Merge pull request #705 from hannes14/hs/mres_with_map

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 +107,16 @@ 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, y )
+   v2 = vector(R, x)
+   v3 = vector(R, x+y)
+
+   M = Singular.Module(R, v1, v2, v3)
+   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