Homogenize wrt. weights of ideals (#675)

* Homogenize wrt. weights odf ideals

* use homogenize_ideal, homogenize_ideal_with_weights

deps/src/ideals.cpp

@@ -308,6 +308,14 @@ void singular_define_ideals(jlcxx::Module & Singular)
 
     Singular.method("rank", [](ideal m) { return (int)m->rank; });
 
+    Singular.method("id_Homogenize", &id_Homogenize);
+
+    Singular.method("id_HomogenizeW", [](ideal a, int v, jlcxx::ArrayRef<int> w, ring r) {
+        intvec * ww = to_intvec(w);
+        ideal id = id_HomogenizeW(a, v, ww, r);
+        return id;
+    });
+
     Singular.method("id_Quotient", [](ideal a, ideal b, bool c, ring d) {
         const ring origin = currRing;
         rChangeCurrRing(d);

src/ideal/ideal.jl

@@ -1,7 +1,7 @@
 export sideal, IdealSet, syz, lead, normalize!, is_constant, is_zerodim, fglm,
        fres, dimension, highcorner, jet, kbase, minimal_generating_set,
        independent_sets, maximal_independent_set, mres, ngens, nres, sres,
-       intersection,
+       intersection, homogenize_ideal, homogenize_ideal_with_weights,
        quotient, reduce, eliminate, kernel, equal, contains, is_var_generated,
        saturation, saturation2, satstd, slimgb, std, vdim, interreduce, degree, mult,
        hilbert_series, std_hilbert, is_homogeneous, division, divrem, mstd
@@ -197,6 +197,46 @@ function homogenize(I::sideal{S}, v::S) where S <: spoly
     end
 end
 
+@doc raw"""
+    homogenize_ideal(I::sideal{S}, v::S) where S <: spoly
+
+Homogenization of the ideal `I` by homogenization of the generators
+of a suitable Groebner Basis of `I` by the variable `v` and
+return the corresponding homogeneous ideal.
+The variable `v` must have weight `1`.
+"""
+function homogenize_ideal(I::sideal{S}, v::S) where S <: spoly
+   R = base_ring(I)
+   R == parent(v) || error("incompatible parents")
+   i = var_index(v)
+   GC.@preserve I v R begin
+      isone(libSingular.p_WTotaldegree(v.ptr, R.ptr)) ||
+               error("variable must have weight 1")
+      ptr = libSingular.id_Homogenize(I.ptr, i, R.ptr)
+      return sideal{S}(R, ptr)
+    end
+end
+
+@doc raw"""
+    homogenize_ideal_with_weights(I::sideal{S}, v::S, w::Vector{Int32}) where S <: spoly
+
+Homogenization of the ideal `I` wrt. weights `w` by homogenization of the
+generators of a suitable Groebner Basis of `I` by the variable `v` and
+return the corresponding homogeneous ideal.
+The variable `v` must have weight `1`.
+"""
+function homogenize_ideal_with_weights(I::sideal{S}, v::S,  w::Vector{Int32}) where S <: spoly
+   R = base_ring(I)
+   R == parent(v) || error("incompatible parents")
+   i = var_index(v)
+   GC.@preserve I v R begin
+      isone(libSingular.p_WTotaldegree(v.ptr, R.ptr)) ||
+               error("variable must have weight 1")
+      ptr = libSingular.id_HomogenizeW(I.ptr, i, w, R.ptr)
+      return sideal{S}(R, ptr)
+    end
+end
+
 
 @doc raw"""
     normalize!(I::sideal)