Add hilbert_series

deps/src/ideals.cpp

@@ -677,6 +677,22 @@ void singular_define_ideals(jlcxx::Module & Singular)
  delete v;
  rChangeCurrRing(origin);
  });
+ Singular.method("scHilbPoly", [](ideal I, ring r, ring Qt) {
+ const ring origin = currRing;
+ rChangeCurrRing(r);
+ poly h=hFirstSeries0p(I,r->qideal,NULL,r,Qt);
+ rChangeCurrRing(origin);
+ return h;
+ });
+ Singular.method("scHilbPolyWeighted", [](ideal I, ring r, jlcxx::ArrayRef<int> weights, ring Qt) {
+ intvec *w = to_intvec(weights);
+ const ring origin = currRing;
+ rChangeCurrRing(r);
+ poly h=hFirstSeries0p(I,r->qideal,w,r,Qt);
+ delete w;
+ rChangeCurrRing(origin);
+ return h;
+ });
  Singular.method("id_Homogen", id_Homogen);
  Singular.method("id_HomModule", [](jlcxx::ArrayRef<int> weights, ideal I, ring r) {
  intvec* w = NULL;

src/ideal/ideal.jl

@@ -1278,6 +1278,38 @@ function hilbert_series(I::sideal{spoly{T}}, w::Vector{<:Integer}) where T <: Ne
  return z
 end
 
+@doc raw"""
+ hilbert_series(I::sideal{spoly{T}}, Qt::PolyRing) where T <: Nemo.FieldElem
+
+Return the polynomial $Q(t)$ as element of Qt where `Q(t)/(1-t)^nvars(base_ring(I))`
+is the Hilbert-Poincare series of $I$ for weights $(1, \dots, 1)$.
+The generators of $I$ must be given as a Groebner basis.
+"""
+function hilbert_series(I::sideal{spoly{T}}, Qt::PolyRing) where T <: Nemo.FieldElem
+ I.isGB || error("Not a Groebner basis")
+ R = base_ring(I)
+ GC.@preserve I R Qt new_ptr = libSingular.scHilbPoly(I.ptr, R.ptr, Qt.ptr)
+ return Qt(new_ptr)
+end
+
+@doc raw"""
+ hilbert_series(I::sideal{spoly{T}}, w::Vector{<:Integer}) where T <: Nemo.FieldElem
+
+Return the polynomial $Q(t)$ of Qt where $\frac{Q(t)}{\prod_i (1-t^{w_i})}$
+is the Hilbert-Poincare series of $I$ for weights $\{w_i\}$. Each weight must be
+positive $w_i > 0$.
+The generators of $I$ must be given as a Groebner basis.
+"""
+function hilbert_series(I::sideal{spoly{T}}, w::Vector{<:Integer}, Qt::PolyRing) where T <: Nemo.FieldElem
+ I.isGB || error("Not a Groebner basis")
+ R = base_ring(I)
+ length(w) == nvars(R) || error("wrong number of weights")
+ all(x -> x > 0, w) || error("weights must be positive")
+ w = convert(Vector{Int32}, w)
+ GC.@preserve I R Qt new_ptr = libSingular.scHilbPolyWeighted(I.ptr, R.ptr, w, Qt.ptr)
+ return Qt(new_ptr)
+end
+
 @doc raw"""
  std_hilbert(I::sideal{spoly{T}}, hs::Vector{Int32}; complete_reduction::Bool=false) where T <: Nemo.FieldElem
 

test/ideal/sideal-test.jl

@@ -686,6 +686,10 @@ end
 
  @test ngens(std_hilbert(j, h, w, complete_reduction = true)) == 
  ngens(std(j, complete_reduction = true))
+ Qt,(t,)= polynomial_ring(QQ, ["t"])
+ I=Ideal(R,[x,y,z])
+ I=std(I)
+ @test hilbert_series(I,Qt) == -t^3+3*t^2-3*t+1
 end
 
 @testset "sideal.oscar#1702" begin