kalmar/GroupRings.jl
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use GroupOrNCRing[Elem]

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in AbstractAlgebra Rings are not groups
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kalmarek 2019-07-01 01:05:48 +02:00
parent fbd7b940e9
commit af1ca3e6e7
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2 changed files with 75 additions and 58 deletions
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23
src/GroupRings.jl
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@ -1,7 +1,7 @@
module GroupRings module GroupRings
using AbstractAlgebra using AbstractAlgebra
import AbstractAlgebra: Group, GroupElem, Ring, RingElem, parent, elem_type, parent_type, addeq!, mul! import AbstractAlgebra: Group, NCRing, NCRingElem, parent, elem_type, parent_type, addeq!, mul!
using SparseArrays using SparseArrays
using LinearAlgebra using LinearAlgebra
@ -9,13 +9,16 @@ using Markdown
import Base: convert, show, hash, ==, +, -, *, ^, //, /, length, getindex, setindex!, eltype, one, zero import Base: convert, show, hash, ==, +, -, *, ^, //, /, length, getindex, setindex!, eltype, one, zero
GroupOrNCRing = Union{AbstractAlgebra.Group, AbstractAlgebra.NCRing}
GroupOrNCRingElem = Union{AbstractAlgebra.GroupElem, AbstractAlgebra.NCRingElem}
############################################################################### ###############################################################################
# #
# GroupRings / GroupRingsElem # GroupRings / GroupRingsElem
# #
############################################################################### ###############################################################################
mutable struct GroupRing{Gr<:Group, T<:GroupElem} <: Ring mutable struct GroupRing{Gr<:GroupOrNCRing, T<:GroupOrNCRingElem} <: NCRing
group::Gr group::Gr
basis::Vector{T} basis::Vector{T}
basis_dict::Dict{T, Int} basis_dict::Dict{T, Int}
@ -39,7 +42,7 @@ mutable struct GroupRing{Gr<:Group, T<:GroupElem} <: Ring
end end
end end
mutable struct GroupRingElem{T, A<:AbstractVector, GR<:GroupRing} <: RingElem mutable struct GroupRingElem{T, A<:AbstractVector, GR<:GroupRing} <: NCRingElem
coeffs::A coeffs::A
parent::GR parent::GR
@ -131,13 +134,13 @@ function (RG::GroupRing{<:AbstractAlgebra.NCRing})(i::Int, T::Type=Int)
return elt return elt
end end
function (RG::GroupRing)(g::GroupElem, T::Type=Int) function (RG::GroupRing)(g::GroupOrNCRingElem, T::Type=Int)
result = RG(T) result = RG(T)
result[RG.group(g)] = one(T) result[RG.group(g)] = one(T)
return result return result
end end
function (RG::GroupRing{Gr,T})(V::Vector{T}, S::Type=Int) where {Gr<:Group, T<:GroupElem} function (RG::GroupRing{Gr,T})(V::Vector{T}, S::Type=Int) where {Gr, T}
res = RG(S) res = RG(S)
for g in V for g in V
res[g] += one(S) res[g] += one(S)
@ -181,7 +184,7 @@ function getindex(X::GroupRingElem, n::Int)
return X.coeffs[n] return X.coeffs[n]
end end
function getindex(X::GroupRingElem, g::GroupElem) function getindex(X::GroupRingElem, g::GroupOrNCRingElem)
return X.coeffs[parent(X).basis_dict[g]] return X.coeffs[parent(X).basis_dict[g]]
end end
@ -189,7 +192,7 @@ function setindex!(X::GroupRingElem, value, n::Int)
X.coeffs[n] = value X.coeffs[n] = value
end end
function setindex!(X::GroupRingElem, value, g::GroupElem) function setindex!(X::GroupRingElem, value, g::GroupOrNCRingElem)
RG = parent(X) RG = parent(X)
if !(g in keys(RG.basis_dict)) if !(g in keys(RG.basis_dict))
g = (RG.group)(g) g = (RG.group)(g)
@ -525,8 +528,8 @@ end
reverse_dict(iter) = reverse_dict(Int, iter) reverse_dict(iter) = reverse_dict(Int, iter)
function create_pm(basis::Vector{T}, basis_dict::Dict{T, Int}, function create_pm(basis::AbstractVector{T}, basis_dict::Dict{T, Int},
limit::Int=length(basis); twisted::Bool=false, check=true) where {T<:GroupElem} limit::Int=length(basis); twisted::Bool=false, check=true) where T
product_matrix = zeros(Int, (limit,limit)) product_matrix = zeros(Int, (limit,limit))
Threads.@threads for i in 1:limit Threads.@threads for i in 1:limit
x = basis[i] x = basis[i]
@ -543,7 +546,7 @@ function create_pm(basis::Vector{T}, basis_dict::Dict{T, Int},
return product_matrix return product_matrix
end end
create_pm(b::Vector{T}) where {T<:GroupElem} = create_pm(b, reverse_dict(b)) create_pm(b::AbstractVector{<:GroupOrNCRingElem}) = create_pm(b, reverse_dict(b))
function check_pm(product_matrix, basis, twisted=false) function check_pm(product_matrix, basis, twisted=false)
idx = findfirst(product_matrix' .== 0) idx = findfirst(product_matrix' .== 0)

18
test/runtests.jl
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@ -9,7 +9,7 @@ using SparseArrays
@testset "Constructors: PermutationGroup" begin @testset "Constructors: PermutationGroup" begin
G = PermutationGroup(3) G = PermutationGroup(3)
@test isa(GroupRing(G), AbstractAlgebra.Ring) @test isa(GroupRing(G), AbstractAlgebra.NCRing)
@test isa(GroupRing(G), GroupRing) @test isa(GroupRing(G), GroupRing)
RG = GroupRing(G) RG = GroupRing(G)
@ -115,6 +115,20 @@ using SparseArrays
@test string(-a) == " - 2() - 1(1,2,3)" @test string(-a) == " - 2() - 1(1,2,3)"
@test length(a) == 2 @test length(a) == 2
@testset "RSL(3,Z)" begin
N = 3
halfradius = 2
M = MatrixAlgebra(zz, N)
E(M, i,j) = (e_ij = one(M); e_ij[i,j] = 1; e_ij)
S = [E(M, i,j) for i in 1:N for j in 1:N if i≠j]
S = unique([S; inv.(S)])
E_R, sizes = Groups.generate_balls(S, radius=2*halfradius)
E_rdict = GroupRings.reverse_dict(E_R)
pm = GroupRings.create_pm(E_R, E_rdict, sizes[halfradius]; twisted=true);
@test GroupRing(M, E_R, E_rdict, pm) isa GroupRing
end
end end
@testset "Arithmetic" begin @testset "Arithmetic" begin
@ -153,7 +167,7 @@ using SparseArrays
@test isa(b//4, GroupRingElem) @test isa(b//4, GroupRingElem)
@test eltype(b//4) == Rational{Int} @test eltype(b//4) == Rational{Int}
@test isa(b//big(4), RingElem) @test isa(b//big(4), NCRingElem)
@test eltype(b//(big(4)//1)) == Rational{BigInt} @test eltype(b//(big(4)//1)) == Rational{BigInt}
@test isa(a//1, GroupRingElem) @test isa(a//1, GroupRingElem)