Dimension and Hilbert: handle zero ideal

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))
 

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

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

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))