More signatures for quotient_ring_as_module and ideal_as_module (#…

…4174) * More signatures for `quotient_ring_as_module` and `ideal_as_module` * add test * extend doctest
oscar-system · Oct 4, 2024 · ca727c8 · ca727c8
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diff --git a/docs/doc.main b/docs/doc.main
@@ -133,6 +133,7 @@
         "CommutativeAlgebra/ModulesOverMultivariateRings/intro.md",
         "CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md",
         "CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md",
+	"CommutativeAlgebra/ModulesOverMultivariateRings/ideals_quorings_as_modules.md",
         "CommutativeAlgebra/ModulesOverMultivariateRings/module_operations.md",
         "CommutativeAlgebra/ModulesOverMultivariateRings/hom_operations.md",
         "CommutativeAlgebra/ModulesOverMultivariateRings/complexes.md",

diff --git a/...c/CommutativeAlgebra/ModulesOverMultivariateRings/ideals_quorings_as_modules.md b/...c/CommutativeAlgebra/ModulesOverMultivariateRings/ideals_quorings_as_modules.md
@@ -0,0 +1,20 @@
+```@meta
+CurrentModule = Oscar
+```
+
+# Ideals and Quotient Rings as Modules
+
+## Ideals as Modules
+
+```@docs
+ideal_as_module(I::Union{MPolyIdeal, MPolyQuoIdeal, MPolyLocalizedIdeal, MPolyQuoLocalizedIdeal})
+```
+
+# Quotient Rings as Modules
+
+```@docs
+quotient_ring_as_module(A::MPolyQuoRing)
+```
+
+
+
diff --git a/docs/src/CommutativeAlgebra/affine_algebras.md b/docs/src/CommutativeAlgebra/affine_algebras.md
@@ -672,9 +672,3 @@ multi_hilbert_series(A::MPolyQuoRing; algorithm::Symbol=:BayerStillmanA)
 multi_hilbert_series_reduced(A::MPolyQuoRing; algorithm::Symbol=:BayerStillmanA)
 multi_hilbert_function(A::MPolyQuoRing, g::FinGenAbGroupElem)
 ```
-
-## Affine Algebras as Modules
-
-```@docs
-quotient_ring_as_module(A::MPolyQuoRing)
-```
diff --git a/docs/src/CommutativeAlgebra/ideals.md b/docs/src/CommutativeAlgebra/ideals.md
@@ -285,13 +285,6 @@ julia> DH(Ih) == I   # dehomogenization of Ih
 true
 ```
 
-
-## Ideals as Modules
-
-```@docs
-ideal_as_module(I::MPolyIdeal)
-```
-
 ## Generating Special Ideals
 
 ### Katsura-n

diff --git a/src/Modules/ModulesGraded.jl b/src/Modules/ModulesGraded.jl
@@ -2879,25 +2879,44 @@ end
 
 Return `A` considered as an object of type `SubquoModule`.
 
-    quotient_ring_as_module(I::MPolyIdeal)
+    quotient_ring_as_module(I::Union{MPolyIdeal, MPolyQuoIdeal, MPolyLocalizedIdeal, MPolyQuoLocalizedIdeal})
 
 As above, where `A` is the quotient of `base_ring(I)` modulo `I`.
 
 # Examples
 ```jldoctest
 julia> R, (x, y) = polynomial_ring(QQ, [:x, :y]);
 
-julia> I = ideal(R, [x^2, y^3])
-Ideal generated by
-  x^2
-  y^3
+julia> IR = ideal(R, [x^2, y^3]);
 
-julia> quotient_ring_as_module(I)
+julia> quotient_ring_as_module(IR)
+Subquotient of Submodule with 1 generator
+1 -> e[1]
+by Submodule with 2 generators
+1 -> x^2*e[1]
+2 -> y^3*e[1]
+
+julia> base_ring(ans)
+Multivariate polynomial ring in 2 variables x, y
+  over rational field
+
+julia> A, _ = quo(R, ideal(R,[x*y]));
+
+julia> AI = ideal(A, [x^2, y^3]);
+
+julia> quotient_ring_as_module(AI)
 Subquotient of Submodule with 1 generator
 1 -> e[1]
 by Submodule with 2 generators
 1 -> x^2*e[1]
 2 -> y^3*e[1]
+
+julia> base_ring(ans)
+Quotient
+  of multivariate polynomial ring in 2 variables x, y
+    over rational field
+  by ideal (x*y)
+
 ```
 ```jldoctest
 julia> S, (x, y) = graded_polynomial_ring(QQ, [:x, :y]);
@@ -2920,7 +2939,7 @@ function quotient_ring_as_module(A::MPolyQuoRing)
   return quotient_ring_as_module(modulus(A))
 end
 
-function quotient_ring_as_module(I::MPolyIdeal)
+function quotient_ring_as_module(I::Union{MPolyIdeal, MPolyQuoIdeal, MPolyLocalizedIdeal, MPolyQuoLocalizedIdeal})
   R = base_ring(I)
   F = is_graded(R) ? graded_free_module(R, 1) : free_module(R, 1)
   e1 = F[1]
@@ -2930,7 +2949,7 @@ end
 #####ideals as modules#####
 
 @doc raw"""
-    ideal_as_module(I::MPolyIdeal)
+    ideal_as_module(I::Union{MPolyIdeal, MPolyQuoIdeal, MPolyLocalizedIdeal, MPolyQuoLocalizedIdeal})
 
 Return `I` considered as an object of type `SubquoModule`.
 
@@ -2964,7 +2983,7 @@ Graded submodule of S^1
 represented as subquotient with no relations
 ```
 """
-function ideal_as_module(I::MPolyIdeal)
+function ideal_as_module(I::Union{MPolyIdeal, MPolyQuoIdeal, MPolyLocalizedIdeal, MPolyQuoLocalizedIdeal})
   R = base_ring(I)
   F = is_graded(R) ? graded_free_module(R, 1) : free_module(R, 1)
   e1 = F[1]

diff --git a/test/Modules/ModulesGraded.jl b/test/Modules/ModulesGraded.jl
@@ -1243,5 +1243,30 @@ end
   K, inc = kernel(phi)
 end
 
+@testset "ideal and quotient ring as module" begin
+  R, (x, y) = polynomial_ring(QQ,[:x, :y])
+  I = ideal(R, [y^2-x^3-x^2])
+  II = ideal_as_module(I)
+  M = quotient_ring_as_module(I)
+  Q, pr = quo(R, I)
+  J = ideal(Q, gens(Q))
+  ideal_as_module(J)
+  quotient_ring_as_module(J)
+  U = complement_of_point_ideal(R, [0, 0])
+  Rloc, _ = localization(R, U)
+  Iloc = ideal(Rloc, [y^2-x^3-x^2])
+  Mloc = ideal_as_module(Iloc)
+  @test is_empty(relations(Mloc))
+  QI = quotient_ring_as_module(I)
+  @test rank(ambient_free_module(QI)) == 1
+  Q, pr = quo(Rloc, Iloc)
+  J = ideal(Q, gens(Q))
+  ideal_as_module(J)
+  quotient_ring_as_module(J)
+end
+
+
+
+