime, 0); - ulong nbits_prime = LOG2(prime); - - ulong count_nprimes = 1; - - //max degree reached during multi-mod computation - slong maxdegree = -1; - - - double e = omp_get_wtime(); - nbits_prime = 0; - - fmpz_t coeff; - fmpz_init(coeff); - - double e_mod = 0; - - //On teste si le resultant est square-free - make_nmod_bpoly(heap->a_mod, A, mdegA, prime); - make_nmod_bpoly(heap->b_mod, B, mdegB, prime); - - update_poly_tables_with_prime(heap, 0, prime); - nmod_bpoly_resultant_allocated_feval(heap, mdegA, mdegB, 0); - - fprintf(stderr, "prime = %lu\n", prime); - fprintf(stderr, "Degree of the resultant is %ld\n", heap->res_mod_array[0]->length - 1); - prime = n_nextprime(prime, 0); - double e_res = 0; - int boo = 1; - while(nbits_prime < bound_nbits && boo){ - int pos = 0; - - while(pos < size_table){ - make_nmod_bpoly(heap->a_mod, A, mdegA, prime); - make_nmod_bpoly(heap->b_mod, B, mdegB, prime); - - if(heap->a_mod[mdegA]->length>0 && heap->b_mod[mdegB]->length>0){ - - double start_mod = omp_get_wtime(); - update_poly_tables_with_prime(heap, pos, prime); - double t = omp_get_wtime(); - nmod_bpoly_resultant_allocated_feval(heap, mdegA, mdegB, pos); - e_res += (omp_get_wtime() - t); - e_mod += (omp_get_wtime() - start_mod); - pos++; - fmpz_mul_ui(heap->prod_primes[pos], heap->prod_primes[pos - 1], prime); - - nbits_prime += LOG2(prime); - prime = n_nextprime(prime, 0); - count_nprimes++; - } - else{ - prime = n_nextprime(prime, 0); - } - } - - //on verifie si les images modulaires collent au resultant qu'on a calcule - if(check_modular_images(res, heap, size_table, &maxdegree)){ - fprintf(stderr, "\n\nfinal prime = %lu\n\n", prime); - boo = 0; - } - else{//ca colle pas, on continue la reconstruction. - fmpz_poly_fit_length(res, maxdegree+1); - fmpz_one(coeff); - for(ulong j = 0; j <= maxdegree; j++){ - fmpz_set(coeff, res->coeffs + j); - for(int i = 0; i < size_table; i++){ - myfmpz_CRT_ui(coeff, coeff, - heap->prod_primes[i], (heap->res_mod_array[i]->coeffs)[j], heap->primes_array[i], 1, heap->prod_mod); - } - fmpz_poly_set_coeff_fmpz(res, j, coeff); - } - fmpz_set(heap->prod_primes[0], heap->prod_primes[size_table]); - } - } - - fprintf(stderr, "Wall time spent in modular resultant = %f\n", e_res); - count_nprimes--; - fprintf(stderr, "Number of used primes = %lu\n", count_nprimes); - fprintf(stderr, "Elapsed time (modp): %f\n", e_mod); - fprintf(stderr, "Elapsed time (total): %f\n", omp_get_wtime() - e); - - fprintf(stderr, "Final size coeffs: %ld\n", FLINT_ABS(_fmpz_vec_max_bits(res->coeffs, res->length))); - fprintf(stderr, "Degree of the output: %ld\n", res->length-1); - - fmpz_clear(coeff); - free_data_heap(mdegA, mdegB, size_table, heap); - return; -} - - -static void _fmpz_bpoly_sqfree_resultant_probabilistic(fmpz_poly_t res, - fmpz_poly_t *A, slong mdegA, - fmpz_poly_t *B, slong mdegB){ - - slong tdegA, tdegB, sdegA, sdegB; - ulong nbitsA, nbitsB; - get_degrees_and_nbits(A, mdegA, - B, mdegB, - &tdegA, &tdegB, - &sdegA, &sdegB, - &nbitsA, &nbitsB); - int size_table = 4; - data_heap_t *heap = allocate_data_heap(tdegA, tdegB, - mdegA, mdegB, - sdegA, sdegB, - size_table); - - fprintf(stderr, "Total degrees : %ld %ld\n", tdegA, tdegB); - fprintf(stderr, "numpoints = %lu\n", heap->npts); - - //Hadamard-type (Goldstein-Graham) - ulong bound_nbits = nbitsA*(mdegB) + nbitsB*(mdegA); - - fprintf(stderr, "Bound (nbits) = %lu\n", bound_nbits); - - mp_limb_t prime = 1073741827; - //On devrait mettre un peu d'alea - prime = n_nextprime(1152921504606847009, 0); - ulong nbits_prime = LOG2(prime); - - ulong count_nprimes = 1; - - //max degree reached during multi-mod computation - slong maxdegree = -1; - - double e = omp_get_wtime(); - nbits_prime = 0; - - fmpz_t coeff; - fmpz_init(coeff); - - double e_mod = 0; - - //On teste si le resultant est square-free - make_nmod_bpoly(heap->a_mod, A, mdegA, prime); - make_nmod_bpoly(heap->b_mod, B, mdegB, prime); - - update_poly_tables_with_prime(heap, 0, prime); - nmod_bpoly_resultant_allocated_feval(heap, mdegA, mdegB, 0); - - fprintf(stderr, "prime = %lu\n", prime); - fprintf(stderr, "Degree of the resultant is %ld\n", heap->res_mod_array[0]->length - 1); - if(!is_non_square_free(heap->res_mod_array[0], heap->sqf_part)){ - fprintf(stderr, "The resultant is square-free\n"); - - free_data_heap(mdegA, mdegB, size_table, heap); - fprintf(stderr, "free heap done\n"); - _fmpz_bpoly_resultant_probabilistic(res, - A, mdegA, - B, mdegB); - return; - } - fprintf(stderr, "The resultant is not square-free\n"); - prime = n_nextprime(prime, 0); - - while(nbits_prime < bound_nbits || 0 == 0){ - int pos = 0; - - while(pos < size_table){ - make_nmod_bpoly(heap->a_mod, A, mdegA, prime); - make_nmod_bpoly(heap->b_mod, B, mdegB, prime); - - if(heap->a_mod[mdegA]->length>0 && heap->b_mod[mdegB]->length>0){ - - double start_mod = omp_get_wtime(); - update_poly_tables_with_prime(heap, pos, prime); - nmod_bpoly_resultant_allocated_feval(heap, mdegA, mdegB, pos); - - square_free_part_nmod_poly(heap->res_mod_array[pos], heap->sqf_part); - - e_mod += (omp_get_wtime() - start_mod); - pos++; - fmpz_mul_ui(heap->prod_primes[pos], heap->prod_primes[pos - 1], prime); - nbits_prime += LOG2(prime); - prime = n_nextprime(prime, 0); - count_nprimes++; - } - else{ - prime = n_nextprime(prime, 0); - } - } - - //on verifie si les images modulaires collent au resultant qu'on a calcule - if(check_modular_images(res, heap, size_table, &maxdegree)){ - fprintf(stderr, "\n\nfinal prime = %lu\n\n", prime); - break; - } - else{//ca colle pas, on continue la reconstruction. - fmpz_poly_fit_length(res, maxdegree+1); - fmpz_one(coeff); - for(ulong j = 0; j <= maxdegree; j++){ - fmpz_set(coeff, res->coeffs + j); - for(int i = 0; i < size_table; i++){ - myfmpz_CRT_ui(coeff, coeff, - heap->prod_primes[i], (heap->res_mod_array[i]->coeffs)[j], heap->primes_array[i], 1, heap->prod_mod); - } - fmpz_poly_set_coeff_fmpz(res, j, coeff); - // fmpz_print(coeff);fprintf(stdout, "\n"); - } - fmpz_set(heap->prod_primes[0], heap->prod_primes[size_table]); - } - } - - count_nprimes--; - fprintf(stderr, "Number of used primes = %lu\n", count_nprimes); - fprintf(stderr, "Elapsed time (modp): %f\n", e_mod); - fprintf(stderr, "Elapsed time (total): %f\n", omp_get_wtime() - e); - - fprintf(stderr, "Final size coeffs: %ld\n", FLINT_ABS(_fmpz_vec_max_bits(res->coeffs, res->length))); - fprintf(stderr, "Degree of the output: %ld\n", res->length-1); - - fmpz_clear(coeff); - free_data_heap(mdegA, mdegB, size_table, heap); - return; -} - -/* /\* */ -/* Input: A et B sont des pointeurs sur tableaux de fmpz_poly_t de */ -/* tailles respectives degA + 1 et degB + 1 */ - -/* *\/ */ - - -static void fmpz_bpoly_sqfree_resultant_probabilistic(fmpz_poly_t res, - fmpz_poly_t *A, slong degA, - fmpz_poly_t *B, slong degB){ - if(degA < degB){ - _fmpz_bpoly_sqfree_resultant_probabilistic(res, B, degB, A, degA); - } - else{ - _fmpz_bpoly_sqfree_resultant_probabilistic(res, - A, degA, - B, degB); - } -} - - -static void fmpz_bpoly_resultant_probabilistic(fmpz_poly_t res, - fmpz_poly_t *A, slong degA, - fmpz_poly_t *B, slong degB){ - if(degA < degB){ - _fmpz_bpoly_resultant_probabilistic(res, B, degB, A, degA); - } - else{ - _fmpz_bpoly_resultant_probabilistic(res, - A, degA, - B, degB); - } -} - - -int main(int argc, char **argv){ - - bsolve_flags * flags = allocate_initialize_flags(); - - int binary_format = 0; - getoptions(argc, argv, flags); - - FILE *file = fopen(flags->input_file,"r"); - - if(file==NULL){ - fprintf(stderr, "No such file\n"); - return 1; - } - slong degA = 0, degB = 0; - //Array est un tableau de fmpz_poly_t de lgr degA + degB + 1 - fmpz_poly_t *Array = get_input_polynomials(file, °A, °B); - fmpz_poly_t *bA = Array; - fmpz_poly_t *bB = Array + (degA + 1); - fclose(file); - - if(DEBUG >= 2){ - - fprintf(stderr, "\nA := "); - fmpz_bpoly_fprint_pretty(stderr, bA, degA); - fprintf(stderr, "\n"); - fflush(stderr); - fprintf(stderr, "B := "); - fmpz_bpoly_fprint_pretty(stderr, bB, degB); - fprintf(stderr, "\n"); - fflush(stderr); - } - - - - if(0==1){ - flint_rand_t state; - flint_randinit(state); - fmpz_bpoly_random_dense(bA, degA, degA, state); - fmpz_bpoly_random_dense(bB, degB, degB, state); - flint_randclear(state); - } - - fprintf(stderr, "flags->task = %d\n", flags->task); - if(flags->task == 1){ - fmpz_poly_t res; - fmpz_poly_init(res); - fmpz_bpoly_resultant_probabilistic(res, bA, degA, bB, degB); - display_resutant(res, flags, binary_format); - fmpz_poly_clear(res); - } - if(flags->task == 2){ - fmpz_poly_t res; - fmpz_poly_init(res); - fmpz_bpoly_sqfree_resultant_probabilistic(res, bA, degA, bB, degB); - display_resutant(res, flags, binary_format); - fmpz_poly_clear(res); - } - if(DEBUG>10){ - fmpz_poly_t res; - fmpz_poly_init(res); - fmpz_bpoly_resultant_deterministic(res, bA, degA, bB, degB); - fmpz_poly_clear(res); - } - if(flags->task==0){ - bsolve_fmpz_all_params_t *bs_param = malloc(sizeof(bsolve_fmpz_all_params_t)); - if(fmpz_bpoly_param(bs_param, bA, degA, bB, degB)){ - if(flags->output_file != NULL){ - FILE *ofile = fopen(flags->output_file, "w"); - if(flags->binary){ - print_bs_fmpz_all_params_bin(ofile, bs_param); - } - else{ - print_bs_fmpz_all_params_pretty(ofile, bs_param); - } - fclose(ofile); - } - else{ - if(flags->binary){ - print_bs_fmpz_all_params_bin(stdout, bs_param); - } - else{ - print_bs_fmpz_all_params_pretty(stdout, bs_param); - } - } - - free_bsolve_fmpz_all_params(bs_param); - return 0; - } - free(bs_param); - return 0; - } - - for(ulong i = 0; i <= degA + degB + 1; i++){ - fmpz_poly_clear(Array[i]); - } - free(Array); - free_flags(flags); - return 0; -} diff --git a/src/connectivity/src/resultant/out.txt b/src/connectivity/src/resultant/out.txt deleted file mode 100644 index ce01362..0000000 --- a/src/connectivity/src/resultant/out.txt +++ /dev/null @@ -1 +0,0 @@ -hello diff --git a/src/connectivity/src/resultant/ratreconstruct.c b/src/connectivity/src/resultant/ratreconstruct.c deleted file mode 100644 index bb0fb6f..0000000 --- a/src/connectivity/src/resultant/ratreconstruct.c +++ /dev/null @@ -1,176 +0,0 @@ -#define ROT(u,v,t) \ - do { fmpz _t = *u; *u = *v; *v = *t; *t = _t; } while (0); - -void myfmpz_CRT_ui(fmpz_t out, const fmpz_t r1, const fmpz_t m1, - ulong r2, ulong m2, int sign, fmpz_t *m1m2) -{ - mp_limb_t c; - // fmpz_t m1m2; - - c = fmpz_fdiv_ui(m1, m2); - c = n_invmod(c, m2); - - if (c == 0) - { - flint_printf("Exception (fmpz_CRT_ui). m1 not invertible modulo m2.\n"); - flint_abort(); - } - - // fmpz_init(m1m2); - fmpz_mul_ui(m1m2[0], m1, m2); - - _fmpz_CRT_ui_precomp(out, r1, m1, r2, m2, n_preinvert_limb(m2), - m1m2[0], c, sign); - - // fmpz_clear(m1m2); -} - -int -_myfmpq_reconstruct_fmpz_2(fmpz_t n, fmpz_t d, - const fmpz_t a, const fmpz_t m, const fmpz_t N, const fmpz_t D) -{ - fmpz_t q, r, s, t; - int success = 0; - - /* Quickly identify small integers */ - if (fmpz_cmp(a, N) <= 0) - { - fmpz_set(n, a); - fmpz_one(d); - return 1; - } - fmpz_sub(n, a, m); - if(fmpz_cmp_ui(n, 0)>=0){ - if(fmpz_cmp(n, N) <= 0){ - fmpz_one(d); - return 1; - } - } - else{ - fmpz_neg(n, n); - if(fmpz_cmp(n, N) <= 0){ - fmpz_one(d); - fmpz_neg(n, n); - return 1; - } - } - /* if (fmpz_cmpabs(n, N) <= 0) */ - /* { */ - /* fmpz_one(d); */ - /* fprintf(stderr, "ici?\n"); */ - /* return 1; */ - /* } */ - - fmpz_init(q); - fmpz_init(r); - fmpz_init(s); - fmpz_init(t); - - fmpz_set(r, m); fmpz_zero(s); - fmpz_set(n, a); fmpz_one(d); - - while (fmpz_cmpabs(n, N) > 0) - { - fmpz_fdiv_q(q, r, n); - fmpz_mul(t, q, n); fmpz_sub(t, r, t); ROT(r, n, t); - fmpz_mul(t, q, d); fmpz_sub(t, s, t); ROT(s, d, t); - } - - if (fmpz_sgn(d) < 0) - { - fmpz_neg(n, n); - fmpz_neg(d, d); - } - - if (fmpz_cmp(d, D) <= 0) - { - fmpz_gcd(t, n, d); - success = fmpz_is_one(t); - } - - fmpz_clear(q); - fmpz_clear(r); - fmpz_clear(s); - fmpz_clear(t); - return success; -} - -int -myfmpq_reconstruct_fmpz_2(fmpq_t res, const fmpz_t a, const fmpz_t m, - const fmpz_t N, const fmpz_t D) -{ - return _myfmpq_reconstruct_fmpz_2(fmpq_numref(res), - fmpq_denref(res), a, m, N, D); -} - -int -_myfmpq_reconstruct_fmpz(fmpz_t n, fmpz_t d, - const fmpz_t a, const fmpz_t m) -{ - fmpz_t N; - int result; - - fmpz_init(N); - fmpz_fdiv_q_2exp(N, m, 1); - fmpz_sqrt(N, N); - result = _myfmpq_reconstruct_fmpz_2(n, d, a, m, N, N); - fmpz_clear(N); - - return result; -} - -int -myfmpq_reconstruct_fmpz(mpz_rat_t *res, fmpz_t a, const fmpz_t m) -{ - if(fmpz_cmp_ui(a, 0)>=0){ - return _myfmpq_reconstruct_fmpz(res->numer, - res->denom, a, m); - } - else{ - while(fmpz_cmp_ui(a, 0) < 0){ - // fmpz_fprint(stderr, a); fprintf(stderr, "\n"); - fmpz_add(a, a, m); - } - int b = _myfmpq_reconstruct_fmpz(res->numer, - res->denom, a, m); - return b; - } -} - -/* returns 0 if the rational reconstruction failed */ -int rat_recon(fmpz_poly_t poly, fmpz_poly_t poly_num, fmpz_poly_t poly_den, fmpz_t lcm, - data_heap_t *heap, ulong deg, ulong *rec_poly){ - fprintf(stderr, "[%lu, %lu] ", (*rec_poly), deg); - ulong size = heap->size_mod_array; - fmpz_mul_ui(heap->h_prod, heap->prod_primes[size-1], heap->primes_array[size-1]); - int b = myfmpq_reconstruct_fmpz(heap->coef, poly->coeffs+(*rec_poly), heap->h_prod); - fmpz_lcm(lcm, lcm, heap->coef->denom); - fmpz_set(poly_num->coeffs + (*rec_poly), heap->coef->numer); - fmpz_set(poly_den->coeffs + (*rec_poly), heap->coef->denom); - if(b==0){ - (*rec_poly) = 0; - fmpz_one(lcm); - fprintf(stderr, "--> [%lu, %lu]\n", (*rec_poly), deg); - return b; - } - for(ulong i = (*rec_poly) + 1; i <= deg; i++){ - b = myfmpq_reconstruct_fmpz(heap->coef, poly->coeffs+i, heap->h_prod); - if(b == 0){ - (*rec_poly) = i-1; - fprintf(stderr, "--> [%lu, %lu]\n", (*rec_poly), deg); - return b; - } - fmpz_lcm(lcm, lcm, heap->coef->denom); - fmpz_set(poly_num->coeffs + i, heap->coef->numer); - fmpz_set(poly_den->coeffs + i, heap->coef->denom); - } - (*rec_poly) = deg; - for(ulong i = 0; i <= deg; i++){ - fmpz_divexact(heap->coef->numer, lcm, poly_den->coeffs + i); - fmpz_mul(poly_num->coeffs + i, poly_num->coeffs + i, heap->coef->numer); - } - fprintf(stderr, "--> [%lu, %lu]\n", (*rec_poly), deg); - return b; -} - - diff --git 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z+N-a!fA9VM82`P$ALGB{XuUzV{d1l6A00h(gVKI`z4-*xHt^-B8>cG^?j|CPV* z;)nQO_rK$R6Z8McAcOVmF8#cp&)N3{RjU;H1s%KhIdH8;2ao=3F*k}vo|H#obsKH~aQulKjIeRu!A`y2k4+y8^n z=J88EKbGy+YxR0ZKOXHr@w-0u`v2Y|+E3o`rS9_G|J{1eW!zHwnfxfQTgvqJ%}-wT z)bRO4uPrH5ZjbG-+j}D^6pWtcyi4FZMU?KjzY5b2Ke!1I!!H4~){-- x -> split(x, ": ")[end] * "s") - #elseif v == 2 - # println(stderr(out)) - #end - Ls = usolve_out_to_tuple(fname2) - Is = tuple_to_inter(Ls) - if output == "inter" - return Is - else - ff = open(fname2, "r") - return Ls, Is - end -end - - -#using Nemo -#R, (x,y) = polynomial_ring(ZZ, [:x,:y]) -#f = x^2+5*x-4 diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index 3a0c8cc..f2d7515 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -35,7 +35,7 @@ function trimat_rand(A, n; up=true, range=-100:100) end function int_coeffs(F::Vector{P} where P <: Union{QQMPolyRingElem, QQPolyRingElem}) - CD = [ lcm(map(denominator, collect(coefficients(f)))) for f in F ] + CD = [ iszero(f) ? f : lcm(map(denominator, collect(coefficients(f)))) for f in F ] return (F .* CD) end From 5e5af35bf884005a4ffe594fc2644480a11b60cc Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Thu, 9 Apr 2026 17:34:43 +0200 Subject: [PATCH 135/180] optimize subresultant for finite field --- Manifest.toml | 45 ++++++++++++++++-- Project.toml | 2 + src/connectivity/subresultants.jl | 76 +++++++++++++++++++++++-------- src/exports.jl | 2 +- 4 files changed, 102 insertions(+), 23 deletions(-) diff --git a/Manifest.toml b/Manifest.toml index b99aa50..0c5efb6 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -2,7 +2,7 @@ julia_version = "1.12.5" manifest_format = "2.0" -project_hash = "2c4a2b32eac43961eadb14cefb3546541a48cf2b" +project_hash = "df55572e31ee2a4a5a0c44bb96cd0c13ec9af668" [[deps.AbstractAlgebra]] deps = ["LinearAlgebra", "MacroTools", "PrecompileTools", "Preferences", "Random", "RandomExtensions", "SparseArrays"] @@ -15,7 +15,7 @@ weakdeps = ["Test"] TestExt = "Test" [[deps.AlgebraicSolving]] -deps = ["Colors", "LinearAlgebra", "Logging", "Markdown", "Nemo", "Primes", "Printf", "Random", "StaticArrays", "msolve_jll"] +deps = ["Colors", "LinearAlgebra", "Logging", "Markdown", "Nemo", "Plots", "Primes", "Printf", "Random", "StaticArrays", "msolve_jll"] path = "." uuid = "66b61cbe-0446-4d5d-9090-1ff510639f9d" version = "0.10.4" @@ -38,6 +38,12 @@ version = "1.11.0" uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" version = "1.11.0" +[[deps.BenchmarkTools]] +deps = ["Compat", "JSON", "Logging", "Printf", "Profile", "Statistics", "UUIDs"] +git-tree-sha1 = "6876e30dc02dc69f0613cb6ece242144f2ca9e56" +uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" +version = "1.7.0" + [[deps.BitFlags]] git-tree-sha1 = "0691e34b3bb8be9307330f88d1a3c3f25466c24d" uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35" @@ -95,6 +101,16 @@ git-tree-sha1 = "37ea44092930b1811e666c3bc38065d7d87fcc74" uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" version = "0.13.1" +[[deps.Compat]] +deps = ["TOML", "UUIDs"] +git-tree-sha1 = "9d8a54ce4b17aa5bdce0ea5c34bc5e7c340d16ad" +uuid = "34da2185-b29b-5c13-b0c7-acf172513d20" +version = "4.18.1" +weakdeps = ["Dates", "LinearAlgebra"] + + [deps.Compat.extensions] + CompatLinearAlgebraExt = "LinearAlgebra" + [[deps.CompilerSupportLibraries_jll]] deps = ["Artifacts", "Libdl"] uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" @@ -174,7 +190,7 @@ uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a" version = "0.4.5" [[deps.FFMPEG_jll]] -deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"] +deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libva_jll", "libvorbis_jll", "x264_jll", "x265_jll"] git-tree-sha1 = "01ba9d15e9eae375dc1eb9589df76b3572acd3f2" uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5" version = "8.0.1+0" @@ -674,6 +690,11 @@ deps = ["Unicode"] uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" version = "1.11.0" +[[deps.Profile]] +deps = ["StyledStrings"] +uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79" +version = "1.11.0" + [[deps.PtrArrays]] git-tree-sha1 = "4fbbafbc6251b883f4d2705356f3641f3652a7fe" uuid = "43287f4e-b6f4-7ad1-bb20-aadabca52c3d" @@ -1023,6 +1044,12 @@ git-tree-sha1 = "7ed9347888fac59a618302ee38216dd0379c480d" uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa" version = "0.9.12+0" +[[deps.Xorg_libpciaccess_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"] +git-tree-sha1 = "4909eb8f1cbf6bd4b1c30dd18b2ead9019ef2fad" +uuid = "a65dc6b1-eb27-53a1-bb3e-dea574b5389e" +version = "0.18.1+0" + [[deps.Xorg_libxcb_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXau_jll", "Xorg_libXdmcp_jll"] git-tree-sha1 = "bfcaf7ec088eaba362093393fe11aa141fa15422" @@ -1135,6 +1162,12 @@ git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f" uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f" version = "0.2.2+0" +[[deps.libdrm_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libpciaccess_jll"] +git-tree-sha1 = "63aac0bcb0b582e11bad965cef4a689905456c03" +uuid = "8e53e030-5e6c-5a89-a30b-be5b7263a166" +version = "2.4.125+1" + [[deps.libevdev_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "56d643b57b188d30cccc25e331d416d3d358e557" @@ -1159,6 +1192,12 @@ git-tree-sha1 = "e015f211ebb898c8180887012b938f3851e719ac" uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" version = "1.6.55+0" +[[deps.libva_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll", "Xorg_libXext_jll", "Xorg_libXfixes_jll", "libdrm_jll"] +git-tree-sha1 = "7dbf96baae3310fe2fa0df0ccbb3c6288d5816c9" +uuid = "9a156e7d-b971-5f62-b2c9-67348b8fb97c" +version = "2.23.0+0" + [[deps.libvorbis_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll"] git-tree-sha1 = "11e1772e7f3cc987e9d3de991dd4f6b2602663a5" diff --git a/Project.toml b/Project.toml index 9f7e4dd..1b1790c 100644 --- a/Project.toml +++ b/Project.toml @@ -4,6 +4,7 @@ version = "0.10.4" authors = ["ederc ", "Mohab Safey El Din ", "RĂ©mi Prebet "] [deps] +BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" Colors = "5ae59095-9a9b-59fe-a467-6f913c188581" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" @@ -17,6 +18,7 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" msolve_jll = "6d01cc9a-e8f6-580e-8c54-544227e08205" [compat] +BenchmarkTools = "1.7.0" LinearAlgebra = "1.6" Logging = "1.6" Markdown = "1.6" diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index 046286d..f307ff5 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -69,59 +69,96 @@ function array_to_poly(LP, A) return finish(C) end -# Univariate resultant +""" + subresultants(P, Q) +Compute the subresultant polynomial remainder sequence (PRS) of two univariate polynomials. + +Returns a vector `[S0, S1, ..., Sk]` where: +- S0 = Q (after possible swap) +- each Si is a subresultant +- sequence ends when remainder becomes zero or constant +""" + function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingElement + return _subresultants(P, Q, false) +end + +function subresultants(P::FqPolyRingElem, Q::FqPolyRingElem) + return _subresultants(P, Q, true) +end + +function _subresultants(P::Union{PolyRingElem{T}, FqPolyRingElem}, Q::Union{PolyRingElem{T}, FqPolyRingElem}, Fq::Bool) where T <: RingElement + + # Ensure deg(P) >= deg(Q) if degree(P) < degree(Q) P, Q = Q, P end - S = [Q] - s = leading_coefficient(Q)^(degree(P)-degree(Q)) + + S = Vector{typeof(Q)}() + push!(S, Q) + + # Initial scaling factor (controls normalization of pseudo-remainders) + s = leading_coefficient(Q)^(degree(P) - degree(Q)) + + # rem is faster when working with finite fields (relies on FLINT) A = Q - B = pseudorem(P,-Q) - ring = parent(P) + B = Fq ? (-leading_coefficient(Q))^(degree(P) - degree(Q) + 1) * rem(P, Q) : pseudorem(P, -Q) + while true d = degree(A) e = degree(B) - #println("($d,$e)") + # Termination: exact division reached if iszero(B) return S end - pushfirst!(S, copy(B)) - delta = d - e + pushfirst!(S, B) # prepend current remainder + delta = d - e # degree drop + # --- Compute normalization factor C --- if delta > 1 if length(S) > 1 + # Use previous subresultants to stabilize scaling n = degree(S[2]) - degree(S[1]) - 1 if n == 0 - C = copy(S[1]) + C = S[1] else x = leading_coefficient(S[1]) y = leading_coefficient(S[2]) + + # fast exponentiation (binary powering) a = 1 << (length(bits(ZZ(n))) - 1) c = x - n = n - a + n -= a while a > 1 - a /= 2 + a >>= 1 c = c^2 / y if n >= a c = c * x / y - n = n - a + n -= a end end + C = c * S[1] / y end else - C = leading_coefficient(B)^(delta-1) * B / s^(delta-1) + # First step: fallback normalization + C = leading_coefficient(B)^(delta - 1) * B / s^(delta - 1) end - pushfirst!(S, copy(C)) + pushfirst!(S, C) else - C = copy(B) + C = B end + + # Termination: constant polynomial if e == 0 return S end - #@time - B = pseudorem(A,-B) / (s^delta * leading_coefficient(A)) - A = copy(C) + + # --- Next pseudo-remainder --- + B = Fq ? (-leading_coefficient(B))^(d - e + 1)* rem(A, B) : pseudorem(A, -B) + B /= (s^delta * leading_coefficient(A)) + + # Shift sequence + A = C s = leading_coefficient(A) end end @@ -568,4 +605,5 @@ end return filter(p->length(p[2][1])>0, param_crit) end -param_crit_split(f; v=1) = param_crit_split(f, zero(parent(f)), v=v, detect_app=false) \ No newline at end of file +param_crit_split(f; v=1) = param_crit_split(f, zero(parent(f)), v=v, detect_app=false) + diff --git a/src/exports.jl b/src/exports.jl index ce4142a..9764da9 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -6,4 +6,4 @@ export polynomial_ring, MPolyRing, GFElem, MPolyRingElem, equidimensional_decomposition, homogenize, dimension, FqMPolyRingElem, hilbert_series, hilbert_dimension, hilbert_degree, hilbert_polynomial, rational_curve_parametrization, roadmap, computepolar, all_eqs, - all_base_pts, nb_nodes + all_base_pts, nb_nodes, subresultants \ No newline at end of file From bb5ab5d8d57cf3c88fa9d09ec4d02f3dd6cf8e0c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Fri, 10 Apr 2026 11:02:59 +0200 Subject: [PATCH 136/180] start cleaning auxiliary functions --- src/connectivity/arbtools.jl | 2 +- src/connectivity/boxes.jl | 94 +++++++++++++++--------------------- src/connectivity/isolate.jl | 17 ++----- src/exports.jl | 2 +- 4 files changed, 47 insertions(+), 68 deletions(-) diff --git a/src/connectivity/arbtools.jl b/src/connectivity/arbtools.jl index 9f176cf..c7ab533 100644 --- a/src/connectivity/arbtools.jl +++ b/src/connectivity/arbtools.jl @@ -16,7 +16,7 @@ end Convert rational interval (x1, x2) to Arb ball. """ -function rat_to_arb(interval, field::ArbField) +function rat_to_arb(interval::Vector{QQFieldElem}, field::ArbField) x1, x2 = interval @assert x1 <= x2 "Invalid interval: x1 > x2" diff --git a/src/connectivity/boxes.jl b/src/connectivity/boxes.jl index 11d9713..36eca89 100644 --- a/src/connectivity/boxes.jl +++ b/src/connectivity/boxes.jl @@ -1,63 +1,49 @@ -function in_inter(I, J) - return J[1] <= I[1] && I[2] <= J[2] -end +in_inter(I, J) = J[1] <= I[1] && I[2] <= J[2] +overlap_inter(I,J) = max(I[1], J[1]) <= min(I[2], J[2]) -function overlap_inter(I,J) - return max(I[1], J[1]) <= min(I[2], J[2]) -end +# Helper function to process a single edge of the box +function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v; max_retries=5) + prec = initial_prec -# To try/do : isolate with usolve, call msolve with only one variable -function intersect_box(f, B; prec=100, v=0) - L = Array{Any}(undef, 4) - for i in 1:2 - # Lxi - L[i] = Array{Any}(undef,2) - compt = 0 - while compt < 5 - flag = false - L[i][1] = isolate_eval(f, 2, B[2][i], prec=prec) - L[i][2] = [] - for (j, l) in pairs(L[i][1]) - if in_inter(l, B[1]) - push!(L[i][2], j) - elseif overlap_inter(l, B[1]) - prec *= 2 - v > 0 && println("Increase precision to ", prec) - flag = true - compt += 1 - break - end - end - flag || break - end - if compt >= 5 - error("Problem when isolating on one side of a box") - end - # Lyi - L[i+2] = Array{Any}(undef,2) - compt = 0 - while compt < 5 - flag = false - L[i+2][1] = isolate_eval(f, 1, B[1][i], prec=prec) - L[i+2][2] = [] - for (j, l) in pairs(L[i+2][1]) - if in_inter(l, B[2]) - push!(L[i+2][2], j) - elseif overlap_inter(l, B[2]) - prec *= 2 - v > 0 && println("Increase precision to ", prec) - flag = true - compt += 1 - break - end + for _ in 1:max_retries + roots = isolate_eval(f, fixed_dim, fixed_val, prec=prec) + valid_indices = Int[] + overlap_found = false + + for (j, l) in pairs(roots) + if in_inter(l, target_interval) + push!(valid_indices, j) + elseif overlap_inter(l, target_interval) + prec *= 2 + v > 0 && println("Increase precision to ", prec) + overlap_found = true + break # Break inner for-loop to restart with higher precision end - flag || break end - if compt >= 5 - error("Problem when isolating on one side of a box") + + # If we successfully processed all roots without overlap, return the results + if !overlap_found + return (roots, valid_indices) end end - return L + + error("Problem when isolating on one side of a box after $max_retries attempts") +end + + +function intersect_box(f, B; prec=100, v=0) + # B[1] represents x-bounds, B[2] represents y-bounds + + # Evaluate horizontal edges (fix y to B[2][1] and B[2][2], target x-interval B[1]) + edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v) + edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v) + + # Evaluate vertical edges (fix x to B[1][1] and B[1][2], target y-interval B[2]) + edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v) + edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v) + + # Return as a typed array of Tuples + return [edge_y1, edge_y2, edge_x1, edge_x2] end function refine_xboxes(f::T where T<:Union{PolyRingElem, MPolyRingElem}, LB, prec) diff --git a/src/connectivity/isolate.jl b/src/connectivity/isolate.jl index f292456..f9209be 100644 --- a/src/connectivity/isolate.jl +++ b/src/connectivity/isolate.jl @@ -1,10 +1,8 @@ function isolate(f; prec = 32) - #println(f) - # Univariate isolation using usolve - if total_degree(f) == 0 - return [] - end + # Univariate isolation with msolve + total_degree(f) == 0 && return [] @assert is_univariate(f) "Not univariate polynomial" + sols = real_solutions(Ideal([change_ringvar(f)]), precision=prec, interval=true, info_level=0) return getindex.(sols, 1) end @@ -12,12 +10,7 @@ end function isolate_eval(f, ivar, val; prec=64) # univariate isolation of roots of a bivariate polynomial f # whose ivar-th variable is evaluated at val - # uses msolve fev = change_ringvar(evaluate(f, [ivar], [val])) - CD = lcm(map(denominator, collect(coefficients(fev)))) - fev *= CD - - tmp = isolate(fev, prec=prec) - return tmp - + #fev *= fev |> coefficients .|> denominator |> lcm + return isolate(fev, prec=prec) end \ No newline at end of file diff --git a/src/exports.jl b/src/exports.jl index 9764da9..f1d3afa 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -6,4 +6,4 @@ export polynomial_ring, MPolyRing, GFElem, MPolyRingElem, equidimensional_decomposition, homogenize, dimension, FqMPolyRingElem, hilbert_series, hilbert_dimension, hilbert_degree, hilbert_polynomial, rational_curve_parametrization, roadmap, computepolar, all_eqs, - all_base_pts, nb_nodes, subresultants \ No newline at end of file + all_base_pts, nb_nodes, subresultants, change_ringvar \ No newline at end of file From 4e55cd6070a7b4d07f4234ab490ba75b01cb9ab5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Fri, 10 Apr 2026 15:39:27 +0200 Subject: [PATCH 137/180] continue cleaning, debug and code factoring --- src/connectivity/arbtools.jl | 29 ++---- src/connectivity/boxes.jl | 80 --------------- src/connectivity/connectcurves.jl | 85 +++++----------- src/connectivity/isolate.jl | 16 --- src/connectivity/isolateboxes.jl | 161 ++++++++++++++++++++++++++++++ src/connectivity/tools.jl | 5 +- 6 files changed, 201 insertions(+), 175 deletions(-) delete mode 100644 src/connectivity/boxes.jl delete mode 100644 src/connectivity/isolate.jl create mode 100644 src/connectivity/isolateboxes.jl diff --git a/src/connectivity/arbtools.jl b/src/connectivity/arbtools.jl index c7ab533..4f03aea 100644 --- a/src/connectivity/arbtools.jl +++ b/src/connectivity/arbtools.jl @@ -7,12 +7,12 @@ function arb_to_rat(x::ArbFieldElem) r = radius(x) lo = x - 2r hi = x + 2r - return (simplest_rational_inside(lo), simplest_rational_inside(hi)) + return Vector{QQFieldElem}([simplest_rational_inside(lo), simplest_rational_inside(hi)]) end """ - rat_to_arb(interval::Tuple, field::ArbField) -> ArbFieldElem + rat_to_arb(interval::Vector{QQFieldElem}, field::ArbField) -> ArbFieldElem Convert rational interval (x1, x2) to Arb ball. """ @@ -28,23 +28,12 @@ end """ - evaluate_arb(f, x::ArbFieldElem) - -Evaluate polynomial f at x using Arb arithmetic. -""" -function evaluate_arb(f, x::ArbFieldElem) - is_zero(f) && return zero(parent(x)) - cf = coefficients_of_univariate(f) - return evalpoly(x, cf) -end - - -""" - evaluate_arb(f, g, x::ArbFieldElem) + evaluate_arb(f, g, x::Vector{QQFieldElem}) Evaluate rational function f/g at x. +Return a rational interval enclosing the result, computed using Arb. """ -function evaluate_arb(f, g, x::ArbFieldElem) +function evaluate_arb(f, g, x::Vector{QQFieldElem}, field::ArbField) @assert !is_zero(g) "Denominator must be non-zero" is_zero(f) && return zero(parent(x)) @@ -52,10 +41,11 @@ function evaluate_arb(f, g, x::ArbFieldElem) cf = coefficients_of_univariate(f) cg = coefficients_of_univariate(g) - num = evalpoly(x, cf) - den = evalpoly(x, cg) + x_arb = rat_to_arb(x, field) + num = evalpoly(x_arb, cf) + den = evalpoly(x_arb, cg) - return num / den + return arb_to_rat(num / den) end @@ -63,6 +53,7 @@ end arb_eval(f, B::Vector{Tuple}, prec::Int) Evaluate polynomial f over interval box B. +Return an Arb ball containing the image of B by f. """ function arb_eval(f, B::Vector{Tuple}, field::ArbField) BA = Vector{ArbFieldElem}(undef, length(B)) diff --git a/src/connectivity/boxes.jl b/src/connectivity/boxes.jl deleted file mode 100644 index 36eca89..0000000 --- a/src/connectivity/boxes.jl +++ /dev/null @@ -1,80 +0,0 @@ -in_inter(I, J) = J[1] <= I[1] && I[2] <= J[2] -overlap_inter(I,J) = max(I[1], J[1]) <= min(I[2], J[2]) - -# Helper function to process a single edge of the box -function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v; max_retries=5) - prec = initial_prec - - for _ in 1:max_retries - roots = isolate_eval(f, fixed_dim, fixed_val, prec=prec) - valid_indices = Int[] - overlap_found = false - - for (j, l) in pairs(roots) - if in_inter(l, target_interval) - push!(valid_indices, j) - elseif overlap_inter(l, target_interval) - prec *= 2 - v > 0 && println("Increase precision to ", prec) - overlap_found = true - break # Break inner for-loop to restart with higher precision - end - end - - # If we successfully processed all roots without overlap, return the results - if !overlap_found - return (roots, valid_indices) - end - end - - error("Problem when isolating on one side of a box after $max_retries attempts") -end - - -function intersect_box(f, B; prec=100, v=0) - # B[1] represents x-bounds, B[2] represents y-bounds - - # Evaluate horizontal edges (fix y to B[2][1] and B[2][2], target x-interval B[1]) - edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v) - edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v) - - # Evaluate vertical edges (fix x to B[1][1] and B[1][2], target y-interval B[2]) - edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v) - edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v) - - # Return as a typed array of Tuples - return [edge_y1, edge_y2, edge_x1, edge_x2] -end - -function refine_xboxes(f::T where T<:Union{PolyRingElem, MPolyRingElem}, LB, prec) - # Refine LB along first axis, being roots of f - xnew = isolate(f, prec=prec) - for i in eachindex(xnew) - if xnew[i][1]==xnew[i][2] - xnew[i] = [xnew[i][1]-1//ZZ(1)< 1 && println(f) + precx = precx <= 1 ? 2 : precx v > 0 && println("Compute parametrization of critical pts...") @iftime (v > 0) params = param_crit_split(f,g,v=v-1, detect_app=true) @@ -34,51 +34,12 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen params[-i] = [ [C[i][1] |> intC], C[i][2], C[i][3] ] end - compt = 0 - xcrit, xcritpermut, LBcrit = Dict(), Dict(), Dict() - while compt < 5 - try - # TODO : check that no overlap between different isolations - v > 0 && println("\nIsolating critical values with precision ", precx,"..") - @iftime (v > 0) begin - xcrit = Dict(p[1]=> reduce(vcat, [isolate(pp, prec=precx) for pp in p[2][1]]) for p in params) - # Enlarge exact isolating root intervals - for i in eachindex(xcrit) - for j in eachindex(xcrit[i]) - if xcrit[i][j][1]==xcrit[i][j][2] - xcrit[i][j] = [xcrit[i][j][1]-1//ZZ(1)< 0 && println("Computing isolating critical boxes") + LBcrit = Dict() + @iftime (v > 0) xcritpermut, precx = compute_crit_boxes(params, LBcrit, precx, v) + xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in eachindex(LBcrit)) - v > 0 && println("\nComputing isolating critical boxes using Arb with precision ",precx,"..") - @iftime (v > 0) begin - arbField = ArbField(precx) - Pcrit = Dict( i => [[xc, evaluate_arb(params[i][2], params[i][3], rat_to_arb(xc, arbField))] for xc in xcrit[i]] for i in eachindex(xcrit)) - LBcrit = Dict( i=> [[ map(QQ, pc[1]), map(QQ, arb_to_rat(pc[2])) ] for pc in pcrit] for (i, pcrit) in Pcrit) - # Enlarge exact isolating box vertical side (horizontal lines) - for i in eachindex(LBcrit) - for j in eachindex(LBcrit[i]) - if LBcrit[i][j][2][1]==LBcrit[i][j][2][2] - LBcrit[i][j][2] = [LBcrit[i][j][2][1]-1//ZZ(2)< 0 && println("\nRefine x-precision to $precx") - compt += 1 - else - break - end - end - # TODO: limite du compteur pertinent ? - if compt >= 5 - error("Problem in isolating critical boxes") - end + # println("LBcrit: ", LBcrit) v > 0 && println("\nTest for identifying singular boxes") @iftime (v > 0) begin @@ -88,28 +49,35 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen arbField = ArbField(precx) Lfyk = diff_list(f, 2, max(maximum(eachindex(LBcrit)),2)) for ind in eachindex(LBcrit) - (ind < 0 && ind == 1) && continue # extreme and control pts - m = ind==0 ? 2 : ind # nodes have mult 2 - while true - flag = false + ind < 0 && continue # control pts + m = ind <= 1 ? 2 : ind # nodes and extrems have mult 2 + noisolate = false + for _ in 1:5 + noisolate = false for j in eachindex(LBcrit[ind]) pcrit = [ rat_to_arb(c, arbField) for c in LBcrit[ind][j] ] # Check if the the mult(pcrit)-th derivative of f vanishes on pcrit if contains_zero(evaluate(Lfyk[m+1], pcrit)) - (v > 0) && println("Refine singular boxes of multiplicity ", m) - # TODO refine_boxes(params[k], LBcrit[k]) - #flag = true + # TODO refine only boxes associated to multiplicity m + precx *= 2 + (v > 0) && println("Refine singular boxes of index $ind to $precx bits precision") + xcritpermut, precx = compute_crit_boxes(params, LBcrit, precx, v-1) + xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in eachindex(LBcrit)) + noisolate = true break end end - flag || break + noisolate || break + end + if noisolate + error("Problem in singular boxes refinement") end end end v > 0 && println("\nCompute intersections with critical boxes..") @iftime (v > 0) begin - ## TODO : Refine only the intervals that need to be refined? + ## TODO : Refine only the intervals that need to be refined? only the factor that defines the intervals LPCside = Dict{Int,Any}() ndig = maximum([ndigits(length(LBcrit[i])) for i in eachindex(LBcrit)]) for i in eachindex(LBcrit) @@ -122,14 +90,15 @@ end compt = 0 while compt < 5 flag = false + # println(LBcrit[i]) for j in eachindex(LBcrit[i]) v > 0 && print("$Ptype=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp,v=v) npcside = [length(n) for (I, n) in pcside] - #println("($i, $j): $npcside") + # println("($i, $j): $npcside") if (i == 1 && sum(npcside) > 2) || (i != 1 && sum(npcside[1:2]) != 0) precxtmp *= 2 - v > 0 && println("\nRefine boxes along x-axis to precision ", precxtmp) + v > 0 && println("\nRefine boxes along x-axis to $precxtmp bits precision") refine_xboxes(params[i][1], LBcrit[i], precxtmp) flag = true compt += 1 diff --git a/src/connectivity/isolate.jl b/src/connectivity/isolate.jl deleted file mode 100644 index f9209be..0000000 --- a/src/connectivity/isolate.jl +++ /dev/null @@ -1,16 +0,0 @@ -function isolate(f; prec = 32) - # Univariate isolation with msolve - total_degree(f) == 0 && return [] - @assert is_univariate(f) "Not univariate polynomial" - - sols = real_solutions(Ideal([change_ringvar(f)]), precision=prec, interval=true, info_level=0) - return getindex.(sols, 1) -end - -function isolate_eval(f, ivar, val; prec=64) - # univariate isolation of roots of a bivariate polynomial f - # whose ivar-th variable is evaluated at val - fev = change_ringvar(evaluate(f, [ivar], [val])) - #fev *= fev |> coefficients .|> denominator |> lcm - return isolate(fev, prec=prec) -end \ No newline at end of file diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl new file mode 100644 index 0000000..3c6525a --- /dev/null +++ b/src/connectivity/isolateboxes.jl @@ -0,0 +1,161 @@ +in_inter(I, J) = J[1] <= I[1] && I[2] <= J[2] +overlap_inter(I,J) = max(I[1], J[1]) <= min(I[2], J[2]) + + # Function that isolate roots of a multivariate polynomial with a + # single variable +function isolate(f; prec = 32) + total_degree(f) == 0 && return [] + @assert is_univariate(f) "Not univariate polynomial" + + sols = real_solutions(Ideal([change_ringvar(f)]), precision=prec, interval=true, info_level=0) + return getindex.(sols, 1) +end + +# univariate isolation of roots of a bivariate polynomial f whose +# ivar-th variable is evaluated at val +function isolate_eval(f, ivar, val; prec=64) + fev = change_ringvar(evaluate(f, [ivar], [val])) + # fev *= fev |> coefficients .|> denominator |> lcm + return isolate(fev, prec=prec) +end + +""" + _expand_degenerate_intervals!(xnew, prec) + +Expand intervals where lower == upper to avoid zero-width boxes. +""" +function _expand_degenerate_intervals!(xnew, prec) + d = 1 // (ZZ(1) << prec) + for i in eachindex(xnew) + if xnew[i][1] == xnew[i][2] + x = xnew[i][1] + xnew[i] = [x - d, x + d] + end + end + return xnew +end + +# TODO: add the singularity check here, probably just by calling a function +# make sure we refine only the boxes that need to be refined +function compute_crit_boxes(params, LBcrit, precx, v, max_attempts=5) + compt = 0 + xcrit = Dict() + while compt <= max_attempts + try + v > 0 && compt > 0 && println("ComputeBoxes: refine x-precision to $precx bits") + # TODO : check that no overlap between different isolations + xcrit = Dict(i=> reduce(vcat, [isolate(pp, prec=precx) for pp in p[1]]) for (i, p) in params) + # Enlarge exact isolating root intervals + for xvals in values(xcrit) + _expand_degenerate_intervals!(xvals, precx) + end + arbField = ArbField(precx) + for i in keys(xcrit) + xvals = xcrit[i] + ycrit = [ + evaluate_arb(params[i][2], params[i][3], xc, arbField) + for xc in xvals + ] + _expand_degenerate_intervals!(ycrit, precx) + @inbounds LBcrit[i] = [ + [xvals[j], ycrit[j]] for j in eachindex(ycrit) + ] + end + catch e + precx *= 2 + v > 1 && println("Error in isolating critical boxes: ", e) + compt += 1 + else + break + end + end + # TODO: is that a relevant upper bound? + if compt > max_attempts + error("Problem in isolating critical boxes") + end + + return (order_permut2d(xcrit), precx) +end + +# Helper function to process a single edge of the box +function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v; max_retries=5) + prec = initial_prec + + for _ in 1:max_retries + roots = isolate_eval(f, fixed_dim, fixed_val, prec=prec) + valid_indices = Int[] + overlap_found = false + + for (j, l) in pairs(roots) + if in_inter(l, target_interval) + push!(valid_indices, j) + elseif overlap_inter(l, target_interval) + prec *= 2 + v > 0 && println("IntersectBox: increase precision to $prec bits") + overlap_found = true + break # Break inner for-loop to restart with higher precision + end + end + + # If we successfully processed all roots without overlap, return the results + if !overlap_found + return (roots, valid_indices) + end + end + + error("Problem when isolating on one side of a box after $max_retries attempts") +end + +# Function that computes the intersection of a curve with a box by isolating roots on the edges +function intersect_box(f, B; prec=100, v=0) + # B[1] represents x-bounds, B[2] represents y-bounds + + # Evaluate horizontal edges (fix y to B[2][1] and B[2][2], target x-interval B[1]) + edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v) + edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v) + + # Evaluate vertical edges (fix x to B[1][1] and B[1][2], target y-interval B[2]) + edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v) + edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v) + + # Return as a typed array of Tuples + return [edge_y1, edge_y2, edge_x1, edge_x2] +end + + +""" + _update_LB_first_axis!(LB, xnew) + +Replace first coordinate of each box in LB with corresponding xnew interval. +""" +function _update_LB_first_axis!(LB, xnew) + @inbounds for i in eachindex(LB) + LB[i][1] = xnew[i] + end + return LB +end + +""" + refine_xboxes(f, LB, prec) + +Refine LB along first axis using roots of polynomials in F +The order in F is assumed to match the one in LB +""" +function refine_xboxes(F::Vector{T} where T<:Union{PolyRingElem, MPolyRingElem}, LB, prec) + # Concatenate all roots from isolating each polynomial in F + xnew = reduce(vcat, [isolate(f, prec=prec) for f in F]) + + _expand_degenerate_intervals!(xnew, prec) + return _update_LB_first_axis!(LB, xnew) +end + +""" + refine_ith_xboxes(f, LB, i, prec) + +Refine only the i-th box along first axis using i-th root of f. +""" +function refine_ith_xboxes(f, LB, i, prec) + xnew = isolate(f, prec=prec) + @inbounds LB[i] = [xnew[i], LB[i][2]] + return LB +end \ No newline at end of file diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index f2d7515..4c69d3f 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -19,9 +19,10 @@ function diff(p, v, n) end function diff_list(p, v, n) - Ldp = [p] + Ldp = Vector{typeof(p)}(undef, n+1) + Ldp[1] = p for j in 1:n - push!(Ldp, derivative(Ldp[end], v)) + Ldp[j+1] = derivative(Ldp[j], v) end return Ldp end From 7e66f6c9e94d4fae03d398a272a703299ac8fb27 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 13 Apr 2026 13:02:55 +0200 Subject: [PATCH 138/180] improve and factor build poly --- src/connectivity/arbtools.jl | 2 +- src/connectivity/buildpoly.jl | 212 +++++++++++++----------------- src/connectivity/subresultants.jl | 15 ++- 3 files changed, 104 insertions(+), 125 deletions(-) diff --git a/src/connectivity/arbtools.jl b/src/connectivity/arbtools.jl index 4f03aea..3134133 100644 --- a/src/connectivity/arbtools.jl +++ b/src/connectivity/arbtools.jl @@ -7,7 +7,7 @@ function arb_to_rat(x::ArbFieldElem) r = radius(x) lo = x - 2r hi = x + 2r - return Vector{QQFieldElem}([simplest_rational_inside(lo), simplest_rational_inside(hi)]) + return [simplest_rational_inside(lo), simplest_rational_inside(hi)] end diff --git a/src/connectivity/buildpoly.jl b/src/connectivity/buildpoly.jl index ae668c6..9fa8b42 100644 --- a/src/connectivity/buildpoly.jl +++ b/src/connectivity/buildpoly.jl @@ -1,140 +1,116 @@ -# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables -function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} - R = parent(first(F)) - # Locate variables of R in newvarias - to_varias = Vector{Int}(undef,0) - for v in newvarias_S - ind = findfirst(x->x==v, R.S) - push!(to_varias, typeof(ind)==Nothing ? length(R.S)+1 : ind) - end - - ind_novarias = setdiff(eachindex(R.S), to_varias) - newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) +""" + change_ringvar(F, new_S::Vector{Symbol}) - res = typeof(first(F))[] - ctx = MPolyBuildCtx(newR) +Inject polynomial(s) into a new multivariate polynomial ring defined by `new_S`. +Uses the direct ring constructor `R(coeffs, exps)` to automatically handle +monomial ordering, coalescing, and zero-term removal. +""" +function change_ringvar(F::AbstractVector{<:Union{PolyRingElem, MPolyRingElem}}, new_S::Vector{Symbol}) + isempty(F) && return typeof(first(F))[] - for f in F - for (e, c) in zip(exponent_vectors(f), coefficients(f)) - @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") - push!(e, 0) - push_term!(ctx, c, [e[i] for i in to_varias ]) - end - push!(res, finish(ctx)) - end - - return res -end - -function change_ringvar(F::Vector{P}, newvarias_S::Vector{Symbol}) where {P <: PolyRingElem} R = parent(first(F)) - to_varias = [ v==R.S ? 1 : 2 for v in newvarias_S] - newR, = polynomial_ring(base_ring(R), newvarias_S) - - res = typeof(zero(newR))[] - ctx = MPolyBuildCtx(newR) - - LcF = [ filter!(t->t[2]!=0, collect(enumerate(coefficients(f)))) for f in F ] - for f in LcF - for (ef, c) in f - e = [ef-1, 0] - push_term!(ctx, c, [e[i] for i in to_varias ]) + old_S = symbols(R) + newR, _ = polynomial_ring(base_ring(R), new_S) + + # Pre-calculate index mapping: old_index -> new_index (0 if removed) + idx_map = [isnothing(idx) ? 0 : idx for idx in (findfirst(==(v), new_S) for v in old_S)] + + T = typeof(zero(base_ring(R))) + n_vars = length(new_S) + + return map(F) do f + coeffs = T[] + exps = Vector{Int}[] + + if f isa MPolyRingElem + for (e, c) in zip(exponent_vectors(f), coefficients(f)) + e_new = zeros(Int, n_vars) + for (i, power) in enumerate(e) + if power > 0 + @assert idx_map[i] != 0 "Occurrence of removed variable '$(old_S[i])' found!" + e_new[idx_map[i]] = power + end + end + push!(coeffs, c) + push!(exps, e_new) + end + else # PolyRingElem + @assert idx_map[1] != 0 "Occurrence of removed variable '$(old_S[1])' found!" + for (deg_plus_1, c) in enumerate(coefficients(f)) + if !iszero(c) + e_new = zeros(Int, n_vars) + if deg_plus_1 > 1 + e_new[idx_map[1]] = deg_plus_1 + end + push!(coeffs, c) + push!(exps, e_new) + end + end end - push!(res, finish(ctx)) - end - - return res -end -function change_ringvar(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) - return first(change_ringvar([f], newvarias_S)) -end - -function change_ringvar(F::Vector{P}, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {P <: MPolyRingElem, I <: Int64} - R = parent(first(F)) - return change_ringvar(F, [R.S[i] for i in ind_newvarias]) -end - -function change_ringvar(f::MPolyRingElem, ind_newvarias::Union{Vector{I}, UnitRange{I}}) where {I <: Int64} - R = parent(f) - return first(change_ringvar([f], [R.S[i] for i in ind_newvarias])) -end - -# Return the polynomials in F, but injected in the polynomial ring with the variables occuring in F -function change_ringvar(F::Vector{P}) where {P <: MPolyRingElem} - union_varias = Set{Symbol}() - for f in F - union!(union_varias, map(Symbol, vars(f)) ) + # Create the new polynomial associated to f + return newR(coeffs, exps) end - return change_ringvar(F, collect(union_varias)) end -function change_ringvar(f::MPolyRingElem) - return first(change_ringvar([f])) -end +# Dispatch for a single polynomial +change_ringvar(f::Union{PolyRingElem, MPolyRingElem}, new_S::Vector{Symbol}) = change_ringvar([f], new_S)[1] -# Return the polynomials in F, but injected in the polynomial ring with newvarias_S as new variables -function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: MPolyRingElem} - R = parent(first(F)) - # Locate variables of R in newvarias - to_varias = Vector{Int}(undef,0) - for v in newvarias_S - ind = findfirst(x->x==v, oldvarias_S) - push!(to_varias, typeof(ind)==Nothing ? length(oldvarias_S)+1 : ind) - end +# Dispatch for variable indices instead of symbols +# change_ringvar(F::AbstractVector{<:MPolyRingElem}, ind::Union{AbstractVector{<:Integer}, UnitRange{<:Integer}}) = +# change_ringvar(F, [symbols(parent(first(F)))[i] for i in ind]) - ind_novarias = setdiff(eachindex(oldvarias_S), to_varias) - newR, newvarias = polynomial_ring(base_ring(R), newvarias_S) +# change_ringvar(f::MPolyRingElem, ind::Union{AbstractVector{<:Integer}, UnitRange{<:Integer}}) = +# change_ringvar([f], ind)[1] - res = typeof(first(F))[] - ctx = MPolyBuildCtx(newR) +# """ +# change_ringvar(F) - for f in F - for (e, c) in zip(exponent_vectors(f), coefficients(f)) - @assert(all([ e[i]==0 for i in ind_novarias ]), "Occurence of old variable.s found!") - push!(e, 0) - push_term!(ctx, c, [e[i] for i in to_varias ]) - end - push!(res, finish(ctx)) - end +# Automatically detect all unique variables present in the polynomials and inject them +# into a ring containing only those variables. +# """ +# function change_ringvar(F::AbstractVector{<:MPolyRingElem}) +# used_vars = unique(reduce(vcat, [Symbol.(vars(f)) for f in F])) +# return change_ringvar(F, used_vars) +# end - return res -end +# change_ringvar(f::MPolyRingElem) = change_ringvar([f])[1] -function change_ringvar_mod(F::Vector{P}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) where {P <: PolyRingElem} - R = parent(first(F)) - A, (x,) = polynomial_ring(base_ring(R), oldvarias_S) - return change_ringvar_mod([ evaluate(f, x) for f in F ], newvarias_S, oldvarias_S) -end -function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}, oldvarias_S::Vector{Symbol}) - return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) -end +""" + MPolyBuild(F::Vector{Vector{RingElem}}, new_S::Vector{Symbol}, idx::Int) -#function change_ringvar_mod(f::Union{MPolyRingElem, PolyRingElem}, newvarias_S::Vector{Symbol}) -# return first(change_ringvar_mod([f], newvarias_S, oldvarias_S)) -#end +Construct multivariate polynomials in a single variable. +`F` is a list of coefficient lists in degree-increasing order. +The polynomial will use the variable at index `idx` in `new_S`. +""" +function MPolyBuild(F::AbstractVector{<:AbstractVector{<:RingElement}}, new_S::Vector{Symbol}, idx::Int) + isempty(F) && return [] -function MPolyBuild(F::Vector{Vector{P}}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} A = parent(first(first(F))) - R, = polynomial_ring(A, newvarias_S) - to_varias = [ i==idx ? 1 : 2 for i in eachindex(newvarias_S) ] - - res = typeof(zero(R))[] - ctx = MPolyBuildCtx(R) - - LcF = [ filter!(t->t[2]!=0, collect(enumerate(f))) for f in F ] - for f in LcF - for (ef, c) in f - e = [ef-1, 0] - push_term!(ctx, c, [e[i] for i in to_varias ]) + R, _ = polynomial_ring(A, new_S) + + T = typeof(zero(A)) + n_vars = length(new_S) + + return map(F) do f_coeffs + coeffs = T[] + exps = Vector{Int}[] + + # Construct coeff/exp lists + for (deg_plus_1, c) in enumerate(f_coeffs) + if !iszero(c) + e_new = zeros(Int, n_vars) + e_new[idx] = deg_plus_1 - 1 + push!(coeffs, c) + push!(exps, e_new) + end end - push!(res, finish(ctx)) - end - return res + # Create the polynomial associated to f_coeffs + return R(coeffs, exps) + end end -function MPolyBuild(f::Vector{P}, newvarias_S::Vector{Symbol}, idx::Int) where {P <: RingElem} - return first(MPolyBuild([f], newvarias_S, idx)) -end \ No newline at end of file +# Dispatch for a single coefficient vector +MPolyBuild(f::AbstractVector{<:RingElement}, new_S::Vector{Symbol}, idx::Int) = MPolyBuild([f], new_S, idx)[1] \ No newline at end of file diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index f307ff5..e3c3c9b 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -335,7 +335,7 @@ function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=fa v>1 && println("Convert the coefficients into polynomials") L1Q = [ [QQ.(ss) for ss in s ] for s in L1 ] - @iftime v>0 sr = [ MPolyBuild(s, parent(P).S, (idx+1)%2) for s in L1Q ] + @iftime v>0 sr = [ MPolyBuild(s, symbols(parent(P)), (idx+1)%2) for s in L1Q ] return sr end @@ -352,7 +352,7 @@ end function mmod_param_crit(P::ZZMPolyRingElem, Q::ZZMPolyRingElem; n_threads=Threads.nthreads(), v=0, detect_app=true) prim = ZZ(1)<<(61) - RS = parent(P).S + RS = P |> parent |> symbols L1, L1f, primprod = [], [], ZZ(1) Ltemp = Vector{Vector{Vector{Vector{ZZRingElem}}}}(undef,n_threads+1) dP = derivative(P, 2) @@ -420,7 +420,10 @@ function mmod_param_crit(P::ZZMPolyRingElem, Q::ZZMPolyRingElem; n_threads=Threa v>1 && println("Convert the coefficients into polynomials") L1Q = [ [ QQ.(poly) for poly in param ] for param in L1f ] - @iftime v>0 param = Dict( m => vcat([[int_coeffs(MPolyBuild(param[1], parent(P).S, 1))]], [ int_coeffs(MPolyBuild(poly, parent(P).S, 1)) for poly in param[2:end] ]) for (m, param) in zip([-1,1], L1Q)) + @iftime v>0 param = Dict( m => vcat( + [[int_coeffs(MPolyBuild(param[1], symbols(parent(P)), 1))]], + [ int_coeffs(MPolyBuild(poly, symbols(parent(P)), 1)) for poly in param[2:end] ]) + for (m, param) in zip([-1,1], L1Q)) return param end @@ -465,7 +468,7 @@ function num_biv_rat_mod(A, P, RS) Ahmod = change_coefficient_ring(U, Ah1) Aeval = evaluate(Ahmod, [amod, bmod]) - return change_ringvar_mod(lift(Aeval), RS, newv) + return change_ringvar(lift(Aeval), RS) end function intersect_biv_mod(P::Vector{T} where T<:Any, A::MPolyRingElem, RS::Vector{Symbol}) @@ -480,7 +483,7 @@ function intersect_biv(P::Vector{T} where T<:Any, A::MPolyRingElem) return P[1] end compt = 0 - RS = parent(A).S + RS = A |> parent |> symbols dA, dAf = [], [] pprod, p = 1, ZZ(1) << 60 while compt<12 @@ -521,7 +524,7 @@ end function param_crit_split(f, g; v=0, detect_app=true, RS = nothing) @assert (f|>parent|>base_ring|>characteristic == 0 || !isnothing(RS)) "Variable names must be provided when char>0" if f|>parent|>base_ring|>characteristic == 0 - RS = parent(f).S + RS = f |> parent |> symbols end # Compute subresultants and factor the first subresultant v>0 && println("Compute subresultant sequence") From 70ccebb52f7a08090e3733e7f455ef0b30131220 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 13 Apr 2026 14:50:54 +0200 Subject: [PATCH 139/180] factor compute insulating boxes --- src/connectivity/buildpoly.jl | 26 +++---- src/connectivity/connectcurves.jl | 50 +++---------- src/connectivity/isolateboxes.jl | 120 +++++++++++++++++++++++++++++- 3 files changed, 138 insertions(+), 58 deletions(-) diff --git a/src/connectivity/buildpoly.jl b/src/connectivity/buildpoly.jl index 9fa8b42..c0da303 100644 --- a/src/connectivity/buildpoly.jl +++ b/src/connectivity/buildpoly.jl @@ -56,25 +56,17 @@ end # Dispatch for a single polynomial change_ringvar(f::Union{PolyRingElem, MPolyRingElem}, new_S::Vector{Symbol}) = change_ringvar([f], new_S)[1] -# Dispatch for variable indices instead of symbols -# change_ringvar(F::AbstractVector{<:MPolyRingElem}, ind::Union{AbstractVector{<:Integer}, UnitRange{<:Integer}}) = -# change_ringvar(F, [symbols(parent(first(F)))[i] for i in ind]) + """ + change_ringvar(F) -# change_ringvar(f::MPolyRingElem, ind::Union{AbstractVector{<:Integer}, UnitRange{<:Integer}}) = -# change_ringvar([f], ind)[1] - -# """ -# change_ringvar(F) - -# Automatically detect all unique variables present in the polynomials and inject them -# into a ring containing only those variables. -# """ -# function change_ringvar(F::AbstractVector{<:MPolyRingElem}) -# used_vars = unique(reduce(vcat, [Symbol.(vars(f)) for f in F])) -# return change_ringvar(F, used_vars) -# end +Automatically detect all unique variables present in the polynomials and inject them into a ring containing only those variables. +""" +function change_ringvar(F::AbstractVector{<:MPolyRingElem}) + used_vars = unique(reduce(vcat, [Symbol.(vars(f)) for f in F])) + return change_ringvar(F, used_vars) +end -# change_ringvar(f::MPolyRingElem) = change_ringvar([f])[1] +change_ringvar(f::MPolyRingElem) = change_ringvar([f])[1] """ diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 3c4b61b..788cc28 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -34,47 +34,15 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen params[-i] = [ [C[i][1] |> intC], C[i][2], C[i][3] ] end - v > 0 && println("Computing isolating critical boxes") - LBcrit = Dict() - @iftime (v > 0) xcritpermut, precx = compute_crit_boxes(params, LBcrit, precx, v) - xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in eachindex(LBcrit)) - - # println("LBcrit: ", LBcrit) - - v > 0 && println("\nTest for identifying singular boxes") -@iftime (v > 0) begin - ######################################################## - # For each mult of sing pts (keys) give the corresponding factors of the resultant (values) - ######################################################### - arbField = ArbField(precx) - Lfyk = diff_list(f, 2, max(maximum(eachindex(LBcrit)),2)) - for ind in eachindex(LBcrit) - ind < 0 && continue # control pts - m = ind <= 1 ? 2 : ind # nodes and extrems have mult 2 - noisolate = false - for _ in 1:5 - noisolate = false - for j in eachindex(LBcrit[ind]) - pcrit = [ rat_to_arb(c, arbField) for c in LBcrit[ind][j] ] - # Check if the the mult(pcrit)-th derivative of f vanishes on pcrit - if contains_zero(evaluate(Lfyk[m+1], pcrit)) - # TODO refine only boxes associated to multiplicity m - precx *= 2 - (v > 0) && println("Refine singular boxes of index $ind to $precx bits precision") - xcritpermut, precx = compute_crit_boxes(params, LBcrit, precx, v-1) - xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in eachindex(LBcrit)) - noisolate = true - break - end - end - noisolate || break - end - if noisolate - error("Problem in singular boxes refinement") - end + v > 0 && println("Computing insulating critical boxes") + @iftime (v > 0) + LBcrit, Lprecx = insulate_crit_boxes(f, params, precx) end -end + #println("LBcrit: ", LBcrit) + ############################# + # Compute boxes that intersect curve only on vertical sides + ############################## v > 0 && println("\nCompute intersections with critical boxes..") @iftime (v > 0) begin ## TODO : Refine only the intervals that need to be refined? only the factor that defines the intervals @@ -158,7 +126,9 @@ end # Graph computation fct, typeout = outf ? (Float64, Float64) : (identity, QQFieldElem) - + # Critical values and their order + xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in eachindex(LBcrit)) + xcritpermut = order_permut2d(xcrit) # List of vertex: at index i is the tuple of the coordinates of the i-th vertex Vert = Vector{Tuple{typeout, typeout}}() # List of edges: a tuple (i,j) is an edge between the i-th and j-th vertices diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index 3c6525a..46aeebd 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -74,9 +74,127 @@ function compute_crit_boxes(params, LBcrit, precx, v, max_attempts=5) error("Problem in isolating critical boxes") end - return (order_permut2d(xcrit), precx) + return precx end +function compute_singular_boxes(f, LBcrit, params, precx) + arbField = ArbField(precx) + Lfyk = diff_list(f, 2, max(maximum(eachindex(LBcrit)),2)) + for ind in eachindex(LBcrit) + ind < 0 && continue # control pts + m = ind <= 1 ? 2 : ind # nodes and extrems have mult 2 + noisolate = false + for _ in 1:5 + noisolate = false + for j in eachindex(LBcrit[ind]) + pcrit = [ rat_to_arb(c, arbField) for c in LBcrit[ind][j] ] + # Check if the the mult(pcrit)-th derivative of f vanishes on pcrit + if contains_zero(evaluate(Lfyk[m+1], pcrit)) + # TODO refine only boxes associated to multiplicity m + precx *= 2 + (v > 0) && println("Refine singular boxes of index $ind to $precx bits precision") + precx = compute_crit_boxes(params, LBcrit, precx, v-1) + noisolate = true + break + end + end + noisolate || break + end + if noisolate + error("Problem in singular boxes refinement") + end + end + return precx +end + +###################################3 +# File: critical_boxes.jl + +""" + _compute_boxes_for_index!(i, params, LBcrit, precx) + +Compute isolating boxes for a single index i. +""" +function _compute_boxes_for_index!(i, params, LBcrit, precx) + xvals = reduce(vcat, (isolate(pp, prec=precx) for pp in params[i][1])) + _expand_degenerate_intervals!(xvals, precx) + + arbField = ArbField(precx) + + yvals = [ + evaluate_arb(params[i][2], params[i][3], xc, arbField) + for xc in xvals + ] + _expand_degenerate_intervals!(yvals, precx) + + @inbounds LBcrit[i] = [[xvals[j], yvals[j]] for j in eachindex(xvals)] +end + + +""" + _needs_refinement(i, f, LBcrit, precx) + +Check if boxes at index i require refinement. +""" +function _needs_refinement(i, f, LBcrit, precx) + arbField = ArbField(precx) + m = i <= 1 ? 2 : i + # TODO: input, compute once for all i + Lfyk = diff_list(f, 2, max(i, 2)) + + for box in LBcrit[i] + pcrit = [rat_to_arb(c, arbField) for c in box] + + if contains_zero(evaluate(Lfyk[m+1], pcrit)) + return true + end + end + return false +end + + +""" + compute_crit_and_singular_boxes!(f, params, LBcrit, precx; max_attempts=5, v=0) + +Compute and refine critical boxes per index independently. +""" +function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) + LBcrit, Lprecx = Dict(), Dict() + + for i in keys(params) + attempts, precxi = 0, precx + while attempts <= max_attempts + try + attempts > 0 && v > 0 && + println("Refining index $i -> prec = $precxi") + + _compute_boxes_for_index!(i, params, LBcrit, precxi) + + # singularity check + if ! needs_refinement(i, f, LBcrit, precxi, params) + break + end + + # refine ONLY this index + precxi *= 2 + attempts += 1 + + catch e + precxi *= 2 + attempts += 1 + v > 1 && println("Error at index $i: ", e) + end + end + attempts > max_attempts && + error("Failed to isolate boxes for index $i") + + Lprecx[i] = precxi + end + + return LBcrit, Lprecx +end +####################################################### + # Helper function to process a single edge of the box function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v; max_retries=5) prec = initial_prec From a4770c51003928923526f2d1a7168e71366dab32 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 13 Apr 2026 15:57:19 +0200 Subject: [PATCH 140/180] factor and improve box intersection --- src/connectivity/connectcurves.jl | 88 +---------- src/connectivity/isolateboxes.jl | 233 ++++++++++++++++++++++++++++-- 2 files changed, 221 insertions(+), 100 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 788cc28..f45ba72 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -35,94 +35,10 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen end v > 0 && println("Computing insulating critical boxes") - @iftime (v > 0) - LBcrit, Lprecx = insulate_crit_boxes(f, params, precx) - end - #println("LBcrit: ", LBcrit) + @iftime (v > 0) LBcrit, Lprecx = insulate_crit_boxes(f, params, precx) - ############################# - # Compute boxes that intersect curve only on vertical sides - ############################## v > 0 && println("\nCompute intersections with critical boxes..") -@iftime (v > 0) begin - ## TODO : Refine only the intervals that need to be refined? only the factor that defines the intervals - LPCside = Dict{Int,Any}() - ndig = maximum([ndigits(length(LBcrit[i])) for i in eachindex(LBcrit)]) - for i in eachindex(LBcrit) - LPCside[i] = Array{Any}(undef, length(LBcrit[i])) - # Data printing part - ndigi = ndigits(length(LBcrit[i])) - Ptype = (i > length(LBcrit)-length(C)) ? "Pcon" : "mult" - ### - precxtmp = precx - compt = 0 - while compt < 5 - flag = false - # println(LBcrit[i]) - for j in eachindex(LBcrit[i]) - v > 0 && print("$Ptype=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") - pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp,v=v) - npcside = [length(n) for (I, n) in pcside] - # println("($i, $j): $npcside") - if (i == 1 && sum(npcside) > 2) || (i != 1 && sum(npcside[1:2]) != 0) - precxtmp *= 2 - v > 0 && println("\nRefine boxes along x-axis to $precxtmp bits precision") - refine_xboxes(params[i][1], LBcrit[i], precxtmp) - flag = true - compt += 1 - break - end - LPCside[i][j] = pcside - end - flag || break - end - v > 0 && println("") - if compt >= 5 - error("Problem in computing intersections with boxes") - end - end - LnPCside = Dict(i => [[length(indI) for (L, indI) in PB] for PB in LPCside[i]] for i in eachindex(LPCside)) - - # Update extreme boxes - if haskey(LBcrit, 1) - for j in eachindex(LBcrit[1]) - # If the curve does not intersect the box only on vertical sides - if !(LnPCside[1][j][1:2] == [0, 0]) - PCside, nPCside = LPCside[1][j], LnPCside[1][j] - I = [ l[1] for l in PCside[3:end] ] - nI = [ l[2] for l in PCside[3:end] ] - # Locate the orientation of the extreme point - # s is the index on the side where there are more branches - # s=1: left; s=2: right - s = argmax([length(I[1]), length(I[2])]) - # Ordinate range of the extreme point - ycrit = LBcrit[1][j][2] - # If it intersects on the bottom side - if nPCside[1] == 1 - # yinf: the intersection with the vertical side just below the extreme point - yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[1]]) - # We vertically enlarge the box until it intersects on the horizontal side - push!(LPCside[1][j][s + 2][2], yinf) - LPCside[1][j][1][2] = [] - # We update the intersection numbers - LnPCside[1][j][s + 2] += 1 - LnPCside[1][j][1] = 0 - end - # If it intersects on the top side - if nPCside[2] == 1 - # ymax: the intersection with the vertical side just above the extreme point - ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[2]]) - # We vertically enlarge the box until it intersects on the horizontal side - push!(LPCside[1][j][s + 2][2], ymax) - LPCside[1][j][2][2] = [] - # We update the intersection numbers - LnPCside[1][j][s + 2] += 1 - LnPCside[1][j][2] = 0 - end - end - end - end -end + @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(LBcrit, params, Lprecx) # Graph computation fct, typeout = outf ? (Float64, Float64) : (identity, QQFieldElem) diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index 46aeebd..4ce431f 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -1,3 +1,8 @@ +const Side = Tuple{Vector{QQFieldElem}, Vector{Int}} +const Sides = NTuple{4, Side} +const Boxes = Vector{Side} + + in_inter(I, J) = J[1] <= I[1] && I[2] <= J[2] overlap_inter(I,J) = max(I[1], J[1]) <= min(I[2], J[2]) @@ -229,15 +234,15 @@ function intersect_box(f, B; prec=100, v=0) # B[1] represents x-bounds, B[2] represents y-bounds # Evaluate horizontal edges (fix y to B[2][1] and B[2][2], target x-interval B[1]) - edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v) - edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v) + edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v)::Side + edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v)::Side # Evaluate vertical edges (fix x to B[1][1] and B[1][2], target y-interval B[2]) - edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v) - edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v) + edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v)::Side + edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v)::Side - # Return as a typed array of Tuples - return [edge_y1, edge_y2, edge_x1, edge_x2] + # Return as a 4-Tuple of 2-Tuples + return (edge_y1, edge_y2, edge_x1, edge_x2) end @@ -267,13 +272,213 @@ function refine_xboxes(F::Vector{T} where T<:Union{PolyRingElem, MPolyRingElem}, return _update_LB_first_axis!(LB, xnew) end -""" - refine_ith_xboxes(f, LB, i, prec) +## TODO : Refine only the intervals that need to be refined? only the factor that defines the intervals + + +function intersect_vertical_boxes(LBcrit, params, Lprecx) + LPCside = Dict{Int,Any}() + ndig = maximum([ndigits(length(LBcrit[i])) for i in eachindex(LBcrit)]) + for i in eachindex(LBcrit) + LPCside[i] = Array{Any}(undef, length(LBcrit[i])) + # Data printing part + ndigi = ndigits(length(LBcrit[i])) + Ptype = (i > length(LBcrit)-length(C)) ? "Pcon" : "mult" + ### + precxtmp = Lprecx[i] + compt = 0 + while compt < 5 + flag = false + # println(LBcrit[i]) + for j in eachindex(LBcrit[i]) + v > 0 && print("$Ptype=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") + pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp,v=v) + npcside = [length(n) for (I, n) in pcside] + # println("($i, $j): $npcside") + if (i == 1 && sum(npcside) > 2) || (i != 1 && sum(npcside[1:2]) != 0) + precxtmp *= 2 + v > 0 && println("\nRefine boxes along x-axis to $precxtmp bits precision") + refine_xboxes(params[i][1], LBcrit[i], precxtmp) + flag = true + compt += 1 + break + end + LPCside[i][j] = pcside + end + flag || break + end + v > 0 && println("") + if compt >= 5 + error("Problem in computing intersections with boxes") + end + Lprecx[i] = precxtmp + end + LnPCside = Dict(i => [[length(indI) for (L, indI) in PB] for PB in LPCside[i]] for i in eachindex(LPCside)) + + # Update extreme boxes + if haskey(LBcrit, 1) + for j in eachindex(LBcrit[1]) + # If the curve does not intersect the box only on vertical sides + if !(LnPCside[1][j][1:2] == [0, 0]) + PCside, nPCside = LPCside[1][j], LnPCside[1][j] + # Get the left and right sides + I = [ l[1] for l in PCside[3:end] ] + nI = [ l[2] for l in PCside[3:end] ] + # Locate the orientation of the extreme point + # s is the index on the side where there are more branches + # s=1: left; s=2: right + s = argmax([length(I[1]), length(I[2])]) + # Ordinate range of the extreme point + ycrit = LBcrit[1][j][2] + # If it intersects on the bottom side + if nPCside[1] == 1 + # yinf: the intersection with the vertical side just below the extreme point + yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[1]]) + # We vertically enlarge the box until it intersects on the horizontal side + push!(LPCside[1][j][s + 2][2], yinf) + LPCside[1][j][1][2] = [] + # We update the intersection numbers + LnPCside[1][j][s + 2] += 1 + LnPCside[1][j][1] = 0 + end + # If it intersects on the top side + if nPCside[2] == 1 + # ymax: the intersection with the vertical side just above the extreme point + ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[2]]) + # We vertically enlarge the box until it intersects on the horizontal side + push!(LPCside[1][j][s + 2][2], ymax) + LPCside[1][j][2][2] = [] + # We update the intersection numbers + LnPCside[1][j][s + 2] += 1 + LnPCside[1][j][2] = 0 + end + end + end + end + return LPCside, LnPCside +end -Refine only the i-th box along first axis using i-th root of f. -""" -function refine_ith_xboxes(f, LB, i, prec) - xnew = isolate(f, prec=prec) - @inbounds LB[i] = [xnew[i], LB[i][2]] - return LB +############################### + + + +function intersect_vertical_boxes_bis(LBcrit, params, Lprecx; max_attempts=5, v=0) + + LPCside = Dict{Int, Boxes}() + + for (i, boxes) in pairs(LBcrit) + prec = Lprecx[i] + n = length(boxes) + + sides_vec = Vector{Sides}(undef, n) + + for attempt in 1:max_attempts + refined = false + + @inbounds for j in 1:n + v > 0 && print("i=$i ($j/$n)\r") + + pc = intersect_box(f, boxes[j], prec=prec, v=v)::Sides + + c1 = length(pc[1][2]) + c2 = length(pc[2][2]) + c3 = length(pc[3][2]) + c4 = length(pc[4][2]) + + if (i == 1 && (c1 + c2 + c3 + c4 > 2)) || + (i != 1 && (c1 != 0 || c2 != 0)) + + prec *= 2 + v > 0 && println("\nRefine -> prec = $prec") + + refine_xboxes(params[i][1], boxes, prec) + + refined = true + break + end + + sides_vec[j] = pc + end + + refined || break + attempt == max_attempts && + error("Problem in computing intersections (i=$i)") + end + + LPCside[i] = sides_vec + Lprecx[i] = prec + + v > 0 && println() + end + + # ---- Counts (type-stable) ---- + LnPCside = Dict{Int, Vector{NTuple{4, Int}}}() + + for (i, vec) in pairs(LPCside) + LnPCside[i] = [ + ( + length(pc[1][2]), + length(pc[2][2]), + length(pc[3][2]), + length(pc[4][2]) + ) + for pc in vec + ] + end + + # ---- Extremal case (i == 1) ---- + if haskey(LBcrit, 1) + boxes = LBcrit[1] + pcs = LPCside[1] + cnts = LnPCside[1] + + @inbounds for j in eachindex(boxes) + c1, c2, c3, c4 = cnts[j] + + (c1 == 0 && c2 == 0) && continue + + pc = pcs[j] + ycrit = boxes[j][2] + + I1 = pc[3][1] # left + I2 = pc[4][1] # right + + # Orientation of the curve left(s=1)/right(s=2) + s = length(I1) >= length(I2) ? 1 : 2 + + # ---- intersection on bottom ---- + if c1 == 1 + # Attach to the max intersection below the bow on the correct side + yinf = maximum(i for (i, yy) in pairs((s == 1 ? I1 : I2)) if yy[1] < ycrit[1]) + + push!(pc[s+2][2], yinf) + pc[1][2] = Int[] + + cnts[j] = ( + 0, + c2, + s == 1 ? c3 + 1 : c3, + s == 2 ? c4 + 1 : c4 + ) + + c1, c2, c3, c4 = cnts[j] # for next step + end + + # ---- intersection on top ---- + if c2 == 1 + ymax = minimum(i for (i, yy) in pairs((s == 1 ? I1 : I2)) if yy[2] > ycrit[2]) + + push!(pc[s+2][2], ymax) + pc[2][2] = Int[] + + cnts[j] = ( + c1, + 0, + s == 1 ? c3 + 1 : c3, + s == 2 ? c4 + 1 : c4 + ) + end + end + end + + return LPCside, LnPCside end \ No newline at end of file From 5322f8470ac10ae267846da931410522bedc3a81 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 13 Apr 2026 16:28:14 +0200 Subject: [PATCH 141/180] small trucs --- src/connectivity/subresultants.jl | 1 + 1 file changed, 1 insertion(+) diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index e3c3c9b..c99fc1f 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -477,6 +477,7 @@ function intersect_biv_mod(P::Vector{T} where T<:Any, A::MPolyRingElem, RS::Vect end function intersect_biv(P::Vector{T} where T<:Any, A::MPolyRingElem) + # TODO: test the reconstruction # P = [Lq, a, b] encodes sets (x,a(x)/b(x)) where Lq[i](x)=0 # Compute divisor dA of q that encodes intersection with A(x,y)=0 if iszero(A) From eb687794ada2c2ee1acf0e24665404981df0d280 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Mon, 13 Apr 2026 20:44:17 +0200 Subject: [PATCH 142/180] fixes and TODOs --- src/connectivity/connectcurves.jl | 7 +- src/connectivity/isolateboxes.jl | 193 +++--------------------------- src/connectivity/subresultants.jl | 3 + 3 files changed, 22 insertions(+), 181 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index f45ba72..a87ee59 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -29,16 +29,15 @@ function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); gen v > 0 && println("Compute parametrization of critical pts...") @iftime (v > 0) params = param_crit_split(f,g,v=v-1, detect_app=true) #@iftime (v > 0) params = mmod_param_crit(f, g,v=v-1, detect_app=true) - for i in 1:length(C) params[-i] = [ [C[i][1] |> intC], C[i][2], C[i][3] ] end v > 0 && println("Computing insulating critical boxes") - @iftime (v > 0) LBcrit, Lprecx = insulate_crit_boxes(f, params, precx) + @iftime (v > 0) LBcrit, Lprecx = insulate_crit_boxes(f, params, precx, v=v-1) - v > 0 && println("\nCompute intersections with critical boxes..") - @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(LBcrit, params, Lprecx) + v > 0 && println("Compute intersections with critical boxes..") + @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(f, params, LBcrit, Lprecx, v=v-1) # Graph computation fct, typeout = outf ? (Float64, Float64) : (identity, QQFieldElem) diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index 4ce431f..9e2cc8e 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -1,6 +1,6 @@ -const Side = Tuple{Vector{QQFieldElem}, Vector{Int}} -const Sides = NTuple{4, Side} -const Boxes = Vector{Side} +const side = Tuple{Vector{Vector{QQFieldElem}}, Vector{Int}} +const Sides = NTuple{4, side} +const Boxes = Vector{Sides} in_inter(I, J) = J[1] <= I[1] && I[2] <= J[2] @@ -40,81 +40,6 @@ function _expand_degenerate_intervals!(xnew, prec) return xnew end -# TODO: add the singularity check here, probably just by calling a function -# make sure we refine only the boxes that need to be refined -function compute_crit_boxes(params, LBcrit, precx, v, max_attempts=5) - compt = 0 - xcrit = Dict() - while compt <= max_attempts - try - v > 0 && compt > 0 && println("ComputeBoxes: refine x-precision to $precx bits") - # TODO : check that no overlap between different isolations - xcrit = Dict(i=> reduce(vcat, [isolate(pp, prec=precx) for pp in p[1]]) for (i, p) in params) - # Enlarge exact isolating root intervals - for xvals in values(xcrit) - _expand_degenerate_intervals!(xvals, precx) - end - arbField = ArbField(precx) - for i in keys(xcrit) - xvals = xcrit[i] - ycrit = [ - evaluate_arb(params[i][2], params[i][3], xc, arbField) - for xc in xvals - ] - _expand_degenerate_intervals!(ycrit, precx) - @inbounds LBcrit[i] = [ - [xvals[j], ycrit[j]] for j in eachindex(ycrit) - ] - end - catch e - precx *= 2 - v > 1 && println("Error in isolating critical boxes: ", e) - compt += 1 - else - break - end - end - # TODO: is that a relevant upper bound? - if compt > max_attempts - error("Problem in isolating critical boxes") - end - - return precx -end - -function compute_singular_boxes(f, LBcrit, params, precx) - arbField = ArbField(precx) - Lfyk = diff_list(f, 2, max(maximum(eachindex(LBcrit)),2)) - for ind in eachindex(LBcrit) - ind < 0 && continue # control pts - m = ind <= 1 ? 2 : ind # nodes and extrems have mult 2 - noisolate = false - for _ in 1:5 - noisolate = false - for j in eachindex(LBcrit[ind]) - pcrit = [ rat_to_arb(c, arbField) for c in LBcrit[ind][j] ] - # Check if the the mult(pcrit)-th derivative of f vanishes on pcrit - if contains_zero(evaluate(Lfyk[m+1], pcrit)) - # TODO refine only boxes associated to multiplicity m - precx *= 2 - (v > 0) && println("Refine singular boxes of index $ind to $precx bits precision") - precx = compute_crit_boxes(params, LBcrit, precx, v-1) - noisolate = true - break - end - end - noisolate || break - end - if noisolate - error("Problem in singular boxes refinement") - end - end - return precx -end - -###################################3 -# File: critical_boxes.jl - """ _compute_boxes_for_index!(i, params, LBcrit, precx) @@ -159,9 +84,12 @@ end """ - compute_crit_and_singular_boxes!(f, params, LBcrit, precx; max_attempts=5, v=0) + compute_crit_and_singular_boxes(f, params, precx; max_attempts=5, v=0) -Compute and refine critical boxes per index independently. +Compute insulating boxes for critical points, refining precision if necessary. +Insulating means that each box contains a single critical point and +all branches of the curve intersecting the box are incident to this +critical point. """ function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) LBcrit, Lprecx = Dict(), Dict() @@ -176,7 +104,7 @@ function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) _compute_boxes_for_index!(i, params, LBcrit, precxi) # singularity check - if ! needs_refinement(i, f, LBcrit, precxi, params) + if !_needs_refinement(i, f, LBcrit, precxi) break end @@ -234,12 +162,12 @@ function intersect_box(f, B; prec=100, v=0) # B[1] represents x-bounds, B[2] represents y-bounds # Evaluate horizontal edges (fix y to B[2][1] and B[2][2], target x-interval B[1]) - edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v)::Side - edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v)::Side + edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v)::side + edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v)::side # Evaluate vertical edges (fix x to B[1][1] and B[1][2], target y-interval B[2]) - edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v)::Side - edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v)::Side + edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v)::side + edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v)::side # Return as a 4-Tuple of 2-Tuples return (edge_y1, edge_y2, edge_x1, edge_x2) @@ -272,96 +200,7 @@ function refine_xboxes(F::Vector{T} where T<:Union{PolyRingElem, MPolyRingElem}, return _update_LB_first_axis!(LB, xnew) end -## TODO : Refine only the intervals that need to be refined? only the factor that defines the intervals - - -function intersect_vertical_boxes(LBcrit, params, Lprecx) - LPCside = Dict{Int,Any}() - ndig = maximum([ndigits(length(LBcrit[i])) for i in eachindex(LBcrit)]) - for i in eachindex(LBcrit) - LPCside[i] = Array{Any}(undef, length(LBcrit[i])) - # Data printing part - ndigi = ndigits(length(LBcrit[i])) - Ptype = (i > length(LBcrit)-length(C)) ? "Pcon" : "mult" - ### - precxtmp = Lprecx[i] - compt = 0 - while compt < 5 - flag = false - # println(LBcrit[i]) - for j in eachindex(LBcrit[i]) - v > 0 && print("$Ptype=$i ; $(j)/$(length(LBcrit[i]))$(repeat(" ", ndig-ndigi+1))pts","\r") - pcside = intersect_box(f, LBcrit[i][j], prec=precxtmp,v=v) - npcside = [length(n) for (I, n) in pcside] - # println("($i, $j): $npcside") - if (i == 1 && sum(npcside) > 2) || (i != 1 && sum(npcside[1:2]) != 0) - precxtmp *= 2 - v > 0 && println("\nRefine boxes along x-axis to $precxtmp bits precision") - refine_xboxes(params[i][1], LBcrit[i], precxtmp) - flag = true - compt += 1 - break - end - LPCside[i][j] = pcside - end - flag || break - end - v > 0 && println("") - if compt >= 5 - error("Problem in computing intersections with boxes") - end - Lprecx[i] = precxtmp - end - LnPCside = Dict(i => [[length(indI) for (L, indI) in PB] for PB in LPCside[i]] for i in eachindex(LPCside)) - - # Update extreme boxes - if haskey(LBcrit, 1) - for j in eachindex(LBcrit[1]) - # If the curve does not intersect the box only on vertical sides - if !(LnPCside[1][j][1:2] == [0, 0]) - PCside, nPCside = LPCside[1][j], LnPCside[1][j] - # Get the left and right sides - I = [ l[1] for l in PCside[3:end] ] - nI = [ l[2] for l in PCside[3:end] ] - # Locate the orientation of the extreme point - # s is the index on the side where there are more branches - # s=1: left; s=2: right - s = argmax([length(I[1]), length(I[2])]) - # Ordinate range of the extreme point - ycrit = LBcrit[1][j][2] - # If it intersects on the bottom side - if nPCside[1] == 1 - # yinf: the intersection with the vertical side just below the extreme point - yinf = maximum([i for (i, yy) in pairs(I[s]) if yy[1] < ycrit[1]]) - # We vertically enlarge the box until it intersects on the horizontal side - push!(LPCside[1][j][s + 2][2], yinf) - LPCside[1][j][1][2] = [] - # We update the intersection numbers - LnPCside[1][j][s + 2] += 1 - LnPCside[1][j][1] = 0 - end - # If it intersects on the top side - if nPCside[2] == 1 - # ymax: the intersection with the vertical side just above the extreme point - ymax = minimum([i for (i, yy) in pairs(I[s]) if yy[2] > ycrit[2]]) - # We vertically enlarge the box until it intersects on the horizontal side - push!(LPCside[1][j][s + 2][2], ymax) - LPCside[1][j][2][2] = [] - # We update the intersection numbers - LnPCside[1][j][s + 2] += 1 - LnPCside[1][j][2] = 0 - end - end - end - end - return LPCside, LnPCside -end - -############################### - - - -function intersect_vertical_boxes_bis(LBcrit, params, Lprecx; max_attempts=5, v=0) +function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0) LPCside = Dict{Int, Boxes}() @@ -375,7 +214,7 @@ function intersect_vertical_boxes_bis(LBcrit, params, Lprecx; max_attempts=5, v= refined = false @inbounds for j in 1:n - v > 0 && print("i=$i ($j/$n)\r") + v >= 0 && print("i=$i ($j/$n)\r") pc = intersect_box(f, boxes[j], prec=prec, v=v)::Sides @@ -407,7 +246,7 @@ function intersect_vertical_boxes_bis(LBcrit, params, Lprecx; max_attempts=5, v= LPCside[i] = sides_vec Lprecx[i] = prec - v > 0 && println() + v >= 0 && println() end # ---- Counts (type-stable) ---- diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index c99fc1f..6c19a48 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -528,6 +528,7 @@ function param_crit_split(f, g; v=0, detect_app=true, RS = nothing) RS = f |> parent |> symbols end # Compute subresultants and factor the first subresultant + # TODO: factor f before computing subresultants or at least divide by content v>0 && println("Compute subresultant sequence") if total_degree(f) > 30 && f|>parent|>base_ring|>characteristic == 0 @iftime v>0 sr = mmod_subresultants(f, derivative(f, 2), 2, list=true, n_ssr=2, v=v-1) @@ -539,6 +540,8 @@ function param_crit_split(f, g; v=0, detect_app=true, RS = nothing) return Dict() end + # TODO: sr is univariate? check what's called + # TODO: try full factorization? v>1 && println("Square-free factorization") @iftime v>1 sqr = collect(factor_squarefree(sr[1][1])) From a6ddb2d25824bf9c3495b13bda81dfd089fb364e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Mon, 13 Apr 2026 21:32:38 +0200 Subject: [PATCH 143/180] start plot export --- src/connectivity/connectcurves.jl | 2 +- src/connectivity/plots.jl | 97 +++++++++++++++++++++++++++++++ 2 files changed, 98 insertions(+), 1 deletion(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index a87ee59..a79168e 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -1,6 +1,6 @@ export compute_graph, connected_components, number_connected_components, group_by_component, merge_graphs, - plot_graph, plot_graphs, plot_graph_comp, Bresultant, param_crit_split + plot_graph, plot_graphs, plot_graph_comp, Bresultant, param_crit_split, build_graph_components_data, build_graphs_data, build_graph_data # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index ba1f3c6..e0b28f9 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -79,4 +79,101 @@ function replace_width_height_in_file(filename, x, y) # Write the modified content back to the file write(filename, content) +end + +# ---------- TYPES ---------- + +struct EdgeGroup + edges::Vector{Tuple{Vector{Float64}, Vector{Float64}}} + color::Int64#NTuple{3,Float64} + width::Float64 +end + +struct PointGroup + vertices::Tuple{Vector{Float64}, Vector{Float64}} # (x, y) + color::Int64#NTuple{3,Float64} + marker::Symbol +end + +struct GraphPlotData + edge_groups::Vector{EdgeGroup} + point_groups::Vector{PointGroup} +end + +# ---------- HELPERS ---------- + +function normalize_vemph(Vemph) + if Vemph isa Vector{Vector} + return Vemph + elseif Vemph isa Vector + return [Vemph] + elseif Vemph isa Dict + return collect(values(Vemph)) + else + return Vector{Vector{Int}}() + end +end + +# ---------- CORE BUILDERS ---------- +# TODO: remove the sequence in edge_groups as there should be only one, right? (same for point_groups in build_graph_data) + +function build_graph_data(G, Vemph=Vector{Vector{Int}}(); width=3.0, vert=true) + Vemph = normalize_vemph(Vemph) + V, E = G + + # edges + edges = [ + begin + v1, v2 = [map(Float64, V[idx]) for idx in e] + ([v1[1], v2[1]], [v1[2], v2[2]]) + end + for e in E + ] + + edge_groups = [EdgeGroup(edges, rand(1:666), width)] + + #point groups + point_groups = PointGroup[] + + if vert + vx = map(v -> Float64(v[1]), V) + vy = map(v -> Float64(v[2]), V) + push!(point_groups, PointGroup((vx, vy), rand(1:666), :diamond)) + end + + for group in Vemph + hx = map(j -> Float64(V[j][1]), group) + hy = map(j -> Float64(V[j][2]), group) + push!(point_groups, PointGroup((hx, hy), rand(1:666), :diamond)) + end + + return GraphPlotData(edge_groups, point_groups) +end + +# ---------- MULTI GRAPHS ---------- + +function build_graphs_data(CG; width=3.0, vert=true) + results = GraphPlotData[] + + for item in CG + + G, Vemph = length(item) == 2 ? item : item, Vector{Int}() + data = build_graph_data(G, Vemph; width=width, vert=vert) + + # override edge color per graph + for eg in data.edge_groups + eg = EdgeGroup(eg.edges, rand(1:666), eg.width) + end + + push!(results, data) + end + + return results +end + +# ---------- CONNECTED COMPONENTS ---------- + +function build_graph_components_data(G, Vemph=Vector{Int}(); width=3.0, vert=true) + CG = connected_components(G, Vemph) + return build_graphs_data(CG; width=width, vert=vert) end \ No newline at end of file From 54bea33bfee06be4c06372b1cc949664971f7ff3 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 14 Apr 2026 01:51:50 +0200 Subject: [PATCH 144/180] todo notes --- src/connectivity/isolateboxes.jl | 2 +- src/connectivity/subresultants.jl | 1 + 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index 9e2cc8e..d5b2fc4 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -4,7 +4,7 @@ const Boxes = Vector{Sides} in_inter(I, J) = J[1] <= I[1] && I[2] <= J[2] -overlap_inter(I,J) = max(I[1], J[1]) <= min(I[2], J[2]) +overlap_inter(I, J) = max(I[1], J[1]) <= min(I[2], J[2]) # Function that isolate roots of a multivariate polynomial with a # single variable diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index 6c19a48..4ffdaf7 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -564,6 +564,7 @@ function param_crit_split(f, g; v=0, detect_app=true, RS = nothing) end # Nodes : multiplicity 2 in res + # TODO: first test with interval arithmetics? Most of the time this will suffice v>0 && println("Compute apparent singularities") if 2 in sqrmult if detect_app From f52a0112ac99d9319e6bb1fe258294aaff4247f3 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 14 Apr 2026 16:00:35 +0200 Subject: [PATCH 145/180] plot ok, without removing previous --- Manifest.toml | 4 ++-- src/connectivity/connectcurves.jl | 7 +++++++ src/connectivity/isolateboxes.jl | 2 +- src/connectivity/plots.jl | 35 ++++++++----------------------- 4 files changed, 19 insertions(+), 29 deletions(-) diff --git a/Manifest.toml b/Manifest.toml index 0c5efb6..43a90bf 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -1,6 +1,6 @@ # This file is machine-generated - editing it directly is not advised -julia_version = "1.12.5" +julia_version = "1.12.6" manifest_format = "2.0" project_hash = "df55572e31ee2a4a5a0c44bb96cd0c13ec9af668" @@ -15,7 +15,7 @@ weakdeps = ["Test"] TestExt = "Test" [[deps.AlgebraicSolving]] -deps = ["Colors", "LinearAlgebra", "Logging", "Markdown", "Nemo", "Plots", "Primes", "Printf", "Random", "StaticArrays", "msolve_jll"] +deps = ["BenchmarkTools", "Colors", "LinearAlgebra", "Logging", "Markdown", "Nemo", "Plots", "Primes", "Printf", "Random", "StaticArrays", "msolve_jll"] path = "." uuid = "66b61cbe-0446-4d5d-9090-1ff510639f9d" version = "0.10.4" diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index a79168e..00d3395 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -15,6 +15,13 @@ include("plots.jl") include("arbtools.jl") include("buildpoly.jl") +# Input: +# The space curve is given by f(x,y) = 0 and (df/dy)(x,y)*z = g(x,y) +# it is assumed in generic position of put it using generic parameter +# for now f is assumed to be square-free (future feature) +# C is a list of parametrization [p,a,b] of plane pts i.e. such that p(x)=0,y=a(x)/b(x) +# these points must be on the curve +# Output: Computes a graph homeomorphic to the curve, identitying point in C function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, int_coeff=true, outf=true) where (P <: MPolyRingElem) R = parent(f) x, y = gens(R) diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index d5b2fc4..c8cbe9a 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -318,6 +318,6 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0 end end end - + #TODO: by design bottom/top sides in LnPCside are [0,0] -> remove return LPCside, LnPCside end \ No newline at end of file diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index e0b28f9..c2e8a42 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -96,11 +96,11 @@ struct PointGroup end struct GraphPlotData - edge_groups::Vector{EdgeGroup} + edge_groups::EdgeGroup point_groups::Vector{PointGroup} end -# ---------- HELPERS ---------- +# ---------- HELPER ---------- function normalize_vemph(Vemph) if Vemph isa Vector{Vector} @@ -115,9 +115,7 @@ function normalize_vemph(Vemph) end # ---------- CORE BUILDERS ---------- -# TODO: remove the sequence in edge_groups as there should be only one, right? (same for point_groups in build_graph_data) - -function build_graph_data(G, Vemph=Vector{Vector{Int}}(); width=3.0, vert=true) +function build_graph_data(G, Vemph=Vector{Vector{Int}}(); width=3.0, vert=true, color=rand(1:666)) Vemph = normalize_vemph(Vemph) V, E = G @@ -129,25 +127,24 @@ function build_graph_data(G, Vemph=Vector{Vector{Int}}(); width=3.0, vert=true) end for e in E ] + edge_group = EdgeGroup(edges, color, width) - edge_groups = [EdgeGroup(edges, rand(1:666), width)] - - #point groups + #points point_groups = PointGroup[] if vert vx = map(v -> Float64(v[1]), V) vy = map(v -> Float64(v[2]), V) - push!(point_groups, PointGroup((vx, vy), rand(1:666), :diamond)) + push!(point_groups, PointGroup((vx, vy), 17, :diamond)) end for group in Vemph hx = map(j -> Float64(V[j][1]), group) hy = map(j -> Float64(V[j][2]), group) - push!(point_groups, PointGroup((hx, hy), rand(1:666), :diamond)) + push!(point_groups, PointGroup((hx, hy), color, :diamond)) end - return GraphPlotData(edge_groups, point_groups) + return GraphPlotData(edge_group, point_groups) end # ---------- MULTI GRAPHS ---------- @@ -156,24 +153,10 @@ function build_graphs_data(CG; width=3.0, vert=true) results = GraphPlotData[] for item in CG - G, Vemph = length(item) == 2 ? item : item, Vector{Int}() - data = build_graph_data(G, Vemph; width=width, vert=vert) - - # override edge color per graph - for eg in data.edge_groups - eg = EdgeGroup(eg.edges, rand(1:666), eg.width) - end + data = build_graph_data(G, Vemph; width=width, vert=vert, color=rand(1:666)) push!(results, data) end - return results -end - -# ---------- CONNECTED COMPONENTS ---------- - -function build_graph_components_data(G, Vemph=Vector{Int}(); width=3.0, vert=true) - CG = connected_components(G, Vemph) - return build_graphs_data(CG; width=width, vert=vert) end \ No newline at end of file From 3a0be5ff566f431b3c6be818814b9dbc232e3d01 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 14 Apr 2026 19:08:42 +0200 Subject: [PATCH 146/180] big changes in progress --- src/connectivity/connectcurves.jl | 452 ++++++++++++++++++++---------- src/connectivity/datastruct.jl | 29 ++ src/connectivity/isolateboxes.jl | 334 ++++++++++++++++------ src/connectivity/newgraph.jl | 186 ++++++++++++ src/connectivity/plots.jl | 2 +- src/connectivity/tools.jl | 17 ++ 6 files changed, 791 insertions(+), 229 deletions(-) create mode 100644 src/connectivity/datastruct.jl create mode 100644 src/connectivity/newgraph.jl diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 00d3395..150f0c1 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -10,10 +10,11 @@ export compute_graph, connected_components, number_connected_components, group_b include("tools.jl") include("subresultants.jl") include("isolateboxes.jl") -include("graph.jl") +include("newgraph.jl") include("plots.jl") include("arbtools.jl") include("buildpoly.jl") +include("datastruct.jl") # Input: # The space curve is given by f(x,y) = 0 and (df/dy)(x,y)*z = g(x,y) @@ -22,201 +23,366 @@ include("buildpoly.jl") # C is a list of parametrization [p,a,b] of plane pts i.e. such that p(x)=0,y=a(x)/b(x) # these points must be on the curve # Output: Computes a graph homeomorphic to the curve, identitying point in C -function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, int_coeff=true, outf=true) where (P <: MPolyRingElem) +# function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, int_coeff=true, outf=true) where (P <: MPolyRingElem) +# R = parent(f) +# x, y = gens(R) +# intC = int_coeff ? int_coeffs : identity +# # Pre-processing the input +# f, g = intC([f,g]) +# changemat = generic ? [1 0; 0 1] : trimat_rand(QQ, 2, range=-100:100) +# f = evaluate(f, collect(changemat*[x; y])); +# v > 1 && println(f) +# precx = precx <= 1 ? 2 : precx + +# v > 0 && println("Compute parametrization of critical pts...") +# @iftime (v > 0) params = param_crit_split(f,g,v=v-1, detect_app=true) +# #@iftime (v > 0) params = mmod_param_crit(f, g,v=v-1, detect_app=true) +# for i in 1:length(C) +# params[-i] = [ [C[i][1] |> intC], C[i][2], C[i][3] ] +# end + +# v > 0 && println("Computing insulating critical boxes") +# @iftime (v > 0) LBcrit, Lprecx = insulate_crit_boxes(f, params, precx, v=v-1) + +# v > 0 && println("Compute intersections with critical boxes..") +# @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf, v=v-1) + +# # Graph computation +# fct, typeout = outf ? (Float64, Float64) : (identity, QQFieldElem) +# # Critical values and their order +# xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in eachindex(LBcrit)) +# xcritpermut = order_permut2d(xcrit) +# # List of vertex: at index i is the tuple of the coordinates of the i-th vertex +# Vert = Vector{Tuple{typeout, typeout}}() +# # List of edges: a tuple (i,j) is an edge between the i-th and j-th vertices +# Edg = Vector{Tuple{Int, Int}}() +# Corr = Dict( m => [[[], [[], [], []], []] for j in xcrit[m] ] for m in eachindex(xcrit)) +# Vcon = [ [] for _ in 1:length(C) ] + +# # Keep track of processed isolated & apparent singularities +# Lapp = [[],[]] + +# for ind in eachindex(xcritpermut) +# i, j = xcritpermut[ind] + +# if ind > 1 +# i1, j1 = xcritpermut[ind - 1] +# end +# if ind < length(xcritpermut) +# i2, j2 = xcritpermut[ind + 1] +# I2L, = LPCside[i2][j2][3] +# end + +# PCside = LPCside[i][j] +# I = [ l[1] for l in PCside[3:end] ] +# nI = [ l[2] for l in PCside[3:end] ] + +# xcmid = sum(LBcrit[i][j][1])//2 |> fct +# ycmid = sum(LBcrit[i][j][2])//2 |> fct + +# ymincrit = minimum(vcat(nI[1], nI[2], [length(I[1])+1])) +# # Construct vertices +# ########################### +# # On the vertical left side +# if ind > 1 +# for k in 1:length(I[1]) +# push!(Corr[i][j][1], Corr[i1][j1][3][k]) +# end +# else +# for k in 1:length(I[1]) +# push!(Vert, (xcrit[i][j][1], sum(I[1][k])//2) .|> fct) +# push!(Corr[i][j][1], length(Vert)) +# end +# end +# ########################### +# # On the vertical right side +# if ind < length(xcritpermut) +# for k in 1:length(I[2]) +# push!(Vert, ((xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4) .|> fct) +# push!(Corr[i][j][3], length(Vert)) +# end +# else +# for k in 1:length(I[2]) +# push!(Vert, (xcrit[i][j][2], sum(I[2][k])//2) .|> fct) +# push!(Corr[i][j][3], length(Vert)) +# end +# end +# ########################### +# # Below the critical point +# for k in 1:ymincrit-1 +# push!(Vert, (xcmid, sum(I[1][k] + I[2][k])// 4) .|> fct) +# push!(Corr[i][j][2][1], length(Vert)) +# push!(Edg, (Corr[i][j][1][k], length(Vert))) # left +# push!(Edg, (length(Vert), Corr[i][j][3][k])) # right +# end +# ########################### +# # The critical point +# ########################## +# # If we are dealing with a isolated node +# if i in [0,2] && isempty(nI[1]) && isempty(nI[2]) +# push!(Lapp[1], (i,j)) +# # If we are dealing with an apparent singularity +# elseif i == 0 +# # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 +# push!(Edg, (Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]])) +# push!(Edg, (Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]])) +# push!(Lapp[2], (i,j)) +# else +# # We can add the vertex +# push!(Vert, (xcmid, ycmid)) +# push!(Corr[i][j][2][2], length(Vert)) +# # We connect to the vertical left side of the critical box +# for k in nI[1] +# push!(Edg, (Corr[i][j][1][k], length(Vert))) +# end +# # We connect to the vertical right side of the critical box +# for k in nI[2] +# push!(Edg, (length(Vert), Corr[i][j][3][k])) +# end +# if i < 0 +# # If this is a control point +# push!(Vcon[-i], length(Vert)) +# end +# end +# ########################### +# # Above the critical point +# for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1 +# push!(Vert, (xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4) .|> fct) +# push!(Corr[i][j][2][3], length(Vert)) +# push!(Edg, (Corr[i][j][1][end - k + 1], length(Vert))) # left +# push!(Edg, (length(Vert), Corr[i][j][3][end - k + 1])) # right +# end +# end + +# if v > 0 && Lapp != [[],[]] +# println("Removed apparent singularities: $(length(Lapp[1])) isolated $(length(Lapp[2])) nodes") +# end + +# # Operate inverse change of variable if necessary +# if !(generic) +# for i in eachindex(Vert) +# vx,vy = Vert[i] +# vx,vy = fct.(changemat*[vx, vy]) +# Vert[i] = (vx, vy) +# end +# end + +# if length(C)>0 +# return (Vert, Edg), Vcon +# else +# return Vert, Edg +# end +# end + +# function compute_graph(f::P, g::P, C::Dict{Int,Vector{P}}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) +# G, Vcon = compute_graph(f, g, collect(values(C)), generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf) +# VC = Dict{Int64, Vector{Int}}([ k => Vcon[i] for (i,k) in enumerate(keys(C)) ]) +# return G, VC +# end + +# function compute_graph(f::P, g::P, C::Vector{P}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) +# G, (Vcon,) = compute_graph(f, g, [C], generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf = outf) +# return G, Vcon +# end + +# ################################################################ +# function group_by_component(f::P, C::Vector{P}; generic=true, precx=150, v=0, arb=true, int_coeff=false) where {P <: MPolyRingElem} +# # Compute a graph homeomorphic to Z(F) and return the vertices identified by Z(C) +# G, Vcon = compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff) +# # Compute the partition of the vertices in Vcon according to the connected component in G +# sort!(Vcon) +# CVcon = group_by_component(G, Vcon) + +# # Convert the partition into abscissa order +# index_map = Dict((val, idx) for (idx, val) in enumerate(Vcon)) +# return [map(v -> index_map[v], C) for C in CVcon] +# end + +# function plot_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) +# plot_graph(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +# end + +# function plot_graph(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) +# plot_graph(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +# end + +# function plot_graph_comp(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) +# plot_graph_comp(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +# end + +# function plot_graph_comp(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) +# plot_graph_comp(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +# end + +# function number_connected_components(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) +# number_connected_components(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +# end + +# function number_connected_components(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) +# number_connected_components(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +# end + +#################################### + +function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; + generic=true, precx=150, v=0, int_coeff=true, outf=true) where {P <: MPolyRingElem} + R = parent(f) x, y = gens(R) intC = int_coeff ? int_coeffs : identity + # Pre-processing the input - f, g = intC([f,g]) + f, g = intC([f, g]) changemat = generic ? [1 0; 0 1] : trimat_rand(QQ, 2, range=-100:100) - f = evaluate(f, collect(changemat*[x; y])); + f = evaluate(f, collect(changemat * [x; y])) + precx = max(2, precx) v > 1 && println(f) - precx = precx <= 1 ? 2 : precx v > 0 && println("Compute parametrization of critical pts...") - @iftime (v > 0) params = param_crit_split(f,g,v=v-1, detect_app=true) - #@iftime (v > 0) params = mmod_param_crit(f, g,v=v-1, detect_app=true) + @iftime (v > 0) params = param_crit_split(f, g, v=v-1, detect_app=true) for i in 1:length(C) - params[-i] = [ [C[i][1] |> intC], C[i][2], C[i][3] ] + params[-i] = [ [intC(C[i][1])], C[i][2], C[i][3] ] end v > 0 && println("Computing insulating critical boxes") @iftime (v > 0) LBcrit, Lprecx = insulate_crit_boxes(f, params, precx, v=v-1) - + println(LBcrit) v > 0 && println("Compute intersections with critical boxes..") - @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(f, params, LBcrit, Lprecx, v=v-1) - - # Graph computation - fct, typeout = outf ? (Float64, Float64) : (identity, QQFieldElem) + @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf, v=v-1) + println(LPCside) # Critical values and their order - xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in eachindex(LBcrit)) + xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in keys(LBcrit)) xcritpermut = order_permut2d(xcrit) - # List of vertex: at index i is the tuple of the coordinates of the i-th vertex - Vert = Vector{Tuple{typeout, typeout}}() - # List of edges: a tuple (i,j) is an edge between the i-th and j-th vertices - Edg = Vector{Tuple{Int, Int}}() - Corr = Dict( m => [[[], [[], [], []], []] for j in xcrit[m] ] for m in eachindex(xcrit)) - Vcon = [ [] for _ in 1:length(C) ] - # Keep track of processed isolated & apparent singularities - Lapp = [[],[]] + # Graph data + Vert = Tuple{QQFieldElem, QQFieldElem}[] # List of points (x,y) + Edg = Tuple{Int, Int}[] # List of tuples (idx, idy) + Vcon = Dict{Int, Vector{Int}}(k => Int[] for k in keys(C)) # Index of control vertices - for ind in eachindex(xcritpermut) - i, j = xcritpermut[ind] + Lapp_isolated = Tuple{Int, Int}[] + Lapp_nodes = Tuple{Int, Int}[] - if ind > 1 - i1, j1 = xcritpermut[ind - 1] - end - if ind < length(xcritpermut) - i2, j2 = xcritpermut[ind + 1] - I2L, = LPCside[i2][j2][3] - end + # Keep track of connection between all computed points when increasing x + Corr = Dict(m => [CriticalNodeConnections() for _ in xcrit[m]] for m in keys(xcrit)) + + for (ind, (i, j)) in enumerate(xcritpermut) + i1, j1 = ind > 1 ? xcritpermut[ind - 1] : (0, 0) # previous + i2, j2 = ind < length(xcritpermut) ? xcritpermut[ind + 1] : (0, 0) # next + # Current cylinder above xcrit[i][j] PCside = LPCside[i][j] - I = [ l[1] for l in PCside[3:end] ] - nI = [ l[2] for l in PCside[3:end] ] + I2L_points = ind < length(xcritpermut) ? LPCside[i2][j2].left.points : nothing + + # Midpoints of the critical box itself + xcmid = sum(LBcrit[i][j][1]) / 2 + ycmid = sum(LBcrit[i][j][2]) / 2 - xcmid = sum(LBcrit[i][j][1])//2 |> fct - ycmid = sum(LBcrit[i][j][2])//2 |> fct + nI_left = PCside.left.indices_inside + nI_right = PCside.right.indices_inside + ymincrit = minimum(vcat(nI_left, nI_right, [length(PCside.left.points) + 1])) - ymincrit = minimum(vcat(nI[1], nI[2], [length(I[1])+1])) - # Construct vertices - ########################### - # On the vertical left side + # 1. Left side vertices + # one-to-one connection with previous right side + # TODO: could be improved memory-wise if ind > 1 - for k in 1:length(I[1]) - push!(Corr[i][j][1], Corr[i1][j1][3][k]) + for k in 1:length(PCside.left.points) + push!(Corr[i][j].left, Corr[i1][j1].right[k]) end else - for k in 1:length(I[1]) - push!(Vert, (xcrit[i][j][1], sum(I[1][k])//2) .|> fct) - push!(Corr[i][j][1], length(Vert)) + for k in 1:length(PCside.left.points) + xval = xcrit[i][j][1] - 1 + yval = sum(PCside.left.points[k]) / 2 + push!(Vert, (xval, yval)) + push!(Corr[i][j].left, length(Vert)) end end - ########################### - # On the vertical right side + + # 2. Right side vertices if ind < length(xcritpermut) - for k in 1:length(I[2]) - push!(Vert, ((xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4) .|> fct) - push!(Corr[i][j][3], length(Vert)) + for k in 1:length(PCside.right.points) + xval = (xcrit[i][j][2] + xcrit[i2][j2][1]) / 2 + yval = sum(PCside.right.points[k] + I2L_points[k]) / 4 + push!(Vert, (xval, yval)) + push!(Corr[i][j].right, length(Vert)) end else - for k in 1:length(I[2]) - push!(Vert, (xcrit[i][j][2], sum(I[2][k])//2) .|> fct) - push!(Corr[i][j][3], length(Vert)) + for k in 1:length(PCside.right.points) + xval = xcrit[i][j][2] + yval = sum(PCside.right.points[k]) / 2 + push!(Vert, (xval, yval)) + push!(Corr[i][j].right, length(Vert)) end end - ########################### - # Below the critical point + + # 3. Below the critical point + # TODO: many vertices and edges could be removed here for k in 1:ymincrit-1 - push!(Vert, (xcmid, sum(I[1][k] + I[2][k])// 4) .|> fct) - push!(Corr[i][j][2][1], length(Vert)) - push!(Edg, (Corr[i][j][1][k], length(Vert))) # left - push!(Edg, (length(Vert), Corr[i][j][3][k])) # right + yval = sum(PCside.left.points[k] + PCside.right.points[k]) / 4 + push!(Vert, (xcmid, yval)) + push!(Corr[i][j].bottom, length(Vert)) + push!(Edg, (Corr[i][j].left[k], length(Vert))) + push!(Edg, (length(Vert), Corr[i][j].right[k])) end - ########################### - # The critical point - ########################## - # If we are dealing with a isolated node - if i in [0,2] && isempty(nI[1]) && isempty(nI[2]) - push!(Lapp[1], (i,j)) - # If we are dealing with an apparent singularity + + # 4. The critical point + if i == 0 && isempty(nI_left) && isempty(nI_right) + push!(Lapp_isolated, (i, j)) elseif i == 0 - # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 - push!(Edg, (Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]])) - push!(Edg, (Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]])) - push!(Lapp[2], (i,j)) + push!(Edg, (Corr[i][j].left[nI_left[1]], Corr[i][j].right[nI_right[2]])) + push!(Edg, (Corr[i][j].left[nI_left[2]], Corr[i][j].right[nI_right[1]])) + push!(Lapp_nodes, (i, j)) else - # We can add the vertex push!(Vert, (xcmid, ycmid)) - push!(Corr[i][j][2][2], length(Vert)) - # We connect to the vertical left side of the critical box - for k in nI[1] - push!(Edg, (Corr[i][j][1][k], length(Vert))) - end - # We connect to the vertical right side of the critical box - for k in nI[2] - push!(Edg, (length(Vert), Corr[i][j][3][k])) - end - if i < 0 - # If this is a control point + push!(Corr[i][j].center, length(Vert)) + + for k in nI_left; push!(Edg, (Corr[i][j].left[k], length(Vert))); end + for k in nI_right; push!(Edg, (length(Vert), Corr[i][j].right[k])); end + + if i < 0 # Control point push!(Vcon[-i], length(Vert)) end end - ########################### - # Above the critical point - for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1 - push!(Vert, (xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4) .|> fct) - push!(Corr[i][j][2][3], length(Vert)) - push!(Edg, (Corr[i][j][1][end - k + 1], length(Vert))) # left - push!(Edg, (length(Vert), Corr[i][j][3][end - k + 1])) # right - end - end - if v > 0 && Lapp != [[],[]] - println("Removed apparent singularities: $(length(Lapp[1])) isolated $(length(Lapp[2])) nodes") + # 5. Above the critical point + for k = (length(PCside.left.points) - length(nI_left) - ymincrit + 1):-1:1 + yval = sum(PCside.left.points[end-k+1] + PCside.right.points[end-k+1]) / 4 + push!(Vert, (xcmid, yval)) + push!(Corr[i][j].top, length(Vert)) + push!(Edg, (Corr[i][j].left[end-k+1], length(Vert))) + push!(Edg, (length(Vert), Corr[i][j].right[end-k+1])) + end end - # Operate inverse change of variable if necessary - if !(generic) + # Post processing the data + if !generic for i in eachindex(Vert) - vx,vy = Vert[i] - vx,vy = fct.(changemat*[vx, vy]) - Vert[i] = (vx, vy) + vx, vy = Vert[i] + Vert[i] = Tuple(changemat * [vx, vy]) end end - if length(C)>0 - return (Vert, Edg), Vcon - else - return Vert, Edg + if outf + Vert = [ (Float64(x), Float64(y)) for (x,y) in Vert ] + return CurveGraph{Float64}(Vert, Edg, Vcon) end -end - -function compute_graph(f::P, g::P, C::Dict{Int,Vector{P}}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) - G, Vcon = compute_graph(f, g, collect(values(C)), generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf) - VC = Dict{Int64, Vector{Int}}([ k => Vcon[i] for (i,k) in enumerate(keys(C)) ]) - return G, VC -end - -function compute_graph(f::P, g::P, C::Vector{P}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) - G, (Vcon,) = compute_graph(f, g, [C], generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf = outf) - return G, Vcon -end - -################################################################ -function group_by_component(f::P, C::Vector{P}; generic=true, precx=150, v=0, arb=true, int_coeff=false) where {P <: MPolyRingElem} - # Compute a graph homeomorphic to Z(F) and return the vertices identified by Z(C) - G, Vcon = compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff) - # Compute the partition of the vertices in Vcon according to the connected component in G - sort!(Vcon) - CVcon = group_by_component(G, Vcon) - - # Convert the partition into abscissa order - index_map = Dict((val, idx) for (idx, val) in enumerate(Vcon)) - return [map(v -> index_map[v], C) for C in CVcon] -end -function plot_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - plot_graph(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) + # Return the unified data structure + return CurveGraph{QQFieldElem}(Vert, Edg, Vcon) end -function plot_graph(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - plot_graph(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) -end +# Multi-dispatch wrappers returning the Graph Struct +compute_graph(f::P, g::P; kwargs...) where {P <: MPolyRingElem} = + _compute_graph_core(f, g, Vector{Vector{P}}(); kwargs...) -function plot_graph_comp(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - plot_graph_comp(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) -end - -function plot_graph_comp(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - plot_graph_comp(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) -end +compute_graph(f::P, g::P, C::Vector{Vector{P}}; kwargs...) where {P <: MPolyRingElem} = + _compute_graph_core(f, g, C; kwargs...) -function number_connected_components(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - number_connected_components(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) +function compute_graph(f::P, g::P, C::Dict{Int, Vector{P}}; kwargs...) where {P <: MPolyRingElem} + graph = _compute_graph_core(f, g, collect(values(C)); kwargs...) + # Remap Vcon dictionary keys to match original dict keys + mapped_vcon = Dict{Int, Vector{Int}}(k => graph.control_nodes[i] for (i, k) in enumerate(keys(C))) + return CurveGraph(graph.vertices, graph.edges, mapped_vcon) end -function number_connected_components(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) - number_connected_components(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) -end \ No newline at end of file +compute_graph(f::P, g::P, C::Vector{P}; kwargs...) where {P <: MPolyRingElem} = + _compute_graph_core(f, g, [C]; kwargs...) \ No newline at end of file diff --git a/src/connectivity/datastruct.jl b/src/connectivity/datastruct.jl new file mode 100644 index 0000000..94766e3 --- /dev/null +++ b/src/connectivity/datastruct.jl @@ -0,0 +1,29 @@ +# Represents the isolated points and valid connections on a single box edge +struct BoxEdge{T} + points::Vector{Vector{T}} + indices_inside::Vector{Int} +end + +# Represents a complete critical box intersection profile +struct BoxIntersections{T} + bottom::BoxEdge{T} + top::BoxEdge{T} + left::BoxEdge{T} + right::BoxEdge{T} +end + +# Tracks the vertex IDs attached to different parts of a critical point box +Base.@kwdef struct CriticalNodeConnections + left::Vector{Int} = Int[] + bottom::Vector{Int} = Int[] + center::Vector{Int} = Int[] + top::Vector{Int} = Int[] + right::Vector{Int} = Int[] +end + +# Connectivity graph + control nodes +struct CurveGraph{T} + vertices::Vector{Tuple{T, T}} + edges::Vector{Tuple{Int, Int}} + control_nodes::Dict{Int, Vector{Int}} +end \ No newline at end of file diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index c8cbe9a..8c2b6a7 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -6,6 +6,8 @@ const Boxes = Vector{Sides} in_inter(I, J) = J[1] <= I[1] && I[2] <= J[2] overlap_inter(I, J) = max(I[1], J[1]) <= min(I[2], J[2]) +# TODO: output vector of tuple for the intervals (inside real_solutions?) + # Function that isolate roots of a multivariate polynomial with a # single variable function isolate(f; prec = 32) @@ -128,52 +130,244 @@ function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) end ####################################################### +# # Helper function to process a single edge of the box +# function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v; max_retries=5) +# prec = initial_prec + +# for _ in 1:max_retries +# roots = isolate_eval(f, fixed_dim, fixed_val, prec=prec) +# indices_inside = Int[] +# overlap_found = false + +# for (j, l) in pairs(roots) +# if in_inter(l, target_interval) +# push!(indices_inside, j) +# elseif overlap_inter(l, target_interval) +# prec *= 2 +# v > 0 && println("IntersectBox: increase precision to $prec bits") +# overlap_found = true +# break # Break inner for-loop to restart with higher precision +# end +# end + +# # If we successfully processed all roots without overlap, return the results +# if !overlap_found +# return (roots, indices_inside) +# end +# end + +# error("Problem when isolating on one side of a box after $max_retries attempts") +# end + +# # Function that computes the intersection of a curve with a box by isolating roots on the edges +# function intersect_box(f, B; prec=100, v=0) +# # B[1] represents x-bounds, B[2] represents y-bounds + +# # Evaluate horizontal edges (fix y to B[2][1] and B[2][2], target x-interval B[1]) +# edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v)::side +# edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v)::side + +# # Evaluate vertical edges (fix x to B[1][1] and B[1][2], target y-interval B[2]) +# edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v)::side +# edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v)::side + +# # Return as a 4-Tuple of 2-Tuples +# return (edge_y1, edge_y2, edge_x1, edge_x2) +# end + + +# """ +# _update_LB_first_axis!(LB, xnew) + +# Replace first coordinate of each box in LB with corresponding xnew interval. +# """ +# function _update_LB_first_axis!(LB, xnew) +# @inbounds for i in eachindex(LB) +# LB[i][1] = xnew[i] +# end +# return LB +# end + +# """ +# refine_xboxes(f, LB, prec) + +# Refine LB along first axis using roots of polynomials in F +# The order in F is assumed to match the one in LB +# """ +# function refine_xboxes(F::Vector{T} where T<:Union{PolyRingElem, MPolyRingElem}, LB, prec) +# # Concatenate all roots from isolating each polynomial in F +# xnew = reduce(vcat, [isolate(f, prec=prec) for f in F]) + +# _expand_degenerate_intervals!(xnew, prec) +# return _update_LB_first_axis!(LB, xnew) +# end + +# function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0) + +# LPCside = Dict{Int, Boxes}() + +# for (i, boxes) in pairs(LBcrit) +# prec = Lprecx[i] +# n = length(boxes) + +# sides_vec = Vector{Sides}(undef, n) + +# for attempt in 1:max_attempts +# refined = false + +# @inbounds for j in 1:n +# v >= 0 && print("i=$i ($j/$n)\r") + +# pc = intersect_box(f, boxes[j], prec=prec, v=v)::Sides + +# c1 = length(pc[1][2]) +# c2 = length(pc[2][2]) +# c3 = length(pc[3][2]) +# c4 = length(pc[4][2]) + +# if (i == 1 && (c1 + c2 + c3 + c4 > 2)) || +# (i != 1 && (c1 != 0 || c2 != 0)) + +# prec *= 2 +# v > 0 && println("\nRefine -> prec = $prec") + +# refine_xboxes(params[i][1], boxes, prec) + +# refined = true +# break +# end + +# sides_vec[j] = pc +# end + +# refined || break +# attempt == max_attempts && +# error("Problem in computing intersections (i=$i)") +# end + +# LPCside[i] = sides_vec +# Lprecx[i] = prec + +# v >= 0 && println() +# end + +# # ---- Counts (type-stable) ---- +# LnPCside = Dict{Int, Vector{NTuple{4, Int}}}() + +# for (i, vec) in pairs(LPCside) +# LnPCside[i] = [ +# ( +# length(pc[1][2]), +# length(pc[2][2]), +# length(pc[3][2]), +# length(pc[4][2]) +# ) +# for pc in vec +# ] +# end + +# # ---- Extremal case (i == 1) ---- +# if haskey(LBcrit, 1) +# boxes = LBcrit[1] +# pcs = LPCside[1] +# cnts = LnPCside[1] + +# @inbounds for j in eachindex(boxes) +# c1, c2, c3, c4 = cnts[j] + +# (c1 == 0 && c2 == 0) && continue + +# pc = pcs[j] +# ycrit = boxes[j][2] + +# I1 = pc[3][1] # left +# I2 = pc[4][1] # right + +# # Orientation of the curve left(s=1)/right(s=2) +# s = length(I1) >= length(I2) ? 1 : 2 + +# # ---- intersection on bottom ---- +# if c1 == 1 +# # Attach to the max intersection below the bow on the correct side +# yinf = maximum(i for (i, yy) in pairs((s == 1 ? I1 : I2)) if yy[1] < ycrit[1]) + +# push!(pc[s+2][2], yinf) +# pc[1][2] = Int[] + +# cnts[j] = ( +# 0, +# c2, +# s == 1 ? c3 + 1 : c3, +# s == 2 ? c4 + 1 : c4 +# ) + +# c1, c2, c3, c4 = cnts[j] # for next step +# end + +# # ---- intersection on top ---- +# if c2 == 1 +# ymax = minimum(i for (i, yy) in pairs((s == 1 ? I1 : I2)) if yy[2] > ycrit[2]) + +# push!(pc[s+2][2], ymax) +# pc[2][2] = Int[] + +# cnts[j] = ( +# c1, +# 0, +# s == 1 ? c3 + 1 : c3, +# s == 2 ? c4 + 1 : c4 +# ) +# end +# end +# end +# #TODO: by design bottom/top sides in LnPCside are [0,0] -> remove +# return LPCside, LnPCside +# end + +############################################## + # Helper function to process a single edge of the box -function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v; max_retries=5) +function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v, outf; max_retries=5) prec = initial_prec for _ in 1:max_retries roots = isolate_eval(f, fixed_dim, fixed_val, prec=prec) - valid_indices = Int[] + indices_inside = Int[] overlap_found = false for (j, l) in pairs(roots) if in_inter(l, target_interval) - push!(valid_indices, j) + push!(indices_inside, j) elseif overlap_inter(l, target_interval) prec *= 2 v > 0 && println("IntersectBox: increase precision to $prec bits") overlap_found = true - break # Break inner for-loop to restart with higher precision + break end end - - # If we successfully processed all roots without overlap, return the results + # All roots without overlap on this edge if !overlap_found - return (roots, valid_indices) + T = QQFieldElem + return BoxEdge{T}(roots, indices_inside) end end - error("Problem when isolating on one side of a box after $max_retries attempts") end # Function that computes the intersection of a curve with a box by isolating roots on the edges -function intersect_box(f, B; prec=100, v=0) - # B[1] represents x-bounds, B[2] represents y-bounds - +function intersect_box(f, B, outf; prec=100, v=0) # Evaluate horizontal edges (fix y to B[2][1] and B[2][2], target x-interval B[1]) - edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v)::side - edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v)::side - + edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v, outf) + edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v, outf) # Evaluate vertical edges (fix x to B[1][1] and B[1][2], target y-interval B[2]) - edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v)::side - edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v)::side + edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v, outf) + edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v, outf) - # Return as a 4-Tuple of 2-Tuples - return (edge_y1, edge_y2, edge_x1, edge_x2) + # Return clean struct + T = QQFieldElem + return BoxIntersections{T}(edge_y1, edge_y2, edge_x1, edge_x2) end - """ _update_LB_first_axis!(LB, xnew) @@ -200,42 +394,43 @@ function refine_xboxes(F::Vector{T} where T<:Union{PolyRingElem, MPolyRingElem}, return _update_LB_first_axis!(LB, xnew) end -function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0) - - LPCside = Dict{Int, Boxes}() +# Function computing the intersection of the vertical sides of the critical boxes with the curve defined by f. +# If an intersection on top/bottom side is detected, refine the width until this does not happen or max_attemps is reached. +function intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf; max_attempts=5, v=0) + # Automatically infer the point type based on outf + T = QQFieldElem + LPCside = Dict{Int, Vector{BoxIntersections{T}}}() + LnPCside = Dict{Int, Vector{NTuple{4, Int}}}() for (i, boxes) in pairs(LBcrit) prec = Lprecx[i] n = length(boxes) - - sides_vec = Vector{Sides}(undef, n) + sides_vec = Vector{BoxIntersections{T}}(undef, n) + nsides_vec = Vector{NTuple{4, Int}}(undef,n) for attempt in 1:max_attempts refined = false @inbounds for j in 1:n v >= 0 && print("i=$i ($j/$n)\r") + pc = intersect_box(f, boxes[j], outf, prec=prec, v=v) - pc = intersect_box(f, boxes[j], prec=prec, v=v)::Sides - - c1 = length(pc[1][2]) - c2 = length(pc[2][2]) - c3 = length(pc[3][2]) - c4 = length(pc[4][2]) + c1 = length(pc.bottom.indices_inside) + c2 = length(pc.top.indices_inside) + c3 = length(pc.left.indices_inside) + c4 = length(pc.right.indices_inside) if (i == 1 && (c1 + c2 + c3 + c4 > 2)) || (i != 1 && (c1 != 0 || c2 != 0)) - prec *= 2 v > 0 && println("\nRefine -> prec = $prec") - refine_xboxes(params[i][1], boxes, prec) - refined = true break end sides_vec[j] = pc + nsides_vec[j] = (c1,c2,c3,c4) end refined || break @@ -244,80 +439,49 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0 end LPCside[i] = sides_vec + LnPCside[i] = nsides_vec Lprecx[i] = prec - v >= 0 && println() end - # ---- Counts (type-stable) ---- - LnPCside = Dict{Int, Vector{NTuple{4, Int}}}() - - for (i, vec) in pairs(LPCside) - LnPCside[i] = [ - ( - length(pc[1][2]), - length(pc[2][2]), - length(pc[3][2]), - length(pc[4][2]) - ) - for pc in vec - ] - end - - # ---- Extremal case (i == 1) ---- + # ---- Extremal case (i == 1) we vertically enlarge boxes manually ----- + # TODO: here we modify only LPCside and LnPCside, not LBcrit if haskey(LBcrit, 1) - boxes = LBcrit[1] - pcs = LPCside[1] - cnts = LnPCside[1] + boxes, pcs, npcs = LBcrit[1], LPCside[1], LnPCside[1] @inbounds for j in eachindex(boxes) - c1, c2, c3, c4 = cnts[j] + c1, c2, c3, c4 = npcs[j] - (c1 == 0 && c2 == 0) && continue + (c1 == 0 && c2 == 0) && continue # Nothing to do pc = pcs[j] ycrit = boxes[j][2] - I1 = pc[3][1] # left - I2 = pc[4][1] # right - # Orientation of the curve left(s=1)/right(s=2) - s = length(I1) >= length(I2) ? 1 : 2 + s = length(pc.left.points) >= length(pc.right.points) ? 1 : 2 + side_pts = s == 1 ? pc.left.points : pc.right.points + side_indices = s == 1 ? pc.left.indices_inside : pc.right.indices_inside # ---- intersection on bottom ---- if c1 == 1 - # Attach to the max intersection below the bow on the correct side - yinf = maximum(i for (i, yy) in pairs((s == 1 ? I1 : I2)) if yy[1] < ycrit[1]) - - push!(pc[s+2][2], yinf) - pc[1][2] = Int[] - - cnts[j] = ( - 0, - c2, - s == 1 ? c3 + 1 : c3, - s == 2 ? c4 + 1 : c4 - ) - - c1, c2, c3, c4 = cnts[j] # for next step + # Attach to the max intersection below the box on the correct side + ind_yinf = maximum(i for (i, yy) in pairs(side_pts) if yy < ycrit[1]) + push!(side_indices, ind_yinf) + empty!(pc.bottom.indices_inside) + npcs[j] = (0, c2, s == 1 ? c3 + 1 : c3, s == 2 ? c4 + 1 : c4) end + c1, c2, c3, c4 = npcs[j] # In case this has changed # ---- intersection on top ---- if c2 == 1 - ymax = minimum(i for (i, yy) in pairs((s == 1 ? I1 : I2)) if yy[2] > ycrit[2]) - - push!(pc[s+2][2], ymax) - pc[2][2] = Int[] - - cnts[j] = ( - c1, - 0, - s == 1 ? c3 + 1 : c3, - s == 2 ? c4 + 1 : c4 - ) + # Attach to the min intersection above the bow on the correct side + ind_ymax = minimum(i for (i, yy) in pairs(side_pts) if yy > ycrit[2]) + push!(side_indices, ind_ymax) + empty!(pc.top.indices_inside) + npcs[j] = (c1, 0, s == 1 ? c3 + 1 : c3, s == 2 ? c4 + 1 : c4) end end end - #TODO: by design bottom/top sides in LnPCside are [0,0] -> remove + return LPCside, LnPCside end \ No newline at end of file diff --git a/src/connectivity/newgraph.jl b/src/connectivity/newgraph.jl new file mode 100644 index 0000000..f2d7db7 --- /dev/null +++ b/src/connectivity/newgraph.jl @@ -0,0 +1,186 @@ +# ========================================================================= +# GRAPH DECOMPOSITION +# ========================================================================= + +""" + connected_components(G::CurveGraph{T}) where T + +Decomposes a graph into its connected components. + +# Inputs +- `G::CurveGraph{T}`: The unified curve graph. + +# Outputs +- `Vector{CurveGraph{T}}`: A list of disjoint subgraphs. Each subgraph retains + the mapped coordinates, edges, and control nodes belonging to its component. +""" +function connected_components(G::CurveGraph{T}) where T + nv = length(G.vertices) + + # Work with vertices to avoid missing isolated vertices + adj_list = [Int[] for _ in 1:nv] + for (u, v) in G.edges + push!(adj_list[u], v) + push!(adj_list[v], u) + end + + visited = falses(nv) + components = Vector{Vector{Int}}() + + # Iterative DFS + for i in 1:nv + if !visited[i] + comp = Int[] + stack = [i] + visited[i] = true + while !isempty(stack) + curr = pop!(stack) + push!(comp, curr) + for neighbor in adj_list[curr] + if !visited[neighbor] + visited[neighbor] = true + push!(stack, neighbor) + end + end + end + push!(components, comp) + end + end + + # Mapping global vertex ID -> (component ID, local vertex ID) + vertex_map = Vector{Tuple{Int, Int}}(undef, nv) + for (cid, comp) in enumerate(components) + for (local_id, global_id) in enumerate(comp) + vertex_map[global_id] = (cid, local_id) + end + end + + # Group edges in O(E) time using the map + comp_edges = [Tuple{Int, Int}[] for _ in 1:length(components)] + for (u, v) in G.edges + cid_u, local_u = vertex_map[u] + cid_v, local_v = vertex_map[v] + push!(comp_edges[cid_u], (local_u, local_v)) + end + + # Reconstruct subgraphs into clean CurveGraph structs + subgraphs = CurveGraph{T}[] + for (cid, comp) in enumerate(components) + new_verts = G.vertices[comp] + new_edges = comp_edges[cid] + new_control = Dict{Int, Vector{Int}}() + + # Keep track of control points falling into this specific component + for (k, v_list) in G.control_nodes + local_v_list = Int[] + for global_v in v_list + c, local_v = vertex_map[global_v] + if c == cid + push!(local_v_list, local_v) + end + end + if !isempty(local_v_list) + new_control[k] = local_v_list + end + end + + push!(subgraphs, CurveGraph{T}(new_verts, new_edges, new_control)) + end + + return subgraphs +end + +""" + group_by_component(G::CurveGraph) + +# Outputs +- `Vector{Dict{Int, Vector{Int}}}`: Returns just the control nodes mapped to each connected component. +""" +function group_by_component(G::CurveGraph) + subgraphs = connected_components(G) + return [sg.control_nodes for sg in subgraphs if !isempty(sg.vertices)] +end + +""" + number_connected_components(G::CurveGraph) + +# Outputs +- `Int`: The count of isolated subgraphs in the parent structure. +""" +number_connected_components(G::CurveGraph) = length(connected_components(G)) + + +# ========================================================================= +# GRAPH MERGING +# ========================================================================= + +""" + merge_graphs(graphs::Vector{CurveGraph{T}}) where T + +Merges a collection of disjoint graphs into a single graph, mathematically fusing +vertices that share common `control_nodes` mappings. + +# Inputs +- `graphs::Vector{CurveGraph{T}}`: A list of graphs. `graphs[i].control_nodes[k]` + should contain the local vertex indices in graph `i` that connect to graph `k`. + +# Outputs +- `CurveGraph{T}`: A unified graph struct. +""" +function merge_graphs(graphs::Vector{CurveGraph{T}}) where T + isempty(graphs) && return CurveGraph{T}(Tuple{T,T}[], Tuple{Int,Int}[], Dict{Int, Vector{Int}}()) + length(graphs) == 1 && return deepcopy(graphs[1]) + + Vtot = copy(graphs[1].vertices) + Etot = copy(graphs[1].edges) + + # Dictionary to track: (graph_id, local_vertex_id) -> merged_global_id + global_map = Dict{Tuple{Int, Int}, Int}() + for i in 1:length(graphs[1].vertices) + global_map[(1, i)] = i + end + + for i in 2:length(graphs) + G_i = graphs[i] + + # Step 1: Pre-map common control nodes connected to previously merged graphs + for (k, common_indices_in_i) in G_i.control_nodes + if k < i && haskey(graphs[k].control_nodes, i) + common_indices_in_k = graphs[k].control_nodes[i] + # Zip ensures we pair corresponding control nodes precisely + for (idx_i, idx_k) in zip(common_indices_in_i, common_indices_in_k) + global_map[(i, idx_i)] = global_map[(k, idx_k)] + end + end + end + + # Step 2: Add completely new (unmapped) vertices from G_i to Vtot + for idx_i in 1:length(G_i.vertices) + if !haskey(global_map, (i, idx_i)) + push!(Vtot, G_i.vertices[idx_i]) + global_map[(i, idx_i)] = length(Vtot) + end + end + + # Step 3: Append the edges using the newly mapped global indices + for (u, v) in G_i.edges + push!(Etot, (global_map[(i, u)], global_map[(i, v)])) + end + end + + # Step 4: Preserve external control nodes pointing OUTSIDE the merged structure + merged_control = Dict{Int, Vector{Int}}() + num_graphs = length(graphs) + + for i in 1:num_graphs + for (k, v_list) in graphs[i].control_nodes + # If `k` points to a graph outside of the ones we just merged + if k > num_graphs || k <= 0 + mapped_v = [global_map[(i, v)] for v in v_list] + append!(get!(merged_control, k, Int[]), mapped_v) + end + end + end + + return CurveGraph{T}(Vtot, Etot, merged_control) +end \ No newline at end of file diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index c2e8a42..e160b85 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -4,7 +4,7 @@ function plot_graph(G, Vemph::Vector{Vector{T}} where T<:Any; color="red", width if !subplt plot(legend=false) end - V, E = G + V, E = G.vertices, G.edges #col = distinguishable_colors(length(Vemph)+2) for e in E v1, v2 = [ map(Float64, V[ee]) for ee in e ] diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index 4c69d3f..2bf637d 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -51,3 +51,20 @@ macro iftime(v, ex) end end end + +""" + extract_point(I, outf::Bool) + +Convert an isolation interval `I = [a, b]` into a single representative point. +""" +function extract_point(I, outf::Bool; interval::Bool=false) + a, b = I[1], I[2] + if outf + return interval ? (Float64(a),Float64(b)) : Float64(a + b) / 2.0 + else + return interval ? (a,b) : simplest_between(a, b) # Nemo's native simplest rational function + end +end + +# Helper for averaging two extracted points +average_points(a, b, outf::Bool) = outf ? (a + b) / 2.0 : (a + b) // 2 \ No newline at end of file From d68c292c9066a6be5d53dc1d6946d1f9652001d9 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 14 Apr 2026 19:46:58 +0200 Subject: [PATCH 147/180] new version of whole code with new data structure --- src/connectivity/connectcurves.jl | 205 +------------------------ src/connectivity/graph.jl | 238 +++++++++++++++++++----------- src/connectivity/newgraph.jl | 186 ----------------------- 3 files changed, 150 insertions(+), 479 deletions(-) delete mode 100644 src/connectivity/newgraph.jl diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 150f0c1..3bf4806 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -7,14 +7,14 @@ export compute_graph, connected_components, number_connected_components, group_b rat_to_arb, evaluate_arb, evaluate_arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit +include("datastruct.jl") include("tools.jl") include("subresultants.jl") include("isolateboxes.jl") -include("newgraph.jl") +include("graph.jl") include("plots.jl") include("arbtools.jl") include("buildpoly.jl") -include("datastruct.jl") # Input: # The space curve is given by f(x,y) = 0 and (df/dy)(x,y)*z = g(x,y) @@ -23,207 +23,6 @@ include("datastruct.jl") # C is a list of parametrization [p,a,b] of plane pts i.e. such that p(x)=0,y=a(x)/b(x) # these points must be on the curve # Output: Computes a graph homeomorphic to the curve, identitying point in C -# function compute_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, int_coeff=true, outf=true) where (P <: MPolyRingElem) -# R = parent(f) -# x, y = gens(R) -# intC = int_coeff ? int_coeffs : identity -# # Pre-processing the input -# f, g = intC([f,g]) -# changemat = generic ? [1 0; 0 1] : trimat_rand(QQ, 2, range=-100:100) -# f = evaluate(f, collect(changemat*[x; y])); -# v > 1 && println(f) -# precx = precx <= 1 ? 2 : precx - -# v > 0 && println("Compute parametrization of critical pts...") -# @iftime (v > 0) params = param_crit_split(f,g,v=v-1, detect_app=true) -# #@iftime (v > 0) params = mmod_param_crit(f, g,v=v-1, detect_app=true) -# for i in 1:length(C) -# params[-i] = [ [C[i][1] |> intC], C[i][2], C[i][3] ] -# end - -# v > 0 && println("Computing insulating critical boxes") -# @iftime (v > 0) LBcrit, Lprecx = insulate_crit_boxes(f, params, precx, v=v-1) - -# v > 0 && println("Compute intersections with critical boxes..") -# @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf, v=v-1) - -# # Graph computation -# fct, typeout = outf ? (Float64, Float64) : (identity, QQFieldElem) -# # Critical values and their order -# xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in eachindex(LBcrit)) -# xcritpermut = order_permut2d(xcrit) -# # List of vertex: at index i is the tuple of the coordinates of the i-th vertex -# Vert = Vector{Tuple{typeout, typeout}}() -# # List of edges: a tuple (i,j) is an edge between the i-th and j-th vertices -# Edg = Vector{Tuple{Int, Int}}() -# Corr = Dict( m => [[[], [[], [], []], []] for j in xcrit[m] ] for m in eachindex(xcrit)) -# Vcon = [ [] for _ in 1:length(C) ] - -# # Keep track of processed isolated & apparent singularities -# Lapp = [[],[]] - -# for ind in eachindex(xcritpermut) -# i, j = xcritpermut[ind] - -# if ind > 1 -# i1, j1 = xcritpermut[ind - 1] -# end -# if ind < length(xcritpermut) -# i2, j2 = xcritpermut[ind + 1] -# I2L, = LPCside[i2][j2][3] -# end - -# PCside = LPCside[i][j] -# I = [ l[1] for l in PCside[3:end] ] -# nI = [ l[2] for l in PCside[3:end] ] - -# xcmid = sum(LBcrit[i][j][1])//2 |> fct -# ycmid = sum(LBcrit[i][j][2])//2 |> fct - -# ymincrit = minimum(vcat(nI[1], nI[2], [length(I[1])+1])) -# # Construct vertices -# ########################### -# # On the vertical left side -# if ind > 1 -# for k in 1:length(I[1]) -# push!(Corr[i][j][1], Corr[i1][j1][3][k]) -# end -# else -# for k in 1:length(I[1]) -# push!(Vert, (xcrit[i][j][1], sum(I[1][k])//2) .|> fct) -# push!(Corr[i][j][1], length(Vert)) -# end -# end -# ########################### -# # On the vertical right side -# if ind < length(xcritpermut) -# for k in 1:length(I[2]) -# push!(Vert, ((xcrit[i][j][2] + xcrit[i2][j2][1])//2, sum(I[2][k] + I2L[k])//4) .|> fct) -# push!(Corr[i][j][3], length(Vert)) -# end -# else -# for k in 1:length(I[2]) -# push!(Vert, (xcrit[i][j][2], sum(I[2][k])//2) .|> fct) -# push!(Corr[i][j][3], length(Vert)) -# end -# end -# ########################### -# # Below the critical point -# for k in 1:ymincrit-1 -# push!(Vert, (xcmid, sum(I[1][k] + I[2][k])// 4) .|> fct) -# push!(Corr[i][j][2][1], length(Vert)) -# push!(Edg, (Corr[i][j][1][k], length(Vert))) # left -# push!(Edg, (length(Vert), Corr[i][j][3][k])) # right -# end -# ########################### -# # The critical point -# ########################## -# # If we are dealing with a isolated node -# if i in [0,2] && isempty(nI[1]) && isempty(nI[2]) -# push!(Lapp[1], (i,j)) -# # If we are dealing with an apparent singularity -# elseif i == 0 -# # We connect the pairwise opposite branches nI[1][1][i] and nI[1][2][i+1 mod 2], i=1,2 -# push!(Edg, (Corr[i][j][1][nI[1][1]], Corr[i][j][3][nI[2][2]])) -# push!(Edg, (Corr[i][j][1][nI[1][2]], Corr[i][j][3][nI[2][1]])) -# push!(Lapp[2], (i,j)) -# else -# # We can add the vertex -# push!(Vert, (xcmid, ycmid)) -# push!(Corr[i][j][2][2], length(Vert)) -# # We connect to the vertical left side of the critical box -# for k in nI[1] -# push!(Edg, (Corr[i][j][1][k], length(Vert))) -# end -# # We connect to the vertical right side of the critical box -# for k in nI[2] -# push!(Edg, (length(Vert), Corr[i][j][3][k])) -# end -# if i < 0 -# # If this is a control point -# push!(Vcon[-i], length(Vert)) -# end -# end -# ########################### -# # Above the critical point -# for k=(length(I[1]) - length(nI[1]) - ymincrit+1):-1:1 -# push!(Vert, (xcmid, sum(I[1][end - k + 1] + I[2][end - k + 1])//4) .|> fct) -# push!(Corr[i][j][2][3], length(Vert)) -# push!(Edg, (Corr[i][j][1][end - k + 1], length(Vert))) # left -# push!(Edg, (length(Vert), Corr[i][j][3][end - k + 1])) # right -# end -# end - -# if v > 0 && Lapp != [[],[]] -# println("Removed apparent singularities: $(length(Lapp[1])) isolated $(length(Lapp[2])) nodes") -# end - -# # Operate inverse change of variable if necessary -# if !(generic) -# for i in eachindex(Vert) -# vx,vy = Vert[i] -# vx,vy = fct.(changemat*[vx, vy]) -# Vert[i] = (vx, vy) -# end -# end - -# if length(C)>0 -# return (Vert, Edg), Vcon -# else -# return Vert, Edg -# end -# end - -# function compute_graph(f::P, g::P, C::Dict{Int,Vector{P}}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) -# G, Vcon = compute_graph(f, g, collect(values(C)), generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf) -# VC = Dict{Int64, Vector{Int}}([ k => Vcon[i] for (i,k) in enumerate(keys(C)) ]) -# return G, VC -# end - -# function compute_graph(f::P, g::P, C::Vector{P}; generic=true, precx = 150, v=0, arb=true, int_coeff=false, outf = true) where (P <: MPolyRingElem) -# G, (Vcon,) = compute_graph(f, g, [C], generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf = outf) -# return G, Vcon -# end - -# ################################################################ -# function group_by_component(f::P, C::Vector{P}; generic=true, precx=150, v=0, arb=true, int_coeff=false) where {P <: MPolyRingElem} -# # Compute a graph homeomorphic to Z(F) and return the vertices identified by Z(C) -# G, Vcon = compute_graph(f, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff) -# # Compute the partition of the vertices in Vcon according to the connected component in G -# sort!(Vcon) -# CVcon = group_by_component(G, Vcon) - -# # Convert the partition into abscissa order -# index_map = Dict((val, idx) for (idx, val) in enumerate(Vcon)) -# return [map(v -> index_map[v], C) for C in CVcon] -# end - -# function plot_graph(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) -# plot_graph(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) -# end - -# function plot_graph(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) -# plot_graph(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) -# end - -# function plot_graph_comp(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) -# plot_graph_comp(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) -# end - -# function plot_graph_comp(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) -# plot_graph_comp(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) -# end - -# function number_connected_components(f::P, g::P, C::Vector{Vector{P}}=Vector{Vector{P}}(); generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) -# number_connected_components(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) -# end - -# function number_connected_components(f::P, g::P, C; generic=true, precx = 150, v=0, arb=true, int_coeff=true, outf=true) where (P <: MPolyRingElem) -# number_connected_components(compute_graph(f, g, C, generic=generic, precx=precx, v=v, arb=arb, int_coeff=int_coeff, outf=outf)) -# end - -#################################### - function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; generic=true, precx=150, v=0, int_coeff=true, outf=true) where {P <: MPolyRingElem} diff --git a/src/connectivity/graph.jl b/src/connectivity/graph.jl index 026eda0..ed2dd93 100644 --- a/src/connectivity/graph.jl +++ b/src/connectivity/graph.jl @@ -1,128 +1,186 @@ -## TODO : deal with isolated vertices (not appearing in the edges) -############################ - -function index_of(x, L) - return findfirst(t->t==x,L) -end - -function connected_components(G, Vemph=[]; ind_abs=false) - # Outputs subgraphs of the connected components - ########### - vert, edges = G +# ========================================================================= +# GRAPH DECOMPOSITION +# ========================================================================= + +""" + connected_components(G::CurveGraph{T}) where T + +Decomposes a graph into its connected components. + +# Inputs +- `G::CurveGraph{T}`: The unified curve graph. + +# Outputs +- `Vector{CurveGraph{T}}`: A list of disjoint subgraphs. Each subgraph retains + the mapped coordinates, edges, and control nodes belonging to its component. +""" +function connected_components(G::CurveGraph{T}) where T + nv = length(G.vertices) + + # Work with vertices to avoid missing isolated vertices + adj_list = [Int[] for _ in 1:nv] + for (u, v) in G.edges + push!(adj_list[u], v) + push!(adj_list[v], u) + end - adj_list = Dict{Int, Vector{Int}}() - visited = Set{Int}() + visited = falses(nv) components = Vector{Vector{Int}}() - # Build adjacency list - for (i, j) in edges - push!(get!(adj_list, i, []), j) - push!(get!(adj_list, j, []), i) - end - - # Depth-first search - function dfs(node, component) - push!(visited, node) - push!(component, node) - for neighbor in adj_list[node] - if !(neighbor in visited) - dfs(neighbor, component) + # Iterative DFS + for i in 1:nv + if !visited[i] + comp = Int[] + stack = [i] + visited[i] = true + while !isempty(stack) + curr = pop!(stack) + push!(comp, curr) + for neighbor in adj_list[curr] + if !visited[neighbor] + visited[neighbor] = true + push!(stack, neighbor) + end + end end + push!(components, comp) end end - # Find connected components - for node in keys(adj_list) - if !(node in visited) - component = Vector{Int}() - dfs(node, component) - push!(components, component) + # Mapping global vertex ID -> (component ID, local vertex ID) + vertex_map = Vector{Tuple{Int, Int}}(undef, nv) + for (cid, comp) in enumerate(components) + for (local_id, global_id) in enumerate(comp) + vertex_map[global_id] = (cid, local_id) end end - # Group edges by connected component - grouped_edges = [Tuple{Int, Int}[] for _ in components] - for (idx, component) in enumerate(components) - for node in component - for neighbor in adj_list[node] - if neighbor > node && neighbor in component - push!(grouped_edges[idx], (index_of(node,component), index_of(neighbor,component))) - end - end - end + # Group edges + comp_edges = [Tuple{Int, Int}[] for _ in 1:length(components)] + for (u, v) in G.edges + cid_u, local_u = vertex_map[u] + cid_v, local_v = vertex_map[v] + push!(comp_edges[cid_u], (local_u, local_v)) end - if length(Vemph)>0 - CVemph = [ Dict(k=>[] for k in eachindex(Vemph)) for _ in eachindex(components) ] - for i in eachindex(components) - for j in eachindex(components[i]) - for k in eachindex(Vemph) - if components[i][j] in Vemph[k] - push!(CVemph[i][k], ind_abs ? components[i][j] : j) - end + # Reconstruct subgraphs into CurveGraphs + subgraphs = CurveGraph{T}[] + for (cid, comp) in enumerate(components) + new_verts = G.vertices[comp] + new_edges = comp_edges[cid] + new_control = Dict{Int, Vector{Int}}() + + # Keep track of control points falling into this specific component + for (k, v_list) in G.control_nodes + local_v_list = Int[] + for global_v in v_list + c, local_v = vertex_map[global_v] + if c == cid + push!(local_v_list, local_v) end end + if !isempty(local_v_list) + new_control[k] = local_v_list + end end - end - if length(Vemph)>0 - return [ [[[ vert[cv] for cv in components[i] ], grouped_edges[i]], CVemph[i]] for i in eachindex(components) ] - else - return [ [[ vert[cv] for cv in components[i] ], grouped_edges[i]] for i in eachindex(components) ] + push!(subgraphs, CurveGraph{T}(new_verts, new_edges, new_control)) end -end -function group_by_component(G, V) - CG = connected_components(G, V, ind_abs=true) - return filter(c->length(c)>0, [ C[2] for C in CG ]) + return subgraphs end -function number_connected_components(G) - return length(connected_components(G)) +""" + group_by_component(G::CurveGraph) + +# Outputs +- `Vector{Dict{Int, Vector{Int}}}`: Returns just the control nodes mapped to each connected component. +""" +function group_by_component(G::CurveGraph) + subgraphs = connected_components(G) + return [sg.control_nodes for sg in subgraphs if !isempty(sg.vertices)] end +""" + number_connected_components(G::CurveGraph) + +# Outputs +- `Int`: The count of isolated subgraphs in the parent structure. +""" +number_connected_components(G::CurveGraph) = length(connected_components(G)) + + +# ========================================================================= +# GRAPH MERGING +# ========================================================================= + +""" + merge_graphs(graphs::Vector{CurveGraph{T}}) where T + +Merges a collection of disjoint graphs into a single graph, mathematically fusing +vertices that share common `control_nodes` mappings. + +# Inputs +- `graphs::Vector{CurveGraph{T}}`: A list of graphs. `graphs[i].control_nodes[k]` + should contain the local vertex indices in graph `i` that connect to graph `k`. -function merge_graphs(LG::Vector{Tuple{Vector{Tuple{T,T}}, Vector{Tuple{Int,Int}}}} where T<:Union{Float64, QQFieldElem}, LVC::Vector{Dict{Int, Vector{Int}}}) - # Initialize merged graph with the vertices and edges of the first graph - Vtot, Etot = deepcopy(LG[1]) +# Outputs +- `CurveGraph{T}`: A unified graph struct. +""" +function merge_graphs(graphs::Vector{CurveGraph{T}}) where T + isempty(graphs) && return CurveGraph{T}(Tuple{T,T}[], Tuple{Int,Int}[], Dict{Int, Vector{Int}}()) + length(graphs) == 1 && return deepcopy(graphs[1]) - # To keep track of the mapping of vertices from each graph to the merged graph - all_vertex_maps = [Dict(i => i for i in 1:length(Vtot))] + Vtot = copy(graphs[1].vertices) + Etot = copy(graphs[1].edges) - # Iterate over each graph G_i in LG starting from the second graph - for i in 2:length(LG) - Vi, Ei = LG[i] # Vertices and edges of the current graph + # Dictionary to track: (graph_id, local_vertex_id) -> merged_global_id + global_map = Dict{Tuple{Int, Int}, Int}() + for i in 1:length(graphs[1].vertices) + global_map[(1, i)] = i + end - # Dictionary to map vertices of Gi to their new indices in Vtot - vertex_index_map = Dict() + for i in 2:length(graphs) + G_i = graphs[i] - # Step 1: Map common vertices from Gi to existing vertices in Vtot - for (k, common_indices) in LVC[i] - if k < i - # Map each common vertex in Gi to its corresponding vertex in Gk (already merged) - for (j, idx) in enumerate(common_indices) - vertex_index_map[idx] = all_vertex_maps[k][LVC[k][i][j]] + # Step 1: Pre-map common control nodes connected to previously merged graphs + for (k, common_indices_in_i) in G_i.control_nodes + if k < i && haskey(graphs[k].control_nodes, i) + common_indices_in_k = graphs[k].control_nodes[i] + # Zip ensures we pair corresponding control nodes precisely + for (idx_i, idx_k) in zip(common_indices_in_i, common_indices_in_k) + global_map[(i, idx_i)] = global_map[(k, idx_k)] end end end - # Step 2: Add non-common vertices from Gi to Vtot - for idx in 1:length(Vi) - if !haskey(vertex_index_map, idx) # If not already mapped, it's a new vertex - vertex_index_map[idx] = push!(Vtot, Vi[idx]) |> length + # Step 2: Add completely new (unmapped) vertices from G_i to Vtot + for idx_i in 1:length(G_i.vertices) + if !haskey(global_map, (i, idx_i)) + push!(Vtot, G_i.vertices[idx_i]) + global_map[(i, idx_i)] = length(Vtot) end end - # Step 3: Merge edges of Gi into the merged graph - new_edges = [(vertex_index_map[i], vertex_index_map[j]) for (i, j) in Ei] - append!(Etot, new_edges) - # Store the vertex index mapping for Gi for future merges - push!(all_vertex_maps, vertex_index_map) + # Step 3: Append the edges using the newly mapped global indices + for (u, v) in G_i.edges + push!(Etot, (global_map[(i, u)], global_map[(i, v)])) + end end - return Vtot, Etot -end + # Step 4: Preserve external control nodes pointing OUTSIDE the merged structure + merged_control = Dict{Int, Vector{Int}}() + num_graphs = length(graphs) + + for i in 1:num_graphs + for (k, v_list) in graphs[i].control_nodes + # If `k` points to a graph outside of the ones we just merged + if k > num_graphs || k <= 0 + mapped_v = [global_map[(i, v)] for v in v_list] + append!(get!(merged_control, k, Int[]), mapped_v) + end + end + end -function merge_graphs(LGVC::Vector{Tuple{Tuple{Vector{Tuple{T, T}}, Vector{Tuple{Int64, Int64}}}, Dict{Int64, Vector{Int64}}}} where T<:Union{Float64, QQFieldElem}) - return merge_graphs(first.(LGVC), last.(LGVC)) + return CurveGraph{T}(Vtot, Etot, merged_control) end \ No newline at end of file diff --git a/src/connectivity/newgraph.jl b/src/connectivity/newgraph.jl deleted file mode 100644 index f2d7db7..0000000 --- a/src/connectivity/newgraph.jl +++ /dev/null @@ -1,186 +0,0 @@ -# ========================================================================= -# GRAPH DECOMPOSITION -# ========================================================================= - -""" - connected_components(G::CurveGraph{T}) where T - -Decomposes a graph into its connected components. - -# Inputs -- `G::CurveGraph{T}`: The unified curve graph. - -# Outputs -- `Vector{CurveGraph{T}}`: A list of disjoint subgraphs. Each subgraph retains - the mapped coordinates, edges, and control nodes belonging to its component. -""" -function connected_components(G::CurveGraph{T}) where T - nv = length(G.vertices) - - # Work with vertices to avoid missing isolated vertices - adj_list = [Int[] for _ in 1:nv] - for (u, v) in G.edges - push!(adj_list[u], v) - push!(adj_list[v], u) - end - - visited = falses(nv) - components = Vector{Vector{Int}}() - - # Iterative DFS - for i in 1:nv - if !visited[i] - comp = Int[] - stack = [i] - visited[i] = true - while !isempty(stack) - curr = pop!(stack) - push!(comp, curr) - for neighbor in adj_list[curr] - if !visited[neighbor] - visited[neighbor] = true - push!(stack, neighbor) - end - end - end - push!(components, comp) - end - end - - # Mapping global vertex ID -> (component ID, local vertex ID) - vertex_map = Vector{Tuple{Int, Int}}(undef, nv) - for (cid, comp) in enumerate(components) - for (local_id, global_id) in enumerate(comp) - vertex_map[global_id] = (cid, local_id) - end - end - - # Group edges in O(E) time using the map - comp_edges = [Tuple{Int, Int}[] for _ in 1:length(components)] - for (u, v) in G.edges - cid_u, local_u = vertex_map[u] - cid_v, local_v = vertex_map[v] - push!(comp_edges[cid_u], (local_u, local_v)) - end - - # Reconstruct subgraphs into clean CurveGraph structs - subgraphs = CurveGraph{T}[] - for (cid, comp) in enumerate(components) - new_verts = G.vertices[comp] - new_edges = comp_edges[cid] - new_control = Dict{Int, Vector{Int}}() - - # Keep track of control points falling into this specific component - for (k, v_list) in G.control_nodes - local_v_list = Int[] - for global_v in v_list - c, local_v = vertex_map[global_v] - if c == cid - push!(local_v_list, local_v) - end - end - if !isempty(local_v_list) - new_control[k] = local_v_list - end - end - - push!(subgraphs, CurveGraph{T}(new_verts, new_edges, new_control)) - end - - return subgraphs -end - -""" - group_by_component(G::CurveGraph) - -# Outputs -- `Vector{Dict{Int, Vector{Int}}}`: Returns just the control nodes mapped to each connected component. -""" -function group_by_component(G::CurveGraph) - subgraphs = connected_components(G) - return [sg.control_nodes for sg in subgraphs if !isempty(sg.vertices)] -end - -""" - number_connected_components(G::CurveGraph) - -# Outputs -- `Int`: The count of isolated subgraphs in the parent structure. -""" -number_connected_components(G::CurveGraph) = length(connected_components(G)) - - -# ========================================================================= -# GRAPH MERGING -# ========================================================================= - -""" - merge_graphs(graphs::Vector{CurveGraph{T}}) where T - -Merges a collection of disjoint graphs into a single graph, mathematically fusing -vertices that share common `control_nodes` mappings. - -# Inputs -- `graphs::Vector{CurveGraph{T}}`: A list of graphs. `graphs[i].control_nodes[k]` - should contain the local vertex indices in graph `i` that connect to graph `k`. - -# Outputs -- `CurveGraph{T}`: A unified graph struct. -""" -function merge_graphs(graphs::Vector{CurveGraph{T}}) where T - isempty(graphs) && return CurveGraph{T}(Tuple{T,T}[], Tuple{Int,Int}[], Dict{Int, Vector{Int}}()) - length(graphs) == 1 && return deepcopy(graphs[1]) - - Vtot = copy(graphs[1].vertices) - Etot = copy(graphs[1].edges) - - # Dictionary to track: (graph_id, local_vertex_id) -> merged_global_id - global_map = Dict{Tuple{Int, Int}, Int}() - for i in 1:length(graphs[1].vertices) - global_map[(1, i)] = i - end - - for i in 2:length(graphs) - G_i = graphs[i] - - # Step 1: Pre-map common control nodes connected to previously merged graphs - for (k, common_indices_in_i) in G_i.control_nodes - if k < i && haskey(graphs[k].control_nodes, i) - common_indices_in_k = graphs[k].control_nodes[i] - # Zip ensures we pair corresponding control nodes precisely - for (idx_i, idx_k) in zip(common_indices_in_i, common_indices_in_k) - global_map[(i, idx_i)] = global_map[(k, idx_k)] - end - end - end - - # Step 2: Add completely new (unmapped) vertices from G_i to Vtot - for idx_i in 1:length(G_i.vertices) - if !haskey(global_map, (i, idx_i)) - push!(Vtot, G_i.vertices[idx_i]) - global_map[(i, idx_i)] = length(Vtot) - end - end - - # Step 3: Append the edges using the newly mapped global indices - for (u, v) in G_i.edges - push!(Etot, (global_map[(i, u)], global_map[(i, v)])) - end - end - - # Step 4: Preserve external control nodes pointing OUTSIDE the merged structure - merged_control = Dict{Int, Vector{Int}}() - num_graphs = length(graphs) - - for i in 1:num_graphs - for (k, v_list) in graphs[i].control_nodes - # If `k` points to a graph outside of the ones we just merged - if k > num_graphs || k <= 0 - mapped_v = [global_map[(i, v)] for v in v_list] - append!(get!(merged_control, k, Int[]), mapped_v) - end - end - end - - return CurveGraph{T}(Vtot, Etot, merged_control) -end \ No newline at end of file From 3d447b90221328746791d4fd2b9edd7ca343cb02 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 14 Apr 2026 19:55:55 +0200 Subject: [PATCH 148/180] cleaning remain plot --- src/connectivity/connectcurves.jl | 47 ++++--- src/connectivity/graph.jl | 2 +- src/connectivity/isolateboxes.jl | 202 ------------------------------ 3 files changed, 30 insertions(+), 221 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 3bf4806..8268856 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -16,6 +16,34 @@ include("plots.jl") include("arbtools.jl") include("buildpoly.jl") +# ========================================================================= +# MULTIPLE DISPATCH WRAPPERS (Clean, concise, and DRY) +# ========================================================================= + +# Base case: No 'C' provided +compute_graph(f::P, g::P; kwargs...) where {P <: MPolyRingElem} = + _compute_graph_core(f, g, Vector{Vector{P}}(); kwargs...) + +# Case 1: C is a Vector of Vectors +compute_graph(f::P, g::P, C::Vector{Vector{P}}; kwargs...) where {P <: MPolyRingElem} = + _compute_graph_core(f, g, C; kwargs...) + +# Case 2: C is a Dictionary +function compute_graph(f::P, g::P, C::Dict{Int, Vector{P}}; kwargs...) where {P <: MPolyRingElem} + graph = _compute_graph_core(f, g, collect(values(C)); kwargs...) + # Remap Vcon dictionary keys to match original dict keys + mapped_vcon = Dict{Int, Vector{Int}}(k => graph.control_nodes[i] for (i, k) in enumerate(keys(C))) + return CurveGraph(graph.vertices, graph.edges, mapped_vcon) +end + +# Case 3: C is a single Vector +compute_graph(f::P, g::P, C::Vector{P}; kwargs...) where {P <: MPolyRingElem} = + _compute_graph_core(f, g, [C]; kwargs...) + +# ========================================================================= +# CORE IMPLEMENTATION +# ========================================================================= + # Input: # The space curve is given by f(x,y) = 0 and (df/dy)(x,y)*z = g(x,y) # it is assumed in generic position of put it using generic parameter @@ -167,21 +195,4 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; # Return the unified data structure return CurveGraph{QQFieldElem}(Vert, Edg, Vcon) -end - -# Multi-dispatch wrappers returning the Graph Struct -compute_graph(f::P, g::P; kwargs...) where {P <: MPolyRingElem} = - _compute_graph_core(f, g, Vector{Vector{P}}(); kwargs...) - -compute_graph(f::P, g::P, C::Vector{Vector{P}}; kwargs...) where {P <: MPolyRingElem} = - _compute_graph_core(f, g, C; kwargs...) - -function compute_graph(f::P, g::P, C::Dict{Int, Vector{P}}; kwargs...) where {P <: MPolyRingElem} - graph = _compute_graph_core(f, g, collect(values(C)); kwargs...) - # Remap Vcon dictionary keys to match original dict keys - mapped_vcon = Dict{Int, Vector{Int}}(k => graph.control_nodes[i] for (i, k) in enumerate(keys(C))) - return CurveGraph(graph.vertices, graph.edges, mapped_vcon) -end - -compute_graph(f::P, g::P, C::Vector{P}; kwargs...) where {P <: MPolyRingElem} = - _compute_graph_core(f, g, [C]; kwargs...) \ No newline at end of file +end \ No newline at end of file diff --git a/src/connectivity/graph.jl b/src/connectivity/graph.jl index ed2dd93..2ec31c5 100644 --- a/src/connectivity/graph.jl +++ b/src/connectivity/graph.jl @@ -11,7 +11,7 @@ Decomposes a graph into its connected components. - `G::CurveGraph{T}`: The unified curve graph. # Outputs -- `Vector{CurveGraph{T}}`: A list of disjoint subgraphs. Each subgraph retains +- `Vector{CurveGraph{T}}`: A list of disjoint subgraphs. Each subgraph retains the mapped coordinates, edges, and control nodes belonging to its component. """ function connected_components(G::CurveGraph{T}) where T diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index 8c2b6a7..d895eaf 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -1,8 +1,3 @@ -const side = Tuple{Vector{Vector{QQFieldElem}}, Vector{Int}} -const Sides = NTuple{4, side} -const Boxes = Vector{Sides} - - in_inter(I, J) = J[1] <= I[1] && I[2] <= J[2] overlap_inter(I, J) = max(I[1], J[1]) <= min(I[2], J[2]) @@ -128,203 +123,6 @@ function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) return LBcrit, Lprecx end -####################################################### - -# # Helper function to process a single edge of the box -# function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v; max_retries=5) -# prec = initial_prec - -# for _ in 1:max_retries -# roots = isolate_eval(f, fixed_dim, fixed_val, prec=prec) -# indices_inside = Int[] -# overlap_found = false - -# for (j, l) in pairs(roots) -# if in_inter(l, target_interval) -# push!(indices_inside, j) -# elseif overlap_inter(l, target_interval) -# prec *= 2 -# v > 0 && println("IntersectBox: increase precision to $prec bits") -# overlap_found = true -# break # Break inner for-loop to restart with higher precision -# end -# end - -# # If we successfully processed all roots without overlap, return the results -# if !overlap_found -# return (roots, indices_inside) -# end -# end - -# error("Problem when isolating on one side of a box after $max_retries attempts") -# end - -# # Function that computes the intersection of a curve with a box by isolating roots on the edges -# function intersect_box(f, B; prec=100, v=0) -# # B[1] represents x-bounds, B[2] represents y-bounds - -# # Evaluate horizontal edges (fix y to B[2][1] and B[2][2], target x-interval B[1]) -# edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v)::side -# edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v)::side - -# # Evaluate vertical edges (fix x to B[1][1] and B[1][2], target y-interval B[2]) -# edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v)::side -# edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v)::side - -# # Return as a 4-Tuple of 2-Tuples -# return (edge_y1, edge_y2, edge_x1, edge_x2) -# end - - -# """ -# _update_LB_first_axis!(LB, xnew) - -# Replace first coordinate of each box in LB with corresponding xnew interval. -# """ -# function _update_LB_first_axis!(LB, xnew) -# @inbounds for i in eachindex(LB) -# LB[i][1] = xnew[i] -# end -# return LB -# end - -# """ -# refine_xboxes(f, LB, prec) - -# Refine LB along first axis using roots of polynomials in F -# The order in F is assumed to match the one in LB -# """ -# function refine_xboxes(F::Vector{T} where T<:Union{PolyRingElem, MPolyRingElem}, LB, prec) -# # Concatenate all roots from isolating each polynomial in F -# xnew = reduce(vcat, [isolate(f, prec=prec) for f in F]) - -# _expand_degenerate_intervals!(xnew, prec) -# return _update_LB_first_axis!(LB, xnew) -# end - -# function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0) - -# LPCside = Dict{Int, Boxes}() - -# for (i, boxes) in pairs(LBcrit) -# prec = Lprecx[i] -# n = length(boxes) - -# sides_vec = Vector{Sides}(undef, n) - -# for attempt in 1:max_attempts -# refined = false - -# @inbounds for j in 1:n -# v >= 0 && print("i=$i ($j/$n)\r") - -# pc = intersect_box(f, boxes[j], prec=prec, v=v)::Sides - -# c1 = length(pc[1][2]) -# c2 = length(pc[2][2]) -# c3 = length(pc[3][2]) -# c4 = length(pc[4][2]) - -# if (i == 1 && (c1 + c2 + c3 + c4 > 2)) || -# (i != 1 && (c1 != 0 || c2 != 0)) - -# prec *= 2 -# v > 0 && println("\nRefine -> prec = $prec") - -# refine_xboxes(params[i][1], boxes, prec) - -# refined = true -# break -# end - -# sides_vec[j] = pc -# end - -# refined || break -# attempt == max_attempts && -# error("Problem in computing intersections (i=$i)") -# end - -# LPCside[i] = sides_vec -# Lprecx[i] = prec - -# v >= 0 && println() -# end - -# # ---- Counts (type-stable) ---- -# LnPCside = Dict{Int, Vector{NTuple{4, Int}}}() - -# for (i, vec) in pairs(LPCside) -# LnPCside[i] = [ -# ( -# length(pc[1][2]), -# length(pc[2][2]), -# length(pc[3][2]), -# length(pc[4][2]) -# ) -# for pc in vec -# ] -# end - -# # ---- Extremal case (i == 1) ---- -# if haskey(LBcrit, 1) -# boxes = LBcrit[1] -# pcs = LPCside[1] -# cnts = LnPCside[1] - -# @inbounds for j in eachindex(boxes) -# c1, c2, c3, c4 = cnts[j] - -# (c1 == 0 && c2 == 0) && continue - -# pc = pcs[j] -# ycrit = boxes[j][2] - -# I1 = pc[3][1] # left -# I2 = pc[4][1] # right - -# # Orientation of the curve left(s=1)/right(s=2) -# s = length(I1) >= length(I2) ? 1 : 2 - -# # ---- intersection on bottom ---- -# if c1 == 1 -# # Attach to the max intersection below the bow on the correct side -# yinf = maximum(i for (i, yy) in pairs((s == 1 ? I1 : I2)) if yy[1] < ycrit[1]) - -# push!(pc[s+2][2], yinf) -# pc[1][2] = Int[] - -# cnts[j] = ( -# 0, -# c2, -# s == 1 ? c3 + 1 : c3, -# s == 2 ? c4 + 1 : c4 -# ) - -# c1, c2, c3, c4 = cnts[j] # for next step -# end - -# # ---- intersection on top ---- -# if c2 == 1 -# ymax = minimum(i for (i, yy) in pairs((s == 1 ? I1 : I2)) if yy[2] > ycrit[2]) - -# push!(pc[s+2][2], ymax) -# pc[2][2] = Int[] - -# cnts[j] = ( -# c1, -# 0, -# s == 1 ? c3 + 1 : c3, -# s == 2 ? c4 + 1 : c4 -# ) -# end -# end -# end -# #TODO: by design bottom/top sides in LnPCside are [0,0] -> remove -# return LPCside, LnPCside -# end - -############################################## # Helper function to process a single edge of the box function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v, outf; max_retries=5) From 17dfd53fdc7c88dec7221f0fadc05aeda7863cf1 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 14 Apr 2026 22:52:18 +0200 Subject: [PATCH 149/180] clean a bit everything + some small optimination --- src/connectivity/connectcurves.jl | 7 +- src/connectivity/datastruct.jl | 19 ++++++ src/connectivity/isolateboxes.jl | 21 ++++-- src/connectivity/plots.jl | 106 +++++++++++------------------- src/connectivity/tools.jl | 35 +--------- src/imports.jl | 2 +- 6 files changed, 76 insertions(+), 114 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 8268856..e9c7aa9 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -17,7 +17,7 @@ include("arbtools.jl") include("buildpoly.jl") # ========================================================================= -# MULTIPLE DISPATCH WRAPPERS (Clean, concise, and DRY) +# MULTIPLE DISPATCH WRAPPERS # ========================================================================= # Base case: No 'C' provided @@ -73,10 +73,10 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; v > 0 && println("Computing insulating critical boxes") @iftime (v > 0) LBcrit, Lprecx = insulate_crit_boxes(f, params, precx, v=v-1) - println(LBcrit) + v > 0 && println("Compute intersections with critical boxes..") @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf, v=v-1) - println(LPCside) + # Critical values and their order xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in keys(LBcrit)) xcritpermut = order_permut2d(xcrit) @@ -110,7 +110,6 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; # 1. Left side vertices # one-to-one connection with previous right side - # TODO: could be improved memory-wise if ind > 1 for k in 1:length(PCside.left.points) push!(Corr[i][j].left, Corr[i1][j1].right[k]) diff --git a/src/connectivity/datastruct.jl b/src/connectivity/datastruct.jl index 94766e3..9a138b2 100644 --- a/src/connectivity/datastruct.jl +++ b/src/connectivity/datastruct.jl @@ -26,4 +26,23 @@ struct CurveGraph{T} vertices::Vector{Tuple{T, T}} edges::Vector{Tuple{Int, Int}} control_nodes::Dict{Int, Vector{Int}} +end + +# ---------- PLOT ---------- + +struct EdgeGroup + edges::Vector{Tuple{Vector{Float64}, Vector{Float64}}} + color::Int64 + width::Float64 +end + +struct PointGroup + vertices::Tuple{Vector{Float64}, Vector{Float64}} # (x, y) + color::Int64 + marker::Symbol +end + +struct GraphPlotData + edge_group::EdgeGroup + point_groups::Vector{PointGroup} end \ No newline at end of file diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index d895eaf..f025646 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -16,8 +16,9 @@ end # univariate isolation of roots of a bivariate polynomial f whose # ivar-th variable is evaluated at val function isolate_eval(f, ivar, val; prec=64) - fev = change_ringvar(evaluate(f, [ivar], [val])) + fev = evaluate(f, [ivar], [val]) # fev *= fev |> coefficients .|> denominator |> lcm + fev = fev / content(fev) return isolate(fev, prec=prec) end @@ -47,7 +48,6 @@ function _compute_boxes_for_index!(i, params, LBcrit, precx) _expand_degenerate_intervals!(xvals, precx) arbField = ArbField(precx) - yvals = [ evaluate_arb(params[i][2], params[i][3], xc, arbField) for xc in xvals @@ -63,12 +63,9 @@ end Check if boxes at index i require refinement. """ -function _needs_refinement(i, f, LBcrit, precx) +function _needs_refinement(i, Lfyk, LBcrit, precx) arbField = ArbField(precx) m = i <= 1 ? 2 : i - # TODO: input, compute once for all i - Lfyk = diff_list(f, 2, max(i, 2)) - for box in LBcrit[i] pcrit = [rat_to_arb(c, arbField) for c in box] @@ -79,6 +76,15 @@ function _needs_refinement(i, f, LBcrit, precx) return false end +# Compute the list of the n-th first derivative of p w.r.t v +function diff_list(p, v, n) + L = Vector{typeof(p)}(undef, n + 1) + L[1] = p + @inbounds for j in 2:n+1 + L[j] = derivative(L[j-1], v) + end + return L +end """ compute_crit_and_singular_boxes(f, params, precx; max_attempts=5, v=0) @@ -90,6 +96,7 @@ critical point. """ function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) LBcrit, Lprecx = Dict(), Dict() + Lfyk = diff_list(f, 2, max(maximum(keys(params)), 2)) for i in keys(params) attempts, precxi = 0, precx @@ -101,7 +108,7 @@ function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) _compute_boxes_for_index!(i, params, LBcrit, precxi) # singularity check - if !_needs_refinement(i, f, LBcrit, precxi) + if !_needs_refinement(i, Lfyk, LBcrit, precxi) break end diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index e160b85..66ed551 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,10 +1,10 @@ ## Plot functions -function plot_graph(G, Vemph::Vector{Vector{T}} where T<:Any; color="red", width=3, vert=true, subplt=false) +function plot_graph(G; color="red", width=3, vert=true, subplt=false) if !subplt plot(legend=false) end - V, E = G.vertices, G.edges + V, Vcon, E = G.vertices, G.control_nodes, G.edges #col = distinguishable_colors(length(Vemph)+2) for e in E v1, v2 = [ map(Float64, V[ee]) for ee in e ] @@ -13,42 +13,28 @@ function plot_graph(G, Vemph::Vector{Vector{T}} where T<:Any; color="red", width if vert scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) end - for i in 1:length(Vemph) - scatter!( map(Float64, [V[j][1] for j in Vemph[i]]), map(Float64, [V[j][2] for j in Vemph[i]]), mc=color, m=:diamond) + for i in 1:length(Vcon) + scatter!( map(Float64, [V[j][1] for j in Vcon[i]]), map(Float64, [V[j][2] for j in Vcon[i]]), mc=color, m=:diamond) end subplt || gui() end -function plot_graph(G; color="red", width=3, vert=true, subplt=false) - plot_graph(G, Vector{Vector{QQMPolyRingElem}}(); color=color, width=width, vert=vert, subplt=subplt) -end - -function plot_graph(G, Vemph::Vector{T} where T<:Any; color="red", width=3, vert=true, subplt=false) - plot_graph(G, [Vemph], color=color, width=width, vert=vert, subplt=subplt) -end - -function plot_graph(G, Vemph::Dict{Int, Vector{T}} where T<:Any; color="red", width=3, vert=true, subplt=false) - plot_graph(G, Vemph|>values|>collect, color=color, width=width, vert=vert, subplt=subplt) -end - function plot_graphs(CG; width=3, vert=true, subplt=false) if !subplt plot(legend=false) end col = distinguishable_colors(length(CG)+2) - for j in eachindex(CG) - G, CVemph = length(CG[j][1])==2 ? CG[j] : (CG[j], Vector{Int}()) - plot_graph(G, CVemph, color=col[j+2], vert=vert, subplt=true) + for (j, G) in enumerate(CG) + plot_graph(G, color=col[j+2], vert=vert, subplt=true) end subplt || gui() #savefig("/home/remi/Documents/gittravail/test.html") #replace_width_height_in_file("/home/remi/Documents/gittravail/test.html", 1000, 750) end -function plot_graph_comp(G, Vemph=[]; width=3, vert=true, subplt=false) +function plot_graph_comp(G; width=3, vert=true, subplt=false) plot(legend=false) - CG = connected_components(G, Vemph) - #println(Vemph) + CG = connected_components(G) plot_graphs(CG, width=width, vert=vert, subplt=true) subplt || gui()#savefig("/tmp/test.html") end @@ -81,43 +67,20 @@ function replace_width_height_in_file(filename, x, y) write(filename, content) end -# ---------- TYPES ---------- - -struct EdgeGroup - edges::Vector{Tuple{Vector{Float64}, Vector{Float64}}} - color::Int64#NTuple{3,Float64} - width::Float64 -end - -struct PointGroup - vertices::Tuple{Vector{Float64}, Vector{Float64}} # (x, y) - color::Int64#NTuple{3,Float64} - marker::Symbol -end - -struct GraphPlotData - edge_groups::EdgeGroup - point_groups::Vector{PointGroup} -end - -# ---------- HELPER ---------- - -function normalize_vemph(Vemph) - if Vemph isa Vector{Vector} - return Vemph - elseif Vemph isa Vector - return [Vemph] - elseif Vemph isa Dict - return collect(values(Vemph)) - else - return Vector{Vector{Int}}() - end -end - # ---------- CORE BUILDERS ---------- -function build_graph_data(G, Vemph=Vector{Vector{Int}}(); width=3.0, vert=true, color=rand(1:666)) - Vemph = normalize_vemph(Vemph) - V, E = G +# How to plot: +# function plot_graph(P) +# plot(legend=false) +# E = P.edge_group +# plot!(E.edges, color=E.color, width = E.width) +# scatter!(V.vertices, color=V.color, marker = V.marker) for V in P.point_groups ] +# gui() +# end +# +# plot_graph(build_graphs_data(G)) + +function build_graph_data(G; width=3.0, vert=true, color=rand(1:666)) + V, Vcon, E = G.vertices, G.control_nodes, G.edges # edges edges = [ @@ -138,7 +101,7 @@ function build_graph_data(G, Vemph=Vector{Vector{Int}}(); width=3.0, vert=true, push!(point_groups, PointGroup((vx, vy), 17, :diamond)) end - for group in Vemph + for group in Vcon hx = map(j -> Float64(V[j][1]), group) hy = map(j -> Float64(V[j][2]), group) push!(point_groups, PointGroup((hx, hy), color, :diamond)) @@ -149,14 +112,21 @@ end # ---------- MULTI GRAPHS ---------- -function build_graphs_data(CG; width=3.0, vert=true) - results = GraphPlotData[] - - for item in CG - G, Vemph = length(item) == 2 ? item : item, Vector{Int}() - data = build_graph_data(G, Vemph; width=width, vert=vert, color=rand(1:666)) +# How to plot: +# function plot_graphs(P) +# plot(legend=false) +# for P in CP +# E = P.edge_group +# plot!(E.edges, color=E.color, width = E.width) +# [ scatter!(V.vertices, color=V.color, marker = V.marker) for V in P.point_groups ] +# end +# gui() +# end +# +# plot_graphs(build_graphs_data(CG)) - push!(results, data) - end - return results +function build_graphs_data(CG; width=3.0, vert=true) + c = randperm(666)[1:length(CG)] # Distinct numbers + return [build_graph_data(G; width=width, vert=vert, color=c[i]) + for (i, G) in enumerate(CG)] end \ No newline at end of file diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index 2bf637d..ce3326f 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -10,22 +10,6 @@ function order_permut2d(L) return sorted_ind end -function diff(p, v, n) - dp = p - for j in 1:n - dp = derivative(dp, v) - end - return dp -end - -function diff_list(p, v, n) - Ldp = Vector{typeof(p)}(undef, n+1) - Ldp[1] = p - for j in 1:n - Ldp[j+1] = derivative(Ldp[j], v) - end - return Ldp -end function trimat_rand(A, n; up=true, range=-100:100) if up @@ -50,21 +34,4 @@ macro iftime(v, ex) $(esc(ex)) end end -end - -""" - extract_point(I, outf::Bool) - -Convert an isolation interval `I = [a, b]` into a single representative point. -""" -function extract_point(I, outf::Bool; interval::Bool=false) - a, b = I[1], I[2] - if outf - return interval ? (Float64(a),Float64(b)) : Float64(a + b) / 2.0 - else - return interval ? (a,b) : simplest_between(a, b) # Nemo's native simplest rational function - end -end - -# Helper for averaging two extracted points -average_points(a, b, outf::Bool) = outf ? (a + b) / 2.0 : (a + b) // 2 \ No newline at end of file +end \ No newline at end of file diff --git a/src/imports.jl b/src/imports.jl index 8b14b88..cccee04 100644 --- a/src/imports.jl +++ b/src/imports.jl @@ -7,7 +7,7 @@ using Plots, Colors #pythonplot() import Plots: plot -import Random: MersenneTwister +import Random: MersenneTwister, randperm import Logging: ConsoleLogger, with_logger, Warn, Info import Printf: @sprintf, @printf From dc0562a3d622856abb674f616f345c47682fe4d1 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 14 Apr 2026 23:04:12 +0200 Subject: [PATCH 150/180] remove comment --- src/connectivity/connectcurves.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index e9c7aa9..f413e9d 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -20,7 +20,7 @@ include("buildpoly.jl") # MULTIPLE DISPATCH WRAPPERS # ========================================================================= -# Base case: No 'C' provided +# Base case: No 'C' (control points) provided compute_graph(f::P, g::P; kwargs...) where {P <: MPolyRingElem} = _compute_graph_core(f, g, Vector{Vector{P}}(); kwargs...) From ff45f94ffc3716f62497cb40af2d9428480cc6eb Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 14 Apr 2026 23:05:30 +0200 Subject: [PATCH 151/180] clean plots --- src/connectivity/plots.jl | 68 --------------------------------------- 1 file changed, 68 deletions(-) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 66ed551..f30d8f9 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,72 +1,4 @@ -## Plot functions -function plot_graph(G; color="red", width=3, vert=true, subplt=false) - if !subplt - plot(legend=false) - end - V, Vcon, E = G.vertices, G.control_nodes, G.edges - #col = distinguishable_colors(length(Vemph)+2) - for e in E - v1, v2 = [ map(Float64, V[ee]) for ee in e ] - plot!([v1[1], v2[1]], [v1[2], v2[2]], lc=color, lw=width) - end - if vert - scatter!( map(Float64, [v[1] for v in V]), map(Float64, [v[2] for v in V]), mc="black", m=:diamond) - end - for i in 1:length(Vcon) - scatter!( map(Float64, [V[j][1] for j in Vcon[i]]), map(Float64, [V[j][2] for j in Vcon[i]]), mc=color, m=:diamond) - end - subplt || gui() -end - -function plot_graphs(CG; width=3, vert=true, subplt=false) - if !subplt - plot(legend=false) - end - col = distinguishable_colors(length(CG)+2) - for (j, G) in enumerate(CG) - plot_graph(G, color=col[j+2], vert=vert, subplt=true) - end - subplt || gui() - #savefig("/home/remi/Documents/gittravail/test.html") - #replace_width_height_in_file("/home/remi/Documents/gittravail/test.html", 1000, 750) -end - -function plot_graph_comp(G; width=3, vert=true, subplt=false) - plot(legend=false) - CG = connected_components(G) - plot_graphs(CG, width=width, vert=vert, subplt=true) - subplt || gui()#savefig("/tmp/test.html") -end - -function replace_width_height_in_file(filename, x, y) - # Open the file and read its content as a string - content = read(filename, String) - - # Build the patterns to search for and the replacements - width_pattern = "\"width\": 600" - height_pattern = "\"height\": 400" - - # Create the replacement strings with new values of x and y - new_width = "\"width\": $x" - new_height = "\"height\": $y" - - # Replace the last occurrence of "width": 600 - last_width_pos = findlast(occursin(width_pattern), Base.split(content, "\n")) - if last_width_pos !== nothing - content = replace(content, width_pattern => new_width; count=1) - end - - # Replace the last occurrence of "height": 400 - last_height_pos = findlast(occursin(height_pattern), Base.split(content, "\n")) - if last_height_pos !== nothing - content = replace(content, height_pattern => new_height; count=1) - end - - # Write the modified content back to the file - write(filename, content) -end - # ---------- CORE BUILDERS ---------- # How to plot: # function plot_graph(P) From 69d97be919f41c8b8bb6a617cd5f555adc3db24d Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Tue, 14 Apr 2026 23:08:45 +0200 Subject: [PATCH 152/180] other cleanings --- src/connectivity/isolateboxes.jl | 4 +--- src/connectivity/tools.jl | 2 -- 2 files changed, 1 insertion(+), 5 deletions(-) diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index f025646..dde1d52 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -1,8 +1,6 @@ in_inter(I, J) = J[1] <= I[1] && I[2] <= J[2] overlap_inter(I, J) = max(I[1], J[1]) <= min(I[2], J[2]) -# TODO: output vector of tuple for the intervals (inside real_solutions?) - # Function that isolate roots of a multivariate polynomial with a # single variable function isolate(f; prec = 32) @@ -250,7 +248,7 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf; max_attempts= end # ---- Extremal case (i == 1) we vertically enlarge boxes manually ----- - # TODO: here we modify only LPCside and LnPCside, not LBcrit + # TODO: should we also modify LBcrit? if haskey(LBcrit, 1) boxes, pcs, npcs = LBcrit[1], LPCside[1], LnPCside[1] diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index ce3326f..0ab4b4b 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -4,13 +4,11 @@ function order_permut2d(L) # Sort the enumerated list based on the values sorted_LL = sort(LL, by = x -> x[1]) # Extract the sorted values and their corresponding indices - #sorted_L = [pair[1] for pair in sorted_LL] sorted_ind = [pair[2] for pair in sorted_LL] return sorted_ind end - function trimat_rand(A, n; up=true, range=-100:100) if up return [ i==j ? one(A) : (i Date: Tue, 14 Apr 2026 23:23:24 +0200 Subject: [PATCH 153/180] keep naive subresultant and paramcrit --- src/connectivity/connectcurves.jl | 2 +- src/connectivity/plots.jl | 44 ++--- src/connectivity/subresultants.jl | 270 ++---------------------------- 3 files changed, 38 insertions(+), 278 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index f413e9d..67e367f 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -116,7 +116,7 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; end else for k in 1:length(PCside.left.points) - xval = xcrit[i][j][1] - 1 + xval = xcrit[i][j][1] yval = sum(PCside.left.points[k]) / 2 push!(Vert, (xval, yval)) push!(Corr[i][j].left, length(Vert)) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index f30d8f9..77b28c1 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,15 +1,17 @@ # ---------- CORE BUILDERS ---------- +""" # How to plot: -# function plot_graph(P) -# plot(legend=false) -# E = P.edge_group -# plot!(E.edges, color=E.color, width = E.width) -# scatter!(V.vertices, color=V.color, marker = V.marker) for V in P.point_groups ] -# gui() -# end -# -# plot_graph(build_graphs_data(G)) +function plot_graph(P) + plot(legend=false) + E = P.edge_group + plot!(E.edges, color=E.color, width = E.width) + [scatter!(V.vertices, color=V.color, marker = V.marker) for V in P.point_groups] + gui() +end + +plot_graph(build_graphs_data(G)) +""" function build_graph_data(G; width=3.0, vert=true, color=rand(1:666)) V, Vcon, E = G.vertices, G.control_nodes, G.edges @@ -44,18 +46,20 @@ end # ---------- MULTI GRAPHS ---------- +""" # How to plot: -# function plot_graphs(P) -# plot(legend=false) -# for P in CP -# E = P.edge_group -# plot!(E.edges, color=E.color, width = E.width) -# [ scatter!(V.vertices, color=V.color, marker = V.marker) for V in P.point_groups ] -# end -# gui() -# end -# -# plot_graphs(build_graphs_data(CG)) +function plot_graphs(P) + plot(legend=false) + for P in CP + E = P.edge_group + plot!(E.edges, color=E.color, width = E.width) + [ scatter!(V.vertices, color=V.color, marker = V.marker) for V in P.point_groups ] + end + gui() +end + +plot_graphs(build_graphs_data(CG)) +""" function build_graphs_data(CG; width=3.0, vert=true) c = randperm(666)[1:length(CG)] # Distinct numbers diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl index 4ffdaf7..b0f9012 100644 --- a/src/connectivity/subresultants.jl +++ b/src/connectivity/subresultants.jl @@ -181,7 +181,7 @@ function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false if list for (k,lsr) in enumerate(Lsr) mlsr = [] - for i in 1:k#length(lsr) + for i in 1:k tmp = [[],[]] if i in eachindex(lsr) for j in 1:length(lsr[i]) @@ -212,222 +212,6 @@ function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false return newsr end -function interp_subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, iv; list=false, Dmax=nothing) where T <: RingElement - R = parent(P) - A = coefficient_ring(R) - iu = iv%2+1 - Vu, Vv = [:x, :y] - # Modern computer Algebra Th 6.51. - degs = degrees(P) - n, d = degs[iv], degs[iu] - if isnothing(Dmax) - Dmax = [ (2*n-1-2*k)*d for k=0:d-1 ][1] - #Dmax = degsmax[end]>>1+1 - end - ## - B,t =polynomial_ring(A, Vv) - xs = A.(-Dmax//2:Dmax//2) - Srev = Vector{Vector{typeof(t)}}(undef, length(xs)) - evPQ = [ [ B(0) for pq in [P,Q] ] for xx in xs] -@time begin - Threads.@threads for i in eachindex(xs) - evPQ[i][1] = B(coefficients_of_univariate(evaluate(P,[iu],[xs[i]]))) - evPQ[i][2] = B(coefficients_of_univariate(evaluate(Q,[iu],[xs[i]]))) - end -end -@time begin - Threads.@threads for i in 1:length(xs) - Srev[i] = subresultants(evPQ[i][1], evPQ[i][2]) - end -end - Srev = [ [ collect(coefficients(ss)) for ss in s] for s in Srev ] - C, = Nemo.polynomial_ring(A,Vu) - Sr = [ [ C(0) for _=1:i] for i=1:n ] - Lys = [ [ [ (try A(Srev[l][i][j]) catch; A(0) end) for l in eachindex(Srev) ] for j in 1:i ] for i in 1:n ] -@time begin - Threads.@threads for i = 1:2 - # For the i-th subresultant - Threads.@threads for j in 0:i-1 - # Each coefficient is interpolated - Sr[i][end-j] = interpolate(C, xs, Lys[i][end-j]) - end - end -end - return Sr -end - -function mmod_subresultants(P::QQMPolyRingElem, Q::QQMPolyRingElem, idx; list=false, n_threads=Threads.nthreads(), n_ssr=-1,v=0) - PZ, QZ = change_coefficient_ring.(Ref(ZZ), int_coeffs.([P,Q])) - sr = mmod_subresultants(PZ, QZ, idx; list=list, n_threads=n_threads, n_ssr=n_ssr, v=v) - return sr - if list - return [ change_coefficient_ring.(Ref(QQ),srp) for srp in sr ] - else - return change_coefficient_ring.(Ref(QQ),sr) - end -end - -function mmod_subresultants(P::ZZMPolyRingElem, Q::ZZMPolyRingElem, idx; list=false, n_threads=Threads.nthreads(), n_ssr=0, v=0) - prim = ZZ(1)<<(61) - L1, primprod = [], ZZ(1) - Ltemp = Vector{Vector{Vector{Vector{ZZRingElem}}}}(undef,n_threads+1) - lcpq = [ evaluate(leading_coefficient(l, 2),[0,0]) for l in [P,Q] ] - compt = n_threads - while true - v > 0 && print("$compt primes ") - LP, LQ, Lprim = MPolyRingElem[], MPolyRingElem[], ZZRingElem[] - while length(Lprim) < n_threads - prim = next_prime(prim) - if !any(getindex.(divides.(lcpq, Ref(prim)),1)) - Pprim, Qprim = [ change_coefficient_ring(residue_ring(ZZ, prim)[1], poly) for poly in [P,Q] ] - #Pprim, Qprim = [ change_coefficient_ring(GF(prim), poly) for poly in [P,Q] ] - push!.([LP,LQ,Lprim], [Pprim,Qprim,prim]) - else - return prim, lcpq - end - end - @iftime v>1 begin - Threads.@threads for j in 1:n_threads - sr = subresultants(LP[j], LQ[j], idx, list=true) - Ltemp[j] = [ [ lift.(Ref(ZZ), coefficients_of_univariate(srii)) for srii in sri ] for sri in sr ] - #sr = interp_subresultants(LP[j], LQ[j], idx)[1][1] - #Ltemp[j] = lift.(Ref(ZZ), coefficients(sr)) - end - end - - if n_ssr > 0 - for j in 1:n_threads - for k in eachindex(Ltemp[j]) - Ltemp[j][k] = Ltemp[j][k][end-min(k,n_ssr)+1:end] - end - end - end - - if L1 != [] - Ltemp[n_threads+1] = copy(L1) - push!(Lprim, primprod) - end - #@assert allequal(length.(Ltemp[1:nthreads])) "Specialization problem" - Nssr = n_ssr<0 ? length(last(first(Ltemp))) : n_ssr - #println(Ltemp) - L2 = deepcopy(L1) - L1 = Vector{Vector{Vector{ZZRingElem}}}(undef, length(first(Ltemp))) - @iftime v>1 begin - Threads.@threads for i in eachindex(L1) - L1[i] = Vector{Vector{ZZRingElem}}(undef, min(i, Nssr)) - Threads.@threads for j in eachindex(L1[i]) - #println("($i,$j)") - L1[i][j] = Vector{ZZRingElem}(undef, length(Ltemp[1][i][j])) - Threads.@threads for k in eachindex(L1[i][j]) - cfs = [ try Ltemp[p][i][j][k] catch; ZZ(0) end for p in eachindex(Lprim) ] - L1[i][j][k] = crt(cfs, Lprim, true) - end - end - end - end - #println(L1) - primprod = prod(Lprim) - compt+=n_threads - v > 0 && println(ndigits(primprod, 10), " digits") - L1 != L2 || break - #compt < 20 || break - end - - v>1 && println("Convert the coefficients into polynomials") - L1Q = [ [QQ.(ss) for ss in s ] for s in L1 ] - @iftime v>0 sr = [ MPolyBuild(s, symbols(parent(P)), (idx+1)%2) for s in L1Q ] - return sr -end - -function mmod_param_crit(P::QQMPolyRingElem, Q::QQMPolyRingElem; n_threads=Threads.nthreads(), detect_app=true, v=0) - PZ, QZ = change_coefficient_ring.(Ref(ZZ), int_coeffs.([P,Q])) - pc = mmod_param_crit(PZ, QZ, n_threads=n_threads, detect_app=detect_app, v=v) - return pc - if list - return [ change_coefficient_ring.(Ref(QQ),srp) for srp in sr ] - else - return change_coefficient_ring.(Ref(QQ),sr) - end -end - -function mmod_param_crit(P::ZZMPolyRingElem, Q::ZZMPolyRingElem; n_threads=Threads.nthreads(), v=0, detect_app=true) - prim = ZZ(1)<<(61) - RS = P |> parent |> symbols - L1, L1f, primprod = [], [], ZZ(1) - Ltemp = Vector{Vector{Vector{Vector{ZZRingElem}}}}(undef,n_threads+1) - dP = derivative(P, 2) - lcpq = [ evaluate(leading_coefficient(l, 2),[0,0]) for l in [P,dP,Q] ] - compt = n_threads - while true - v > 0 && print("$compt primes ") - LP, LQ, Lprim = MPolyRingElem[], MPolyRingElem[], ZZRingElem[] - while length(Lprim) < n_threads - prim = next_prime(prim) - if !any(getindex.(divides.(lcpq, Ref(prim)),1)) - #Pprim, Qprim = [ change_coefficient_ring(residue_ring(ZZ, prim)[1], poly) for poly in [P,Q] ] - Pprim, Qprim = [ change_coefficient_ring(GF(prim), poly) for poly in [P,Q] ] - push!.([LP,LQ,Lprim], [Pprim,Qprim,prim]) - end - end - @iftime v>1 begin - Threads.@threads for j in 1:n_threads - pc = param_crit_split(LP[j], LQ[j], RS = RS, v=v-2, detect_app=detect_app) - Ltemp[j] = Vector{Vector{ZZMPolyRingElem}}(undef, length(pc)) - for (ik, k) in enumerate(eachindex(pc)) - q, a, b = pc[k] - q = first(q) - dq = derivative(q,1) - Pnum = mod(dq*gcdinv(b,q)[2]*a, q) - Ltemp[j][ik] = [ lift.(Ref(ZZ), coefficients_of_univariate(poly)) for poly in [q, Pnum, dq] ] - end - #sr = interp_subresultants(LP[j], LQ[j], idx)[1][1] - #Ltemp[j] = lift.(Ref(ZZ), coefficients(sr)) - end - end - - if L1 != [] - Ltemp[n_threads+1] = copy(L1) - push!(Lprim, primprod) - end - #println(Ltemp) - L1 = Vector{Vector{Vector{ZZRingElem}}}(undef, length(Ltemp[1])) - @iftime v>1 begin - Threads.@threads for i in eachindex(L1) - #println("($i,$j)") - L1[i] = Vector{ZZRingElem}(undef, length(Ltemp[1][i])) - Threads.@threads for j in eachindex(L1[i]) - L1[i][j] = Vector{ZZRingElem}(undef, length(Ltemp[1][i][j])) - for k in eachindex(L1[i][j]) - cfs = [ try Ltemp[p][i][j][k] catch; ZZ(0) end for p in eachindex(Lprim) ] - L1[i][j][k] = crt(cfs, Lprim, false) - end - end - end - end - primprod = prod(Lprim) - L2f = deepcopy(L1f) - try - @iftime v>1 L1f = [ [ [ reconstruct(c, primprod) for c in poly ] for poly in param ] for param in L1 ] - #println(L1f) - L1f != L2f || break - catch - println("No rational rec") - end - compt+=n_threads - v > 0 && println(ndigits(primprod, 10), " digits") - #compt < 20 || break - end - - v>1 && println("Convert the coefficients into polynomials") - L1Q = [ [ QQ.(poly) for poly in param ] for param in L1f ] - @iftime v>0 param = Dict( m => vcat( - [[int_coeffs(MPolyBuild(param[1], symbols(parent(P)), 1))]], - [ int_coeffs(MPolyBuild(poly, symbols(parent(P)), 1)) for poly in param[2:end] ]) - for (m, param) in zip([-1,1], L1Q)) - return param -end - - function fact_gcd(delta::T, LP::Vector{T}) where (T <:PolyRingElem) # delta : poly to factor w.r.t the polynomials in LP Lphi = [gcd(delta, LP[1])] @@ -442,18 +226,11 @@ function fact_gcd(delta::T, LP::Vector{T}) where (T <:PolyRingElem) return filter(s->degree(s[2])>0, Dict(enumerate(Ldelta))) end -function fact_gcd(delta::T, LP::Vector{T}, RS::Vector{Symbol}) where (T <:MPolyRingElem) - @assert is_univariate(delta) && all(is_univariate.(LP)) "Not univariate polynomial" - R = parent(delta) - A, = polynomial_ring(coefficient_ring(R), first(RS)) - out = fact_gcd(A(coefficients_of_univariate(delta)), A.(coefficients_of_univariate.(LP))) - return Dict([ (i, change_ringvar(f, [first(RS)]) ) for (i,f) in out ]) -end - -function num_biv_rat_mod(A, P, RS) +function num_biv_rat_mod(A, P) # Computes the numerator of the polynomial A(x,a(x)//b(x)) mod q # where P = [q, a, b] B = base_ring(parent(A)) + RS = symbols(B) T, = polynomial_ring(B, RS[1]) Puniv = [ T(coefficients_of_univariate(p)) for p in P ] @@ -471,10 +248,6 @@ function num_biv_rat_mod(A, P, RS) return change_ringvar(lift(Aeval), RS) end -function intersect_biv_mod(P::Vector{T} where T<:Any, A::MPolyRingElem, RS::Vector{Symbol}) - Aev = num_biv_rat_mod(A, P, RS) - return gcd(P[1], Aev) -end function intersect_biv(P::Vector{T} where T<:Any, A::MPolyRingElem) # TODO: test the reconstruction @@ -522,35 +295,24 @@ function intersect_biv(P::Vector{T} where T<:Any, A::MPolyRingElem) return int_coeffs(change_ringvar(B(dAf), RS)) end -function param_crit_split(f, g; v=0, detect_app=true, RS = nothing) - @assert (f|>parent|>base_ring|>characteristic == 0 || !isnothing(RS)) "Variable names must be provided when char>0" - if f|>parent|>base_ring|>characteristic == 0 - RS = f |> parent |> symbols - end - # Compute subresultants and factor the first subresultant - # TODO: factor f before computing subresultants or at least divide by content +function param_crit_split(f, g; v=0, detect_app=true) + # Compute subresultants v>0 && println("Compute subresultant sequence") - if total_degree(f) > 30 && f|>parent|>base_ring|>characteristic == 0 - @iftime v>0 sr = mmod_subresultants(f, derivative(f, 2), 2, list=true, n_ssr=2, v=v-1) - else - @iftime v>0 sr = subresultants(f, derivative(f, 2), 2, list=true) - end + @iftime v>0 sr = subresultants(f, derivative(f, 2), 2, list=true) if total_degree(sr[1][1]) == 0 return Dict() end # TODO: sr is univariate? check what's called - # TODO: try full factorization? - v>1 && println("Square-free factorization") - @iftime v>1 sqr = collect(factor_squarefree(sr[1][1])) + v>1 && println("Factorization") + @iftime v>1 sqr = collect(factor(sr[1][1])) # Filter out factors with zero multiplicity and sort by multiplicity sqr = sort!(filter(t -> t[2] > 0, sqr), by = t -> t[2]) # Group factors by multiplicity sqrmult = unique(getindex.(sqr, 2)) group_sqr = Dict(m => [r[1] for r in sqr if r[2] == m] for m in sqrmult) - #println(group_sqr) v>0 && println("Compute crit partition w.r.t to multiplicity") # Initalization @@ -564,35 +326,29 @@ function param_crit_split(f, g; v=0, detect_app=true, RS = nothing) end # Nodes : multiplicity 2 in res - # TODO: first test with interval arithmetics? Most of the time this will suffice v>0 && println("Compute apparent singularities") if 2 in sqrmult if detect_app @iftime v>0 begin A = derivative(derivative(f,2),2)*derivative(g,1) - derivative(derivative(f,1),2)*derivative(g,2) - if f|>parent|>base_ring|>characteristic > 0 - dA = [ (intersect_biv_mod([q, -sr[2][end-1], sr[2][end]], A, RS)) for q in group_sqr[2] ] - else - dA = [ (intersect_biv([q, -sr[2][end-1], sr[2][end]], A)) for q in group_sqr[2] ] - end - push!(param_crit, 0=>[group_sqr[2]./dA, -sr[2][end-1], sr[2][end]]) + dA = [ (intersect_biv([q, -sr[2][end-1], sr[2][end]], A)) for q in group_sqr[2] ] + push!(param_crit, 0 => [group_sqr[2]./dA, -sr[2][end-1], sr[2][end]]) append!(param_crit[2][1], dA) end else - push!(param_crit, 0=>[group_sqr[2], -sr[2][end-1], sr[2][end]]) + push!(param_crit, 0 => [group_sqr[2], -sr[2][end-1], sr[2][end]]) end end # Other sing filter!(m->!(m in [1,2]), sqrmult) - #TODO: simpler criterion for mult=p*(p-1)? lsr = [ try sr[p][end] catch; one(parent(f)) end for p in 2:(singmult[end]+1) ] Ld = Vector{Vector{Dict{Int, MPolyRingElem}}}(undef, length(sqrmult)) v>0 && println("Compute gcd decomposition") @iftime v>0 begin - Threads.@threads for k in eachindex(sqrmult) + for k in eachindex(sqrmult) Ld[k] = Vector{Dict{Int, MPolyRingElem}}(undef,length(group_sqr[sqrmult[k]])) for l in eachindex(group_sqr[sqrmult[k]]) - Ld[k][l] = fact_gcd(group_sqr[sqrmult[k]][l], lsr, RS) + Ld[k][l] = fact_gcd(group_sqr[sqrmult[k]][l], lsr) end end for k in eachindex(Ld) From 6ed305b71d8c526c8a7aa533f211987f8e88a941 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Wed, 15 Apr 2026 02:41:25 +0200 Subject: [PATCH 154/180] improvement of subresultant but bug --- src/connectivity/connectcurves.jl | 2 +- src/connectivity/subresultants-bis.jl | 310 ++++++++++++++++++++++++++ 2 files changed, 311 insertions(+), 1 deletion(-) create mode 100644 src/connectivity/subresultants-bis.jl diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 67e367f..c3344c9 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -9,7 +9,7 @@ export compute_graph, connected_components, number_connected_components, group_b include("datastruct.jl") include("tools.jl") -include("subresultants.jl") +include("subresultants-bis.jl") include("isolateboxes.jl") include("graph.jl") include("plots.jl") diff --git a/src/connectivity/subresultants-bis.jl b/src/connectivity/subresultants-bis.jl new file mode 100644 index 0000000..e996312 --- /dev/null +++ b/src/connectivity/subresultants-bis.jl @@ -0,0 +1,310 @@ +# ========================================================================= +# RING COERCION TOOLS (Replaces array wrangling and homogenize) +# ========================================================================= + +# TODO: use MPolyBuildCtx? + +""" + to_univariate(P::MPolyRingElem, var_idx::Int) + +Converts a bivariate polynomial in `K[x, y]` into a univariate polynomial in `(K[x])[y]`. +""" +function to_univariate(P::MPolyRingElem, var_idx::Int) + R = parent(P) + K = base_ring(R) + coeff_idx = 3 - var_idx # The variable to be pushed to the coefficients + + Rx, x = polynomial_ring(K, symbols(R)[coeff_idx]) + Rxy, y = polynomial_ring(Rx, symbols(R)[var_idx]) + + res = zero(Rxy) + for (c, exp) in zip(coefficients(P), exponent_vectors(P)) + # Build the coefficient in Rx, then attach to y in Rxy + res += (c * x^exp[coeff_idx]) * y^exp[var_idx] + end + return res +end + +""" + to_bivariate(P::PolyRingElem, R_orig::MPolyRing) + +Maps a univariate polynomial in `(K[x])[y]` back to the original bivariate ring `K[x, y]`. +""" +function to_bivariate(P::PolyRingElem, R_orig::MPolyRing) + ctx = MPolyBuildCtx(R_orig) + for (deg_y, c_y) in enumerate(coefficients(P)) + for (deg_x, c_x) in enumerate(coefficients(c_y)) + push_term!(ctx, c_x, [deg_x,deg_y]) + end + end + return finish(ctx) +end + + +# ========================================================================= +# MODULAR ARITHMETIC & INTERSECTION +# ========================================================================= + +""" + num_biv_rat_mod(A::MPolyRingElem, P::Vector) + +Computes the numerator of `A(x, a(x)/b(x)) mod q(x)` efficiently using Residue Rings. +`P = [q, a, b]`. +""" +function num_biv_rat_mod(A::MPolyRingElem, P::Vector) + q, a, b = P[1], P[2], P[3] + Rx = parent(q) + + # Do math natively inside the quotient ring Rx / + U, mod_q = residue_ring(Rx, q) + a_u, b_u, x_u = mod_q(a), mod_q(b), mod_q(gens(Rx)[1]) + + deg_y = maximum(e[2] for e in exponent_vectors(A); init=0) + res_u = zero(U) + + # Avoids homogenization entirely. b^(deg_y - j) clears the denominator. + for (c, exp) in zip(coefficients(A), exponent_vectors(A)) + i, j = exp[1], exp[2] + res_u += c * (x_u^i) * (a_u^j) * (b_u^(deg_y - j)) + end + + return lift(res_u) +end + +""" + intersect_biv(P::Vector, A::MPolyRingElem) + +P = [q, a, b] encodes a finite set (x,a(x)/b(x)) where q(x)=0 +Computes the divisor of `q` that encodes the intersection with `A(x,y)=0`. +Uses a modular CRT loop. +""" +function intersect_biv(P::Vector, A::MPolyRingElem) + iszero(A) && return P[1] + + RS = symbols(parent(A)) + B, x = polynomial_ring(QQ, RS[1]) + + dA_prev, dA_final = Int[], Int[] + pprod, p = ZZ(1), ZZ(1) << 60 + compt = 0 + + while compt < 12 + p = next_prime(p) + Fp = GF(p) + + # Map polynomials natively to Fp + Pp = [map_coefficients(Fp, poly) for poly in P] + Ap = map_coefficients(Fp, A) + + Apev = num_biv_rat_mod(Ap, Pp) + dAp = gcd(Pp[1], Apev) + + # Lift coefficients back to integers for CRT + dA_current = [lift(ZZ, c) for c in coefficients(dAp)] + + if compt > 0 + dA_current = [crt([d1, d2], [pprod, p]) for (d1, d2) in zip(dA_prev, dA_current)] + end + + count(!iszero, dA_current) <= 1 && return one(B) # Trivial GCD + + pprod *= p + try + dA_final = [reconstruct(c, pprod) for c in dA_current] + (compt > 0 && dA_final == dA_prev) && break + catch + # Rational reconstruction failed, try next prime + end + + dA_prev = dA_final + compt += 1 + end + + return B(dA_final) +end + + +# ========================================================================= +# SUBRESULTANTS +# ========================================================================= + +# Univariate resultant +function subresultants(P::Union{PolyRingElem{T}, FqPolyRingElem}, Q::Union{PolyRingElem{T}, FqPolyRingElem}, is_Fq::Bool=false) where T <: RingElem + degree(P) < degree(Q) && ((P, Q) = (Q, P)) + + S = typeof(P)[Q] + s = leading_coefficient(Q)^(degree(P) - degree(Q)) # Initial scaling factor + # rem is faster when working with finite fields (relies on FLINT) + A = Q + B = is_Fq ? (-leading_coefficient(Q))^(degree(P) - degree(Q) + 1) * rem(P, Q) : pseudorem(P, -Q) + + while !iszero(B) + d, e = degree(A), degree(B) + pushfirst!(S, B) # current remainder + delta = d - e # degree drop + + if delta > 1 + if length(S) > 1 + n = degree(S[2]) - degree(S[1]) - 1 # stabilize scaling + if n == 0 + C = S[1] + else + x, y = leading_coefficient(S[1]), leading_coefficient(S[2]) + a = 1 << (length(bits(ZZ(n))) - 1) + c, n = x, n - a + while a > 1 + a >>= 1 + c = divexact(c^2, y) + if n >= a + c = divexact(c * x, y) + n -= a + end + end + C = divexact(c * S[1], y) + end + else + # First step: fallback normalization + C = divexact(leading_coefficient(B)^(delta - 1) * B, s^(delta - 1)) + end + pushfirst!(S, C) + else + C = B # no degree drop + end + + # Termination: constant polynomial + e == 0 && return S + + # --- Next pseudo-remainder --- + B = is_Fq ? (-leading_coefficient(B))^(d - e + 1) * rem(A, B) : pseudorem(A, -B) + B = divexact(B, s^delta * leading_coefficient(A)) + + A = C + s = leading_coefficient(A) + end + return S +end + +# Bivariate resultant +function subresultants(P::MPolyRingElem, Q::MPolyRingElem, var_idx::Int; list=false) + UP, UQ = to_univariate(P, var_idx), to_univariate(Q, var_idx) + sr_uni = subresultants(UP, UQ) + + R_orig = parent(P) + #x_orig = symbols(R_orig)[3 - var_idx] + v_orig = symbols(R_orig) + + if list + # TODO: avoid evaluate, use change_ringvar? + # Extract coefficients as bivariate polynomials evaluated at y=0 + return [change_ringvar(collect(coefficients(sr)), v_orig) for sr in sr_uni] + else + return [to_bivariate(sr, R_orig) for sr in sr_uni] + end +end + + +# ========================================================================= +# CORE ALGEBRAIC ENGINE +# ========================================================================= + +# delta : poly to factor w.r.t the polynomials in LP +function fact_gcd(delta::T, LP::Vector{T}) where T <: PolyRingElem + Ldelta = Dict{Int, T}() + curr_phi = gcd(delta, LP[1]) + Ldelta[1] = divexact(delta, curr_phi) + + for i in 2:length(LP) + degree(curr_phi) == 0 && break + next_phi = gcd(curr_phi, LP[i]) + Ldelta[i] = divexact(curr_phi, next_phi) + curr_phi = next_phi + end + return filter(kv -> degree(kv.second) > 0, Ldelta) +end + +# wrapper for the above function +function fact_gcd(delta::T, LP::Vector{T}) where (T <:MPolyRingElem) + @assert is_univariate(delta) && all(is_univariate.(LP)) "Not univariate polynomial" + R = parent(delta) + K, RS = coefficient_ring(R), symbols(R) + A, = polynomial_ring(K, RS[1]) + + d_uni = A(coefficients_of_univariate(delta)) + LP_uni = [A(coefficients_of_univariate(p)) for p in LP] + out = fact_gcd(d_uni, LP_uni) + + return Dict([ (i, change_ringvar(f, [first(RS)]) ) for (i,f) in out ]) +end + +""" + param_crit_split(f::MPolyRingElem; v=0, detect_app=true) + +Computes the critical points of a curve `f(x, y) = 0` grouped by multiplicity. +""" +function param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, detect_app=true) + v > 0 && println("Compute subresultant sequence") + f_y = derivative(f, 2) + @iftime v>0 sr = subresultants(f, f_y, 2, list=true) + + (isempty(sr) || total_degree(sr[1][1]) == 0) && return Dict{Int, Vector}() + + v > 1 && println("Factorization") + sqr_factors = factor(sr[1][1]) + + # Filter non-zero multiplicity and sort + sqr = sort([(fac, mult) for (fac, mult) in sqr_factors if mult > 0], by = x -> x[2]) + isempty(sqr) && return Dict{Int, Vector}() + + sqrmult = unique([s[2] for s in sqr]) + group_sqr = Dict(m => [s[1] for s in sqr if s[2] == m] for m in sqrmult) + + v > 0 && println("Compute crit partition w.r.t to multiplicity") + param_crit = Dict{Int, Vector}() + + # Helper function to prevent out-of-bounds access on subresultant lists + get_sr = (p, idx) -> (length(sr) >= p && length(sr[p]) >= abs(idx)) ? sr[p][end+idx] : zero(parent(f)) + + singmult = filter(p -> p*(p-1) <= sqrmult[end], 2:sqrmult[end]) + for p in singmult + param_crit[p] = [MPolyRingElem[], -get_sr(p, -1), (p-1)*get_sr(p, 0)] + end + + # Critical points : multiplicity 1 in res + (1 in sqrmult) && (param_crit[1] = [group_sqr[1], -get_sr(2, -1), get_sr(2, 0)]) + isempty(singmult) && return filter(p -> length(p.second[1]) > 0, param_crit) + + # Nodes : multiplicity 2 in res + v > 0 && println("Compute apparent singularities") + if 2 in sqrmult + if detect_app + f_x = derivative(f, 1) + A = derivative(f_y, 2) * derivative(g, 1) - derivative(f_x, 2) * derivative(g, 2) + + dA = [intersect_biv([q, -get_sr(2, -1), get_sr(2, 0)], A) for q in group_sqr[2]] + + param_crit[0] = [group_sqr[2] ./ dA, -get_sr(2, -1), get_sr(2, 0)] + append!(param_crit[2][1], dA) + else + param_crit[0] = [group_sqr[2], -get_sr(2, -1), get_sr(2, 0)] + end + end + + # Other singularities + filter!(m -> !(m in [1, 2]), sqrmult) + lsr = [get_sr(p, 0) for p in 2:(singmult[end]+1)] + + v > 0 && println("Compute gcd decomposition") + for m in sqrmult + for q in group_sqr[m] + for (i, dji) in fact_gcd(q, lsr) + haskey(param_crit, i+1) ? push!(param_crit[i+1][1], dji) : error("Curve not generic") + end + end + end + + for v in values(param_crit) + filter!(p -> total_degree(p) > 0, v[1]) + end + + return filter(p -> length(p.second[1]) > 0, param_crit) +end \ No newline at end of file From ebcd9d4d4dbbe6062b8c8b2c398a62bec644bd84 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Wed, 15 Apr 2026 03:20:36 +0200 Subject: [PATCH 155/180] fix bug + distinguishable colors plot --- src/connectivity/buildpoly.jl | 62 +++++++++++++-------------- src/connectivity/connectcurves.jl | 2 +- src/connectivity/datastruct.jl | 4 +- src/connectivity/plots.jl | 59 ++++++++++++++++++++++--- src/connectivity/subresultants-bis.jl | 12 +++--- 5 files changed, 94 insertions(+), 45 deletions(-) diff --git a/src/connectivity/buildpoly.jl b/src/connectivity/buildpoly.jl index c0da303..3b6c1e7 100644 --- a/src/connectivity/buildpoly.jl +++ b/src/connectivity/buildpoly.jl @@ -40,7 +40,7 @@ function change_ringvar(F::AbstractVector{<:Union{PolyRingElem, MPolyRingElem}}, if !iszero(c) e_new = zeros(Int, n_vars) if deg_plus_1 > 1 - e_new[idx_map[1]] = deg_plus_1 + e_new[idx_map[1]] = deg_plus_1 - 1 end push!(coeffs, c) push!(exps, e_new) @@ -69,40 +69,40 @@ end change_ringvar(f::MPolyRingElem) = change_ringvar([f])[1] -""" - MPolyBuild(F::Vector{Vector{RingElem}}, new_S::Vector{Symbol}, idx::Int) +# """ +# MPolyBuild(F::Vector{Vector{RingElem}}, new_S::Vector{Symbol}, idx::Int) -Construct multivariate polynomials in a single variable. -`F` is a list of coefficient lists in degree-increasing order. -The polynomial will use the variable at index `idx` in `new_S`. -""" -function MPolyBuild(F::AbstractVector{<:AbstractVector{<:RingElement}}, new_S::Vector{Symbol}, idx::Int) - isempty(F) && return [] +# Construct multivariate polynomials in a single variable. +# `F` is a list of coefficient lists in degree-increasing order. +# The polynomial will use the variable at index `idx` in `new_S`. +# """ +# function MPolyBuild(F::AbstractVector{<:AbstractVector{<:RingElement}}, new_S::Vector{Symbol}, idx::Int) +# isempty(F) && return [] - A = parent(first(first(F))) - R, _ = polynomial_ring(A, new_S) +# A = parent(first(first(F))) +# R, _ = polynomial_ring(A, new_S) - T = typeof(zero(A)) - n_vars = length(new_S) +# T = typeof(zero(A)) +# n_vars = length(new_S) - return map(F) do f_coeffs - coeffs = T[] - exps = Vector{Int}[] +# return map(F) do f_coeffs +# coeffs = T[] +# exps = Vector{Int}[] - # Construct coeff/exp lists - for (deg_plus_1, c) in enumerate(f_coeffs) - if !iszero(c) - e_new = zeros(Int, n_vars) - e_new[idx] = deg_plus_1 - 1 - push!(coeffs, c) - push!(exps, e_new) - end - end +# # Construct coeff/exp lists +# for (deg_plus_1, c) in enumerate(f_coeffs) +# if !iszero(c) +# e_new = zeros(Int, n_vars) +# e_new[idx] = deg_plus_1 - 1 +# push!(coeffs, c) +# push!(exps, e_new) +# end +# end - # Create the polynomial associated to f_coeffs - return R(coeffs, exps) - end -end +# # Create the polynomial associated to f_coeffs +# return R(coeffs, exps) +# end +# end -# Dispatch for a single coefficient vector -MPolyBuild(f::AbstractVector{<:RingElement}, new_S::Vector{Symbol}, idx::Int) = MPolyBuild([f], new_S, idx)[1] \ No newline at end of file +# # Dispatch for a single coefficient vector +# MPolyBuild(f::AbstractVector{<:RingElement}, new_S::Vector{Symbol}, idx::Int) = MPolyBuild([f], new_S, idx)[1] \ No newline at end of file diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index c3344c9..7a93993 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -1,6 +1,6 @@ export compute_graph, connected_components, number_connected_components, group_by_component, merge_graphs, - plot_graph, plot_graphs, plot_graph_comp, Bresultant, param_crit_split, build_graph_components_data, build_graphs_data, build_graph_data + plot_graph, plot_graphs, plot_graph_comp, Bresultant, param_crit_split, build_graphs_data, build_graph_data # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, diff --git a/src/connectivity/datastruct.jl b/src/connectivity/datastruct.jl index 9a138b2..fa04d1f 100644 --- a/src/connectivity/datastruct.jl +++ b/src/connectivity/datastruct.jl @@ -32,13 +32,13 @@ end struct EdgeGroup edges::Vector{Tuple{Vector{Float64}, Vector{Float64}}} - color::Int64 + color::String width::Float64 end struct PointGroup vertices::Tuple{Vector{Float64}, Vector{Float64}} # (x, y) - color::Int64 + color::String marker::Symbol end diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 77b28c1..51275ff 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,3 +1,52 @@ +# Distinguishable Colors + +# file: utils/colors.jl + +""" + distinguishable_colors(n; s=0.8, v=0.9) + +Return `n` visually distinct HEX colors using manual HSV→RGB conversion. +No external libraries used. +""" +function distinguishable_colors(n::Int; s::Float64=0.8, v::Float64=0.9) + n <= 0 && return String[] + + colors = Vector{String}(undef, n) + + for i in 0:n-1 + h = i / n # [0,1) + + c = v * s + h6 = h * 6 + x = c * (1 - abs(mod(h6, 2) - 1)) + m = v - c + + r1 = g1 = b1 = 0.0 + + if 0 ≤ h6 < 1 + r1, g1, b1 = c, x, 0 + elseif 1 ≤ h6 < 2 + r1, g1, b1 = x, c, 0 + elseif 2 ≤ h6 < 3 + r1, g1, b1 = 0, c, x + elseif 3 ≤ h6 < 4 + r1, g1, b1 = 0, x, c + elseif 4 ≤ h6 < 5 + r1, g1, b1 = x, 0, c + else + r1, g1, b1 = c, 0, x + end + + r = Int(round((r1 + m) * 255)) + g = Int(round((g1 + m) * 255)) + b = Int(round((b1 + m) * 255)) + + colors[i+1] = @sprintf("#%02X%02X%02X", r, g, b) + end + + return colors +end + # ---------- CORE BUILDERS ---------- """ @@ -13,7 +62,7 @@ end plot_graph(build_graphs_data(G)) """ -function build_graph_data(G; width=3.0, vert=true, color=rand(1:666)) +function build_graph_data(G; width=3.0, vert=true, color="#FF0000") V, Vcon, E = G.vertices, G.control_nodes, G.edges # edges @@ -32,13 +81,13 @@ function build_graph_data(G; width=3.0, vert=true, color=rand(1:666)) if vert vx = map(v -> Float64(v[1]), V) vy = map(v -> Float64(v[2]), V) - push!(point_groups, PointGroup((vx, vy), 17, :diamond)) + push!(point_groups, PointGroup((vx, vy), color, :x)) end for group in Vcon hx = map(j -> Float64(V[j][1]), group) hy = map(j -> Float64(V[j][2]), group) - push!(point_groups, PointGroup((hx, hy), color, :diamond)) + push!(point_groups, PointGroup((hx, hy), color, :+)) end return GraphPlotData(edge_group, point_groups) @@ -48,7 +97,7 @@ end """ # How to plot: -function plot_graphs(P) +function plot_graphs(CP) plot(legend=false) for P in CP E = P.edge_group @@ -62,7 +111,7 @@ plot_graphs(build_graphs_data(CG)) """ function build_graphs_data(CG; width=3.0, vert=true) - c = randperm(666)[1:length(CG)] # Distinct numbers + c = distinguishable_colors(length(CG)) return [build_graph_data(G; width=width, vert=vert, color=c[i]) for (i, G) in enumerate(CG)] end \ No newline at end of file diff --git a/src/connectivity/subresultants-bis.jl b/src/connectivity/subresultants-bis.jl index e996312..70924d9 100644 --- a/src/connectivity/subresultants-bis.jl +++ b/src/connectivity/subresultants-bis.jl @@ -34,7 +34,7 @@ function to_bivariate(P::PolyRingElem, R_orig::MPolyRing) ctx = MPolyBuildCtx(R_orig) for (deg_y, c_y) in enumerate(coefficients(P)) for (deg_x, c_x) in enumerate(coefficients(c_y)) - push_term!(ctx, c_x, [deg_x,deg_y]) + push_term!(ctx, c_x, [deg_x - 1, deg_y - 1]) end end return finish(ctx) @@ -144,23 +144,23 @@ function subresultants(P::Union{PolyRingElem{T}, FqPolyRingElem}, Q::Union{PolyR delta = d - e # degree drop if delta > 1 - if length(S) > 1 - n = degree(S[2]) - degree(S[1]) - 1 # stabilize scaling + if length(S) > 2 + n = degree(S[3]) - degree(S[2]) - 1 # stabilize scaling if n == 0 C = S[1] else - x, y = leading_coefficient(S[1]), leading_coefficient(S[2]) + x, y = leading_coefficient(S[2]), leading_coefficient(S[3]) a = 1 << (length(bits(ZZ(n))) - 1) c, n = x, n - a while a > 1 a >>= 1 c = divexact(c^2, y) if n >= a - c = divexact(c * x, y) + c = c * divexact(x, y) n -= a end end - C = divexact(c * S[1], y) + C = c * divexact(S[2], y) end else # First step: fallback normalization From 095b49cfdf596a24c32bc4fb6c463fd04c7680c2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 15 Apr 2026 18:19:27 +0200 Subject: [PATCH 156/180] bug fixes and improvement of num_biv_rat_mod --- src/connectivity/buildpoly.jl | 111 +++++++++----- src/connectivity/connectcurves.jl | 2 +- src/connectivity/isolateboxes.jl | 7 +- src/connectivity/subresultants-bis.jl | 211 ++++++++++---------------- 4 files changed, 162 insertions(+), 169 deletions(-) diff --git a/src/connectivity/buildpoly.jl b/src/connectivity/buildpoly.jl index 3b6c1e7..08f8a84 100644 --- a/src/connectivity/buildpoly.jl +++ b/src/connectivity/buildpoly.jl @@ -69,40 +69,77 @@ end change_ringvar(f::MPolyRingElem) = change_ringvar([f])[1] -# """ -# MPolyBuild(F::Vector{Vector{RingElem}}, new_S::Vector{Symbol}, idx::Int) - -# Construct multivariate polynomials in a single variable. -# `F` is a list of coefficient lists in degree-increasing order. -# The polynomial will use the variable at index `idx` in `new_S`. -# """ -# function MPolyBuild(F::AbstractVector{<:AbstractVector{<:RingElement}}, new_S::Vector{Symbol}, idx::Int) -# isempty(F) && return [] - -# A = parent(first(first(F))) -# R, _ = polynomial_ring(A, new_S) - -# T = typeof(zero(A)) -# n_vars = length(new_S) - -# return map(F) do f_coeffs -# coeffs = T[] -# exps = Vector{Int}[] - -# # Construct coeff/exp lists -# for (deg_plus_1, c) in enumerate(f_coeffs) -# if !iszero(c) -# e_new = zeros(Int, n_vars) -# e_new[idx] = deg_plus_1 - 1 -# push!(coeffs, c) -# push!(exps, e_new) -# end -# end - -# # Create the polynomial associated to f_coeffs -# return R(coeffs, exps) -# end -# end - -# # Dispatch for a single coefficient vector -# MPolyBuild(f::AbstractVector{<:RingElement}, new_S::Vector{Symbol}, idx::Int) = MPolyBuild([f], new_S, idx)[1] \ No newline at end of file +""" + MPolyBuild(F::Vector{Vector{RingElem}}, new_S::Vector{Symbol}, idx::Int) + +Construct multivariate polynomials in a single variable. +`F` is a list of coefficient lists in degree-increasing order. +The polynomial will use the variable at index `idx` in `new_S`. +""" +function MPolyBuild(F::AbstractVector{<:AbstractVector{<:RingElement}}, new_S::Vector{Symbol}, idx::Int) + isempty(F) && return [] + + A = parent(first(first(F))) + R, _ = polynomial_ring(A, new_S) + + T = typeof(zero(A)) + n_vars = length(new_S) + + return map(F) do f_coeffs + coeffs = T[] + exps = Vector{Int}[] + + # Construct coeff/exp lists + for (deg_plus_1, c) in enumerate(f_coeffs) + if !iszero(c) + e_new = zeros(Int, n_vars) + e_new[idx] = deg_plus_1 - 1 + push!(coeffs, c) + push!(exps, e_new) + end + end + + # Create the polynomial associated to f_coeffs + return R(coeffs, exps) + end +end + +# Dispatch for a single coefficient vector +MPolyBuild(f::AbstractVector{<:RingElement}, new_S::Vector{Symbol}, idx::Int) = MPolyBuild([f], new_S, idx)[1] + +""" + to_univariate(P::MPolyRingElem, var_idx::Int) + +Converts a bivariate polynomial in `K[x, y]` into a univariate polynomial in `(K[x])[y]`. +""" +function to_univariate(P::MPolyRingElem, var_idx::Int) + R = parent(P) + K = base_ring(R) + coeff_idx = 3 - var_idx # The variable to be pushed to the coefficients + + Rx, x = polynomial_ring(K, symbols(R)[coeff_idx]) + Rxy, y = polynomial_ring(Rx, symbols(R)[var_idx]) + + res = zero(Rxy) + for (c, exp) in zip(coefficients(P), exponent_vectors(P)) + # Build the coefficient in Rx, then attach to y in Rxy + res += (c * x^exp[coeff_idx]) * y^exp[var_idx] + end + return res +end + + +""" + to_bivariate(P::PolyRingElem, R_orig::MPolyRing) + +Maps a univariate polynomial in `(K[x])[y]` back to the original bivariate ring `K[x, y]`. +""" +function to_bivariate(P::PolyRingElem, R_orig::MPolyRing) + ctx = MPolyBuildCtx(R_orig) + for (deg_y, c_y) in enumerate(coefficients(P)) + for (deg_x, c_x) in enumerate(coefficients(c_y)) + push_term!(ctx, c_x, [deg_x - 1, deg_y - 1]) + end + end + return finish(ctx) +end \ No newline at end of file diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 7a93993..0c7bcd9 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -5,7 +5,7 @@ export compute_graph, connected_components, number_connected_components, group_b # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, rat_to_arb, evaluate_arb, evaluate_arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, - intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit + intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit, MPolyBuild, change_ringvar include("datastruct.jl") include("tools.jl") diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index dde1d52..5d4424e 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -94,7 +94,7 @@ critical point. """ function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) LBcrit, Lprecx = Dict(), Dict() - Lfyk = diff_list(f, 2, max(maximum(keys(params)), 2)) + Lfyk = diff_list(f, 2, maximum(keys(params), init=2)) for i in keys(params) attempts, precxi = 0, precx @@ -248,7 +248,6 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf; max_attempts= end # ---- Extremal case (i == 1) we vertically enlarge boxes manually ----- - # TODO: should we also modify LBcrit? if haskey(LBcrit, 1) boxes, pcs, npcs = LBcrit[1], LPCside[1], LnPCside[1] @@ -268,7 +267,7 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf; max_attempts= # ---- intersection on bottom ---- if c1 == 1 # Attach to the max intersection below the box on the correct side - ind_yinf = maximum(i for (i, yy) in pairs(side_pts) if yy < ycrit[1]) + ind_yinf = maximum(i for (i, yy) in pairs(side_pts) if yy[1] < ycrit[1]) push!(side_indices, ind_yinf) empty!(pc.bottom.indices_inside) npcs[j] = (0, c2, s == 1 ? c3 + 1 : c3, s == 2 ? c4 + 1 : c4) @@ -278,7 +277,7 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf; max_attempts= # ---- intersection on top ---- if c2 == 1 # Attach to the min intersection above the bow on the correct side - ind_ymax = minimum(i for (i, yy) in pairs(side_pts) if yy > ycrit[2]) + ind_ymax = minimum(i for (i, yy) in pairs(side_pts) if yy[2] > ycrit[2]) push!(side_indices, ind_ymax) empty!(pc.top.indices_inside) npcs[j] = (c1, 0, s == 1 ? c3 + 1 : c3, s == 2 ? c4 + 1 : c4) diff --git a/src/connectivity/subresultants-bis.jl b/src/connectivity/subresultants-bis.jl index 70924d9..47dc731 100644 --- a/src/connectivity/subresultants-bis.jl +++ b/src/connectivity/subresultants-bis.jl @@ -1,46 +1,80 @@ # ========================================================================= -# RING COERCION TOOLS (Replaces array wrangling and homogenize) +# SUBRESULTANTS # ========================================================================= -# TODO: use MPolyBuildCtx? +# Univariate resultant +function subresultants(P::Union{PolyRingElem{T}, FqPolyRingElem}, Q::Union{PolyRingElem{T}, FqPolyRingElem}, is_Fq::Bool=false) where T <: RingElem + degree(P) < degree(Q) && ((P, Q) = (Q, P)) -""" - to_univariate(P::MPolyRingElem, var_idx::Int) + S = typeof(P)[Q] + s = leading_coefficient(Q)^(degree(P) - degree(Q)) # Initial scaling factor + # rem is faster when working with finite fields (relies on FLINT) + A = Q + B = is_Fq ? (-leading_coefficient(Q))^(degree(P) - degree(Q) + 1) * rem(P, Q) : pseudorem(P, -Q) -Converts a bivariate polynomial in `K[x, y]` into a univariate polynomial in `(K[x])[y]`. -""" -function to_univariate(P::MPolyRingElem, var_idx::Int) - R = parent(P) - K = base_ring(R) - coeff_idx = 3 - var_idx # The variable to be pushed to the coefficients - - Rx, x = polynomial_ring(K, symbols(R)[coeff_idx]) - Rxy, y = polynomial_ring(Rx, symbols(R)[var_idx]) - - res = zero(Rxy) - for (c, exp) in zip(coefficients(P), exponent_vectors(P)) - # Build the coefficient in Rx, then attach to y in Rxy - res += (c * x^exp[coeff_idx]) * y^exp[var_idx] + while !iszero(B) + d, e = degree(A), degree(B) + push!(S, B) # current remainder + delta = d - e # degree drop + + if delta > 1 + if length(S) > 2 + last_add, prev_add = S[end], S[end-1] + n = degree(prev_add) - degree(last_add) - 1 # stabilize scaling + if n == 0 + C = last_add + else + x, y = leading_coefficient(last_add), leading_coefficient(prev_add) + a = 1 << (length(bits(ZZ(n))) - 1) + c, n = x, n - a + while a > 1 + a >>= 1 + c = divexact(c^2, y) + if n >= a + c = c * divexact(x, y) + n -= a + end + end + C = c * divexact(last_add, y) + end + else + # First step: fallback normalization + C = divexact(leading_coefficient(B)^(delta - 1) * B, s^(delta - 1)) + end + push!(S, C) + else + C = B # no degree drop + end + + # Termination: constant polynomial + e == 0 && return reverse!(S) + + # --- Next pseudo-remainder --- + B = is_Fq ? (-leading_coefficient(B))^(d - e + 1) * rem(A, B) : pseudorem(A, -B) + B = divexact(B, s^delta * leading_coefficient(A)) + + A = C + s = leading_coefficient(A) end - return res + return reverse!(S) end -""" - to_bivariate(P::PolyRingElem, R_orig::MPolyRing) +# Bivariate resultant +function subresultants(P::MPolyRingElem, Q::MPolyRingElem, var_idx::Int; list=false) + UP, UQ = to_univariate(P, var_idx), to_univariate(Q, var_idx) + sr_uni = subresultants(UP, UQ) -Maps a univariate polynomial in `(K[x])[y]` back to the original bivariate ring `K[x, y]`. -""" -function to_bivariate(P::PolyRingElem, R_orig::MPolyRing) - ctx = MPolyBuildCtx(R_orig) - for (deg_y, c_y) in enumerate(coefficients(P)) - for (deg_x, c_x) in enumerate(coefficients(c_y)) - push_term!(ctx, c_x, [deg_x - 1, deg_y - 1]) - end + R_orig = parent(P) + v_orig = symbols(R_orig) + + if list + # Extract coefficients as bivariate polynomials + return [change_ringvar(collect(coefficients(sr)), v_orig) for sr in sr_uni] + else + return [to_bivariate(sr, R_orig) for sr in sr_uni] end - return finish(ctx) end - # ========================================================================= # MODULAR ARITHMETIC & INTERSECTION # ========================================================================= @@ -55,18 +89,21 @@ function num_biv_rat_mod(A::MPolyRingElem, P::Vector) q, a, b = P[1], P[2], P[3] Rx = parent(q) - # Do math natively inside the quotient ring Rx / + # Work modulo q and compute y = a/b in the quotient ring U, mod_q = residue_ring(Rx, q) - a_u, b_u, x_u = mod_q(a), mod_q(b), mod_q(gens(Rx)[1]) + y_u = mod_q(a) / mod_q(b) - deg_y = maximum(e[2] for e in exponent_vectors(A); init=0) - res_u = zero(U) - - # Avoids homogenization entirely. b^(deg_y - j) clears the denominator. + # Build coefficients of A as polynomials in y with coefficients in U + degA_y = maximum(e[2] for e in exponent_vectors(A)) + coeff_A_u = [ MPolyBuildCtx(Rx) for _ in 0:degA_y ] for (c, exp) in zip(coefficients(A), exponent_vectors(A)) - i, j = exp[1], exp[2] - res_u += c * (x_u^i) * (a_u^j) * (b_u^(deg_y - j)) + push_term!(coeff_A_u[exp[2] + 1], c, [exp[1], 0]) end + coeff_A_u = [ mod_q(finish(a)) for a in coeff_A_u ] + + # Evaluate the univariate polynomial at y_u in the quotient ring + U_y,_ = polynomial_ring(U) + res_u = evaluate(U_y(coeff_A_u), y_u) return lift(res_u) end @@ -81,9 +118,6 @@ Uses a modular CRT loop. function intersect_biv(P::Vector, A::MPolyRingElem) iszero(A) && return P[1] - RS = symbols(parent(A)) - B, x = polynomial_ring(QQ, RS[1]) - dA_prev, dA_final = Int[], Int[] pprod, p = ZZ(1), ZZ(1) << 60 compt = 0 @@ -106,7 +140,9 @@ function intersect_biv(P::Vector, A::MPolyRingElem) dA_current = [crt([d1, d2], [pprod, p]) for (d1, d2) in zip(dA_prev, dA_current)] end - count(!iszero, dA_current) <= 1 && return one(B) # Trivial GCD + # Trivial GCD : reduced gcd has larger degree + # Then, A(x,y) does not vanish on the points defined by q(x)=0 + all(iszero(c) for c in dA_current[2:end]) && return one(parent(A)) pprod *= p try @@ -120,94 +156,12 @@ function intersect_biv(P::Vector, A::MPolyRingElem) compt += 1 end - return B(dA_final) + return MPolyBuild(dA_final, RSA, 1) end - -# ========================================================================= -# SUBRESULTANTS # ========================================================================= -# Univariate resultant -function subresultants(P::Union{PolyRingElem{T}, FqPolyRingElem}, Q::Union{PolyRingElem{T}, FqPolyRingElem}, is_Fq::Bool=false) where T <: RingElem - degree(P) < degree(Q) && ((P, Q) = (Q, P)) - - S = typeof(P)[Q] - s = leading_coefficient(Q)^(degree(P) - degree(Q)) # Initial scaling factor - # rem is faster when working with finite fields (relies on FLINT) - A = Q - B = is_Fq ? (-leading_coefficient(Q))^(degree(P) - degree(Q) + 1) * rem(P, Q) : pseudorem(P, -Q) - - while !iszero(B) - d, e = degree(A), degree(B) - pushfirst!(S, B) # current remainder - delta = d - e # degree drop - - if delta > 1 - if length(S) > 2 - n = degree(S[3]) - degree(S[2]) - 1 # stabilize scaling - if n == 0 - C = S[1] - else - x, y = leading_coefficient(S[2]), leading_coefficient(S[3]) - a = 1 << (length(bits(ZZ(n))) - 1) - c, n = x, n - a - while a > 1 - a >>= 1 - c = divexact(c^2, y) - if n >= a - c = c * divexact(x, y) - n -= a - end - end - C = c * divexact(S[2], y) - end - else - # First step: fallback normalization - C = divexact(leading_coefficient(B)^(delta - 1) * B, s^(delta - 1)) - end - pushfirst!(S, C) - else - C = B # no degree drop - end - - # Termination: constant polynomial - e == 0 && return S - - # --- Next pseudo-remainder --- - B = is_Fq ? (-leading_coefficient(B))^(d - e + 1) * rem(A, B) : pseudorem(A, -B) - B = divexact(B, s^delta * leading_coefficient(A)) - - A = C - s = leading_coefficient(A) - end - return S -end - -# Bivariate resultant -function subresultants(P::MPolyRingElem, Q::MPolyRingElem, var_idx::Int; list=false) - UP, UQ = to_univariate(P, var_idx), to_univariate(Q, var_idx) - sr_uni = subresultants(UP, UQ) - - R_orig = parent(P) - #x_orig = symbols(R_orig)[3 - var_idx] - v_orig = symbols(R_orig) - - if list - # TODO: avoid evaluate, use change_ringvar? - # Extract coefficients as bivariate polynomials evaluated at y=0 - return [change_ringvar(collect(coefficients(sr)), v_orig) for sr in sr_uni] - else - return [to_bivariate(sr, R_orig) for sr in sr_uni] - end -end - - -# ========================================================================= -# CORE ALGEBRAIC ENGINE -# ========================================================================= - -# delta : poly to factor w.r.t the polynomials in LP +# delta : poly to factor w.r.t the factor of the polynomials in LP function fact_gcd(delta::T, LP::Vector{T}) where T <: PolyRingElem Ldelta = Dict{Int, T}() curr_phi = gcd(delta, LP[1]) @@ -236,6 +190,9 @@ function fact_gcd(delta::T, LP::Vector{T}) where (T <:MPolyRingElem) return Dict([ (i, change_ringvar(f, [first(RS)]) ) for (i,f) in out ]) end + +# ========================================================================= + """ param_crit_split(f::MPolyRingElem; v=0, detect_app=true) From b558cf68a01b28ba590808e8e09a093aee2e5479 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 15 Apr 2026 18:27:59 +0200 Subject: [PATCH 157/180] get rid of ols subresultants + renam subresultants + improve error message --- src/connectivity/connectcurves.jl | 8 +- src/connectivity/isolateboxes.jl | 2 +- .../{subresultants-bis.jl => paramcrit.jl} | 0 src/connectivity/subresultants.jl | 373 ------------------ 4 files changed, 5 insertions(+), 378 deletions(-) rename src/connectivity/{subresultants-bis.jl => paramcrit.jl} (100%) delete mode 100644 src/connectivity/subresultants.jl diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 0c7bcd9..95b0eef 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -7,14 +7,14 @@ export compute_graph, connected_components, number_connected_components, group_b rat_to_arb, evaluate_arb, evaluate_arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit, MPolyBuild, change_ringvar -include("datastruct.jl") include("tools.jl") -include("subresultants-bis.jl") +include("datastruct.jl") +include("buildpoly.jl") +include("subresultants.jl") +include("arbtools.jl") include("isolateboxes.jl") include("graph.jl") include("plots.jl") -include("arbtools.jl") -include("buildpoly.jl") # ========================================================================= # MULTIPLE DISPATCH WRAPPERS diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index 5d4424e..f83b37a 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -154,7 +154,7 @@ function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_pre return BoxEdge{T}(roots, indices_inside) end end - error("Problem when isolating on one side of a box after $max_retries attempts") + error("Problem when isolating on one side of a box after $max_retries attempts\n Consider increasing the initial precision or genericity position.") end # Function that computes the intersection of a curve with a box by isolating roots on the edges diff --git a/src/connectivity/subresultants-bis.jl b/src/connectivity/paramcrit.jl similarity index 100% rename from src/connectivity/subresultants-bis.jl rename to src/connectivity/paramcrit.jl diff --git a/src/connectivity/subresultants.jl b/src/connectivity/subresultants.jl deleted file mode 100644 index b0f9012..0000000 --- a/src/connectivity/subresultants.jl +++ /dev/null @@ -1,373 +0,0 @@ -# Some tools - -function homogenize(P::MPolyRingElem, i::Int, S::Vector{T} where T<:Union{Symbol, String}) - A = base_ring(parent(P)) - if iszero(P) - return zero(polynomial_ring(A, S)[1]) - end - # Homogenize w.r.t to the i-th variables - LPc, LPe = poly_to_array(P) - deg, N = maximum(getindex.(LPe, i)), length(LPe[1]) - for j in eachindex(LPe) - push!(LPe[j], deg-LPe[j][i]) - end - R, = polynomial_ring(A, S) - return array_to_poly([LPc,LPe], R) -end - -function homogenize(LP::Vector{P} where P<:MPolyRingElem, i::Int, S::Vector{T} where T<:Union{Symbol, String}) - return [ homogenize(lp, 2, S) for lp in LP ] -end - -function poly_to_array(P::MPolyRingElem) - # return P as two lists ci and vi of resp. coeffs and exponents - return [collect(coefficients(P)), collect(exponent_vectors(P))] -end - -function rem_ind(L,i) - # remove element at index i - return [ L[1:i-1]; L[i+1:end] ] -end - -function add_ind(L,i,x) - # add element x at index i - return [ L[1:i-1]; [x]; L[i:end] ] -end - -function parray_asvarcoeff(LP, idx) - # takes the above representation of a poly P - # and outputs a representation of P with univariate coeffs in the i-th variable - A = parent(LP[1][1]) - NLP = [ Vector{typeof(LP[1][1])}[], [] ] - for (c,e) in zip(LP[1], LP[2]) - vcat(zeros(A, e[idx]), [c]) - push!(NLP[1], vcat(zeros(A, e[idx]), [c])) - push!(NLP[2], rem_ind(e, idx)) - end - return NLP -end - -function parray_asvar(LP, idx) - # takes the above representation of a poly P - # and outputs a representation of P seen as a univariate poly in the i-th variable - deg = sort(LP[2], by= x->x[idx])[end][idx] - NLP = [ [[],[]] for _ in 1:deg+1 ] - for i in eachindex(LP[2]) - di = LP[2][i][idx]+1 - push!(NLP[di][1], LP[1][i]) - push!(NLP[di][2], rem_ind(LP[2][i], idx)) - end - return NLP -end - -function array_to_poly(LP, A) - C = MPolyBuildCtx(A) - R = base_ring(A) - for i in eachindex(LP[1]) - push_term!(C, R(LP[1][i]), LP[2][i]); - end - return finish(C) -end - -""" - subresultants(P, Q) -Compute the subresultant polynomial remainder sequence (PRS) of two univariate polynomials. - -Returns a vector `[S0, S1, ..., Sk]` where: -- S0 = Q (after possible swap) -- each Si is a subresultant -- sequence ends when remainder becomes zero or constant -""" - -function subresultants(P::PolyRingElem{T}, Q::PolyRingElem{T}) where T <: RingElement - return _subresultants(P, Q, false) -end - -function subresultants(P::FqPolyRingElem, Q::FqPolyRingElem) - return _subresultants(P, Q, true) -end - -function _subresultants(P::Union{PolyRingElem{T}, FqPolyRingElem}, Q::Union{PolyRingElem{T}, FqPolyRingElem}, Fq::Bool) where T <: RingElement - - # Ensure deg(P) >= deg(Q) - if degree(P) < degree(Q) - P, Q = Q, P - end - - S = Vector{typeof(Q)}() - push!(S, Q) - - # Initial scaling factor (controls normalization of pseudo-remainders) - s = leading_coefficient(Q)^(degree(P) - degree(Q)) - - # rem is faster when working with finite fields (relies on FLINT) - A = Q - B = Fq ? (-leading_coefficient(Q))^(degree(P) - degree(Q) + 1) * rem(P, Q) : pseudorem(P, -Q) - - while true - d = degree(A) - e = degree(B) - # Termination: exact division reached - if iszero(B) - return S - end - pushfirst!(S, B) # prepend current remainder - delta = d - e # degree drop - # --- Compute normalization factor C --- - if delta > 1 - if length(S) > 1 - # Use previous subresultants to stabilize scaling - n = degree(S[2]) - degree(S[1]) - 1 - if n == 0 - C = S[1] - else - x = leading_coefficient(S[1]) - y = leading_coefficient(S[2]) - - # fast exponentiation (binary powering) - a = 1 << (length(bits(ZZ(n))) - 1) - c = x - n -= a - while a > 1 - a >>= 1 - c = c^2 / y - if n >= a - c = c * x / y - n -= a - end - end - - C = c * S[1] / y - end - else - # First step: fallback normalization - C = leading_coefficient(B)^(delta - 1) * B / s^(delta - 1) - end - pushfirst!(S, C) - else - C = B - end - - # Termination: constant polynomial - if e == 0 - return S - end - - # --- Next pseudo-remainder --- - B = Fq ? (-leading_coefficient(B))^(d - e + 1)* rem(A, B) : pseudorem(A, -B) - B /= (s^delta * leading_coefficient(A)) - - # Shift sequence - A = C - s = leading_coefficient(A) - end -end - -#Bivariate subresultants -function subresultants(P::MPolyRingElem{T}, Q::MPolyRingElem{T}, idx; list=false) where T <: RingElement - LPQ = map(poly_to_array, [P,Q]) - ULPQ = [ parray_asvar(lpq, idx) for lpq in LPQ ] - - R, x = polynomial_ring(base_ring(parent(P)), "x") - S, y = polynomial_ring(R, "y") - - UP, UQ = [ S([ array_to_poly(l, R) for l in lpq ]) for lpq in ULPQ ] - - sr = subresultants(UP, UQ) - - # Get it back to initial polynomial ring - Lsr = [ [collect(coefficients(csr)) for csr in coefficients(sr)] for sr in sr] - newsr = [] - if list - for (k,lsr) in enumerate(Lsr) - mlsr = [] - for i in 1:k - tmp = [[],[]] - if i in eachindex(lsr) - for j in 1:length(lsr[i]) - push!(tmp[1], lsr[i][j]) - push!(tmp[2],add_ind([j-1],idx, 0)) - end - else - tmp = [[P|>parent|>base_ring|>zero], [[0,0]]] - end - push!(mlsr, tmp) - end - mlsr = [ array_to_poly(tmp, parent(P)) for tmp in mlsr ] - push!(newsr, mlsr) - end - else - for lsr in Lsr - mlsr = [[],[]] - for i in 1:length(lsr) - for j in 1:length(lsr[i]) - push!(mlsr[1], lsr[i][j]) - push!(mlsr[2],add_ind([j-1],idx, i-1)) - end - end - push!(newsr, array_to_poly(mlsr, parent(P))) - end - end - - return newsr -end - -function fact_gcd(delta::T, LP::Vector{T}) where (T <:PolyRingElem) - # delta : poly to factor w.r.t the polynomials in LP - Lphi = [gcd(delta, LP[1])] - Ldelta = [delta/Lphi[1]] - i = 2 - while degree(Lphi[end])>0 - #println.([Lphi,Ldelta,""]) - push!(Lphi, gcd(Lphi[i-1], LP[i])) - push!(Ldelta, Lphi[i-1]/Lphi[i]) - i+=1 - end - return filter(s->degree(s[2])>0, Dict(enumerate(Ldelta))) -end - -function num_biv_rat_mod(A, P) - # Computes the numerator of the polynomial A(x,a(x)//b(x)) mod q - # where P = [q, a, b] - B = base_ring(parent(A)) - RS = symbols(B) - - T, = polynomial_ring(B, RS[1]) - Puniv = [ T(coefficients_of_univariate(p)) for p in P ] - - U, fU = Nemo.residue_ring(T, Puniv[1]) - amod, bmod = fU.(Puniv[2:end]) - - newv = vcat(RS, [:t]) - Tbiv, = polynomial_ring(T, newv[2:end]) - Ah = homogenize(A, 2, newv) - Ah1 = array_to_poly(parray_asvarcoeff(poly_to_array(Ah), 1), Tbiv) - Ahmod = change_coefficient_ring(U, Ah1) - - Aeval = evaluate(Ahmod, [amod, bmod]) - return change_ringvar(lift(Aeval), RS) -end - - -function intersect_biv(P::Vector{T} where T<:Any, A::MPolyRingElem) - # TODO: test the reconstruction - # P = [Lq, a, b] encodes sets (x,a(x)/b(x)) where Lq[i](x)=0 - # Compute divisor dA of q that encodes intersection with A(x,y)=0 - if iszero(A) - return P[1] - end - compt = 0 - RS = A |> parent |> symbols - dA, dAf = [], [] - pprod, p = 1, ZZ(1) << 60 - while compt<12 - #print("$compt,") - if compt>0 - dAfold, dAold = copy(dAf), copy(dA) - end - p = next_prime(p) - Pp = change_coefficient_ring.(Ref(GF(p)), P) - Ap = change_coefficient_ring(GF(p), A) - #@time "Eval" - Apev = num_biv_rat_mod(Ap, Pp, RS) - dAp = gcd(Pp[1], Apev) - dA = lift.(Ref(ZZ), coefficients_of_univariate(dAp)) - if compt>0 - dA = [ crt([d1, d2], [pprod, p], false) for (d1, d2) in zip(dAold, dA) ] - end - if length(filter(!is_zero, dA)) <= 1 - #println("Trivial gcd") - return one(polynomial_ring(QQ, RS)[1]) - end - pprod = pprod*p - try - dAf = [ reconstruct(c, pprod) for c in dA ] - if compt>0 - dAf != dAfold || break - end - catch - #println("No rational rec..") - end - compt += 1 - end - #println() - B, = polynomial_ring(QQ, RS[1]) - return int_coeffs(change_ringvar(B(dAf), RS)) -end - -function param_crit_split(f, g; v=0, detect_app=true) - # Compute subresultants - v>0 && println("Compute subresultant sequence") - @iftime v>0 sr = subresultants(f, derivative(f, 2), 2, list=true) - - if total_degree(sr[1][1]) == 0 - return Dict() - end - - # TODO: sr is univariate? check what's called - v>1 && println("Factorization") - @iftime v>1 sqr = collect(factor(sr[1][1])) - - # Filter out factors with zero multiplicity and sort by multiplicity - sqr = sort!(filter(t -> t[2] > 0, sqr), by = t -> t[2]) - # Group factors by multiplicity - sqrmult = unique(getindex.(sqr, 2)) - group_sqr = Dict(m => [r[1] for r in sqr if r[2] == m] for m in sqrmult) - - v>0 && println("Compute crit partition w.r.t to multiplicity") - # Initalization - singmult = filter(p->p*(p-1)<=sqrmult[end], 2:sqrmult[end]) - param_crit = Dict(p => [[], -sr[p][end-1], (p-1)*sr[p][end]] for p in singmult) - - # Critical points : multiplicity 1 in res - (1 in sqrmult) && push!(param_crit, 1=>[group_sqr[1], -sr[2][end-1], sr[2][end]]) - if length(singmult) == 0 - return filter(p->length(p[2][1])>0, param_crit) - end - - # Nodes : multiplicity 2 in res - v>0 && println("Compute apparent singularities") - if 2 in sqrmult - if detect_app - @iftime v>0 begin - A = derivative(derivative(f,2),2)*derivative(g,1) - derivative(derivative(f,1),2)*derivative(g,2) - dA = [ (intersect_biv([q, -sr[2][end-1], sr[2][end]], A)) for q in group_sqr[2] ] - push!(param_crit, 0 => [group_sqr[2]./dA, -sr[2][end-1], sr[2][end]]) - append!(param_crit[2][1], dA) - end - else - push!(param_crit, 0 => [group_sqr[2], -sr[2][end-1], sr[2][end]]) - end - end - # Other sing - filter!(m->!(m in [1,2]), sqrmult) - lsr = [ try sr[p][end] catch; one(parent(f)) end for p in 2:(singmult[end]+1) ] - Ld = Vector{Vector{Dict{Int, MPolyRingElem}}}(undef, length(sqrmult)) - v>0 && println("Compute gcd decomposition") -@iftime v>0 begin - for k in eachindex(sqrmult) - Ld[k] = Vector{Dict{Int, MPolyRingElem}}(undef,length(group_sqr[sqrmult[k]])) - for l in eachindex(group_sqr[sqrmult[k]]) - Ld[k][l] = fact_gcd(group_sqr[sqrmult[k]][l], lsr) - end - end - for k in eachindex(Ld) - for l in eachindex(Ld[k]) - for (i, dji) in Ld[k][l] - if haskey(param_crit, i+1) - push!(param_crit[i+1][1], dji) - else - error("Curve not in generic position") - end - end - end - end -end - for i in eachindex(param_crit) - filter!(p->total_degree(p)>0, param_crit[i][1]) - end - return filter(p->length(p[2][1])>0, param_crit) -end - -param_crit_split(f; v=1) = param_crit_split(f, zero(parent(f)), v=v, detect_app=false) - From d6cb10bdbe7bf6442ad3626a8fbc808fc1db495a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 15 Apr 2026 18:30:04 +0200 Subject: [PATCH 158/180] change also include --- src/connectivity/connectcurves.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 95b0eef..fc30a28 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -10,7 +10,7 @@ export compute_graph, connected_components, number_connected_components, group_b include("tools.jl") include("datastruct.jl") include("buildpoly.jl") -include("subresultants.jl") +include("paramcrit.jl") include("arbtools.jl") include("isolateboxes.jl") include("graph.jl") From 2a67ccf34e68e954e92dfdfd4268b869c9fb42db Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 15 Apr 2026 19:37:48 +0200 Subject: [PATCH 159/180] manage special cases + consistence LBcrit --- src/connectivity/connectcurves.jl | 14 +++++++++++--- src/connectivity/isolateboxes.jl | 21 ++++++++++++--------- 2 files changed, 23 insertions(+), 12 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index fc30a28..442a280 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -75,7 +75,7 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; @iftime (v > 0) LBcrit, Lprecx = insulate_crit_boxes(f, params, precx, v=v-1) v > 0 && println("Compute intersections with critical boxes..") - @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf, v=v-1) + @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(f, params, LBcrit, Lprecx, v=v-1) # Critical values and their order xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in keys(LBcrit)) @@ -85,6 +85,15 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; Vert = Tuple{QQFieldElem, QQFieldElem}[] # List of points (x,y) Edg = Tuple{Int, Int}[] # List of tuples (idx, idy) Vcon = Dict{Int, Vector{Int}}(k => Int[] for k in keys(C)) # Index of control vertices + typeout = outf ? Float64 : QQFieldElem + + # Empty or unbounded real curves + if isempty(xcrit) + Vert = reduce(vcat, [ (typeout(e), typeout(yy[1])) for e=0:1 for yy in isolate_eval(f,1,1-2*e)]) + nV = length(Vert) / 2 + Edg = [ (i, i + nV) for i=1:nV ] + return CurveGraph{typeout}(Vert, Edg, Vcon) + end Lapp_isolated = Tuple{Int, Int}[] Lapp_nodes = Tuple{Int, Int}[] @@ -189,9 +198,8 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; if outf Vert = [ (Float64(x), Float64(y)) for (x,y) in Vert ] - return CurveGraph{Float64}(Vert, Edg, Vcon) end # Return the unified data structure - return CurveGraph{QQFieldElem}(Vert, Edg, Vcon) + return CurveGraph{typeout}(Vert, Edg, Vcon) end \ No newline at end of file diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index f83b37a..a521d0b 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -130,7 +130,7 @@ function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) end # Helper function to process a single edge of the box -function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v, outf; max_retries=5) +function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v; max_retries=5) prec = initial_prec for _ in 1:max_retries @@ -158,13 +158,13 @@ function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_pre end # Function that computes the intersection of a curve with a box by isolating roots on the edges -function intersect_box(f, B, outf; prec=100, v=0) +function intersect_box(f, B; prec=100, v=0) # Evaluate horizontal edges (fix y to B[2][1] and B[2][2], target x-interval B[1]) - edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v, outf) - edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v, outf) + edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v) + edge_y2 = _isolate_box_edge(f, 2, B[2][2], B[1], prec, v) # Evaluate vertical edges (fix x to B[1][1] and B[1][2], target y-interval B[2]) - edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v, outf) - edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v, outf) + edge_x1 = _isolate_box_edge(f, 1, B[1][1], B[2], prec, v) + edge_x2 = _isolate_box_edge(f, 1, B[1][2], B[2], prec, v) # Return clean struct T = QQFieldElem @@ -199,8 +199,7 @@ end # Function computing the intersection of the vertical sides of the critical boxes with the curve defined by f. # If an intersection on top/bottom side is detected, refine the width until this does not happen or max_attemps is reached. -function intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf; max_attempts=5, v=0) - # Automatically infer the point type based on outf +function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0) T = QQFieldElem LPCside = Dict{Int, Vector{BoxIntersections{T}}}() LnPCside = Dict{Int, Vector{NTuple{4, Int}}}() @@ -216,7 +215,7 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf; max_attempts= @inbounds for j in 1:n v >= 0 && print("i=$i ($j/$n)\r") - pc = intersect_box(f, boxes[j], outf, prec=prec, v=v) + pc = intersect_box(f, boxes[j], prec=prec, v=v) c1 = length(pc.bottom.indices_inside) c2 = length(pc.top.indices_inside) @@ -271,6 +270,8 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf; max_attempts= push!(side_indices, ind_yinf) empty!(pc.bottom.indices_inside) npcs[j] = (0, c2, s == 1 ? c3 + 1 : c3, s == 2 ? c4 + 1 : c4) + # Update also LBcrit for consistency purpose only + boxes[j][2] = (side_pts[ind_yinf][1], boxes[j][2][2]) end c1, c2, c3, c4 = npcs[j] # In case this has changed @@ -281,6 +282,8 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx, outf; max_attempts= push!(side_indices, ind_ymax) empty!(pc.top.indices_inside) npcs[j] = (c1, 0, s == 1 ? c3 + 1 : c3, s == 2 ? c4 + 1 : c4) + # Update also LBcrit for consistency purpose only + boxes[j][2] = (boxes[j][2][1], side_pts[ind_ymax][2]) end end end From e8d551b9e77a348ec10cdf4dd2c55dedbe6cbf36 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 15 Apr 2026 20:00:29 +0200 Subject: [PATCH 160/180] add test on mmod intersect_biv --- src/connectivity/paramcrit.jl | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/src/connectivity/paramcrit.jl b/src/connectivity/paramcrit.jl index 47dc731..b38f6ec 100644 --- a/src/connectivity/paramcrit.jl +++ b/src/connectivity/paramcrit.jl @@ -125,6 +125,9 @@ function intersect_biv(P::Vector, A::MPolyRingElem) while compt < 12 p = next_prime(p) Fp = GF(p) + # Prime check + lcA, lcP = ZZ(leading_coefficient(A)), ZZ(leading_coefficient(P[1])) + divides(p, gcd(lcA, lcP))[1] && continue # Map polynomials natively to Fp Pp = [map_coefficients(Fp, poly) for poly in P] @@ -147,7 +150,10 @@ function intersect_biv(P::Vector, A::MPolyRingElem) pprod *= p try dA_final = [reconstruct(c, pprod) for c in dA_current] - (compt > 0 && dA_final == dA_prev) && break + if (compt > 0 && dA_final == dA_prev) + fact = MPolyBuild(dA_final, RSA, 1) + divides(fact, P[1])[1] && return fact + end catch # Rational reconstruction failed, try next prime end @@ -156,7 +162,7 @@ function intersect_biv(P::Vector, A::MPolyRingElem) compt += 1 end - return MPolyBuild(dA_final, RSA, 1) + error("Failed multi-modular computation of apparent sing: $compt primes used") end # ========================================================================= From 787b4cd61bbce72a3cc07210de85b01ad8930b06 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Wed, 15 Apr 2026 20:51:19 +0200 Subject: [PATCH 161/180] finish documenting compute_graph --- src/connectivity/connectcurves.jl | 54 ++++++++++++++++++++++++++----- src/connectivity/graph.jl | 4 +-- src/connectivity/isolateboxes.jl | 4 +-- src/connectivity/paramcrit.jl | 9 ++++-- 4 files changed, 57 insertions(+), 14 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 442a280..fc4fc4a 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -1,5 +1,5 @@ -export compute_graph, connected_components, number_connected_components, group_by_component, merge_graphs, +export compute_graph, connected_components, number_of_connected_components, group_by_component, merge_graphs, plot_graph, plot_graphs, plot_graph_comp, Bresultant, param_crit_split, build_graphs_data, build_graph_data # DEBUG @@ -20,6 +20,51 @@ include("plots.jl") # MULTIPLE DISPATCH WRAPPERS # ========================================================================= +@doc Markdown.doc""" + compute_graph(f::P, g::P; generic=true, precx=150, v=0, int_coeff=true, outf=true) where {P <: MPolyRingElem} + compute_graph(f::P, g::P, C::Vector{P}; kwargs...) + compute_graph(f::P, g::P, C::Vector{Vector{P}}; kwargs...) + compute_graph(f::P, g::P, C::Dict{Int, Vector{P}}; kwargs...) + +Computes a planar straight-line graph that is homeomorphic to a 3D space curve. + +The input space curve is defined by a 1D parameterization consisting of its planar projection `f(x,y) = 0` and its vertical lift `z = g(x,y) / df/dy(x,y)`. A key feature of this function is its ability to identify and resolve "apparent singularities" in the planar projection—points where two non-singular branches of the 3D curve cross in the 2D projection but do not intersect in 3D space. This is describe in the paper: + + A.Poteaux, N.Islam, R.PrĂ©bet - Algorithm for Connectivity Queries on Real Algebraic Curves - ISSAC'23 + +### Output Data Structure +Returns a `CurveGraph{T}` object (where `T` is determined by the `outf` flag), containing: +* `Vert::Vector{Tuple{T, T}}`: A list of 2D coordinates representing the vertices of the graph (critical points, structural routing nodes, and injected control points). +* `Edg::Vector{Tuple{Int, Int}}`: A list of index pairs defining the undirected edges between vertices in `Vert`. +* `Vcon::Dict{Int, Vector{Int}}`: A mapping from the original 1-based index of a control point in the input array `C` to its resulting vertex index in the `Vert` array. + +### Arguments +* **`f`** (`MPolyRingElem`): The bivariate polynomial defining the planar projection `f(x,y) = 0` +* **`g`** (`MPolyRingElem`): The auxiliary polynomial defining the z-coordinate via `z = g / f_y`. +* **`C`** (`Vector{P}`, Vector{Vector{MPolyRingElem}}`, or `Dict{Int, Vector{P}}`, optionnal): A single/list/dictionnary of user-defined plane points on the curve (control points). Each point is given as a parameterization `[p, a, b]` such that `p(x) = 0` and `y = a(x)/b(x)`. +* **`generic`** (`Bool`, default `true`): If `false`, applies a random shear transformation to put the curve into generic position (preventing vertical alignments of critical points) and inverses it at the end. +* **`precx`** (`Int`, default `150`): Base numerical precision used for the real root isolation of critical x-coordinates. +* **`v`** (`Int`, default `0`): Verbosity level for tracking computational progress. +* **`int_coeff`** (`Bool`, default `true`): If `true`, coerces the polynomials to integer coefficients for optimized exact arithmetic. +* **`outf`** (`Bool`, default `true`): If `true`, outputs the vertex coordinates as machine `Float64`. If `false`, preserves exact rational coordinates (`QQFieldElem`). + +### Examples +```jldoctest +julia> using AlgebraicSolving + +julia> R, (x,y) = polynomial_ring(QQ, ["x","y"]) +(Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x, y]) + + +julia> # Define a space curve projection and its z-lift + f = -49303382*x^4 + 9395599*x^3*y + 67366686*x^3 - 27407214*x^2*y^2 - 71298014*x^2*y - 24150320*x^2 - 12067817*x*y^3 + 6797370*x*y^2 + 20838420*x*y - 18118613*x + 2357706*y^4 - 13736522*y^3 - 37604516*y^2 - 13868221*y + 6980802; + g = 32091920*x^4 - 97772598*x^3*y - 245256584*x^3 + 99093410*x^2*y^2 + 162335273*x^2*y + 239310556*x^2 + 28995368*x*y^3 - 59544597*x*y^2 - 20499914*x*y + 98243402*x + 22738226*y^3 + 111105506*y^2 + 86287748*y - 62439535; + +julia> graph = compute_graph(f, g); + +julia> number_of_connected_components(graph) +3 +""" # Base case: No 'C' (control points) provided compute_graph(f::P, g::P; kwargs...) where {P <: MPolyRingElem} = _compute_graph_core(f, g, Vector{Vector{P}}(); kwargs...) @@ -44,13 +89,6 @@ compute_graph(f::P, g::P, C::Vector{P}; kwargs...) where {P <: MPolyRingElem} = # CORE IMPLEMENTATION # ========================================================================= -# Input: -# The space curve is given by f(x,y) = 0 and (df/dy)(x,y)*z = g(x,y) -# it is assumed in generic position of put it using generic parameter -# for now f is assumed to be square-free (future feature) -# C is a list of parametrization [p,a,b] of plane pts i.e. such that p(x)=0,y=a(x)/b(x) -# these points must be on the curve -# Output: Computes a graph homeomorphic to the curve, identitying point in C function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; generic=true, precx=150, v=0, int_coeff=true, outf=true) where {P <: MPolyRingElem} diff --git a/src/connectivity/graph.jl b/src/connectivity/graph.jl index 2ec31c5..291ce64 100644 --- a/src/connectivity/graph.jl +++ b/src/connectivity/graph.jl @@ -102,12 +102,12 @@ function group_by_component(G::CurveGraph) end """ - number_connected_components(G::CurveGraph) + number_of_connected_components(G::CurveGraph) # Outputs - `Int`: The count of isolated subgraphs in the parent structure. """ -number_connected_components(G::CurveGraph) = length(connected_components(G)) +number_of_connected_components(G::CurveGraph) = length(connected_components(G)) # ========================================================================= diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index a521d0b..c042fbc 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -271,7 +271,7 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0 empty!(pc.bottom.indices_inside) npcs[j] = (0, c2, s == 1 ? c3 + 1 : c3, s == 2 ? c4 + 1 : c4) # Update also LBcrit for consistency purpose only - boxes[j][2] = (side_pts[ind_yinf][1], boxes[j][2][2]) + boxes[j][2][1] = side_pts[ind_yinf][1] end c1, c2, c3, c4 = npcs[j] # In case this has changed @@ -283,7 +283,7 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0 empty!(pc.top.indices_inside) npcs[j] = (c1, 0, s == 1 ? c3 + 1 : c3, s == 2 ? c4 + 1 : c4) # Update also LBcrit for consistency purpose only - boxes[j][2] = (boxes[j][2][1], side_pts[ind_ymax][2]) + boxes[j][2][2] = side_pts[ind_ymax][2] end end end diff --git a/src/connectivity/paramcrit.jl b/src/connectivity/paramcrit.jl index b38f6ec..cd282cb 100644 --- a/src/connectivity/paramcrit.jl +++ b/src/connectivity/paramcrit.jl @@ -200,9 +200,14 @@ end # ========================================================================= """ - param_crit_split(f::MPolyRingElem; v=0, detect_app=true) + param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, detect_app=true) -Computes the critical points of a curve `f(x, y) = 0` grouped by multiplicity. +Computes the critical points (grouped by multiplicity) and apparent singularities +of the space curve defined by: + `f(x, y) = 0` and `(df/dy)(x,y) * z = g(x,y)` + +This relies on subresultant computations and apparent singularity criterion from: +A.Poteaux, N.Islam, R.PrĂ©bet - Algorithm for Connectivity Queries on Real Algebraic Curves - ISSAC'23 """ function param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, detect_app=true) v > 0 && println("Compute subresultant sequence") From bd46e148ab439c2acaa5aee4a53f95dfb7e5ad8b Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 16 Apr 2026 01:17:17 +0200 Subject: [PATCH 162/180] bug fixes + genericity tests --- src/connectivity/arbtools.jl | 4 ++-- src/connectivity/connectcurves.jl | 27 +++++++++++++++++++++------ src/connectivity/paramcrit.jl | 25 ++++++++++++------------- 3 files changed, 35 insertions(+), 21 deletions(-) diff --git a/src/connectivity/arbtools.jl b/src/connectivity/arbtools.jl index 3134133..3d2ad1a 100644 --- a/src/connectivity/arbtools.jl +++ b/src/connectivity/arbtools.jl @@ -38,8 +38,8 @@ function evaluate_arb(f, g, x::Vector{QQFieldElem}, field::ArbField) is_zero(f) && return zero(parent(x)) - cf = coefficients_of_univariate(f) - cg = coefficients_of_univariate(g) + cf = field.(coefficients_of_univariate(f)) + cg = field.(coefficients_of_univariate(g)) x_arb = rat_to_arb(x, field) num = evalpoly(x_arb, cf) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index fc4fc4a..171a432 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -90,21 +90,37 @@ compute_graph(f::P, g::P, C::Vector{P}; kwargs...) where {P <: MPolyRingElem} = # ========================================================================= function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; - generic=true, precx=150, v=0, int_coeff=true, outf=true) where {P <: MPolyRingElem} + generic=true, precx=150, v=0, detect_app=true, outf=true) where {P <: MPolyRingElem} + + @assert !iszero(f) "Input does not define a curve" R = parent(f) x, y = gens(R) - intC = int_coeff ? int_coeffs : identity + typeout = outf ? Float64 : QQFieldElem + + # Empty set + total_degree(f) == 0 && + return CurveGraph( + Tuple{typeout, typeout}[], + Tuple{Int, Int}[], + Dict{Int, Vector{Int}}() + ) # Pre-processing the input - f, g = intC([f, g]) - changemat = generic ? [1 0; 0 1] : trimat_rand(QQ, 2, range=-100:100) + f, g = int_coeffs([f, g]) + changemat = generic ? [1 0; 0 1] : [ QQ(rand(-100:100)) for i=1:2, j=1:2 ] + f = evaluate(f, collect(changemat * [x; y])) precx = max(2, precx) v > 1 && println(f) + # Zero-dim param conditions + d = total_degree(f) + @assert degree(f, 2) == d && degree(f, 1) == d && degree(g, 2) < d && + is_squarefree(f) "Curve not in generic position. Try with generic=false." + v > 0 && println("Compute parametrization of critical pts...") - @iftime (v > 0) params = param_crit_split(f, g, v=v-1, detect_app=true) + @iftime (v > 0) params = param_crit_split(f, g, v=v-1, detect_app=detect_app) for i in 1:length(C) params[-i] = [ [intC(C[i][1])], C[i][2], C[i][3] ] end @@ -123,7 +139,6 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; Vert = Tuple{QQFieldElem, QQFieldElem}[] # List of points (x,y) Edg = Tuple{Int, Int}[] # List of tuples (idx, idy) Vcon = Dict{Int, Vector{Int}}(k => Int[] for k in keys(C)) # Index of control vertices - typeout = outf ? Float64 : QQFieldElem # Empty or unbounded real curves if isempty(xcrit) diff --git a/src/connectivity/paramcrit.jl b/src/connectivity/paramcrit.jl index cd282cb..4dbd643 100644 --- a/src/connectivity/paramcrit.jl +++ b/src/connectivity/paramcrit.jl @@ -213,7 +213,6 @@ function param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, detect_app=tr v > 0 && println("Compute subresultant sequence") f_y = derivative(f, 2) @iftime v>0 sr = subresultants(f, f_y, 2, list=true) - (isempty(sr) || total_degree(sr[1][1]) == 0) && return Dict{Int, Vector}() v > 1 && println("Factorization") @@ -226,25 +225,28 @@ function param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, detect_app=tr sqrmult = unique([s[2] for s in sqr]) group_sqr = Dict(m => [s[1] for s in sqr if s[2] == m] for m in sqrmult) - v > 0 && println("Compute crit partition w.r.t to multiplicity") param_crit = Dict{Int, Vector}() # Helper function to prevent out-of-bounds access on subresultant lists - get_sr = (p, idx) -> (length(sr) >= p && length(sr[p]) >= abs(idx)) ? sr[p][end+idx] : zero(parent(f)) + get_sr = (p, idx)-> (length(sr) >= p && length(sr[p]) >= abs(idx) + 1) ? sr[p][end+idx] : zero(parent(f)) + + # Critical points : multiplicity 1 in res + (1 in sqrmult) && (param_crit[1] = [group_sqr[1], -get_sr(2, -1), get_sr(2, 0)]) + # Singular points singmult = filter(p -> p*(p-1) <= sqrmult[end], 2:sqrmult[end]) + isempty(singmult) && return filter(p -> length(p.second[1]) > 0, param_crit) + + @assert length(sr) >= singmult[end] "Curve not in generic position. Try with generic=false." for p in singmult + @assert length(sr[p]) >= 2 "Curve not in generic position. Try with generic=false." param_crit[p] = [MPolyRingElem[], -get_sr(p, -1), (p-1)*get_sr(p, 0)] end - # Critical points : multiplicity 1 in res - (1 in sqrmult) && (param_crit[1] = [group_sqr[1], -get_sr(2, -1), get_sr(2, 0)]) - isempty(singmult) && return filter(p -> length(p.second[1]) > 0, param_crit) - # Nodes : multiplicity 2 in res - v > 0 && println("Compute apparent singularities") if 2 in sqrmult if detect_app + v > 0 && println("Compute apparent singularities") f_x = derivative(f, 1) A = derivative(f_y, 2) * derivative(g, 1) - derivative(f_x, 2) * derivative(g, 2) @@ -265,14 +267,11 @@ function param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, detect_app=tr for m in sqrmult for q in group_sqr[m] for (i, dji) in fact_gcd(q, lsr) - haskey(param_crit, i+1) ? push!(param_crit[i+1][1], dji) : error("Curve not generic") + @assert haskey(param_crit, i+1) "Curve not in generic position. Try with generic=false." + push!(param_crit[i+1][1], dji) end end end - for v in values(param_crit) - filter!(p -> total_degree(p) > 0, v[1]) - end - return filter(p -> length(p.second[1]) > 0, param_crit) end \ No newline at end of file From 1b783eb665f5047b8c645ec56673f73a0dcf5746 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Thu, 16 Apr 2026 10:36:21 +0200 Subject: [PATCH 163/180] one function for plot --- src/connectivity/plots.jl | 10 +++------- 1 file changed, 3 insertions(+), 7 deletions(-) diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 51275ff..ed5bb29 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,7 +1,3 @@ -# Distinguishable Colors - -# file: utils/colors.jl - """ distinguishable_colors(n; s=0.8, v=0.9) @@ -62,7 +58,7 @@ end plot_graph(build_graphs_data(G)) """ -function build_graph_data(G; width=3.0, vert=true, color="#FF0000") +function build_graph_data(G::CurveGraph{T}; width=3.0, vert=true, color="#FF0000") where T <: Union{Float64,QQFieldElem} V, Vcon, E = G.vertices, G.control_nodes, G.edges # edges @@ -107,10 +103,10 @@ function plot_graphs(CP) gui() end -plot_graphs(build_graphs_data(CG)) +plot_graphs(build_graph_data(CG)) """ -function build_graphs_data(CG; width=3.0, vert=true) +function build_graph_data(CG::Vector{CurveGraph{T}}; width=3.0, vert=true) where T <: Union{Float64,QQFieldElem} c = distinguishable_colors(length(CG)) return [build_graph_data(G; width=width, vert=vert, color=c[i]) for (i, G) in enumerate(CG)] From f0d419e4cd5ec4e6f66b7079f7743b511695c147 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Thu, 16 Apr 2026 16:33:11 +0200 Subject: [PATCH 164/180] documentation of graph + start examples --- src/connectivity/graph.jl | 57 ++++++++++++++++++++++----- src/connectivity/plots.jl | 2 + test/algorithms/curve-connectivity.jl | 24 +++++++++++ 3 files changed, 74 insertions(+), 9 deletions(-) create mode 100644 test/algorithms/curve-connectivity.jl diff --git a/src/connectivity/graph.jl b/src/connectivity/graph.jl index 291ce64..afddb06 100644 --- a/src/connectivity/graph.jl +++ b/src/connectivity/graph.jl @@ -2,17 +2,26 @@ # GRAPH DECOMPOSITION # ========================================================================= -""" +@doc Markdown.doc""" connected_components(G::CurveGraph{T}) where T -Decomposes a graph into its connected components. +Decomposes a graph into its topologically connected components using a Depth-First Search (DFS). + +This function is particularly useful when a single algebraic curve resolves into multiple +disconnected real branches in space. It guarantees that isolated vertices are preserved as +their own zero-edge components. + +Crucially, this function preserves the `control_nodes` mappings. If a global control node +belonged to a specific vertex, it is correctly remapped to that vertex's new local index +within its specific disconnected subgraph. # Inputs -- `G::CurveGraph{T}`: The unified curve graph. +- `G::CurveGraph{T}`: The unified curve graph to be decomposed. # Outputs - `Vector{CurveGraph{T}}`: A list of disjoint subgraphs. Each subgraph retains the mapped coordinates, edges, and control nodes belonging to its component. + """ function connected_components(G::CurveGraph{T}) where T nv = length(G.vertices) @@ -90,22 +99,38 @@ function connected_components(G::CurveGraph{T}) where T return subgraphs end -""" +@doc Markdown.doc""" group_by_component(G::CurveGraph) +Extracts the control_nodes dictionaries partitioned by the graph's connected components. +This is primarily used to determine which external connections (or user-defined points) +belong to which isolated branch of the curve. + +# Inputs +- `G::CurveGraph{T}`: The parent graph structure. + # Outputs -- `Vector{Dict{Int, Vector{Int}}}`: Returns just the control nodes mapped to each connected component. +- `Vector{Dict{Int, Vector{Int}}}`: A list of dictionaries, one for each connected component, +detailing the local vertex indices mapped to specific control IDs. + """ function group_by_component(G::CurveGraph) subgraphs = connected_components(G) return [sg.control_nodes for sg in subgraphs if !isempty(sg.vertices)] end -""" +@doc Markdown.doc""" number_of_connected_components(G::CurveGraph) +Computes the total number of topologically disconnected branches/components in the graph. +This is a convenience wrapper for topological validation. + +# Inputs +- `G::CurveGraph{T}`: The parent graph structure. + # Outputs -- `Int`: The count of isolated subgraphs in the parent structure. +- `Int`: The count of isolated subgraphs. + """ number_of_connected_components(G::CurveGraph) = length(connected_components(G)) @@ -118,11 +143,23 @@ number_of_connected_components(G::CurveGraph) = length(connected_components(G)) merge_graphs(graphs::Vector{CurveGraph{T}}) where T Merges a collection of disjoint graphs into a single graph, mathematically fusing -vertices that share common `control_nodes` mappings. +vertices based on their control_nodes dictionnaries that describe a one-to-one +correspondance between subset of vertices of each graph. + + +# Fusion Mechanism: +This work as follows. Given V1 = [u1,u2] and V2 = [w1,w2,w3] the vertices of two graphs G1 and G2. +Let C1= {2 => [1]} and C2 = {1 => [2]} be their respective control_nodes disctionnary. +Then it merges the first vertex w1 of G2 with the second vertex u2 of G1. +The merged graph has vertices [u1,u2,w2,w3]. + +Note that control nodes that refer to external bounds (e.g., indices k <= 0 or k > length(graphs)) +are preserved in the final merged graph to allow for subsequent higher-level merging or tracking. # Inputs - `graphs::Vector{CurveGraph{T}}`: A list of graphs. `graphs[i].control_nodes[k]` should contain the local vertex indices in graph `i` that connect to graph `k`. + This vertex correspondance must be one-to-one. # Outputs - `CurveGraph{T}`: A unified graph struct. @@ -145,8 +182,10 @@ function merge_graphs(graphs::Vector{CurveGraph{T}}) where T # Step 1: Pre-map common control nodes connected to previously merged graphs for (k, common_indices_in_i) in G_i.control_nodes - if k < i && haskey(graphs[k].control_nodes, i) + if k < i && !isempty(common_indices_in_i) + @assert haskey(graphs[k].control_nodes, i) "Correspondance is not one-to-one" common_indices_in_k = graphs[k].control_nodes[i] + @assert length(common_indices_in_i) == length(common_indices_in_k) "Correspondance is not one-to-one" # Zip ensures we pair corresponding control nodes precisely for (idx_i, idx_k) in zip(common_indices_in_i, common_indices_in_k) global_map[(i, idx_i)] = global_map[(k, idx_k)] diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index ed5bb29..75cbe48 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -47,6 +47,7 @@ end # ---------- CORE BUILDERS ---------- """ # How to plot: +using Plots function plot_graph(P) plot(legend=false) E = P.edge_group @@ -93,6 +94,7 @@ end """ # How to plot: +using Plots function plot_graphs(CP) plot(legend=false) for P in CP diff --git a/test/algorithms/curve-connectivity.jl b/test/algorithms/curve-connectivity.jl new file mode 100644 index 0000000..cd4a9b7 --- /dev/null +++ b/test/algorithms/curve-connectivity.jl @@ -0,0 +1,24 @@ + +# param2 +f = -49303382*x^4 + 9395599*x^3*y + 67366686*x^3 - 27407214*x^2*y^2 - 71298014*x^2*y - 24150320*x^2 - 12067817*x*y^3 + 6797370*x*y^2 + 20838420*x*y - 18118613*x + 2357706*y^4 - 13736522*y^3 - 37604516*y^2 - 13868221*y + 6980802 +g = 32091920*x^4 - 97772598*x^3*y - 245256584*x^3 + 99093410*x^2*y^2 + 162335273*x^2*y + 239310556*x^2 + 28995368*x*y^3 - 59544597*x*y^2 - 20499914*x*y + 98243402*x + 22738226*y^3 + 111105506*y^2 + 86287748*y - 62439535 + +# Not generic +f = y^2-x^2*(x+1) + +# Crunode (after generic change of variable) +-2744*x^3 - 34692*x^2*y + 8085*x^2 - 146202*x*y^2 + 896*x*y - 205379*y^3 - 3285*y^2 + +# Acnode +157464*x^3 + 297432*x^2*y + 7012*x^2 + 187272*x*y^2 + 1496*x*y + 39304*y^3 + 1445*y^2 + +# Ordinary cusp +79507*x^3 + 543606*x^2*y + 9604*x^2 + 1238916*x*y^2 - 3528*x*y + 941192*y^3 + 324*y^2 + +# Rhamphoid cusp +-3077056399*x^5 - 16359034020*x^4*y - 28398241*x^4 - 34788831840*x^3*y^2 + 9336408*x^3*y - 36990656640*x^2*y^3 - 1151064*x^2*y^2 + 5329*x^2 - 19665918720*x*y^4 + 63072*x*y^3 - 876*x*y - 4182119424*y^5 - 1296*y^4 + 36*y^2 +or +-243*x^5 - 25515*x^4*y - 1071630*x^3*y^2 - 22504230*x^2*y^3 + 8464*x^2 - 236294415*x*y^4 + 18216*x*y - 992436543*y^5 + 9801*y^2 + +# Non-generic because two crit-point above (but rat_cur_param works) +x^4 - x^3 + 2*x^2*y^2 - 7//4*x^2 - x*y^2 + x + y^4 - 7//4*y^2 + 3//4 From 7d9e921626c6bc538d4745fca1b64bb27d4ef6af Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Thu, 16 Apr 2026 16:54:08 +0200 Subject: [PATCH 165/180] more documentation --- src/connectivity/isolateboxes.jl | 68 +++++++++++++++++++++++--------- 1 file changed, 49 insertions(+), 19 deletions(-) diff --git a/src/connectivity/isolateboxes.jl b/src/connectivity/isolateboxes.jl index c042fbc..8e7edbd 100644 --- a/src/connectivity/isolateboxes.jl +++ b/src/connectivity/isolateboxes.jl @@ -1,8 +1,11 @@ in_inter(I, J) = J[1] <= I[1] && I[2] <= J[2] overlap_inter(I, J) = max(I[1], J[1]) <= min(I[2], J[2]) - # Function that isolate roots of a multivariate polynomial with a - # single variable +""" + isolate(f; prec = 32) + +Isolate real roots of a multivariate polynomial with a single variable +""" function isolate(f; prec = 32) total_degree(f) == 0 && return [] @assert is_univariate(f) "Not univariate polynomial" @@ -11,11 +14,14 @@ function isolate(f; prec = 32) return getindex.(sols, 1) end -# univariate isolation of roots of a bivariate polynomial f whose -# ivar-th variable is evaluated at val +""" + isolate_eval(f, ivar, val; prec=64) + +Isolate real roots of a bivariate polynomial whose ivar-th variable is +evaluated at val +""" function isolate_eval(f, ivar, val; prec=64) fev = evaluate(f, [ivar], [val]) - # fev *= fev |> coefficients .|> denominator |> lcm fev = fev / content(fev) return isolate(fev, prec=prec) end @@ -74,8 +80,12 @@ function _needs_refinement(i, Lfyk, LBcrit, precx) return false end -# Compute the list of the n-th first derivative of p w.r.t v -function diff_list(p, v, n) +""" + _diff_list(p, v, n) + +Compute the list of the n-th first derivative of p w.r.t v +""" +function _diff_list(p, v, n) L = Vector{typeof(p)}(undef, n + 1) L[1] = p @inbounds for j in 2:n+1 @@ -87,14 +97,14 @@ end """ compute_crit_and_singular_boxes(f, params, precx; max_attempts=5, v=0) -Compute insulating boxes for critical points, refining precision if necessary. -Insulating means that each box contains a single critical point and -all branches of the curve intersecting the box are incident to this -critical point. +Compute insulating boxes for critical points, refining precision if +necessary. Insulating means that each box contains a single critical +point and all branches of the curve intersecting the box are incident +to this critical point. """ function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) LBcrit, Lprecx = Dict(), Dict() - Lfyk = diff_list(f, 2, maximum(keys(params), init=2)) + Lfyk = _diff_list(f, 2, maximum(keys(params), init=2)) for i in keys(params) attempts, precxi = 0, precx @@ -129,7 +139,14 @@ function insulate_crit_boxes(f, params, precx; max_attempts=5, v=0) return LBcrit, Lprecx end -# Helper function to process a single edge of the box +""" + _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v; max_retries=5) + +Function that computes the intersection of a curve with a vertical +(fixed_dim=1)/horizontal (fixed_dim=2) line, and identify those in +target interval. +Returns isolating intervals and indices of the interval in target_interval +""" function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_prec, v; max_retries=5) prec = initial_prec @@ -154,10 +171,16 @@ function _isolate_box_edge(f, fixed_dim, fixed_val, target_interval, initial_pre return BoxEdge{T}(roots, indices_inside) end end - error("Problem when isolating on one side of a box after $max_retries attempts\n Consider increasing the initial precision or genericity position.") + error("Problem when isolating on one side of a box after $max_retries attempts\n + Consider increasing the initial precision or genericity position.") end -# Function that computes the intersection of a curve with a box by isolating roots on the edges +""" + intersect_box(f, B; prec=100, v=0) + +Computes the intersection of a curve with a box by +isolating roots on the edges. +""" function intersect_box(f, B; prec=100, v=0) # Evaluate horizontal edges (fix y to B[2][1] and B[2][2], target x-interval B[1]) edge_y1 = _isolate_box_edge(f, 2, B[2][1], B[1], prec, v) @@ -197,8 +220,16 @@ function refine_xboxes(F::Vector{T} where T<:Union{PolyRingElem, MPolyRingElem}, return _update_LB_first_axis!(LB, xnew) end -# Function computing the intersection of the vertical sides of the critical boxes with the curve defined by f. -# If an intersection on top/bottom side is detected, refine the width until this does not happen or max_attemps is reached. +""" + intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0) + +Computes the intersection of the vertical sides of the critical boxes +in LBcrit with the curve defined by f. + +If an intersection on top/bottom side is detected, refine the width +using params and Lprecx until this does not happen or max_attemps is +reached. +""" function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0) T = QQFieldElem LPCside = Dict{Int, Vector{BoxIntersections{T}}}() @@ -239,11 +270,10 @@ function intersect_vertical_boxes(f, params, LBcrit, Lprecx; max_attempts=5, v=0 attempt == max_attempts && error("Problem in computing intersections (i=$i)") end - + v > 0 && print("\n") LPCside[i] = sides_vec LnPCside[i] = nsides_vec Lprecx[i] = prec - v >= 0 && println() end # ---- Extremal case (i == 1) we vertically enlarge boxes manually ----- From 55c687eb3c966122ca18c19e693993e48b05dc11 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Thu, 16 Apr 2026 18:07:10 +0200 Subject: [PATCH 166/180] more doc (type) --- docs/src/types.md | 105 ++++++++++++++++++++++++++++++++- src/connectivity/datastruct.jl | 26 -------- src/connectivity/plots.jl | 75 ++++++++++++++--------- src/types.jl | 31 +++++++++- 4 files changed, 181 insertions(+), 56 deletions(-) diff --git a/docs/src/types.md b/docs/src/types.md index 1a18966..af668a5 100644 --- a/docs/src/types.md +++ b/docs/src/types.md @@ -186,4 +186,107 @@ The reason of this tree arrangement is mainly because of the following property: of the other's*. In many cases, one can even replace "descendant" by "parent". -See the documentation of the [roadmap](@ref) function for further details. \ No newline at end of file +See the documentation of the [roadmap](@ref) function for further details. + +# Graph Data Structures & Visualization + +## Curve Graphs + +The `CurveGraph{T}` structure represents a planar straight-line graph +that is homeomorphic to a real algebraic curve. It is the output of +algorithms [compute_graph](@ref), which compute the planar projection +of curves while resolving apparent singularities. + +These real algebraic curves are typically output of roadmap algorithms +presented above. Hence `CurveGraph{T}` object can provide a +discretized skeleton of real algebraic sets that preserves +connectivity properties. In particular they share the same number of +connected components (respectively as graphs and as semi-algebraic +sets) + + +The type `CurveGraph{T}` (where `T` is typically `Float64` or `QQFieldElem`) caches the following attributes: + + * `vertices::Vector{Tuple{T, T}}`: a list of 2D coordinates representing the nodes of the graph (critical points, regular routing points, and user-defined control points). + + * `edges::Vector{Tuple{Int, Int}}`: a list of index pairs defining the undirected edges connecting the vertices in `vertices`. + + * `control_nodes::Dict{Int, Vector{Int}}`: a dictionary mapping user-defined control point IDs to their corresponding local vertex indices in the `vertices` array. These IDs typically refer to other `CurveGraph{T}` and the associated vertices: their mutual intersection. This is useful when computing arrangement of curves using [merge_graphs](@ref). + +```julia +struct CurveGraph{T} + vertices::Vector{Tuple{T, T}} + edges::Vector{Tuple{Int, Int}} + control_nodes::Dict{Int, Vector{Int}} +end +``` + +## Graph Plotting Data + +To seamlessly visualize `CurveGraph` objects using standard plotting libraries (such as `Plots.jl`), AlgebraicSolving provides an intermediate geometric representation. + +The primary structure is `GraphPlotData`, which decomposes a mathematical graph into purely visual components: + +* `edges::EdgeGroup`: contains the geometric line segments representing the graph's connections, alongside styling data (color and width). + +* `points::Vector{PointGroup}`: separates standard vertices and special control nodes into distinct scatter groups with specific markers (e.g., `:x` for standard vertices, `:+` for control nodes). + +```julia +struct EdgeGroup + edges::Vector{Tuple{Vector{Float64}, Vector{Float64}}} + color::String + width::Float64 +end + +struct PointGroup + vertices::Tuple{Vector{Float64}, Vector{Float64}} + color::String + marker::Symbol +end + +struct GraphPlotData + edge_group::EdgeGroup + point_groups::Vector{PointGroup} +end +``` + +### Core Builders + +The functions [build_graph_data](@ref) allow to compute such `GraphPlotData` from `CurveGraph{T}` objects. These former objects can be plotted with `Plot.jl` as follows. Below, `G` is a `CurveGraph{T}`. + +```julia +using Plots + +function plot_graph(P) + plot(legend=false) + E = P.edge_group + plot!(E.edges, color=E.color, width = E.width) + [scatter!(V.vertices, color=V.color, marker = V.marker) for V in P.point_groups] + gui() +end + +plot_graph(build_graphs_data(G)) +``` + +If one has `CG` a list of `CurveGraph{T}` (typically the connected +components of `G` obtained with [connected_components](@ref)). + +```julia +# How to plot: +using Plots + +function plot_graphs(CP) + plot(legend=false) + for P in CP + E = P.edge_group + plot!(E.edges, color=E.color, width = E.width) + [ scatter!(V.vertices, color=V.color, marker = V.marker) for V in P.point_groups ] + end + gui() +end + +plot_graphs(build_graph_data(CG)) +``` + +This will plot graphs in CG with distinct and distinguishable colors. +See the documentation of the [build_graph_data](@ref) function for further details. \ No newline at end of file diff --git a/src/connectivity/datastruct.jl b/src/connectivity/datastruct.jl index fa04d1f..e0349a0 100644 --- a/src/connectivity/datastruct.jl +++ b/src/connectivity/datastruct.jl @@ -19,30 +19,4 @@ Base.@kwdef struct CriticalNodeConnections center::Vector{Int} = Int[] top::Vector{Int} = Int[] right::Vector{Int} = Int[] -end - -# Connectivity graph + control nodes -struct CurveGraph{T} - vertices::Vector{Tuple{T, T}} - edges::Vector{Tuple{Int, Int}} - control_nodes::Dict{Int, Vector{Int}} -end - -# ---------- PLOT ---------- - -struct EdgeGroup - edges::Vector{Tuple{Vector{Float64}, Vector{Float64}}} - color::String - width::Float64 -end - -struct PointGroup - vertices::Tuple{Vector{Float64}, Vector{Float64}} # (x, y) - color::String - marker::Symbol -end - -struct GraphPlotData - edge_group::EdgeGroup - point_groups::Vector{PointGroup} end \ No newline at end of file diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 75cbe48..6f37d18 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -1,10 +1,10 @@ """ distinguishable_colors(n; s=0.8, v=0.9) -Return `n` visually distinct HEX colors using manual HSV→RGB conversion. +Return `n` visually distinct HEX colors using manual HSV->RGB conversion. No external libraries used. """ -function distinguishable_colors(n::Int; s::Float64=0.8, v::Float64=0.9) +function distinguishable_colors(n::Int; s::Float64=0.6, v::Float64=0.9) n <= 0 && return String[] colors = Vector{String}(undef, n) @@ -45,18 +45,35 @@ end # ---------- CORE BUILDERS ---------- -""" -# How to plot: -using Plots -function plot_graph(P) - plot(legend=false) - E = P.edge_group - plot!(E.edges, color=E.color, width = E.width) - [scatter!(V.vertices, color=V.color, marker = V.marker) for V in P.point_groups] - gui() -end -plot_graph(build_graphs_data(G)) +@doc Markdown.doc""" + build_graph_data(G::CurveGraph{T}; width=3.0, vert=true, color="#FF0000") where T <: Union{Float64,QQFieldElem} + +Construct plotting data from a `CurveGraph`. + +This function converts the piecewise linear structure encoded in `G` into a +`GraphPlotData` object, separating edges and point groups (vertices and control points), +ready for visualization with plotting libraries such as `Plots.jl` (see documentation +of `GraphPlotData`) + +# Arguments +- `G::CurveGraph{T}`: Input graph containing vertices, control nodes, and edges. +- `width::Real=3.0`: Line width used for rendering edges. +- `vert::Bool=true`: If `true`, include vertices in the graph. +- `color::AbstractString="#FF0000"`: Color used for both edges and points. + +# Behavior +- Edges are converted into line segments between vertex coordinates. +- Vertices (if enabled) are displayed with marker `:x`. +- Control nodes are grouped and displayed with marker `:+`. + +# Returns +- `GraphPlotData`: A structure containing: + - one `EdgeGroup` for all edges + - multiple `PointGroup`s for vertices and control nodes + +# Notes +- All coordinates are converted to `Float64` for compatibility with plotting backends. """ function build_graph_data(G::CurveGraph{T}; width=3.0, vert=true, color="#FF0000") where T <: Union{Float64,QQFieldElem} @@ -90,24 +107,26 @@ function build_graph_data(G::CurveGraph{T}; width=3.0, vert=true, color="#FF0000 return GraphPlotData(edge_group, point_groups) end -# ---------- MULTI GRAPHS ---------- - """ -# How to plot: -using Plots -function plot_graphs(CP) - plot(legend=false) - for P in CP - E = P.edge_group - plot!(E.edges, color=E.color, width = E.width) - [ scatter!(V.vertices, color=V.color, marker = V.marker) for V in P.point_groups ] - end - gui() -end + build_graph_data(CG::Vector{CurveGraph{T}}; width=3.0, vert=true) where T <: Union{Float64,QQFieldElem} -plot_graphs(build_graph_data(CG)) -""" +Construct plotting data for multiple `CurveGraph`s with automatically assigned colors. + +# Arguments +- `CG::Vector{CurveGraph{T}}`: Collection of curve graphs to visualize. +- `width::Real=3.0`: Line width used for rendering edges. +- `vert::Bool=true`: If `true`, include vertices in each graph. +# Behavior +- Colors are generated using `distinguishable_colors` to ensure visual contrast. +- Each graph is assigned a unique color consistently across its edges and points. + +# Returns +- `Vector{GraphPlotData}`: One plotting data object per input graph. + +# Notes +- The number of colors scales with `length(CG)`. +""" function build_graph_data(CG::Vector{CurveGraph{T}}; width=3.0, vert=true) where T <: Union{Float64,QQFieldElem} c = distinguishable_colors(length(CG)) return [build_graph_data(G; width=width, vert=vert, color=c[i]) diff --git a/src/types.jl b/src/types.jl index 56f1c08..47cbb17 100644 --- a/src/types.jl +++ b/src/types.jl @@ -78,6 +78,8 @@ Base.getindex(I::Ideal, idx::Union{Int, UnitRange}) = I.gens[idx] Base.lastindex(I::Ideal) = lastindex(I.gens) +# ---------- ROADMAPS ---------- + mutable struct RMnode base_pt::Vector{QQFieldElem} polar_eqs::Vector{QQMPolyRingElem} @@ -119,4 +121,31 @@ end Base.show(io::IO, RM::Roadmap) = print(io, all_base_pts(RM)) Base.getindex(RM::Roadmap, idx::Union{Int, UnitRange}) = all_eqs(RM)[idx] Base.lastindex(RM::Roadmap) = nb_nodes(RM) -Base.length(RM::Roadmap) = nb_nodes(RM) \ No newline at end of file +Base.length(RM::Roadmap) = nb_nodes(RM) + +# ---------- CURVE CONNECTIVITY ---------- + +struct CurveGraph{T} + vertices::Vector{Tuple{T, T}} + edges::Vector{Tuple{Int, Int}} + control_nodes::Dict{Int, Vector{Int}} +end + +# ----- PLOT ---- + +struct EdgeGroup + edges::Vector{Tuple{Vector{Float64}, Vector{Float64}}} + color::String + width::Float64 +end + +struct PointGroup + vertices::Tuple{Vector{Float64}, Vector{Float64}} + color::String + marker::Symbol +end + +struct GraphPlotData + edge_group::EdgeGroup + point_groups::Vector{PointGroup} +end \ No newline at end of file From a21d3253e512c43f2425ba8ffb2d4985c7f62529 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Thu, 16 Apr 2026 18:32:54 +0200 Subject: [PATCH 167/180] more doc --- src/connectivity/connectcurves.jl | 6 ++--- src/connectivity/paramcrit.jl | 44 ++++++++++++++++++++----------- src/connectivity/tools.jl | 25 +++++++++++++++++- 3 files changed, 56 insertions(+), 19 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 171a432..6e39780 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -45,7 +45,7 @@ Returns a `CurveGraph{T}` object (where `T` is determined by the `outf` flag), c * **`generic`** (`Bool`, default `true`): If `false`, applies a random shear transformation to put the curve into generic position (preventing vertical alignments of critical points) and inverses it at the end. * **`precx`** (`Int`, default `150`): Base numerical precision used for the real root isolation of critical x-coordinates. * **`v`** (`Int`, default `0`): Verbosity level for tracking computational progress. -* **`int_coeff`** (`Bool`, default `true`): If `true`, coerces the polynomials to integer coefficients for optimized exact arithmetic. +* **`force_app`** (`Bool`, default `false`): If `true`, all nodes are considered apparent singularities and the detection step is skipped. This is useful when the original curve is known to have no nodes. * **`outf`** (`Bool`, default `true`): If `true`, outputs the vertex coordinates as machine `Float64`. If `false`, preserves exact rational coordinates (`QQFieldElem`). ### Examples @@ -90,7 +90,7 @@ compute_graph(f::P, g::P, C::Vector{P}; kwargs...) where {P <: MPolyRingElem} = # ========================================================================= function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; - generic=true, precx=150, v=0, detect_app=true, outf=true) where {P <: MPolyRingElem} + generic=true, precx=150, v=0, force_app=false, outf=true) where {P <: MPolyRingElem} @assert !iszero(f) "Input does not define a curve" @@ -120,7 +120,7 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; is_squarefree(f) "Curve not in generic position. Try with generic=false." v > 0 && println("Compute parametrization of critical pts...") - @iftime (v > 0) params = param_crit_split(f, g, v=v-1, detect_app=detect_app) + @iftime (v > 0) params = param_crit_split(f, g, v=v-1, force_app=force_app) for i in 1:length(C) params[-i] = [ [intC(C[i][1])], C[i][2], C[i][3] ] end diff --git a/src/connectivity/paramcrit.jl b/src/connectivity/paramcrit.jl index 4dbd643..22c077e 100644 --- a/src/connectivity/paramcrit.jl +++ b/src/connectivity/paramcrit.jl @@ -2,7 +2,7 @@ # SUBRESULTANTS # ========================================================================= -# Univariate resultant +# Univariate subresultants function subresultants(P::Union{PolyRingElem{T}, FqPolyRingElem}, Q::Union{PolyRingElem{T}, FqPolyRingElem}, is_Fq::Bool=false) where T <: RingElem degree(P) < degree(Q) && ((P, Q) = (Q, P)) @@ -59,7 +59,7 @@ function subresultants(P::Union{PolyRingElem{T}, FqPolyRingElem}, Q::Union{PolyR return reverse!(S) end -# Bivariate resultant +# Bivariate subresultants seen in (K[x])[y] function subresultants(P::MPolyRingElem, Q::MPolyRingElem, var_idx::Int; list=false) UP, UQ = to_univariate(P, var_idx), to_univariate(Q, var_idx) sr_uni = subresultants(UP, UQ) @@ -167,19 +167,30 @@ end # ========================================================================= -# delta : poly to factor w.r.t the factor of the polynomials in LP -function fact_gcd(delta::T, LP::Vector{T}) where T <: PolyRingElem +@doc Markdown.doc""" + fact_gcd(delta::T, LP::Vector{T}) where T <: Union{PolyRingElem, MPolyRingElem} + +Decomposes the polynomial `delta` by separating it into factors based on its greatest common divisors with the sequence of polynomials in `LP`. +The $i$-th entry corresponds to the exact factor of `delta` that divides $LP[1], \dots, LP[i-1]$, but is coprime to $LP[i]$. Factors of degree $0$ are discarded. +""" +function fact_gcd(delta::T, LP::Vector{T}) where {T <: PolyRingElem} Ldelta = Dict{Int, T}() - curr_phi = gcd(delta, LP[1]) - Ldelta[1] = divexact(delta, curr_phi) + curr_phi = delta - for i in 2:length(LP) + for (i, p) in pairs(LP) degree(curr_phi) == 0 && break - next_phi = gcd(curr_phi, LP[i]) - Ldelta[i] = divexact(curr_phi, next_phi) + + next_phi = gcd(curr_phi, p) + q = divexact(curr_phi, next_phi) + + if degree(q) > 0 + Ldelta[i] = q + end + curr_phi = next_phi end - return filter(kv -> degree(kv.second) > 0, Ldelta) + + return Ldelta end # wrapper for the above function @@ -189,18 +200,19 @@ function fact_gcd(delta::T, LP::Vector{T}) where (T <:MPolyRingElem) K, RS = coefficient_ring(R), symbols(R) A, = polynomial_ring(K, RS[1]) + # Convert to standard univariate ring d_uni = A(coefficients_of_univariate(delta)) LP_uni = [A(coefficients_of_univariate(p)) for p in LP] - out = fact_gcd(d_uni, LP_uni) - return Dict([ (i, change_ringvar(f, [first(RS)]) ) for (i,f) in out ]) + out = fact_gcd(d_uni, LP_uni) + return Dict(i => change_ringvar(f, [first(RS)]) for (i,f) in out) end # ========================================================================= """ - param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, detect_app=true) + param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, force_app=false) Computes the critical points (grouped by multiplicity) and apparent singularities of the space curve defined by: @@ -208,8 +220,10 @@ of the space curve defined by: This relies on subresultant computations and apparent singularity criterion from: A.Poteaux, N.Islam, R.PrĂ©bet - Algorithm for Connectivity Queries on Real Algebraic Curves - ISSAC'23 + +If force_app, it assumes that all nodes are apparent singularities. """ -function param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, detect_app=true) +function param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, force_app=false) v > 0 && println("Compute subresultant sequence") f_y = derivative(f, 2) @iftime v>0 sr = subresultants(f, f_y, 2, list=true) @@ -245,7 +259,7 @@ function param_crit_split(f::MPolyRingElem, g::MPolyRingElem; v=0, detect_app=tr # Nodes : multiplicity 2 in res if 2 in sqrmult - if detect_app + if !(force_app) v > 0 && println("Compute apparent singularities") f_x = derivative(f, 1) A = derivative(f_y, 2) * derivative(g, 1) - derivative(f_x, 2) * derivative(g, 2) diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index 0ab4b4b..b1bf7ff 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -1,3 +1,12 @@ +""" + order_permut2d(L) + +Return the indices that sort a 2D collection by its values. + +Given a nested array `L` (e.g. a matrix or vector of vectors), this function +flattens all entries, sorts them by value, and returns the corresponding +2D indices. +""" function order_permut2d(L) # Create a list of tuples with elements and their corresponding indices LL = [(L[i][j], (i, j)) for i in eachindex(L) for j in eachindex(L[i])] @@ -9,14 +18,28 @@ function order_permut2d(L) return sorted_ind end +""" + trimat_rand(A, n; up=true, range=-100:100) + +Generate a random triangular matrix over a given coefficient domain. +""" function trimat_rand(A, n; up=true, range=-100:100) if up return [ i==j ? one(A) : (ij ? A(rand(range)) : zero(A)) for i in 1:3, j in 1:3 ] + return [ i==j ? one(A) : (i>j ? A(rand(range)) : zero(A)) for i in 1:n, j in 1:n ] end end +""" + int_coeffs(F::Vector{P}) where P <: Union{QQMPolyRingElem, QQPolyRingElem} + int_coeffs(f::Union{QQMPolyRingElem, QQPolyRingElem}) + +Clear denominators of polynomial coefficients. + +This function rescales each polynomial so that all coefficients become integers +(by multiplying with the least common multiple of denominators). +""" function int_coeffs(F::Vector{P} where P <: Union{QQMPolyRingElem, QQPolyRingElem}) CD = [ iszero(f) ? f : lcm(map(denominator, collect(coefficients(f)))) for f in F ] return (F .* CD) From 21232a0f1bac13d7c46dfb3932dbcc975b91a3ed Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20P=2E?= Date: Thu, 16 Apr 2026 18:41:38 +0200 Subject: [PATCH 168/180] new function with the ideal --- src/connectivity/connectcurves.jl | 11 ++++++++--- 1 file changed, 8 insertions(+), 3 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 6e39780..5fd1180 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -65,6 +65,11 @@ julia> graph = compute_graph(f, g); julia> number_of_connected_components(graph) 3 """ +function compute_graph(I::Ideal{P} where P <: QQMPolyRingElem; generic=true, kwargs...) + p = rational_curve_parametrization(I, use_lfs = !generic) + return compute_graph(p.elim, p.param[1], kwargs...) +end + # Base case: No 'C' (control points) provided compute_graph(f::P, g::P; kwargs...) where {P <: MPolyRingElem} = _compute_graph_core(f, g, Vector{Vector{P}}(); kwargs...) @@ -90,7 +95,7 @@ compute_graph(f::P, g::P, C::Vector{P}; kwargs...) where {P <: MPolyRingElem} = # ========================================================================= function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; - generic=true, precx=150, v=0, force_app=false, outf=true) where {P <: MPolyRingElem} + plane_generic=true, precx=150, v=0, force_app=false, outf=true) where {P <: MPolyRingElem} @assert !iszero(f) "Input does not define a curve" @@ -108,7 +113,7 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; # Pre-processing the input f, g = int_coeffs([f, g]) - changemat = generic ? [1 0; 0 1] : [ QQ(rand(-100:100)) for i=1:2, j=1:2 ] + changemat = plane_generic ? [1 0; 0 1] : [ QQ(rand(-100:100)) for i=1:2, j=1:2 ] f = evaluate(f, collect(changemat * [x; y])) precx = max(2, precx) @@ -242,7 +247,7 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; end # Post processing the data - if !generic + if !plane_generic for i in eachindex(Vert) vx, vy = Vert[i] Vert[i] = Tuple(changemat * [vx, vy]) From 23725c364b232e926a7bda69e0adc1c448924010 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 17 Apr 2026 01:11:06 +0200 Subject: [PATCH 169/180] bug fixes + arbtools more robust --- src/connectivity/arbtools.jl | 24 ++++++++++++++++-------- src/connectivity/paramcrit.jl | 2 +- test/algorithms/curve-connectivity.jl | 5 +++++ 3 files changed, 22 insertions(+), 9 deletions(-) diff --git a/src/connectivity/arbtools.jl b/src/connectivity/arbtools.jl index 3d2ad1a..eb98a10 100644 --- a/src/connectivity/arbtools.jl +++ b/src/connectivity/arbtools.jl @@ -5,9 +5,13 @@ Return a rational interval enclosing the Arb ball. """ function arb_to_rat(x::ArbFieldElem) r = radius(x) - lo = x - 2r - hi = x + 2r - return [simplest_rational_inside(lo), simplest_rational_inside(hi)] + for i in 2:5 + lo = x - i*r + hi = x + i*r + I = map(simplest_rational_inside, [lo, hi]) + contains(rat_to_arb(I, parent(x)), x) && return I + end + error("Problem in boxes computations with Arb. Try increasing precision.") end @@ -19,11 +23,15 @@ Convert rational interval (x1, x2) to Arb ball. function rat_to_arb(interval::Vector{QQFieldElem}, field::ArbField) x1, x2 = interval @assert x1 <= x2 "Invalid interval: x1 > x2" - - mid = field((x1 + x2) / 2) - rad = field((x2 - x1) / 2) - - return ball(mid, rad) + new_field = field + for i in 2:5 + mid = field((x1 + x2) / 2) + rad = field((x2 - x1) / 2) + I = ball(mid, rad) + all(contains(I, x) for x in interval) && return I + new_field = ArbField(i * field.prec) + end + error("Problem in boxes computations with Arb. Try increasing precision.") end diff --git a/src/connectivity/paramcrit.jl b/src/connectivity/paramcrit.jl index 22c077e..268c67a 100644 --- a/src/connectivity/paramcrit.jl +++ b/src/connectivity/paramcrit.jl @@ -158,7 +158,7 @@ function intersect_biv(P::Vector, A::MPolyRingElem) # Rational reconstruction failed, try next prime end - dA_prev = dA_final + dA_prev = dA_current compt += 1 end diff --git a/test/algorithms/curve-connectivity.jl b/test/algorithms/curve-connectivity.jl index cd4a9b7..8700ffc 100644 --- a/test/algorithms/curve-connectivity.jl +++ b/test/algorithms/curve-connectivity.jl @@ -22,3 +22,8 @@ or # Non-generic because two crit-point above (but rat_cur_param works) x^4 - x^3 + 2*x^2*y^2 - 7//4*x^2 - x*y^2 + x + y^4 - 7//4*y^2 + 3//4 + +# Parametrization of a circle with z=0 but with two new generic variables +# bug in arb_to_rat fixed +f = 6829*x^2 - 1482*x*y + 9565*y^2 - 64770304, +g = -1110*x^2 + 11526*x*y + 2076384 \ No newline at end of file From fc56fa4c0eb91e3c29a6db01b131b1582f1f6365 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 17 Apr 2026 03:25:04 +0200 Subject: [PATCH 170/180] Finally get all graph functions --- src/connectivity/connectcurves.jl | 155 ++++++++++++++++++------------ src/connectivity/tools.jl | 9 ++ 2 files changed, 101 insertions(+), 63 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 5fd1180..4eb2936 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -5,7 +5,7 @@ export compute_graph, connected_components, number_of_connected_components, grou # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, rat_to_arb, evaluate_arb, evaluate_arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, - intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit, MPolyBuild, change_ringvar + intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit, MPolyBuild, change_ringvar, curve_graph, curve_ratparam_graph include("tools.jl") include("datastruct.jl") @@ -16,86 +16,127 @@ include("isolateboxes.jl") include("graph.jl") include("plots.jl") + # ========================================================================= # MULTIPLE DISPATCH WRAPPERS # ========================================================================= @doc Markdown.doc""" - compute_graph(f::P, g::P; generic=true, precx=150, v=0, int_coeff=true, outf=true) where {P <: MPolyRingElem} - compute_graph(f::P, g::P, C::Vector{P}; kwargs...) - compute_graph(f::P, g::P, C::Vector{Vector{P}}; kwargs...) - compute_graph(f::P, g::P, C::Dict{Int, Vector{P}}; kwargs...) + curve_graph(I::Ideal; generic=true, outf=true, kwargs...) + curve_ratparam_graph(P::RationalCurveParametrization; kwargs...) -Computes a planar straight-line graph that is homeomorphic to a 3D space curve. + # Both functions accept optional control points C in various formats: + curve_graph(I, C::Vector{P}; kwargs...) + curve_graph(I, C::Vector{Vector{P}}; kwargs...) + curve_graph(I, C::Dict{Int, Vector{P}}; kwargs...) -The input space curve is defined by a 1D parameterization consisting of its planar projection `f(x,y) = 0` and its vertical lift `z = g(x,y) / df/dy(x,y)`. A key feature of this function is its ability to identify and resolve "apparent singularities" in the planar projection—points where two non-singular branches of the 3D curve cross in the 2D projection but do not intersect in 3D space. This is describe in the paper: +Computes a planar straight-line graph that is homeomorphic to a real algebraic (space) curve. - A.Poteaux, N.Islam, R.PrĂ©bet - Algorithm for Connectivity Queries on Real Algebraic Curves - ISSAC'23 +### Core Workflow & Pre-processing +1. **Parametrization (`curve_graph` only):** If given an `Ideal`, it first computes a `RationalCurveParametrization`. + If `generic=false`, it applies a random integer shear transformation to place the curve into generic position. +2. **Coefficient Extraction:** Pulls the planar projection `f(x,y) = 0` and the vertical lift `z = g(x,y) / df/dy(x,y)` from the parametrization. +3. **Graph Construction:** Computes bounding boxes for critical points, routes connections, + and identifies "apparent singularities" (2D crossings that do not intersect in 3D). ### Output Data Structure Returns a `CurveGraph{T}` object (where `T` is determined by the `outf` flag), containing: -* `Vert::Vector{Tuple{T, T}}`: A list of 2D coordinates representing the vertices of the graph (critical points, structural routing nodes, and injected control points). -* `Edg::Vector{Tuple{Int, Int}}`: A list of index pairs defining the undirected edges between vertices in `Vert`. -* `Vcon::Dict{Int, Vector{Int}}`: A mapping from the original 1-based index of a control point in the input array `C` to its resulting vertex index in the `Vert` array. +* `Vert::Vector{Tuple{T, T}}`: 2D coordinates of the graph vertices (critical points, routing nodes, control points). +* `Edg::Vector{Tuple{Int, Int}}`: Index pairs defining undirected edges between `Vert` indices. +* `Vcon::Dict{Int, Vector{Int}}`: A mapping from the original index of a control point keys its vertex index in `Vert`. ### Arguments -* **`f`** (`MPolyRingElem`): The bivariate polynomial defining the planar projection `f(x,y) = 0` -* **`g`** (`MPolyRingElem`): The auxiliary polynomial defining the z-coordinate via `z = g / f_y`. -* **`C`** (`Vector{P}`, Vector{Vector{MPolyRingElem}}`, or `Dict{Int, Vector{P}}`, optionnal): A single/list/dictionnary of user-defined plane points on the curve (control points). Each point is given as a parameterization `[p, a, b]` such that `p(x) = 0` and `y = a(x)/b(x)`. -* **`generic`** (`Bool`, default `true`): If `false`, applies a random shear transformation to put the curve into generic position (preventing vertical alignments of critical points) and inverses it at the end. -* **`precx`** (`Int`, default `150`): Base numerical precision used for the real root isolation of critical x-coordinates. -* **`v`** (`Int`, default `0`): Verbosity level for tracking computational progress. -* **`force_app`** (`Bool`, default `false`): If `true`, all nodes are considered apparent singularities and the detection step is skipped. This is useful when the original curve is known to have no nodes. -* **`outf`** (`Bool`, default `true`): If `true`, outputs the vertex coordinates as machine `Float64`. If `false`, preserves exact rational coordinates (`QQFieldElem`). +* **`I`** (`Ideal`): The algebraic ideal defining the curve. +* **`P`** (`RationalCurveParametrization`): A pre-computed rational parametrization. +* **`C`** (Optional): User-defined plane points on the curve (control points). Given either as Ideal or RationalParametrization. +* **`generic`** (`Bool`, default `true`): If `false`, applies a random shear transformation. +* **`precx`** (`Int`, default `150`): Base numerical precision for real root isolation. +* **`v`** (`Int`, default `0`): Verbosity level. +* **`force_app`** (`Bool`, default `false`): Skips 3D intersection checks, treating all 2D nodes as apparent singularities. +* **`outf`** (`Bool`, default `true`): Output coordinates as `Float64`. If `false`, outputs exact `QQFieldElem`. +""" +function curve_graph(I::Ideal{P}, args...; generic=true, outf=true, v=0, kwargs...) where {P <: QQMPolyRingElem} + R = parent(I) + n = nvars(R) + typeout = outf ? Float64 : QQFieldElem -### Examples -```jldoctest -julia> using AlgebraicSolving + # Base Case: 1D Ideal (Points) + if n == 1 + sols = real_solutions(I) + Vert = [(typeout(xi[1]), zero(typeout)) for xi in sols] + # If C is a Dict, instantiate keys. If it's a Vector or absent, return empty Dict + C_keys = length(args) > 0 && args[1] isa Dict ? keys(args[1]) : Int[] + Vcon = Dict{Int, Vector{Int}}(k => Int[] for k in C_keys) + return CurveGraph{typeout}(Vert, Tuple{Int, Int}[], Vcon) + end -julia> R, (x,y) = polynomial_ring(QQ, ["x","y"]) -(Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x, y]) + # Pre-processing: Generic Position Shear + # We explicitly define linear forms if !generic to share them with C + v > 0 && println("Compute curve rational parametrization...") + lfs = nothing + if !generic + make_vec(i) = [j <= n ? ZZRingElem(rand(-100:100)) : (j == n+i ? one(ZZRingElem) : zero(ZZRingElem)) for j in 1:n+3] + lfs = make_vec.(1:3) + p_I = rational_curve_parametrization(I, cfs_lfs = lfs) + else + p_I = rational_curve_parametrization(I) + end + # 2. Process Control Ideals (C) if provided + if length(args) > 0 + C = args[1] + new_RS = symbols(parent(p_I.elim)) -julia> # Define a space curve projection and its z-lift - f = -49303382*x^4 + 9395599*x^3*y + 67366686*x^3 - 27407214*x^2*y^2 - 71298014*x^2*y - 24150320*x^2 - 12067817*x*y^3 + 6797370*x*y^2 + 20838420*x*y - 18118613*x + 2357706*y^4 - 13736522*y^3 - 37604516*y^2 - 13868221*y + 6980802; - g = 32091920*x^4 - 97772598*x^3*y - 245256584*x^3 + 99093410*x^2*y^2 + 162335273*x^2*y + 239310556*x^2 + 28995368*x*y^3 - 59544597*x*y^2 - 20499914*x*y + 98243402*x + 22738226*y^3 + 111105506*y^2 + 86287748*y - 62439535; + # Maps Ideal to the new ring and parameterize it with aligned linear forms + C_param = [ is_nothing(lfs) ? rational_parametrization(c) : param_use_lfs(c, lfs, new_RS) for c in C ] -julia> graph = compute_graph(f, g); + # Map C based on its input structure + if C_input isa AbstractDict + C_param = Dict(k => param_C(v) for (k, v) in C_input) + else + C_input isa AbstractVector || error("Control points C must be a Vector or Dict of Ideals.") + end -julia> number_of_connected_components(graph) -3 -""" -function compute_graph(I::Ideal{P} where P <: QQMPolyRingElem; generic=true, kwargs...) - p = rational_curve_parametrization(I, use_lfs = !generic) - return compute_graph(p.elim, p.param[1], kwargs...) + return curve_ratparam_graph(p_I, C_param; outf=outf, kwargs...) + end + + # Delegate to the parametrization function, blindly passing any `C` format down + return curve_ratparam_graph(p, args...; outf=outf, kwargs...) end -# Base case: No 'C' (control points) provided -compute_graph(f::P, g::P; kwargs...) where {P <: MPolyRingElem} = - _compute_graph_core(f, g, Vector{Vector{P}}(); kwargs...) +# ========================================================================= +# MULTIPLE DISPATCH WRAPPERS (INTERNAL) +# ========================================================================= + +# Case 1: No control points +curve_ratparam_graph(p::CurveRationalParametrization; kwargs...) = + _compute_graph_core(p.elim, length(p.param) > 0 ? p.param[end] : zero(parent(p.elim)), Vector{Vector{typeof(p.elim)}}(); kwargs...) + +# Case 2: C is a Vector of Parametrizations +curve_ratparam_graph(p::CurveRationalParametrization, C::Vector{RationalParametrization}; kwargs...) = + _compute_graph_core(p.elim, length(p.param) > 0 ? p.param[end] : zero(parent(p.elim)), + [ [c.elim, c.param[end], c.denom] for c in C]; kwargs...) -# Case 1: C is a Vector of Vectors -compute_graph(f::P, g::P, C::Vector{Vector{P}}; kwargs...) where {P <: MPolyRingElem} = - _compute_graph_core(f, g, C; kwargs...) +# Case 3: C is a Dictionary of Parametrizations (Remaps keys post-computation) +function curve_ratparam_graph(p::CurveRationalParametrization, C::Dict{Int, RationalParametrization}; kwargs...) + f = p.elim + g = length(p.param) > 0 ? p.param[end] : one(parent(f)) -# Case 2: C is a Dictionary -function compute_graph(f::P, g::P, C::Dict{Int, Vector{P}}; kwargs...) where {P <: MPolyRingElem} - graph = _compute_graph_core(f, g, collect(values(C)); kwargs...) - # Remap Vcon dictionary keys to match original dict keys + # Compute graph using the raw vector of parametrizations + pC = [ [c.elim, c.param[end], c.denom] for c in values(C)] + graph = _compute_graph_core(f, g, pC; kwargs...) + + # Remap Vcon dictionary keys to match the user's original dictionary mapped_vcon = Dict{Int, Vector{Int}}(k => graph.control_nodes[i] for (i, k) in enumerate(keys(C))) return CurveGraph(graph.vertices, graph.edges, mapped_vcon) end -# Case 3: C is a single Vector -compute_graph(f::P, g::P, C::Vector{P}; kwargs...) where {P <: MPolyRingElem} = - _compute_graph_core(f, g, [C]; kwargs...) - # ========================================================================= # CORE IMPLEMENTATION # ========================================================================= function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; - plane_generic=true, precx=150, v=0, force_app=false, outf=true) where {P <: MPolyRingElem} + precx=150, v=0, force_app=false, outf=true) where {P <: MPolyRingElem} @assert !iszero(f) "Input does not define a curve" @@ -113,11 +154,8 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; # Pre-processing the input f, g = int_coeffs([f, g]) - changemat = plane_generic ? [1 0; 0 1] : [ QQ(rand(-100:100)) for i=1:2, j=1:2 ] - - f = evaluate(f, collect(changemat * [x; y])) precx = max(2, precx) - v > 1 && println(f) + v > 1 && println("f = $f"); println("g = $g") # Zero-dim param conditions d = total_degree(f) @@ -135,7 +173,7 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; v > 0 && println("Compute intersections with critical boxes..") @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(f, params, LBcrit, Lprecx, v=v-1) - + return LBcrit, LPCside # Critical values and their order xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in keys(LBcrit)) xcritpermut = order_permut2d(xcrit) @@ -208,7 +246,6 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; end # 3. Below the critical point - # TODO: many vertices and edges could be removed here for k in 1:ymincrit-1 yval = sum(PCside.left.points[k] + PCside.right.points[k]) / 4 push!(Vert, (xcmid, yval)) @@ -246,14 +283,6 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; end end - # Post processing the data - if !plane_generic - for i in eachindex(Vert) - vx, vy = Vert[i] - Vert[i] = Tuple(changemat * [vx, vy]) - end - end - if outf Vert = [ (Float64(x), Float64(y)) for (x,y) in Vert ] end diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index b1bf7ff..1ebae1c 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -55,4 +55,13 @@ macro iftime(v, ex) $(esc(ex)) end end +end + + +function param_use_lfs(I::Ideal, cfs_lfs::Vector{Vector{T}} where T<: RingElem, new_RS::Symbol) + new_R = polynomial_ring(base_ring(I), new_RS) + new_gens = [change_ringvar(f, new_RS) for f in gens(I)] + I_new = Ideal(vcat(new_gens, [transpose(cfs_lf) * gens(new_R) for cfs_lf in cfs_lfs])) + + return rational_parametrization(I_new) end \ No newline at end of file From 3742fc352604c95f6cec81b1d1e18e328738bdba Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 17 Apr 2026 13:31:50 +0200 Subject: [PATCH 171/180] introduce arrangement curves (little bug) + several bug fixes --- src/connectivity/connectcurves.jl | 98 +++++++++++++++++++++---------- src/connectivity/paramcrit.jl | 25 ++++---- 2 files changed, 80 insertions(+), 43 deletions(-) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 4eb2936..acf3c89 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -5,7 +5,7 @@ export compute_graph, connected_components, number_of_connected_components, grou # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, rat_to_arb, evaluate_arb, evaluate_arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, - intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit, MPolyBuild, change_ringvar, curve_graph, curve_ratparam_graph + intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit, MPolyBuild, change_ringvar, curve_graph, curve_ratparam_graph, curve_arrangement_graph include("tools.jl") include("datastruct.jl") @@ -16,14 +16,57 @@ include("isolateboxes.jl") include("graph.jl") include("plots.jl") +@doc Markdown.doc""" + curve_arrangement_graph(curves::Vector{Ideal}; generic=true, outf=true, kwargs...) + curve_arrangement_graph(curves::Vector{Ideal}, C::Vector; kwargs...) -# ========================================================================= -# MULTIPLE DISPATCH WRAPPERS -# ========================================================================= +Computes the combined planar graph of an arrangement of multiple space curves. +Automatically computes the mutual intersections between all curves and guarantees +they are projected using a shared, unified linear form. +""" +function curve_arrangement_graph(curves::Vector{Ideal{P}}; generic=true, outf=true, kwargs...) where {P <: QQMPolyRingElem} + N = length(curves) + @assert N > 0 "Must provide at least one curve." + + R = parent(curves[1]) + n = nvars(R) + + # 1. Establish the Shared Projection Context + # We MUST generate the linear forms here and force all curves/intersections to use them. + lfs = nothing + if !generic + make_vec(i) = [j <= n ? ZZRingElem(rand(-100:100)) : (j == n+i ? one(ZZRingElem) : zero(ZZRingElem)) for j in 1:n+3] + lfs = make_vec.(1:3) + end + + # 3. Compute Intersections and Build Individual Graphs + graphs = Vector{CurveGraph}(undef, N) + p_inter = Dict{Set{Int}, RationalParametrization}() + for i in 1:N + p_I = lfs === nothing ? rational_curve_parametrization(curves[i]) : + rational_curve_parametrization(curves[i], cfs_lfs=lfs) + new_RS = symbols(parent(p_I.elim)) + + # Control pts are intersections with all other curves; use Dict to avoid re-computation + C_i = Dict{Int, RationalParametrization}( j => p_inter[Set((i,j))] for j in 1:i-1) + for j in i+1:N + I_ij = vcat(curves[i].gens, curves[j].gens) |> Ideal + C_i[j] = isnothing(lfs) ? rational_parametrization(I_ij) : param_use_lfs(I_ij, lfs, new_RS) + p_inter[Set((i,j))] = + RationalParametrization(C_i[j].vars, C_i[j].cfs_lf, C_i[j].elim, C_i[j].denom, C_i[j].param) + end + + graphs[i] = curve_graph(p_I, C_i; outf=outf, kwargs...) + graphs[i] = _compute_graph_core(p_I.elim, length(p_I.param) > 0 ? p_I.param[end] : zero(parent(p_I.elim)), C_i; kwargs...) + end + + # 4. Merge the graph according to their intersections + return merge_graphs(graphs...) +end @doc Markdown.doc""" curve_graph(I::Ideal; generic=true, outf=true, kwargs...) - curve_ratparam_graph(P::RationalCurveParametrization; kwargs...) + curve_graph(P::RationalCurveParametrization; kwargs...) # Both functions accept optional control points C in various formats: curve_graph(I, C::Vector{P}; kwargs...) @@ -33,7 +76,7 @@ include("plots.jl") Computes a planar straight-line graph that is homeomorphic to a real algebraic (space) curve. ### Core Workflow & Pre-processing -1. **Parametrization (`curve_graph` only):** If given an `Ideal`, it first computes a `RationalCurveParametrization`. +1. **Parametrization:** If given an `Ideal`, it first computes a `RationalCurveParametrization`. If `generic=false`, it applies a random integer shear transformation to place the curve into generic position. 2. **Coefficient Extraction:** Pulls the planar projection `f(x,y) = 0` and the vertical lift `z = g(x,y) / df/dy(x,y)` from the parametrization. 3. **Graph Construction:** Computes bounding boxes for critical points, routes connections, @@ -97,45 +140,38 @@ function curve_graph(I::Ideal{P}, args...; generic=true, outf=true, v=0, kwargs. C_input isa AbstractVector || error("Control points C must be a Vector or Dict of Ideals.") end - return curve_ratparam_graph(p_I, C_param; outf=outf, kwargs...) + return curve_graph(p_I, C_param; outf=outf, v=v, kwargs...) end # Delegate to the parametrization function, blindly passing any `C` format down - return curve_ratparam_graph(p, args...; outf=outf, kwargs...) + return curve_graph(p_I, args...; outf=outf, v=v, kwargs...) end # ========================================================================= # MULTIPLE DISPATCH WRAPPERS (INTERNAL) # ========================================================================= + + # Case 1: No control points -curve_ratparam_graph(p::CurveRationalParametrization; kwargs...) = - _compute_graph_core(p.elim, length(p.param) > 0 ? p.param[end] : zero(parent(p.elim)), Vector{Vector{typeof(p.elim)}}(); kwargs...) +curve_graph(p::RationalCurveParametrization; generic=true, kwargs...) = + _compute_graph_core(p.elim, length(p.param) > 0 ? p.param[end] : zero(parent(p.elim)), Dict{Int, Vector{typeof(p.elim)}}(); kwargs...) # Case 2: C is a Vector of Parametrizations -curve_ratparam_graph(p::CurveRationalParametrization, C::Vector{RationalParametrization}; kwargs...) = +curve_graph(p::RationalCurveParametrization, C::Vector{RationalParametrization}; generic=true, kwargs...) = _compute_graph_core(p.elim, length(p.param) > 0 ? p.param[end] : zero(parent(p.elim)), - [ [c.elim, c.param[end], c.denom] for c in C]; kwargs...) - -# Case 3: C is a Dictionary of Parametrizations (Remaps keys post-computation) -function curve_ratparam_graph(p::CurveRationalParametrization, C::Dict{Int, RationalParametrization}; kwargs...) - f = p.elim - g = length(p.param) > 0 ? p.param[end] : one(parent(f)) + Dict( i => [c.elim, c.param[end], c.denom] for (i,c) in enumerate(C)); kwargs...) - # Compute graph using the raw vector of parametrizations - pC = [ [c.elim, c.param[end], c.denom] for c in values(C)] - graph = _compute_graph_core(f, g, pC; kwargs...) - - # Remap Vcon dictionary keys to match the user's original dictionary - mapped_vcon = Dict{Int, Vector{Int}}(k => graph.control_nodes[i] for (i, k) in enumerate(keys(C))) - return CurveGraph(graph.vertices, graph.edges, mapped_vcon) -end +# Case 3: C is a Dictionary of Parametrizations +curve_graph(p::RationalCurveParametrization, C::Dict{Int, RationalParametrization}; generic=true, kwargs...) = + _compute_graph_core(p.elim, length(p.param) > 0 ? p.param[end] : zero(parent(p.elim)), + Dict( i => [c.elim, c.param[end], c.denom] for (i,c) in C); kwargs...) # ========================================================================= # CORE IMPLEMENTATION # ========================================================================= -function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; +function _compute_graph_core(f::P, g::P, C::Dict{Int, Vector{P}}; precx=150, v=0, force_app=false, outf=true) where {P <: MPolyRingElem} @assert !iszero(f) "Input does not define a curve" @@ -155,7 +191,7 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; # Pre-processing the input f, g = int_coeffs([f, g]) precx = max(2, precx) - v > 1 && println("f = $f"); println("g = $g") + v > 2 && println("f = $f \n g = $g") # Zero-dim param conditions d = total_degree(f) @@ -164,8 +200,8 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; v > 0 && println("Compute parametrization of critical pts...") @iftime (v > 0) params = param_crit_split(f, g, v=v-1, force_app=force_app) - for i in 1:length(C) - params[-i] = [ [intC(C[i][1])], C[i][2], C[i][3] ] + for (i, k) in enumerate(keys(C)) + params[-i] = [ [intC(C[k][1])], C[k][2], C[k][3] ] end v > 0 && println("Computing insulating critical boxes") @@ -173,7 +209,7 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; v > 0 && println("Compute intersections with critical boxes..") @iftime (v > 0) LPCside, LnPCside = intersect_vertical_boxes(f, params, LBcrit, Lprecx, v=v-1) - return LBcrit, LPCside + # Critical values and their order xcrit = Dict(i => [LBcrit[i][j][1] for j in eachindex(LBcrit[i])] for i in keys(LBcrit)) xcritpermut = order_permut2d(xcrit) @@ -269,7 +305,7 @@ function _compute_graph_core(f::P, g::P, C::Vector{Vector{P}}; for k in nI_right; push!(Edg, (length(Vert), Corr[i][j].right[k])); end if i < 0 # Control point - push!(Vcon[-i], length(Vert)) + push!(Vcon[keys(C)[-i]], length(Vert)) end end diff --git a/src/connectivity/paramcrit.jl b/src/connectivity/paramcrit.jl index 268c67a..043fda3 100644 --- a/src/connectivity/paramcrit.jl +++ b/src/connectivity/paramcrit.jl @@ -118,7 +118,9 @@ Uses a modular CRT loop. function intersect_biv(P::Vector, A::MPolyRingElem) iszero(A) && return P[1] - dA_prev, dA_final = Int[], Int[] + RSA = symbols(parent(A)) + dA_Q_prev, dA_Q_final = QQFieldElem[], QQFieldElem[] + dA_Z_curr = ZZRingElem[] pprod, p = ZZ(1), ZZ(1) << 60 compt = 0 @@ -127,7 +129,7 @@ function intersect_biv(P::Vector, A::MPolyRingElem) Fp = GF(p) # Prime check lcA, lcP = ZZ(leading_coefficient(A)), ZZ(leading_coefficient(P[1])) - divides(p, gcd(lcA, lcP))[1] && continue + iszero(rem(gcd(lcA, lcP), p)) && continue # Map polynomials natively to Fp Pp = [map_coefficients(Fp, poly) for poly in P] @@ -137,31 +139,30 @@ function intersect_biv(P::Vector, A::MPolyRingElem) dAp = gcd(Pp[1], Apev) # Lift coefficients back to integers for CRT - dA_current = [lift(ZZ, c) for c in coefficients(dAp)] + dA_Z_next = [lift(ZZ, c) for c in coefficients_of_univariate(dAp)] if compt > 0 - dA_current = [crt([d1, d2], [pprod, p]) for (d1, d2) in zip(dA_prev, dA_current)] + dA_Z_next = [crt([d1, d2], [pprod, p]) for (d1, d2) in zip(dA_Z_curr, dA_Z_next)] end # Trivial GCD : reduced gcd has larger degree # Then, A(x,y) does not vanish on the points defined by q(x)=0 - all(iszero(c) for c in dA_current[2:end]) && return one(parent(A)) + all(iszero(c) for c in dA_Z_next[2:end]) && return one(parent(A)) pprod *= p try - dA_final = [reconstruct(c, pprod) for c in dA_current] - if (compt > 0 && dA_final == dA_prev) - fact = MPolyBuild(dA_final, RSA, 1) - divides(fact, P[1])[1] && return fact + dA_Q_final = [reconstruct(c, pprod) for c in dA_Z_next] + if (compt > 0 && dA_Q_final == dA_Q_prev) + fact = MPolyBuild(dA_Q_final, RSA, 1) + divides(P[1], fact)[1] && return fact end catch - # Rational reconstruction failed, try next prime end - dA_prev = dA_current + dA_Z_curr = dA_Z_next + dA_Q_prev = dA_Q_final compt += 1 end - error("Failed multi-modular computation of apparent sing: $compt primes used") end From 840b3a289e4cb6e0fb3d244763115e5dd5200f2a Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 17 Apr 2026 17:51:18 +0200 Subject: [PATCH 172/180] several bug fixes --- src/connectivity/arbtools.jl | 16 ++++++----- src/connectivity/connectcurves.jl | 46 ++++++++++++++++++++----------- src/connectivity/tools.jl | 12 +++++--- 3 files changed, 47 insertions(+), 27 deletions(-) diff --git a/src/connectivity/arbtools.jl b/src/connectivity/arbtools.jl index eb98a10..d31d312 100644 --- a/src/connectivity/arbtools.jl +++ b/src/connectivity/arbtools.jl @@ -4,14 +4,16 @@ Return a rational interval enclosing the Arb ball. """ function arb_to_rat(x::ArbFieldElem) - r = radius(x) - for i in 2:5 - lo = x - i*r - hi = x + i*r + m, r = midpoint(x), 2*radius(x) + for _ in 2:10 + lo = m - r + hi = m + r + I = map(simplest_rational_inside, [lo, hi]) - contains(rat_to_arb(I, parent(x)), x) && return I + I[1] <= x <= I[2] && return I + r *= 10 end - error("Problem in boxes computations with Arb. Try increasing precision.") + error("Problem in boxes computations with Arb (arb_to_rat). Try increasing precision.") end @@ -31,7 +33,7 @@ function rat_to_arb(interval::Vector{QQFieldElem}, field::ArbField) all(contains(I, x) for x in interval) && return I new_field = ArbField(i * field.prec) end - error("Problem in boxes computations with Arb. Try increasing precision.") + error("Problem in boxes computations with Arb (rat_to_arb). Try increasing precision.") end diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index acf3c89..f5fab7e 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -5,7 +5,8 @@ export compute_graph, connected_components, number_of_connected_components, grou # DEBUG export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, rat_to_arb, evaluate_arb, evaluate_arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, - intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit, MPolyBuild, change_ringvar, curve_graph, curve_ratparam_graph, curve_arrangement_graph + intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit, MPolyBuild, change_ringvar, curve_graph, curve_ratparam_graph, + curve_arrangement_graph, arb_to_rat include("tools.jl") include("datastruct.jl") @@ -24,12 +25,14 @@ Computes the combined planar graph of an arrangement of multiple space curves. Automatically computes the mutual intersections between all curves and guarantees they are projected using a shared, unified linear form. """ -function curve_arrangement_graph(curves::Vector{Ideal{P}}; generic=true, outf=true, kwargs...) where {P <: QQMPolyRingElem} +function curve_arrangement_graph(curves::Vector{Ideal{P}}; generic=true, outf=true, v=0, kwargs...) where {P <: QQMPolyRingElem} N = length(curves) @assert N > 0 "Must provide at least one curve." R = parent(curves[1]) n = nvars(R) + typeout = outf ? Float64 : QQFieldElem + # 1. Establish the Shared Projection Context # We MUST generate the linear forms here and force all curves/intersections to use them. @@ -37,12 +40,14 @@ function curve_arrangement_graph(curves::Vector{Ideal{P}}; generic=true, outf=tr if !generic make_vec(i) = [j <= n ? ZZRingElem(rand(-100:100)) : (j == n+i ? one(ZZRingElem) : zero(ZZRingElem)) for j in 1:n+3] lfs = make_vec.(1:3) + u_lfs = lfs[2][1:end-3] # for zero-dim param of intersect pts end # 3. Compute Intersections and Build Individual Graphs - graphs = Vector{CurveGraph}(undef, N) + graphs = Vector{CurveGraph{typeout}}(undef, N) p_inter = Dict{Set{Int}, RationalParametrization}() for i in 1:N + v > 0 && println("Compute graph of curve number $i/$N...A,") p_I = lfs === nothing ? rational_curve_parametrization(curves[i]) : rational_curve_parametrization(curves[i], cfs_lfs=lfs) new_RS = symbols(parent(p_I.elim)) @@ -51,17 +56,17 @@ function curve_arrangement_graph(curves::Vector{Ideal{P}}; generic=true, outf=tr C_i = Dict{Int, RationalParametrization}( j => p_inter[Set((i,j))] for j in 1:i-1) for j in i+1:N I_ij = vcat(curves[i].gens, curves[j].gens) |> Ideal - C_i[j] = isnothing(lfs) ? rational_parametrization(I_ij) : param_use_lfs(I_ij, lfs, new_RS) + C_i[j] = isnothing(lfs) ? rational_parametrization(I_ij) : param_use_lfs(I_ij, u_lfs, new_RS[end-1]) p_inter[Set((i,j))] = RationalParametrization(C_i[j].vars, C_i[j].cfs_lf, C_i[j].elim, C_i[j].denom, C_i[j].param) end - - graphs[i] = curve_graph(p_I, C_i; outf=outf, kwargs...) - graphs[i] = _compute_graph_core(p_I.elim, length(p_I.param) > 0 ? p_I.param[end] : zero(parent(p_I.elim)), C_i; kwargs...) + @show C_i + @show graphs + graphs[i] = curve_graph(p_I, C_i; outf=outf, v=v-1, kwargs...) end # 4. Merge the graph according to their intersections - return merge_graphs(graphs...) + return merge_graphs(graphs) end @doc Markdown.doc""" @@ -120,6 +125,7 @@ function curve_graph(I::Ideal{P}, args...; generic=true, outf=true, v=0, kwargs. if !generic make_vec(i) = [j <= n ? ZZRingElem(rand(-100:100)) : (j == n+i ? one(ZZRingElem) : zero(ZZRingElem)) for j in 1:n+3] lfs = make_vec.(1:3) + u_lfs = lfs[2][1:end-3] # for zero-dim param of control pts p_I = rational_curve_parametrization(I, cfs_lfs = lfs) else p_I = rational_curve_parametrization(I) @@ -131,7 +137,7 @@ function curve_graph(I::Ideal{P}, args...; generic=true, outf=true, v=0, kwargs. new_RS = symbols(parent(p_I.elim)) # Maps Ideal to the new ring and parameterize it with aligned linear forms - C_param = [ is_nothing(lfs) ? rational_parametrization(c) : param_use_lfs(c, lfs, new_RS) for c in C ] + C_param = [ is_nothing(lfs) ? rational_parametrization(c) : param_use_lfs(c, u_lfs, new_RS[end-1]) for c in C ] # Map C based on its input structure if C_input isa AbstractDict @@ -151,21 +157,28 @@ end # MULTIPLE DISPATCH WRAPPERS (INTERNAL) # ========================================================================= +# Small helper +function prepare_param(P,Q) + R = parent(Q) + param = is_constant(P.elim) ? [P.elim,P.elim,P.elim] : [P.elim, P.param[end], P.denom] + return [ evaluate(p, gens(R)[1]) for p in param ] +end # Case 1: No control points curve_graph(p::RationalCurveParametrization; generic=true, kwargs...) = - _compute_graph_core(p.elim, length(p.param) > 0 ? p.param[end] : zero(parent(p.elim)), Dict{Int, Vector{typeof(p.elim)}}(); kwargs...) + _compute_graph_core(p.elim, length(p.param) > 0 ? p.param[end] : zero(parent(p.elim)), + Dict{Int, Vector{typeof(p.elim)}}(); kwargs...) # Case 2: C is a Vector of Parametrizations curve_graph(p::RationalCurveParametrization, C::Vector{RationalParametrization}; generic=true, kwargs...) = _compute_graph_core(p.elim, length(p.param) > 0 ? p.param[end] : zero(parent(p.elim)), - Dict( i => [c.elim, c.param[end], c.denom] for (i,c) in enumerate(C)); kwargs...) + Dict( i => prepare_param(c, p.elim) for (i,c) in enumerate(C)); kwargs...) # Case 3: C is a Dictionary of Parametrizations curve_graph(p::RationalCurveParametrization, C::Dict{Int, RationalParametrization}; generic=true, kwargs...) = _compute_graph_core(p.elim, length(p.param) > 0 ? p.param[end] : zero(parent(p.elim)), - Dict( i => [c.elim, c.param[end], c.denom] for (i,c) in C); kwargs...) + Dict( i => prepare_param(c, p.elim) for (i,c) in C); kwargs...) # ========================================================================= # CORE IMPLEMENTATION @@ -191,7 +204,7 @@ function _compute_graph_core(f::P, g::P, C::Dict{Int, Vector{P}}; # Pre-processing the input f, g = int_coeffs([f, g]) precx = max(2, precx) - v > 2 && println("f = $f \n g = $g") + v > 2 && println("f = $f \n g = $g\n $C") # Zero-dim param conditions d = total_degree(f) @@ -200,8 +213,9 @@ function _compute_graph_core(f::P, g::P, C::Dict{Int, Vector{P}}; v > 0 && println("Compute parametrization of critical pts...") @iftime (v > 0) params = param_crit_split(f, g, v=v-1, force_app=force_app) - for (i, k) in enumerate(keys(C)) - params[-i] = [ [intC(C[k][1])], C[k][2], C[k][3] ] + keys_C = collect(keys(C)) + for (i, k) in enumerate(keys_C) + params[-i] = [ [int_coeffs(C[k][1])], int_coeffs(C[k][2]), int_coeffs(C[k][3]) ] end v > 0 && println("Computing insulating critical boxes") @@ -305,7 +319,7 @@ function _compute_graph_core(f::P, g::P, C::Dict{Int, Vector{P}}; for k in nI_right; push!(Edg, (length(Vert), Corr[i][j].right[k])); end if i < 0 # Control point - push!(Vcon[keys(C)[-i]], length(Vert)) + push!(Vcon[keys_C[-i]], length(Vert)) end end diff --git a/src/connectivity/tools.jl b/src/connectivity/tools.jl index 1ebae1c..6ceb7ae 100644 --- a/src/connectivity/tools.jl +++ b/src/connectivity/tools.jl @@ -57,11 +57,15 @@ macro iftime(v, ex) end end +# We compute a zero-dim param of I w.r.t. a new generic variable v +# given by Sv (Symbol) and defined by the linear form in cfs_lf +function param_use_lfs(I::Ideal, cfs_lf::Vector{T} where T<: RingElem, Sv::Symbol) + R = parent(I) + new_RS = vcat(symbols(R), Sv) + _, new_V = polynomial_ring(base_ring(R), new_RS) -function param_use_lfs(I::Ideal, cfs_lfs::Vector{Vector{T}} where T<: RingElem, new_RS::Symbol) - new_R = polynomial_ring(base_ring(I), new_RS) - new_gens = [change_ringvar(f, new_RS) for f in gens(I)] - I_new = Ideal(vcat(new_gens, [transpose(cfs_lf) * gens(new_R) for cfs_lf in cfs_lfs])) + new_gens = [change_ringvar(f, new_RS) for f in I.gens] + I_new = Ideal(vcat(new_gens, [new_V[end] + transpose(cfs_lf) * new_V[1:end-1]])) return rational_parametrization(I_new) end \ No newline at end of file From beb2897215f59fb1541f07bc52d3729e832a4d87 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 17 Apr 2026 18:46:57 +0200 Subject: [PATCH 173/180] docs+ start tests --- docs/src/connectivity.md | 90 +++++++++++++++++++++++++++ src/connectivity/plots.jl | 1 - test/algorithms/curve-connectivity.jl | 39 +++--------- 3 files changed, 100 insertions(+), 30 deletions(-) diff --git a/docs/src/connectivity.md b/docs/src/connectivity.md index a932210..ea4f765 100644 --- a/docs/src/connectivity.md +++ b/docs/src/connectivity.md @@ -45,4 +45,94 @@ In addition, AlgebraicSolving can compute equations definition critical loci of dimproj = length(J)-1, only_mins = false ) where (P <: MPolyRingElem) +``` + +# Algorithms for connectivity queries on real algebraic curve + +## Introduction + +AlgebraicSolving allows to compute a graph whose associated (3D) piecewise linear curve is semi-algebraically homeomorphic to a real algebraic curve given as input. +This input can be: + * an `Ideal` given by generators over the rationals, whose real trace is the curve; + * a one-dimensionnal parametrization given as a `RationalCurveParametrization`. We refer to the `Types` page for such a structure. + +It is also possible to compute the arrangement of several curves by simply providing the corresponding vector of Ideals. + +In both cases, user can, in addition, provide control points that will be correctly identified in the final graph, from a topological point of view. + +The underlying engines are + * internal subresultants computations for paramtrization of critical points; + * `msolve` for univariate real root isolation. + +## Computing curve graphs + +```@docs + curve_graph( + I::Ideal{P}, args...; + generic=true, + outf=true, + v=0, + kwargs... + ) where {P <: QQMPolyRingElem} +``` + +```@docs + curve_arrangement_graph( + curves::Vector{Ideal{P}}; + generic=true, + outf=true, + v=0, + kwargs... + ) where (P <: MPolyRingElem) +``` + +## Computing with curve graphs + +Once such a graph is computed, it is encoded in a CurveGraph object, whose description can be found in the Types section of this documentation. +These are nothing but sets of verteices and nodes. +One can perform different operations on such strutures. + +```@docs + connected_components( + G::CurveGraph{T} + ) where T +``` + +```@docs + group_by_components( + G::CurveGraph{T} + ) +``` + +```@docs + number_of_connected_components( + G::CurveGraph{T} + ) +``` + +```@docs + merge_graphs( + graphs::Vector{CurveGraph{T}} + ) where T +``` + +## Displaying curve graph + +As e.g. Plots.jl is not part of AlgebraicSolving.jl, it cannot provide direct functions for plotting curve graphs. However, functions for exporting curve graphs in a format adapted to most ploting libraries, encoded in a `GraphPlotData` object. We refer to the Types section for more information on this structuree. + +```@docs + build_graph_data( + G::CurveGraph{T}; + width=3.0, + vert=true, + color="#FF0000" + ) where T <: Union{Float64,QQFieldElem} +``` + +```@docs + build_graph_data( + CG::Vector{CurveGraph{T}}; + width=3.0, + vert=true + ) where T <: Union{Float64,QQFieldElem} ``` \ No newline at end of file diff --git a/src/connectivity/plots.jl b/src/connectivity/plots.jl index 6f37d18..cec0ce7 100644 --- a/src/connectivity/plots.jl +++ b/src/connectivity/plots.jl @@ -75,7 +75,6 @@ of `GraphPlotData`) # Notes - All coordinates are converted to `Float64` for compatibility with plotting backends. """ - function build_graph_data(G::CurveGraph{T}; width=3.0, vert=true, color="#FF0000") where T <: Union{Float64,QQFieldElem} V, Vcon, E = G.vertices, G.control_nodes, G.edges diff --git a/test/algorithms/curve-connectivity.jl b/test/algorithms/curve-connectivity.jl index 8700ffc..ea1fcbe 100644 --- a/test/algorithms/curve-connectivity.jl +++ b/test/algorithms/curve-connectivity.jl @@ -1,29 +1,10 @@ - -# param2 -f = -49303382*x^4 + 9395599*x^3*y + 67366686*x^3 - 27407214*x^2*y^2 - 71298014*x^2*y - 24150320*x^2 - 12067817*x*y^3 + 6797370*x*y^2 + 20838420*x*y - 18118613*x + 2357706*y^4 - 13736522*y^3 - 37604516*y^2 - 13868221*y + 6980802 -g = 32091920*x^4 - 97772598*x^3*y - 245256584*x^3 + 99093410*x^2*y^2 + 162335273*x^2*y + 239310556*x^2 + 28995368*x*y^3 - 59544597*x*y^2 - 20499914*x*y + 98243402*x + 22738226*y^3 + 111105506*y^2 + 86287748*y - 62439535 - -# Not generic -f = y^2-x^2*(x+1) - -# Crunode (after generic change of variable) --2744*x^3 - 34692*x^2*y + 8085*x^2 - 146202*x*y^2 + 896*x*y - 205379*y^3 - 3285*y^2 - -# Acnode -157464*x^3 + 297432*x^2*y + 7012*x^2 + 187272*x*y^2 + 1496*x*y + 39304*y^3 + 1445*y^2 - -# Ordinary cusp -79507*x^3 + 543606*x^2*y + 9604*x^2 + 1238916*x*y^2 - 3528*x*y + 941192*y^3 + 324*y^2 - -# Rhamphoid cusp --3077056399*x^5 - 16359034020*x^4*y - 28398241*x^4 - 34788831840*x^3*y^2 + 9336408*x^3*y - 36990656640*x^2*y^3 - 1151064*x^2*y^2 + 5329*x^2 - 19665918720*x*y^4 + 63072*x*y^3 - 876*x*y - 4182119424*y^5 - 1296*y^4 + 36*y^2 -or --243*x^5 - 25515*x^4*y - 1071630*x^3*y^2 - 22504230*x^2*y^3 + 8464*x^2 - 236294415*x*y^4 + 18216*x*y - 992436543*y^5 + 9801*y^2 - -# Non-generic because two crit-point above (but rat_cur_param works) -x^4 - x^3 + 2*x^2*y^2 - 7//4*x^2 - x*y^2 + x + y^4 - 7//4*y^2 + 3//4 - -# Parametrization of a circle with z=0 but with two new generic variables -# bug in arb_to_rat fixed -f = 6829*x^2 - 1482*x*y + 9565*y^2 - 64770304, -g = -1110*x^2 + 11526*x*y + 2076384 \ No newline at end of file +@testset "Algorithms -> Curve Graph" begin + R, (x,y) = polynomial_ring(QQ, [:x,:y]) + + # param2 (generic) + f = -49303382*x^4 + 9395599*x^3*y + 67366686*x^3 - 27407214*x^2*y^2 - 71298014*x^2*y - 24150320*x^2 - 12067817*x*y^3 + 6797370*x*y^2 + 20838420*x*y - 18118613*x + 2357706*y^4 - 13736522*y^3 - 37604516*y^2 - 13868221*y + 6980802 + g = 32091920*x^4 - 97772598*x^3*y - 245256584*x^3 + 99093410*x^2*y^2 + 162335273*x^2*y + 239310556*x^2 + 28995368*x*y^3 - 59544597*x*y^2 - 20499914*x*y + 98243402*x + 22738226*y^3 + 111105506*y^2 + 86287748*y - 62439535 + P = AlgebraicSolving.RationalCurveParametrization([:z,:x,:y], Vector{Vector{ZZRingElem}}(), f, derivative(f, 2), [g]) + G = curve_graph(P) + @test number_of_connected_components(G) == 3 +end \ No newline at end of file From f1e13892b1932b1bf8e9e6cb8c1a5b36db84d140 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Fri, 17 Apr 2026 19:03:40 +0200 Subject: [PATCH 174/180] clean and add inclusion --- src/AlgebraicSolving.jl | 5 +++++ src/connectivity/connectcurves.jl | 11 ++--------- src/exports.jl | 4 +++- test/runtests.jl | 3 ++- 4 files changed, 12 insertions(+), 11 deletions(-) diff --git a/src/AlgebraicSolving.jl b/src/AlgebraicSolving.jl index f48e3d3..2c7802f 100644 --- a/src/AlgebraicSolving.jl +++ b/src/AlgebraicSolving.jl @@ -22,8 +22,13 @@ include("siggb/siggb.jl") include("progress/main.jl") #= interp =# include("interp/main.jl") +#= connectivity =# +include("connectivity/connectcurves.jl") +include("connectivity/graph.jl") +include("connectivity/plots.jl") #= examples =# include("examples/katsura.jl") include("examples/cyclic.jl") + end # module AlgebraicSolving diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index f5fab7e..6c0360c 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -1,14 +1,7 @@ -export compute_graph, connected_components, number_of_connected_components, group_by_component, merge_graphs, - plot_graph, plot_graphs, plot_graph_comp, Bresultant, param_crit_split, build_graphs_data, build_graph_data +export connected_components, number_of_connected_components, group_by_component, merge_graphs, build_graph_data,curve_graph,curve_arrangement_graph - # DEBUG - export interp_subresultants, mmod_subresultants, subresultants, diff, diff_list, trimat_rand, fact_gcd, isolate_eval, isolate, - rat_to_arb, evaluate_arb, evaluate_arb_rat, int_coeffs, array_to_poly, parray_asvar, poly_to_array, homogenize, rem_var, - intersect_biv, num_biv_rat_mod, parray_asvarcoeff, mmod_param_crit, MPolyBuild, change_ringvar, curve_graph, curve_ratparam_graph, - curve_arrangement_graph, arb_to_rat - -include("tools.jl") + include("tools.jl") include("datastruct.jl") include("buildpoly.jl") include("paramcrit.jl") diff --git a/src/exports.jl b/src/exports.jl index f1d3afa..3ac8301 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -6,4 +6,6 @@ export polynomial_ring, MPolyRing, GFElem, MPolyRingElem, equidimensional_decomposition, homogenize, dimension, FqMPolyRingElem, hilbert_series, hilbert_dimension, hilbert_degree, hilbert_polynomial, rational_curve_parametrization, roadmap, computepolar, all_eqs, - all_base_pts, nb_nodes, subresultants, change_ringvar \ No newline at end of file + all_base_pts, nb_nodes, connected_components, number_of_connected_components, + group_by_component, merge_graphs, build_graph_data,curve_graph, + curve_arrangement_graph \ No newline at end of file diff --git a/test/runtests.jl b/test/runtests.jl index f6cda36..ec44662 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -11,8 +11,9 @@ include("algorithms/hilbert.jl") include("algorithms/decomposition.jl") include("algorithms/param-curves.jl") include("examples/katsura.jl") -include("interp/thiele.jl") +include("interp/thiele.jl") include("interp/newton.jl") include("interp/cuyt_lee.jl") include("interp/resultant.jl") +include("algorithms/curve-connectivity.jl") end From 2f5b4359e47c93d530fa52747003eaa3a143e587 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 20 Apr 2026 14:49:13 +0200 Subject: [PATCH 175/180] fix dependancies --- Project.toml | 13 ++++++++----- 1 file changed, 8 insertions(+), 5 deletions(-) diff --git a/Project.toml b/Project.toml index 764a2c4..fac42ed 100644 --- a/Project.toml +++ b/Project.toml @@ -1,7 +1,7 @@ name = "AlgebraicSolving" uuid = "66b61cbe-0446-4d5d-9090-1ff510639f9d" -version = "0.10.4" authors = ["ederc ", "Mohab Safey El Din ", "RĂ©mi Prebet "] +version = "0.10.4" [deps] Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b" @@ -9,25 +9,28 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" -Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" -Primes = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae" Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" REPL = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" msolve_jll = "6d01cc9a-e8f6-580e-8c54-544227e08205" +[extras] +Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" + +[targets] +test = ["Test"] + [compat] Distributed = "1.6" LinearAlgebra = "1.6" Logging = "1.6" Markdown = "1.6" Nemo = "0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.50, 0.51, 0.52, 0.53, 0.54" -Plots = "1.41.0" Printf = "1.6" Random = "1.6" REPL = "1.6" StaticArrays = "1" Test = "1.6" julia = "1.10" -msolve_jll = "0.900.502" +msolve_jll = "0.900.502" \ No newline at end of file From a0ed6077a08b2a853454fe593faf1a1d4f1ccb83 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 20 Apr 2026 14:54:38 +0200 Subject: [PATCH 176/180] change test location --- test/{algorithms => connectivity}/curve-connectivity.jl | 0 test/runtests.jl | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) rename test/{algorithms => connectivity}/curve-connectivity.jl (100%) diff --git a/test/algorithms/curve-connectivity.jl b/test/connectivity/curve-connectivity.jl similarity index 100% rename from test/algorithms/curve-connectivity.jl rename to test/connectivity/curve-connectivity.jl diff --git a/test/runtests.jl b/test/runtests.jl index ec44662..c1c4b78 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -15,5 +15,5 @@ include("interp/thiele.jl") include("interp/newton.jl") include("interp/cuyt_lee.jl") include("interp/resultant.jl") -include("algorithms/curve-connectivity.jl") +include("connectivity/curve-connectivity.jl") end From 5eacc92057852e8c20cc35090a77a060c67be650 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 20 Apr 2026 15:23:44 +0200 Subject: [PATCH 177/180] remove dependancies --- src/imports.jl | 5 +---- 1 file changed, 1 insertion(+), 4 deletions(-) diff --git a/src/imports.jl b/src/imports.jl index c2af46b..632b29a 100644 --- a/src/imports.jl +++ b/src/imports.jl @@ -3,11 +3,8 @@ using msolve_jll using Nemo using LinearAlgebra using StaticArrays -using Plots, Colors -#pythonplot() -import Plots: plot -import Random: MersenneTwister, randperm +import Random: MersenneTwister import Logging: ConsoleLogger, with_logger, Warn, Info import Printf: @sprintf, @printf import Distributed: AbstractWorkerPool, remotecall_fetch From 5e5a612eb7fdcbadd2335524d8ae0bd11c606f65 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 20 Apr 2026 15:23:53 +0200 Subject: [PATCH 178/180] update doc --- src/connectivity/connectcurves.jl | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 6c0360c..57cd9a6 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -95,6 +95,23 @@ Returns a `CurveGraph{T}` object (where `T` is determined by the `outf` flag), c * **`v`** (`Int`, default `0`): Verbosity level. * **`force_app`** (`Bool`, default `false`): Skips 3D intersection checks, treating all 2D nodes as apparent singularities. * **`outf`** (`Bool`, default `true`): Output coordinates as `Float64`. If `false`, outputs exact `QQFieldElem`. + +### Example +```jldoctest +julia> using AlgebraicSolving + +julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]); + +julia> f = -42*x^2 + 101*x*y - 8*x*z - 88*x + 53*y^2 + 71*y*z + 154*y + 53*z^2 + 2*z - 32; + g = -7*x^2 - 144*x*y - 126*x*z - 7*x + 30*y^2 - 34*y*z + 72*y + 71*z^2 + 46*z + 5; + +julia> I = Ideal([f, g]); + +julia> G = curve_graph(I); + +julia> number_of_connected_components(G) +3 +``` """ function curve_graph(I::Ideal{P}, args...; generic=true, outf=true, v=0, kwargs...) where {P <: QQMPolyRingElem} R = parent(I) From d1831efb785391dd14e218e34c1d505b87727775 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 20 Apr 2026 15:25:25 +0200 Subject: [PATCH 179/180] remove manifest.toml --- Manifest.toml | 1245 ------------------------------------------------- 1 file changed, 1245 deletions(-) delete mode 100644 Manifest.toml diff --git a/Manifest.toml b/Manifest.toml deleted file mode 100644 index 43a90bf..0000000 --- a/Manifest.toml +++ /dev/null @@ -1,1245 +0,0 @@ -# This file is machine-generated - 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-[[deps.xkbcommon_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] -git-tree-sha1 = "a1fc6507a40bf504527d0d4067d718f8e179b2b8" -uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" -version = "1.13.0+0" From 946f5813f4c4a93941b5f797fbbefcbb51ecb557 Mon Sep 17 00:00:00 2001 From: Remi Prebet Date: Mon, 20 Apr 2026 15:52:29 +0200 Subject: [PATCH 180/180] fix doc and multiple inclusion --- docs/src/connectivity.md | 8 ++++---- src/AlgebraicSolving.jl | 2 -- src/connectivity/connectcurves.jl | 5 +---- src/connectivity/graph.jl | 4 ++-- test/connectivity/curve-connectivity.jl | 3 ++- 5 files changed, 9 insertions(+), 13 deletions(-) diff --git a/docs/src/connectivity.md b/docs/src/connectivity.md index ea4f765..b6b20fc 100644 --- a/docs/src/connectivity.md +++ b/docs/src/connectivity.md @@ -100,20 +100,20 @@ One can perform different operations on such strutures. ```@docs group_by_components( - G::CurveGraph{T} + G::CurveGraph ) ``` ```@docs number_of_connected_components( - G::CurveGraph{T} + G::CurveGraph ) ``` ```@docs merge_graphs( - graphs::Vector{CurveGraph{T}} - ) where T + graphs::Vector{CurveGraph} + ) ``` ## Displaying curve graph diff --git a/src/AlgebraicSolving.jl b/src/AlgebraicSolving.jl index 2c7802f..50ac27c 100644 --- a/src/AlgebraicSolving.jl +++ b/src/AlgebraicSolving.jl @@ -24,8 +24,6 @@ include("progress/main.jl") include("interp/main.jl") #= connectivity =# include("connectivity/connectcurves.jl") -include("connectivity/graph.jl") -include("connectivity/plots.jl") #= examples =# include("examples/katsura.jl") include("examples/cyclic.jl") diff --git a/src/connectivity/connectcurves.jl b/src/connectivity/connectcurves.jl index 57cd9a6..82ca459 100644 --- a/src/connectivity/connectcurves.jl +++ b/src/connectivity/connectcurves.jl @@ -1,7 +1,4 @@ - -export connected_components, number_of_connected_components, group_by_component, merge_graphs, build_graph_data,curve_graph,curve_arrangement_graph - - include("tools.jl") +include("tools.jl") include("datastruct.jl") include("buildpoly.jl") include("paramcrit.jl") diff --git a/src/connectivity/graph.jl b/src/connectivity/graph.jl index afddb06..1505beb 100644 --- a/src/connectivity/graph.jl +++ b/src/connectivity/graph.jl @@ -107,7 +107,7 @@ This is primarily used to determine which external connections (or user-defined belong to which isolated branch of the curve. # Inputs -- `G::CurveGraph{T}`: The parent graph structure. +- `G::CurveGraph`: The parent graph structure. # Outputs - `Vector{Dict{Int, Vector{Int}}}`: A list of dictionaries, one for each connected component, @@ -126,7 +126,7 @@ Computes the total number of topologically disconnected branches/components in t This is a convenience wrapper for topological validation. # Inputs -- `G::CurveGraph{T}`: The parent graph structure. +- `G::CurveGraph`: The parent graph structure. # Outputs - `Int`: The count of isolated subgraphs. diff --git a/test/connectivity/curve-connectivity.jl b/test/connectivity/curve-connectivity.jl index ea1fcbe..edfb610 100644 --- a/test/connectivity/curve-connectivity.jl +++ b/test/connectivity/curve-connectivity.jl @@ -3,8 +3,9 @@ # param2 (generic) f = -49303382*x^4 + 9395599*x^3*y + 67366686*x^3 - 27407214*x^2*y^2 - 71298014*x^2*y - 24150320*x^2 - 12067817*x*y^3 + 6797370*x*y^2 + 20838420*x*y - 18118613*x + 2357706*y^4 - 13736522*y^3 - 37604516*y^2 - 13868221*y + 6980802 + df = 9395599*x^3 - 54814428*x^2*y - 71298014*x^2 - 36203451*x*y^2 + 13594740*x*y + 20838420*x + 9430824*y^3 - 41209566*y^2 - 75209032*y - 13868221 g = 32091920*x^4 - 97772598*x^3*y - 245256584*x^3 + 99093410*x^2*y^2 + 162335273*x^2*y + 239310556*x^2 + 28995368*x*y^3 - 59544597*x*y^2 - 20499914*x*y + 98243402*x + 22738226*y^3 + 111105506*y^2 + 86287748*y - 62439535 - P = AlgebraicSolving.RationalCurveParametrization([:z,:x,:y], Vector{Vector{ZZRingElem}}(), f, derivative(f, 2), [g]) + P = AlgebraicSolving.RationalCurveParametrization([:z,:x,:y], Vector{Vector{ZZRingElem}}(), f, df, [g]) G = curve_graph(P) @test number_of_connected_components(G) == 3 end \ No newline at end of file

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