add mres_with_map

deps/src/ideals.cpp

@@ -54,6 +54,30 @@ auto id_res_helper(sip_sideal * I, int n, int minimize, ring R)
     return std::make_tuple(s, minimal);
 }
 
+auto id_mres_map_helper(sip_sideal * I, int n, ring R)
+{
+    auto origin = currRing;
+    rChangeCurrRing(R);
+    ideal T;
+    syStrategy s = syMres_with_map(I, n, NULL, T);
+    matrix TT=id_Module2Matrix(T,currRing);
+    rChangeCurrRing(origin);
+    auto r = s->minres;
+    bool minimal = true;
+    if (r == NULL) {
+        r = s->fullres;
+    }
+    for(int i=0;i<=n+1;i++)
+    {
+      if (r[i]==NULL)
+      {
+        r[i]=idInit(1,1);
+        break;
+      }
+    }
+    return std::make_tuple(s, TT);
+}
+
 ideal id_Syzygies_internal(ideal m, ring o)
 {
     ideal      id = NULL;
@@ -339,6 +363,7 @@ void singular_define_ideals(jlcxx::Module & Singular)
     Singular.method("id_fres", &id_fres_helper);
 
     Singular.method("id_res", &id_res_helper);
+    Singular.method("id_mres_map", &id_mres_map_helper);
 
     Singular.method("id_Slimgb", &id_Slimgb_helper);
 

src/ideal/ideal.jl

@@ -1,6 +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,
+       independent_sets, maximal_independent_set, mres, mres_with_map,
+       ngens, nres, sres,
        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,
@@ -986,6 +987,26 @@ function mres(I::sideal{spoly{T}}, max_length::Int) where T <: Nemo.FieldElem
    return sresolution{spoly{T}}(R, r, Bool(minimal), true)
 end
 
+@doc raw"""
+    mres_with_map(id::sideal{spoly{T}}, max_length::Int) where T <: Nemo.FieldElem
+
+Compute a minimal (free) resolution of the given ideal up to the maximum
+given length. The ideal must be over a polynomial ring over a field.
+The result is given as a resolution, whose i-th entry is
+the syzygy module of the previous module, starting with the given ideal.
+The `max_length` can be set to $0$ if the full free resolution is required.
+Returns the resolution R and the transformation matrix of id to R[1].
+"""
+function mres_with_map(I::sideal{spoly{T}}, max_length::Int) where T <: Nemo.FieldElem
+   R = base_ring(I)
+   if max_length == 0
+        max_length = nvars(R)
+        # TODO: consider qrings
+   end
+   r, TT_ptr = GC.@preserve I R libSingular.id_mres_map(I.ptr, Cint(max_length + 1), R.ptr)
+   return sresolution{spoly{T}}(R, r, true, true),smatrix{spoly{T}}(R,TT_ptr)
+end
+
 @doc raw"""
     nres(id::sideal{spoly{T}}, max_length::Int) where T <: Nemo.FieldElem
 

test/ideal/sideal-test.jl

@@ -469,6 +469,7 @@ end
    F2 = @inferred sres(std(I), 4)
    F3 = @inferred nres(I, 4)
    F4 = @inferred mres(I, 4)
+   F5,TT = @inferred mres_with_map(I, 4)
 
    # check resolution is of the correct length
    @test (@inferred length(F1)) == 2
@@ -494,11 +495,16 @@ end
    M4 = @inferred Singular.Matrix(F4[1])
    N4 = @inferred Singular.Matrix(F4[2])
 
+   M5 = @inferred Singular.Matrix(F5[1])
+   N5 = @inferred Singular.Matrix(F5[2])
+
    # check we have a complex
    @test iszero(M1*N1)
    @test iszero(M2*N2)
    @test iszero(M3*N3)
    @test iszero(M4*N4)
+   @test iszero(M5*N5)
+   @test iszero(Singular.Matrix(I)*TT-M5)
 end
 
 @testset "sideal.syzygy" begin