mres_with_map for smodule

src/module/module.jl

@@ -312,6 +312,26 @@ function mres(I::smodule{spoly{T}}, max_length::Int) where T <: Nemo.FieldElem
  return sresolution{spoly{T}}(R, r, Bool(minimal), false)
 end
 
+@doc raw"""
+ mres_with_map(id::smodule{spoly{T}}, max_length::Int) where T <: Nemo.FieldElem
+
+Compute a minimal (free) resolution of the given module up to the maximum
+given length. The module 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 module.
+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::smodule{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, false),smatrix{spoly{T}}(R,TT_ptr)
+end
+
 @doc raw"""
  nres(id::smodule{spoly{T}}, max_length::Int) where T <: Nemo.FieldElem
 

test/resolution/sresolution-test.jl

@@ -107,3 +107,15 @@ end
  @test iszero(M1*M2)
  @test iszero(M2*M3)
 end
+
+@testset "sresolution.mres_module" begin
+ R, (x, y) = polynomial_ring(QQ, ["x", "y"])
+
+ v1 = vector(R, x + 1, x*y + 1, y)
+ v2 = vector(R, x^2 + 1, 2x + 3y, x)
+
+ M = Singular.Module(R, v1, v2)
+ L,TT = mres_with_map(M,0)
+ @test iszero(Singular.Matrix(M)*TT-Singular.Matrix(L[1]))
+ @test iszero(Singular.Matrix(L[1])*Singular.Matrix(L[2]))
+end