From 175c8b9e7a970e0141e8957df4a1fc019e1ae856 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?R=C3=A9mi=20P=2E?= <remi.prebet@ens-lyon.fr>
Date: Tue, 17 Jun 2025 15:02:46 +0200
Subject: [PATCH] Dimension and Hilbert: handle zero ideal

---
 src/algorithms/dimension.jl  |  6 ++----
 src/algorithms/hilbert.jl    | 11 ++++-------
 test/algorithms/dimension.jl |  4 ++++
 test/algorithms/hilbert.jl   |  9 +++++++++
 4 files changed, 19 insertions(+), 11 deletions(-)

diff --git a/src/algorithms/dimension.jl b/src/algorithms/dimension.jl
index 89ade19..c17e522 100644
--- a/src/algorithms/dimension.jl
+++ b/src/algorithms/dimension.jl
@@ -26,10 +26,7 @@ function dimension(I::Ideal{T}) where T <: MPolyRingElem
     R = parent(first(gb))
 
     res = Set([trues(ngens(R))])
-    lead_exps = Vector{Vector{Int}}(undef, length(gb))
-    for i in eachindex(gb)
-        lead_exps[i] = _lead_exp_ord(gb[i], :degrevlex)
-    end
+    lead_exps = [ _lead_exp_ord(g, :degrevlex) for g in gb if !iszero(g) ]
     for lexp in lead_exps
         nz_exps = (!iszero).(lexp)
         nz_exps_ind = findall(nz_exps)
@@ -62,6 +59,7 @@ function _all_lesseq(a::BitVector, b::BitVector)::Bool
 end
 
 function _lead_exp_ord(p::MPolyRingElem, order::Symbol)
+    @req !iszero(p) "Zero polynomial does not have a leading term"
     R = parent(p)
     internal_ordering(R)==order && return first(exponent_vectors(p))
 
diff --git a/src/algorithms/hilbert.jl b/src/algorithms/hilbert.jl
index 2ff270c..a42103e 100644
--- a/src/algorithms/hilbert.jl
+++ b/src/algorithms/hilbert.jl
@@ -27,11 +27,8 @@ function hilbert_series(I::Ideal{T}) where T <: MPolyRingElem
     gb = get!(I.gb, 0) do
         groebner_basis(I, complete_reduction = true)
     end
-    lead_exps = Vector{Vector{Int}}(undef, length(gb))
-    for i in eachindex(gb)
-        lead_exps[i] = _lead_exp_ord(gb[i], :degrevlex)
-    end
-    return _hilbert_series_mono(lead_exps)
+    lead_exps = [ _lead_exp_ord(g, :degrevlex) for g in gb if !iszero(g) ]
+    return _hilbert_series_mono(lead_exps, nvars(parent(I)))
 end
 
 @doc Markdown.doc"""
@@ -134,11 +131,11 @@ function hilbert_polynomial(I::Ideal{T}) where T <: MPolyRingElem
 end
 
 # Computes hilbert series of a monomial ideal on input list of exponents
-function _hilbert_series_mono(exps::Vector{Vector{Int}})
+function _hilbert_series_mono(exps::Vector{Vector{Int}}, nr_vars::Int)
 
     h = _num_hilbert_series_mono(exps)
     t = gen(parent(h))
-    return h//(1-t)^length(first(exps))
+    return h//(1-t)^nr_vars
 end
 
 # Computes numerator hilbert series of a monomial ideal on input list of exponents
diff --git a/test/algorithms/dimension.jl b/test/algorithms/dimension.jl
index 8fd8458..dc836a4 100644
--- a/test/algorithms/dimension.jl
+++ b/test/algorithms/dimension.jl
@@ -9,6 +9,10 @@
     @test iszero(dimension(I))
     @test iszero(I.dim)
 
+    I = Ideal([R(0)])
+    @test dimension(I) == ngens(R)
+    @test I.dim == ngens(R)
+
     I = Ideal([R(1)])
     @test dimension(I) == -1
     @test I.dim == -1
diff --git a/test/algorithms/hilbert.jl b/test/algorithms/hilbert.jl
index 361e92e..80fedb5 100644
--- a/test/algorithms/hilbert.jl
+++ b/test/algorithms/hilbert.jl
@@ -21,6 +21,15 @@
     @test iszero(hilbert_dimension(I))
     @test 4 == hilbert_degree(I)
 
+    I = Ideal([R(0)])
+    HS = 1//(1-t)^(nvars(R))
+    HP = (1//6*s^3 + s^2 + 11//6*s + 1, 0)
+
+    @test HS == hilbert_series(I)
+    @test HP == hilbert_polynomial(I)
+    @test nvars(R) == hilbert_dimension(I)
+    @test isone(hilbert_degree(I))
+
     I = Ideal([R(1)])
     @test iszero(hilbert_series(I))
     @test all(iszero, hilbert_polynomial(I))