fres for smodule (#695)

* fres for smodule

seperate functions for sideal/smodule analogue to sres,nres,mres

* add test for fres for smodule

src/ideal/ideal.jl

@@ -918,19 +918,18 @@ end
 ###############################################################################
 
 @doc raw"""
-    fres(id::Union{sideal{spoly{T}}, smodule{spoly{T}}},
-      max_length::Int, method::String="complete") where T <: Nemo.FieldElem
+    fres(id::sideal{spoly{T}}, max_length::Int, method::String="complete") where T <: Nemo.FieldElem
 
-Compute a free resolution of the given ideal/module up to the maximum given
-length. The ideal/module must be over a polynomial ring over a field, and
+Compute a free resolution of the given ideal up to the maximum given
+length. The ideal must be over a polynomial ring over a field, and
 a Groebner basis.
 The possible methods are "complete", "frame", "extended frame" and
 "single module". The result is given as a resolution, whose i-th entry is
 the syzygy module of the previous module, starting with the given
 ideal/module.
 The `max_length` can be set to $0$ if the full free resolution is required.
 """
-function fres(id::Union{sideal{spoly{T}}, smodule{spoly{T}}}, max_length::Int, method::String = "complete") where T <: Nemo.FieldElem
+function fres(id::sideal{spoly{T}}, max_length::Int, method::String = "complete") where T <: Nemo.FieldElem
    id.isGB || error("Not a Groebner basis")
    max_length < 0 && error("length for fres must not be negative")
    R = base_ring(id)

src/module/module.jl

@@ -241,6 +241,35 @@ end
 #   Resolutions
 #
 ###############################################################################
+@doc raw"""
+    fres(id::smodule{spoly{T}}, max_length::Int, method::String="complete") where T <: Nemo.FieldElem
+
+Compute a free resolution of the given module up to the maximum given
+length. The module must be over a polynomial ring over a field, and
+a Groebner basis.
+The possible methods are "complete", "frame", "extended frame" and
+"single module". The result is given as a resolution, whose i-th entry is
+the syzygy module of the previous module, starting with the given
+ideal/module.
+The `max_length` can be set to $0$ if the full free resolution is required.
+"""
+function fres(id::smodule{spoly{T}}, max_length::Int, method::String = "complete") where T <: Nemo.FieldElem
+   id.isGB || error("Not a Groebner basis")
+   max_length < 0 && error("length for fres must not be negative")
+   R = base_ring(id)
+   if max_length == 0
+        max_length = nvars(R)
+        # TODO: consider qrings
+   end
+   if (method != "complete"
+         && method != "frame"
+         && method != "extended frame"
+         && method != "single module")
+      error("wrong optional argument for fres")
+   end
+   r, minimal = GC.@preserve id R libSingular.id_fres(id.ptr, Cint(max_length + 1), method, R.ptr)
+   return sresolution{spoly{T}}(R, r, Bool(minimal), false)
+end
 
 @doc raw"""
     sres(I::smodule{spoly{T}}, max_length::Int) where T <: Singular.FieldElem

test/resolution/sresolution-test.jl

@@ -81,3 +81,29 @@ end
    @test iszero(M1*M2)
 end
 
+@testset "sresolution.fres_module" begin
+   R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
+
+   I = Singular.Ideal(R, y*z + z^2, y^2 + x*z, x*y + z^2, z^3, x*z^2, x^2*z)
+   M = std(syz(I))
+
+   F = fres(M, 0)
+
+   # We have R^6 <- R^9 <- R^5 <- R^1
+   # All references agree that when written as follows:
+   # 0 <- M <- R^6 <- R^9 <- R^5 <- R^1 <- 0
+   # the length is 3, as numbering starts at index 0 with R^6
+
+   @test length(F) == 3
+   @test F[1] isa smodule
+   @test F[2] isa smodule
+
+   M1 = Singular.Matrix(F[1])
+   M2 = Singular.Matrix(F[2])
+   M3 = Singular.Matrix(F[3])
+
+   @test Singular.Matrix(Singular.Module(M1)) == M1
+
+   @test iszero(M1*M2)
+   @test iszero(M2*M3)
+end