From b3be7273c1b895f705b34dc1c8822920f62a004a Mon Sep 17 00:00:00 2001
From: Hans Schoenemann <hannes@mathematik.uni-kl.de>
Date: Fri, 1 Sep 2023 14:58:03 +0200
Subject: [PATCH 1/2] mres_with_map for smodule

---
 src/module/module.jl                | 20 ++++++++++++++++++++
 test/resolution/sresolution-test.jl | 12 ++++++++++++
 2 files changed, 32 insertions(+)

diff --git a/src/module/module.jl b/src/module/module.jl
index 002ee98ea..5f8766923 100644
--- a/src/module/module.jl
+++ b/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
 
diff --git a/test/resolution/sresolution-test.jl b/test/resolution/sresolution-test.jl
index 4feb7b3fb..cb904457a 100644
--- a/test/resolution/sresolution-test.jl
+++ b/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

From 7566d61c351c2606e0062b2b1c8532cd818cf49e Mon Sep 17 00:00:00 2001
From: Hans Schoenemann <hannes@mathematik.uni-kl.de>
Date: Fri, 1 Sep 2023 15:18:53 +0200
Subject: [PATCH 2/2] fix test

---
 test/resolution/sresolution-test.jl | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/test/resolution/sresolution-test.jl b/test/resolution/sresolution-test.jl
index cb904457a..de70527ae 100644
--- a/test/resolution/sresolution-test.jl
+++ b/test/resolution/sresolution-test.jl
@@ -111,10 +111,11 @@ 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)
+   v1 = vector(R, y )
+   v2 = vector(R, x)
+   v3 = vector(R, x+y)
 
-   M = Singular.Module(R, v1, v2)
+   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]))