Fix normal_form for module orderings other than the default ordering

experimental/InjectiveResolutions/src/ModuleFunctionality.jl

@@ -52,7 +52,7 @@ function normal_form(M::ModuleGens{T}, GB::ModuleGens{T}) where {T <: MonoidAlge
 
   P = isdefined(GB, :quo_GB) ? union(GB, GB.quo_GB) : GB
 
-  red = _reduce(singular_generators(M), singular_generators(P))
+  red = _reduce(singular_generators(M, GB.ordering), singular_generators(P))
   res = ModuleGens(oscar_free_module(M), red)
   return res
 end

src/Modules/UngradedModules/ModuleGens.jl

@@ -108,6 +108,23 @@ function singular_generators(M::ModuleGens)
   return M.S
 end
 
+@doc raw"""
+    singular_generators(M::ModuleGens, ordering::ModuleOrdering)
+
+Return the generators of `M` in a Singular module over a Singular polynomial ring with the given `ordering`.
+"""
+function singular_generators(M::ModuleGens, ordering::ModuleOrdering)
+  #= TODO: Maybe cache these 'singular_generators' in a Dict with the 'ModuleOrdering' as a key, 
+  like it is the case for 'groebner_basis'? =#
+  @assert M.F === ordering.M
+  SF = singular_module(M.F, ordering)
+  sr = base_ring(SF)
+  if length(M) == 0
+    return Singular.Module(sr, Singular.vector(sr, sr(0)))
+  end
+  return Singular.Module(sr, [SF(x) for x in oscar_generators(M)]...)
+end
+
 @doc raw"""
     singular_ordering(M::ModuleGens)
 
@@ -462,7 +479,7 @@ function normal_form(M::ModuleGens{T}, GB::ModuleGens{T}) where {T <: MPolyRingE
 
   P = isdefined(GB, :quo_GB) ? union(GB, GB.quo_GB) : GB
 
-  red = _reduce(singular_generators(M), singular_generators(P))
+  red = _reduce(singular_generators(M, GB.ordering), singular_generators(P))
   res = ModuleGens(oscar_free_module(M), red)
   return res
 end
@@ -484,7 +501,7 @@ function normal_form_with_unit(M::ModuleGens{T}, GB::ModuleGens{T}) where {T <:
 
   P = isdefined(GB, :quo_GB) ? union(GB, GB.quo_GB) : GB
 
-  red = _reduce(singular_generators(M), singular_generators(P))
+  red = _reduce(singular_generators(M, GB.ordering), singular_generators(P))
   res = ModuleGens(oscar_free_module(M), red)
   return res, [R(1) for _ in 1:ngens(M)]
 end

test/Modules/UngradedModules.jl

@@ -2171,3 +2171,31 @@ end
   # not a finite module over `QQ`
   @test_throws ErrorException vector_space_basis(S)
 end
+
+@testset "normal form different module orderings" begin
+  R, (x,y) = QQ[:x,:y]
+  F = free_module(R, 3)
+  M, _ = sub(F, [F[1]+F[3], F[2]])
+
+  v = (x^2+x)*F[1]
+  w = F[2]
+
+  # default ordering
+  GB = groebner_basis(M)
+  @test normal_form(v, GB) == (x^2+x)*F[1]
+  @test normal_form(w, GB) == zero(F)
+  @test Oscar.normal_form_with_unit(v, GB) == ((x^2+x)*F[1], one(R))
+
+  # another global ordering
+  ord = invlex(F)*deglex(R)
+  GB_ord = groebner_basis(M, ordering = ord)
+  @test normal_form(v, GB_ord) == -(x^2+x)*F[3]
+  @test normal_form(w, GB_ord) == zero(F)
+  @test Oscar.normal_form_with_unit(v, GB_ord) == (-(x^2+x)*F[3], one(R))
+
+  # local ordering
+  ord_loc = invlex(F)*negdeglex(R)
+  SB = standard_basis(M, ordering = ord_loc)
+  @test normal_form(v, SB) == -x*F[3]
+  @test normal_form(w, SB) == zero(F)
+end