add prune_with_map_projection (#751)

* add prune_with_map_projection

* test prune_with_map_projection

* Update src/module/module.jl

Co-authored-by: Max Horn <max@quendi.de>

* docstring for prune_with_map_projection

* Update src/module/module.jl

---------

Co-authored-by: Max Horn <max@quendi.de>
Co-authored-by: ederc <ederc@mathematik.uni-kl.de>

src/module/module.jl

@@ -1,5 +1,6 @@
 export jet, minimal_generating_set, ModuleClass, rank, smodule, slimgb,
-       eliminate, modulo, lift, division, divrem, prune_with_map
+       eliminate, modulo, lift, division, divrem, prune_with_map,
+       prune_with_map_projection
 
 ###############################################################################
 #
@@ -407,6 +408,23 @@ function prune_with_map(I::smodule{spoly{T}}) where T <: Nemo.FieldElem
    return smodule{spoly{T}}(R, r),smatrix{spoly{T}}(R,TT_ptr)
 end
 
+@doc raw"""
+    prune_with_map_projection(id::smodule{spoly{T}}) where T <: Nemo.FieldElem
+
+Return a module `R`, a transformation matrix `M` and a projection map `p`
+satisfying the following properties: `R` is minimally embedded in a free
+module `parent(R)` such that the quotient `parent(R)/R` is isomorphic to
+`parent(id)/id`, with `M` together with the projection given by the vector `p`
+describing this isomorphism.
+`p` maps `gen(parent(id),i)` to `gen(parent(R),p[i])`
+"""
+function prune_with_map_projection(I::smodule{spoly{T}}) where T <: Nemo.FieldElem
+   R = base_ring(I)
+   a = Vector{Int32}()
+   r, TT_ptr = GC.@preserve I R libSingular.id_prune_map_v(I.ptr, a, R.ptr)
+   return smodule{spoly{T}}(R, r),smatrix{spoly{T}}(R,TT_ptr),a
+end
+
 @doc raw"""
     nres(id::smodule{spoly{T}}, max_length::Int) where T <: Nemo.FieldElem
 

test/module/smodule-test.jl

@@ -324,4 +324,9 @@ end
    @test G[1] == vector(R, z)
    @test T[3,1] == R(1)
 
+   G,T,p = prune_with_map_projection(M)
+   @test p[1] == 1
+   @test p[2] == 1
+   @test p[3] == 2
+
 end