Gröbner basis + elimination order = miscellaneous error (macOS-only)

[wegank]

The following example

using AlgebraicSolving
using Nemo

R = @polynomial_ring(QQ, [:x1, :x2, :x3])

f = [
    x1 + x2 + x3,
    x1 + 2 * x2 + 3 * x3,
    x1 + 3 * x2 + 4 * x3
]

gb = groebner_basis(AlgebraicSolving.Ideal(f), eliminate=2)
println(gb)

fails with high probability on macOS, with an unexpected result

$ julia src/julia/misc/bug2.jl
QQMPolyRingElem[0]

or a SIGTRAP with the following message:

$ julia src/julia/misc/bug2.jl

[93004] signal 4 (1): Illegal instruction: 4
in expression starting at /Users/weijiawang/Projects/phd/src/julia/misc/bug2.jl:13
_xzm_xzone_malloc_freelist_outlined at /usr/lib/system/libsystem_malloc.dylib (unknown line)
_Znwm at /usr/lib/libc++abi.dylib (unknown line)
_ZN4llvm11PassBuilder24registerFunctionAnalysesERNS_15AnalysisManagerINS_8FunctionEJEEE at /Users/weijiawang/.julia/juliaup/julia-1.12.2+0.aarch64.apple.darwin14/lib/julia/libLLVM.dylib (unknown line)
run at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/pipeline.cpp:735
operator() at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/jitlayers.cpp:1459 [inlined]
withModuleDo<(lambda at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/jitlayers.cpp:1420:30)> at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/usr/include/llvm/ExecutionEngine/Orc/ThreadSafeModule.h:136 [inlined]
operator() at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/jitlayers.cpp:1420
operator() at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/jitlayers.cpp:1572 [inlined]
addModule at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/jitlayers.cpp:2031
jl_compile_codeinst_now at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/jitlayers.cpp:626
jl_compile_codeinst_impl at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/jitlayers.cpp:824
jl_compile_method_internal at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/gf.c:3524
_jl_invoke at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/gf.c:4002 [inlined]
ijl_apply_generic at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/gf.c:4210
run_finalizer at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/gc-common.c:180
jl_gc_run_finalizers_in_list at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/gc-common.c:270
run_finalizers at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/gc-common.c:316
finish_nocycle at ./../usr/share/julia/Compiler/src/typeinfer.jl:210
jfptr_finish_nocycle_79329.1 at /Users/weijiawang/.julia/juliaup/julia-1.12.2+0.aarch64.apple.darwin14/lib/julia/sys.dylib (unknown line)
typeinf at ./../usr/share/julia/Compiler/src/abstractinterpretation.jl:4508
typeinf_ext at ./../usr/share/julia/Compiler/src/typeinfer.jl:1252
typeinf_ext_toplevel at ./../usr/share/julia/Compiler/src/typeinfer.jl:1435 [inlined]
typeinf_ext_toplevel at ./../usr/share/julia/Compiler/src/typeinfer.jl:1444
jfptr_typeinf_ext_toplevel_81477.1 at /Users/weijiawang/.julia/juliaup/julia-1.12.2+0.aarch64.apple.darwin14/lib/julia/sys.dylib (unknown line)
jl_apply at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/./julia.h:2391 [inlined]
jl_type_infer at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/gf.c:462
jl_compile_method_internal at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/gf.c:3512
_jl_invoke at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/gf.c:4002 [inlined]
ijl_apply_generic at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/gf.c:4210
jl_apply at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/./julia.h:2391 [inlined]
do_call at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/interpreter.c:123
eval_stmt_value at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/interpreter.c:194
eval_body at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/interpreter.c:689
jl_interpret_toplevel_thunk at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/interpreter.c:898
jl_toplevel_eval_flex at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/toplevel.c:1035
jl_toplevel_eval_flex at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/toplevel.c:975
ijl_toplevel_eval at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/toplevel.c:1047 [inlined]
ijl_toplevel_eval_in at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/toplevel.c:1092
eval at ./boot.jl:489
include_string at ./loading.jl:2867
_include at ./loading.jl:2927
include at ./Base.jl:306
exec_options at ./client.jl:317
_start at ./client.jl:550
jfptr__start_55675.1 at /Users/weijiawang/.julia/juliaup/julia-1.12.2+0.aarch64.apple.darwin14/lib/julia/sys.dylib (unknown line)
jl_apply at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/./julia.h:2391 [inlined]
true_main at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/jlapi.c:971
jl_repl_entrypoint at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-XC9YQX9HH2.0/build/default-honeycrisp-XC9YQX9HH2-0/julialang/julia-release-1-dot-12/src/jlapi.c:1139
Allocations: 3105716 (Pool: 3105657; Big: 59); GC: 4

I suspect the problem lies with Julia or LLVM rather than AlgebraicSolving.jl, but let me know if you think so too; I'll transfer the issue to Julia just in case.

[ederc]

Fixed via #116.