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For Modules over PBWAlgRing and PBWAlgQuo #3900

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For Modules over PBWAlgRing and PBWAlgQuo #3900

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dac9216
modules over PBWAlgRing and PBWAlgQuo
Lax202 Jul 1, 2024
cf1bebe
Merge branch 'master' into pbwmod
Lax202 Jul 1, 2024
9ce925f
priliminary tests
Lax202 Jul 1, 2024
6db5e4a
Merge branch 'master' into pbwmod
Lax202 Jul 29, 2024
c6f419f
changes for GB
Lax202 Sep 18, 2024
2f7ce80
Merge branch 'master' into pbwmod
fingolfin Sep 18, 2024
cb30910
success
Lax202 Sep 18, 2024
90f70e7
made it work for PBWAlgRing
Lax202 Sep 19, 2024
41bec22
- redundancy + tests
Lax202 Sep 19, 2024
813b51b
expressify and extra line
Lax202 Sep 20, 2024
3347794
Merge branch 'master' into pbwmod
Lax202 Sep 20, 2024
fa552f0
PR comments
Lax202 Sep 26, 2024
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6 changes: 3 additions & 3 deletions src/Modules/ModuleTypes.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -70,8 +70,8 @@ Moreover, canonical incoming and outgoing morphisms are stored if the correspond
option is set in suitable functions.
`FreeMod{T}` is a subtype of `AbstractFreeMod{T}`.
"""
@attributes mutable struct FreeMod{T <: RingElem} <: AbstractFreeMod{T}
R::Ring
@attributes mutable struct FreeMod{T <: Union{RingElem, PBWAlgElem, PBWAlgQuoElem}} <: AbstractFreeMod{T}
R::Union{Ring,PBWAlgRing,PBWAlgQuo}
n::Int
S::Vector{Symbol}
d::Union{Vector{FinGenAbGroupElem}, Nothing}
Expand All @@ -91,7 +91,7 @@ option is set in suitable functions.
incoming::WeakKeyIdDict{<:ModuleFP, <:Tuple{<:SMat, <:Any}}
outgoing::WeakKeyIdDict{<:ModuleFP, <:Tuple{<:SMat, <:Any}}

function FreeMod{T}(n::Int,R::Ring,S::Vector{Symbol}) where T <: RingElem
function FreeMod{T}(n::Int,R::Union{Ring, PBWAlgQuo, PBWAlgRing},S::Vector{Symbol}) where T <: Union{RingElem, PBWAlgElem, PBWAlgQuoElem}
r = new{elem_type(R)}()
r.n = n
r.R = R
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18 changes: 18 additions & 0 deletions src/Modules/UngradedModules/FreeMod.jl
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Expand Up @@ -22,6 +22,22 @@ function FreeMod(R::Ring, names::Vector{Symbol}; cached::Bool=false)
return FreeMod{elem_type(R)}(length(names), R, names)
end

function FreeMod(R::PBWAlgQuo, n::Int, name::VarName = :e; cached::Bool = false) # TODO cached?
return FreeMod{elem_type(R)}(n, R, [Symbol("$name[$i]") for i=1:n])
end

function FreeMod(R::PBWAlgRing, n::Int, name::VarName = :e; cached::Bool = false) # TODO cached?
return FreeMod{elem_type(R)}(n, R, [Symbol("$name[$i]") for i=1:n])
end

function FreeMod(R::PBWAlgQuo, names::Vector{String}; cached::Bool=false)
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return FreeMod{elem_type(R)}(length(names), R, Symbol.(names))
end

function FreeMod(R::PBWAlgRing, names::Vector{String}; cached::Bool=false)
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return FreeMod{elem_type(R)}(length(names), R, Symbol.(names))
end

@doc raw"""
free_module(R::MPolyRing, p::Int, name::VarName = :e; cached::Bool = false)
free_module(R::MPolyQuoRing, p::Int, name::VarName = :e; cached::Bool = false)
Expand Down Expand Up @@ -75,6 +91,8 @@ free_module(R::MPolyRing, p::Int, name::VarName = :e; cached::Bool = false) = Fr
free_module(R::MPolyQuoRing, p::Int, name::VarName = :e; cached::Bool = false) = FreeMod(R, p, name, cached = cached)
free_module(R::MPolyLocRing, p::Int, name::VarName = :e; cached::Bool = false) = FreeMod(R, p, name, cached = cached)
free_module(R::MPolyQuoLocRing, p::Int, name::VarName = :e; cached::Bool = false) = FreeMod(R, p, name, cached = cached)
free_module(R::PBWAlgQuo, p::Int, name::VarName = :e; cached::Bool = false) = FreeMod(R,p,name,cached = cached)
free_module(R::PBWAlgRing, p::Int, name::VarName = :e; cached::Bool = false) = FreeMod(R,p,name,cached = cached)

#=XXX this cannot be as it is inherently ambiguous
- FreeModule(R, n)
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2 changes: 2 additions & 0 deletions src/Modules/UngradedModules/FreeModElem.jl
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Expand Up @@ -276,6 +276,8 @@ end
*(a::Int, b::AbstractFreeModElem) = parent(b)(a*coordinates(b))
*(a::Integer, b::AbstractFreeModElem) = parent(b)(base_ring(parent(b))(a)*coordinates(b))
*(a::QQFieldElem, b::AbstractFreeModElem) = parent(b)(base_ring(parent(b))(a)*coordinates(b))
*(a::PBWAlgQuoElem, b::AbstractFreeModElem) = parent(b)(a*coordinates(b))
*(a::PBWAlgElem, b::AbstractFreeModElem) = parent(b)(a*coordinates(b))

@doc raw"""
zero(F::AbstractFreeMod)
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61 changes: 61 additions & 0 deletions test/Modules/PBWModules.jl
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@@ -0,0 +1,61 @@
@testset "modules over PBWAlgQuo" begin
#Free Module tests
E,x = exterior_algebra(QQ, 3)
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This function is part of experimental and should thus not be used in the tests for src/ code

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True. Though maybe we need to look into promoting exterior_algebra one of these days?

In any case, note that this PR is still a very early draft, I mainly asked @Lax202 to open it so we can better see what she's doing and what the state is, and then discuss it. The code still needs to be consolidated into a new source file, and that may very well ultimately end up in the experimental tree. We'll see.

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In the meantime this was merged as part of PR #3988 which copied the tests from here. If we still don't want the exterior_algebra call here, then someone else should remove it from there.

M = free_module(E, 3)
@test ngens(M) == 3
@test gens(M)[1] in M
@test parent(M[1]) == M
v = [x[1], x[1] + x[2], x[1]*x[2]]
@test v == Vector(M(v))

#SubModuleOfFreeModule tests
N = Oscar.SubModuleOfFreeModule(M, gens(M)[1:2])
@test gens(N) == gens(M)[1:2]
@test N[1] in M
#fails! #NEEDS A 'DEFAULT ORDERING' on the PBWAlgQuo ie on E
#@test M(v) in N

#FreeModuleHom tests
W = free_module(E,2)
G = hom(W,M, gens(M)[1:2])
@test ngens(image(G)[1]) == 2

#SubQuoModule tests
Q1 = SubquoModule(M, [x[1]*M[1]])
Q2 = SubquoModule(M, [x[2]*M[1]])
#fail! #NEEDS A 'DEFAULT ORDERING' on the PBWAlgQuo ie on E
#@test !is_canonically_isomorphic(Q2,Q1)
#simplify(Q[1])
end

@testset "modules over PBWAlgRing" begin
R, (x, y, z) = QQ["x", "y", "z"]
L = [x*y, x*z, y*z + 1]
REL = strictly_upper_triangular_matrix(L)
A, (x, y, z) = pbw_algebra(R, REL, deglex(gens(R)))
M = free_module(A, 3)
@test ngens(M) == 3
@test gens(M)[1] in M
@test parent(M[1]) == M
v = [x, x+y, x*y]
@test v == Vector(M(v))

#SubModuleOfFreeModule tests
N = Oscar.SubModuleOfFreeModule(M, gens(M)[1:2])
@test gens(N) == gens(M)[1:2]
@test N[1] in M
#fails! #NEEDS A 'DEFAULT ORDERING' on the PBWAlgQuo ie on E
#@test M(v) in N

#FreeModuleHom tests
W = free_module(A,2)
G = hom(W,M, gens(M)[1:2])
@test ngens(image(G)[1]) == 2

#SubQuoModule tests
Q1 = SubquoModule(M, [x*M[1]])
Q2 = SubquoModule(M, [y*M[1]])
#fail! #NEEDS A 'DEFAULT ORDERING' on the PBWAlgQuo ie on E
#@test !is_canonically_isomorphic(Q2,Q1)
#simplify(Q[1])
end
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