RFC: Add function to obtain underlying abelian group

src/Modules/FreeModules-graded.jl

@@ -1,5 +1,5 @@
 #TODO make d and S a function optionally - to support HUGE degree
-export presentation, decoration
+export presentation, grading_group
 
 abstract type ModuleFP_dec{T} end
 
@@ -29,7 +29,7 @@ mutable struct FreeModule_dec{T} <: ModuleFP_dec{T}
 end
 
 function FreeModule(R::Ring_dec, n::Int, name::String = "e"; cached::Bool = false) 
-  return FreeModule_dec([decoration(R)[0] for i=1:n], R, [Symbol("$name[$i]") for i=1:n])
+  return FreeModule_dec([grading_group(R)[0] for i=1:n], R, [Symbol("$name[$i]") for i=1:n])
 end
 free_module(R::Ring_dec, n::Int, name::String = "e"; cached::Bool = false) = FreeModule(R, n, name, cached = cached)
 
@@ -686,7 +686,7 @@ function syzygie_module(F::BiModArray; sub = 0)
     G = sub
   else
   	[F[Val(:O), i] for i = 1:length(F.O)]
-    z = decoration(base_ring(F.F))[0]
+    z = grading_group(base_ring(F.F))[0]
     G = FreeModule(base_ring(F.F), [iszero(x) ? z : degree(x) for x = F.O])
   end
   return SubQuo_dec(G, s)
@@ -729,9 +729,8 @@ function *(a::FreeModuleElem_dec, b::Array{FreeModuleElem_dec, 1})
   return s
 end
 
-decoration(F::FreeModule_dec) = decoration(F.R)
-decoration(R::MPolyRing_dec) = R.D
-decoration(SQ::SubQuo_dec) = decoration(SQ.F)
+grading_group(F::FreeModule_dec) = grading_group(F.R)
+grading_group(SQ::SubQuo_dec) = grading_group(SQ.F)
 
 function presentation(SQ::SubQuo_dec)
   #A+B/B is generated by A and B
@@ -762,7 +761,7 @@ function presentation(SQ::SubQuo_dec)
     push!(w, degree(q[end]))
   end
   #want R^a -> R^b -> SQ -> 0
-  #TODO sort decoration and fix maps, same decoration should be bundled (to match pretty printing)
+  #TODO sort grading_group and fix maps, same grading_group should be bundled (to match pretty printing)
   G = FreeModule(R, w)
   h_G_F = hom(G, F, q)
   @assert iszero(h_G_F) || iszero(degree(h_G_F))
@@ -1054,7 +1053,7 @@ end
 function free_resolution(S::SubQuo_dec, limit::Int = -1)
   p = presentation(S)
   mp = [map(p, j) for j=1:length(p)]
-  D = decoration(S)
+  D = grading_group(S)
   while true
     k, mk = kernel(mp[1])
     nz = findall(x->!iszero(x), gens(k))
@@ -1109,7 +1108,7 @@ function hom(M::ModuleFP_dec, N::ModuleFP_dec)
   #Janko: have R^t1 -- g1 = map(p2, 0) -> R^t0 -> G
   #kernel g1: k -> R^t1
   #source: Janko's CA script: https://www.mathematik.uni-kl.de/~boehm/lehre/17_CA/ca.pdf
-  D = decoration(M)
+  D = grading_group(M)
   F = FreeModule(base_ring(M), GrpAbFinGenElem[iszero(x) ? D[0] : degree(x) for x = gens(k)])
   g2 = hom(F, codomain(mk), collect(k.sub)) #not clean - but maps not (yet) working
   #step 2
@@ -1364,7 +1363,7 @@ function homogeneous_component(F::T, d::GrpAbFinGenElem) where {T <: Union{FreeM
   #TODO: lazy: ie. no enumeration of points
   #      aparently it is possible to get the number of points faster than the points
   W = base_ring(F)
-  D = decoration(W)
+  D = grading_group(W)
   #have gens for W that can be combined
   #              F that can only be used
   #F ni f = sum c_i,j F[i]*w[j]

src/Rings/MPolyQuo.jl

@@ -858,6 +858,14 @@ end
 #
 ################################################################################
 
+function grading(R::MPolyQuo)
+  if R.R isa MPolyRing_dec
+    return grading(R.R)
+  else
+    error("Underlying polynomialring must be graded")
+  end
+end
+
 function degree(a::MPolyQuoElem{<:MPolyElem_dec})
   simplify!(a)
   @req !iszero(a) "Element must be non-zero"
@@ -883,7 +891,7 @@ function ishomogeneous(a::MPolyQuoElem{<:MPolyElem_dec})
   return ishomogeneous(a.f)
 end
 
-decoration(q::MPolyQuo{<:MPolyElem_dec}) = decoration(q.R)
+grading_group(q::MPolyQuo{<:MPolyElem_dec}) = grading_group(q.R)
 
 function hash(w::MPolyQuoElem, u::UInt)
   simplify!(w)
@@ -894,7 +902,7 @@ function homogeneous_component(W::MPolyQuo{<:MPolyElem_dec}, d::GrpAbFinGenElem)
   #TODO: lazy: ie. no enumeration of points
   #      aparently it is possible to get the number of points faster than the points
   D = parent(d)
-  @assert D == decoration(W)
+  @assert D == grading_group(W)
   R = base_ring(W)
   I = modulus(W)
 

src/Rings/mpoly-graded.jl

@@ -1,6 +1,6 @@
 export weight, decorate, ishomogeneous, homogeneous_components, filtrate,
 grade, GradedPolynomialRing, homogeneous_component, jacobi_matrix, jacobi_ideal,
-HilbertData, hilbert_series, hilbert_series_reduced, hilbert_series_expanded, hilbert_function, hilbert_polynomial,
+HilbertData, hilbert_series, hilbert_series_reduced, hilbert_series_expanded, hilbert_function, hilbert_polynomial, grading,
 homogenization, dehomogenization
 export MPolyRing_dec, MPolyElem_dec
 mutable struct MPolyRing_dec{T, S} <: AbstractAlgebra.MPolyRing{T}
@@ -26,6 +26,8 @@ mutable struct MPolyRing_dec{T, S} <: AbstractAlgebra.MPolyRing{T}
   end
 end
 
+grading_group(W::MPolyRing_dec) = W.D
+
 isgraded(W::MPolyRing_dec) = !isdefined(W, :lt)
 isfiltered(W::MPolyRing_dec) = isdefined(W, :lt)
 

test/Modules/FreeModules-graded-test.jl

@@ -88,7 +88,7 @@ end
         @test Oscar.isgraded(F) == Oscar.isgraded(RR)
         @test Oscar.isfiltered(F) == Oscar.isfiltered(RR)
 
-        G = decoration(F)
+        G = grading_group(F)
         if j == 4
           a = G([convert(fmpz,x) for x = [1,0,1]])
         else

test/Modules/GradedModules.jl

@@ -27,7 +27,7 @@
 
   free_resolution(H)
 
-  homogeneous_component(H, Oscar.decoration(F)[0])
+  homogeneous_component(H, grading_group(F)[0])
 end
 
 @testset "Graded Modules 2" begin

test/Rings/mpoly-graded-test.jl

@@ -32,7 +32,7 @@ function _homogeneous_polys(polys::Vector{<:MPolyElem})
     _monomials = append!(_monomials, monomials(polys[i]))
   end
   hom_polys = []
-  for deg in unique([iszero(mon) ? id(decoration(R)) : degree(mon) for mon = _monomials])
+  for deg in unique([iszero(mon) ? id(grading_group(R)) : degree(mon) for mon = _monomials])
     g = zero(R)
     for i = 1:4
       if haskey(D[i], deg)
@@ -139,7 +139,7 @@ end
         @test Oscar.isfiltered(R_quo) == Oscar.isfiltered(RR)
         @test Oscar.isgraded(R_quo) == Oscar.isgraded(RR)
 
-        @test decoration(R_quo) == decoration(RR)
+        @test grading_group(R_quo) == grading_group(RR)
 
         d_Elem = d_Elems[RR]
 
@@ -186,3 +186,9 @@ end
   R, (x,y) = grade(PolynomialRing(QQ, ["x", "y"])[1]);
   @test_throws ArgumentError degree(zero(R))
 end
+
+@testset "Grading" begin
+  R, (x,y) = grade(PolynomialRing(QQ, ["x", "y"])[1]);
+  D = grading_group(R)
+  @test isisomorphic(D, abelian_group([0]))
+end