Lift std (#313)

* better support for lift_std

- a native version for ideals (as opposed to modules)
- with/out syzygies
- with/out complete_reduction

docs/src/ideal.md

@@ -252,6 +252,14 @@ fglm(::sideal, ::Symbol)
 satstd{T <: AbstractAlgebra.RingElem}(::sideal{T}, ::sideal{T})
 ```
 
+```@docs
+lift_std(::sideal; ::Bool)
+```
+
+```@docs
+lift_std_syz(::sideal; ::Bool)
+```
+
 **Examples**
 
 ```julia

docs/src/module.md

@@ -108,6 +108,13 @@ d = ngens(M)
 std(::smodule; ::Bool)
 ```
 
+```@docs
+lift_std(::smodule; ::Bool)
+```
+
+```@docs
+lift_std_syz(::smodule; ::Bool)
+```
 **Examples**
 
 ```julia

src/ideal/ideal.jl

@@ -521,6 +521,37 @@ function syz(I::sideal)
    return Module(R, ptr)
 end
 
+###############################################################################
+#
+#   LiftStd
+#
+###############################################################################
+
+@doc Markdown.doc"""
+    lift_std_syz(I::sdeal)
+
+computes the Groebner base G of I, the transformation matrix T and the syzygies of M.
+Returns G,T,S
+(Matrix(G) = Matrix(I) * T, 0=Matrix(M)*Matrix(S))
+"""
+function lift_std_syz(M::sideal; complete_reduction::Bool = false)
+   R = base_ring(M)
+   ptr,T_ptr,S_ptr = libSingular.id_LiftStdSyz(M.ptr, R.ptr, complete_reduction)
+   return Ideal(R, ptr), smatrix{elem_type(R)}(R, T_ptr), Module(R,S_ptr)
+end
+
+@doc Markdown.doc"""
+    lift_std(I::sideal)
+
+computes the Groebner base G of I and the transformation matrix T such that
+(Matrix(G) = Matrix(I) * T)
+"""
+function lift_std(M::sideal; complete_reduction::Bool = false)
+   R = base_ring(M)
+   ptr,T_ptr = libSingular.id_LiftStd(M.ptr, R.ptr, complete_reduction)
+   return Ideal(R, ptr), smatrix{elem_type(R)}(R, T_ptr)
+end
+
 ###############################################################################
 #
 #   Resolutions

src/module/module.jl

@@ -285,18 +285,30 @@ end
 ###############################################################################
 
 @doc Markdown.doc"""
-    lift_std(M::smodule)
+    lift_std_syz(M::smodule)
 
 computes the Groebner base G of M, the transformation matrix T and the syzygies of M.
 Returns G,T,S
-(Matrix(G) = (Matrix(T)*Matrix(M), 0=Matrix(S)*Matrix(M))
+(Matrix(G) = Matrix(M) * T, 0=Matrix(M)*Matrix(S))
 """
-function lift_std(M::smodule)
+function lift_std_syz(M::smodule; complete_reduction::Bool = false)
    R = base_ring(M)
-   ptr,T_ptr,S_ptr = libSingular.id_LiftStd(M.ptr, R.ptr)
+   ptr,T_ptr,S_ptr = libSingular.id_LiftStdSyz(M.ptr, R.ptr, complete_reduction)
    return Module(R, ptr), smatrix{elem_type(R)}(R, T_ptr), Module(R,S_ptr)
 end
 
+@doc Markdown.doc"""
+    lift_std(M::smodule)
+
+computes the Groebner base G of M and the transformation matrix T such that
+(Matrix(G) = Matrix(M) * T)
+"""
+function lift_std(M::smodule; complete_reduction::Bool = false)
+   R = base_ring(M)
+   ptr,T_ptr = libSingular.id_LiftStd(M.ptr, R.ptr, complete_reduction)
+   return Module(R, ptr), smatrix{elem_type(R)}(R, T_ptr)
+end
+
 ###############################################################################
 #
 #   Modulo

test/ideal/sideal-test.jl

@@ -337,3 +337,32 @@ end
    @test typeof(L2) == Array{Array{spoly{n_Q}, 1}, 1}
 end
 
+@testset "sideal.lift_std..." begin
+   R, (x, y) = PolynomialRing(QQ, ["x", "y"])
+
+   I = Ideal(R, x, y)
+   G, T = Singular.lift_std(I)
+   @test G[1] == y
+   @test G[2] == x
+   @test T[1,1] == 0
+   @test T[2,2] == 0
+   @test T[2,1] == 1
+   @test T[1,2] == 1
+
+   G, T = Singular.lift_std(I, complete_reduction = true)
+   @test G[1] == y
+   @test G[2] == x
+   @test T[1,1] == 0
+   @test T[2,2] == 0
+   @test T[2,1] == 1
+   @test T[1,2] == 1
+
+   G, T, S = Singular.lift_std_syz(I)
+   mG = Singular.Matrix(G)
+   mI = Singular.Matrix(I)
+   mS = Singular.Matrix(S)
+   @test iszero(mI*mS)
+   # @test mI*T == mG
+   # should be true, but there are additional (invisible) zeros in G 
+   # causing a dimension mismatch
+end