Add hilbert_series (#694)

oscar-system · Aug 15, 2023 · d0bae9a · d0bae9a
1 parent 464a02c
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diff --git a/deps/src/ideals.cpp b/deps/src/ideals.cpp
@@ -669,6 +669,22 @@ 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;

diff --git a/src/ideal/ideal.jl b/src/ideal/ideal.jl
@@ -1277,6 +1277,38 @@ 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
 

diff --git a/test/ideal/sideal-test.jl b/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