mirror of
https://github.com/kalmarek/GroupRings.jl.git
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Merge branch 'master' of github.com:kalmarek/GroupRings.jl
This commit is contained in:
commit
d09d85cbd0
@ -1,7 +1,7 @@
|
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name = "GroupRings"
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uuid = "0befed6a-bd73-11e8-1e41-a1190947c2f5"
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authors = ["Marek Kaluba <kalmar@amu.edu.pl>"]
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version = "0.2.0"
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version = "0.3.0"
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[deps]
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AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
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@ -10,10 +10,8 @@ Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
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SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
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[extras]
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Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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Groups = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
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Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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[targets]
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test = ["Test", "Groups"]
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[compat]
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@ -1,7 +1,7 @@
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module GroupRings
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using AbstractAlgebra
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import AbstractAlgebra: Group, GroupElem, Ring, RingElem, parent, elem_type, parent_type, addeq!, mul!
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import AbstractAlgebra: Group, NCRing, NCRingElem, parent, elem_type, parent_type, addeq!, mul!
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using SparseArrays
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using LinearAlgebra
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@ -9,13 +9,16 @@ using Markdown
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import Base: convert, show, hash, ==, +, -, *, ^, //, /, length, getindex, setindex!, eltype, one, zero
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GroupOrNCRing = Union{AbstractAlgebra.Group, AbstractAlgebra.NCRing}
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GroupOrNCRingElem = Union{AbstractAlgebra.GroupElem, AbstractAlgebra.NCRingElem}
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###############################################################################
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#
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# GroupRings / GroupRingsElem
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#
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###############################################################################
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mutable struct GroupRing{Gr<:Group, T<:GroupElem} <: Ring
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mutable struct GroupRing{Gr<:GroupOrNCRing, T<:GroupOrNCRingElem} <: NCRing
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group::Gr
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basis::Vector{T}
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basis_dict::Dict{T, Int}
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@ -39,7 +42,7 @@ mutable struct GroupRing{Gr<:Group, T<:GroupElem} <: Ring
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end
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end
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mutable struct GroupRingElem{T, A<:AbstractVector, GR<:GroupRing} <: RingElem
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mutable struct GroupRingElem{T, A<:AbstractVector, GR<:GroupRing} <: NCRingElem
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coeffs::A
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parent::GR
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@ -98,7 +101,7 @@ import Base.promote_rule
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promote_rule(::Type{GroupRingElem{T}}, ::Type{GroupRingElem{S}}) where {T,S} =
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GroupRingElem{promote_type(T,S)}
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function convert(::Type{T}, X::GroupRingElem) where {T<:Number}
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function convert(::Type{T}, X::GroupRingElem) where T<:Number
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return GroupRingElem(Vector{T}(X.coeffs), parent(X))
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end
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@ -112,7 +115,7 @@ end
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zero(RG::GroupRing, T::Type=Int) = RG(T)
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one(RG::GroupRing, T::Type=Int) = RG(RG.group(), T)
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one(RG::GroupRing{<:MatSpace}, T::Type=Int) = RG(one(RG.group), T)
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one(RG::GroupRing{<:AbstractAlgebra.NCRing}, T::Type=Int) = RG(one(RG.group), T)
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function (RG::GroupRing)(T::Type=Int)
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isdefined(RG, :basis) || throw("Can not coerce without basis of GroupRing")
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@ -125,19 +128,19 @@ function (RG::GroupRing)(i::Int, T::Type=Int)
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return elt
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end
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function (RG::GroupRing{<:MatSpace})(i::Int, T::Type=Int)
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function (RG::GroupRing{<:AbstractAlgebra.NCRing})(i::Int, T::Type=Int)
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elt = RG(T)
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elt[one(RG.group)] = i
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return elt
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end
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function (RG::GroupRing)(g::GroupElem, T::Type=Int)
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function (RG::GroupRing)(g::GroupOrNCRingElem, T::Type=Int)
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result = RG(T)
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result[RG.group(g)] = one(T)
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return result
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end
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function (RG::GroupRing{Gr,T})(V::Vector{T}, S::Type=Int) where {Gr<:Group, T<:GroupElem}
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function (RG::GroupRing{Gr,T})(V::Vector{T}, S::Type=Int) where {Gr, T}
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res = RG(S)
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for g in V
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res[g] += one(S)
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@ -156,7 +159,7 @@ end
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# keep storage type
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function (RG::GroupRing)(x::AbstractVector{T}) where T<:Number
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function (RG::GroupRing)(x::AbstractVector{T}) where T
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isdefined(RG, :basis) || throw("Basis of GroupRing not defined. For advanced use the direct constructor of GroupRingElem is provided.")
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length(x) == length(RG.basis) || throw("Can not coerce to $RG: lengths differ")
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return GroupRingElem(x, RG)
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@ -181,7 +184,7 @@ function getindex(X::GroupRingElem, n::Int)
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return X.coeffs[n]
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end
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function getindex(X::GroupRingElem, g::GroupElem)
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function getindex(X::GroupRingElem, g::GroupOrNCRingElem)
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return X.coeffs[parent(X).basis_dict[g]]
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end
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@ -189,7 +192,7 @@ function setindex!(X::GroupRingElem, value, n::Int)
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X.coeffs[n] = value
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end
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function setindex!(X::GroupRingElem, value, g::GroupElem)
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function setindex!(X::GroupRingElem, value, g::GroupOrNCRingElem)
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RG = parent(X)
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if !(g in keys(RG.basis_dict))
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g = (RG.group)(g)
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@ -288,15 +291,15 @@ end
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(-)(X::GroupRingElem) = GroupRingElem(-X.coeffs, parent(X))
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function mul!(a::T, X::GroupRingElem{T}) where {T<:Number}
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function mul!(a::T, X::GroupRingElem{T}) where T
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X.coeffs .*= a
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return X
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end
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mul(a::T, X::GroupRingElem{T}) where {T<:Number} = GroupRingElem(a*X.coeffs, parent(X))
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mul(a::T, X::GroupRingElem{T}) where T = GroupRingElem(a*X.coeffs, parent(X))
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function mul(a::T, X::GroupRingElem{S}) where {T<:Number, S<:Number}
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TT = promote_type(T,S)
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function mul(a::T, X::GroupRingElem{S}) where {T<:Number, S}
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TT = promote_type(T,S)
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TT == S || @warn("Scalar and coeffs are in different rings! Promoting result to $(TT)")
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return GroupRingElem(a.*X.coeffs, parent(X))
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end
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@ -343,9 +346,9 @@ end
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fmac!(result::AbstractVector{T},
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X::AbstractVector,
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Y::AbstractVector,
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pm::Array{Int,2}) where {T<:Number}
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pm::Array{Int,2}) where T
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> Fused multiply-add for group ring coeffs using multiplication table `pm`.
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> The result of X*Y in GroupRing is added in-place to `result`.
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> The result of X*Y in GroupRing is added in-place to `result`.
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> Notes:
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> * this method will silently produce false results if `X[k]` is non-zero for
|
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> `k > size(pm,1)`.
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@ -357,11 +360,11 @@ end
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function fmac!(result::AbstractVector{T},
|
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X::AbstractVector,
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Y::AbstractVector,
|
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pm::Array{Int,2}) where {T<:Number}
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pm::Array{Int,2}) where T
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z = zero(T)
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s1 = size(pm,1)
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s2 = size(pm,2)
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@inbounds for j in 1:s2
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if Y[j] != z
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for i in 1:s1
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@ -376,7 +379,7 @@ end
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@doc doc"""
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GRmul!(result::AbstractVector{T}, X::AbstractVector, Y::AbstractVector,
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pm::Matrix{<:Integer}) where {T<:Number}
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pm::Matrix{<:Integer}) where T
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> The most specialised multiplication for `X` and `Y` (intended for `coeffs` of
|
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> `GroupRingElems`), using multiplication table `pm`.
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> Notes:
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@ -389,7 +392,7 @@ end
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function GRmul!(result::AbstractVector{T},
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X::AbstractVector,
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Y::AbstractVector,
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pm::AbstractMatrix{<:Integer}) where {T<:Number}
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pm::AbstractMatrix{<:Integer}) where T
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z = zero(T)
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result .= z
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@ -451,7 +454,7 @@ function mul!(result::GroupRingElem, X::GroupRingElem, Y::GroupRingElem)
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return result
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end
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function *(X::GroupRingElem{T}, Y::GroupRingElem{T}, check::Bool=true) where {T<:Number}
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function *(X::GroupRingElem{T}, Y::GroupRingElem{T}, check::Bool=true) where T
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if check
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parent(X) == parent(Y) || throw("Elements don't seem to belong to the same Group Ring!")
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end
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@ -465,7 +468,7 @@ function *(X::GroupRingElem{T}, Y::GroupRingElem{T}, check::Bool=true) where {T<
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return result
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end
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function *(X::GroupRingElem{T}, Y::GroupRingElem{S}, check::Bool=true) where {T<:Number, S<:Number}
|
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function *(X::GroupRingElem{T}, Y::GroupRingElem{S}, check::Bool=true) where {T,S}
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if check
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parent(X) == parent(Y) || throw("Elements don't seem to belong to the same Group Ring!")
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end
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@ -525,8 +528,8 @@ end
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reverse_dict(iter) = reverse_dict(Int, iter)
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function create_pm(basis::Vector{T}, basis_dict::Dict{T, Int},
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limit::Int=length(basis); twisted::Bool=false, check=true) where {T<:GroupElem}
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function create_pm(basis::AbstractVector{T}, basis_dict::Dict{T, Int},
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limit::Int=length(basis); twisted::Bool=false, check=true) where T
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product_matrix = zeros(Int, (limit,limit))
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Threads.@threads for i in 1:limit
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x = basis[i]
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@ -543,7 +546,7 @@ function create_pm(basis::Vector{T}, basis_dict::Dict{T, Int},
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return product_matrix
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end
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create_pm(b::Vector{T}) where {T<:GroupElem} = create_pm(b, reverse_dict(b))
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create_pm(b::AbstractVector{<:GroupOrNCRingElem}) = create_pm(b, reverse_dict(b))
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function check_pm(product_matrix, basis, twisted=false)
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idx = findfirst(product_matrix' .== 0)
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@ -561,7 +564,7 @@ end
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function complete!(RG::GroupRing)
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isdefined(RG, :basis) || throw(ArgumentError("Provide basis for completion first!"))
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if !isdefined(RG, :pm)
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if !isdefined(RG, :pm)
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initializepm!(RG, fill=false)
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return RG
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end
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110
test/runtests.jl
110
test/runtests.jl
@ -9,7 +9,7 @@ using SparseArrays
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@testset "Constructors: PermutationGroup" begin
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G = PermutationGroup(3)
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@test isa(GroupRing(G), AbstractAlgebra.Ring)
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@test isa(GroupRing(G), AbstractAlgebra.NCRing)
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@test isa(GroupRing(G), GroupRing)
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RG = GroupRing(G)
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@ -115,6 +115,20 @@ using SparseArrays
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@test string(-a) == " - 2() - 1(1,2,3)"
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@test length(a) == 2
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@testset "RSL(3,Z)" begin
|
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N = 3
|
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halfradius = 2
|
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M = MatrixAlgebra(zz, N)
|
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E(M, i,j) = (e_ij = one(M); e_ij[i,j] = 1; e_ij)
|
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S = [E(M, i,j) for i in 1:N for j in 1:N if i≠j]
|
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S = unique([S; inv.(S)])
|
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E_R, sizes = Groups.generate_balls(S, radius=2*halfradius)
|
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E_rdict = GroupRings.reverse_dict(E_R)
|
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pm = GroupRings.create_pm(E_R, E_rdict, sizes[halfradius]; twisted=true);
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@test GroupRing(M, E_R, E_rdict, pm) isa GroupRing
|
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end
|
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end
|
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|
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@testset "Arithmetic" begin
|
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@ -153,7 +167,7 @@ using SparseArrays
|
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@test isa(b//4, GroupRingElem)
|
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@test eltype(b//4) == Rational{Int}
|
||||
|
||||
@test isa(b//big(4), RingElem)
|
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@test isa(b//big(4), NCRingElem)
|
||||
@test eltype(b//(big(4)//1)) == Rational{BigInt}
|
||||
|
||||
@test isa(a//1, GroupRingElem)
|
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@ -208,18 +222,18 @@ using SparseArrays
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@test supp(z) == parent(z).basis
|
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@test supp(RG(1) + RG(perm"(2,3)")) == [G(), perm"(2,3)"]
|
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@test supp(a) == [perm"(3)", perm"(2,3)", perm"(1,2,3)"]
|
||||
|
||||
|
||||
end
|
||||
|
||||
|
||||
@testset "HPC multiplicative operations" begin
|
||||
|
||||
|
||||
G = PermutationGroup(5)
|
||||
RG = GroupRing(G, cachedmul=true)
|
||||
RG2 = GroupRing(G, cachedmul=false)
|
||||
|
||||
|
||||
Z = RG()
|
||||
W = RG()
|
||||
|
||||
|
||||
for g in [rand(G) for _ in 1:30]
|
||||
X = RG(g)
|
||||
Y = -RG(inv(g))
|
||||
@ -227,26 +241,26 @@ using SparseArrays
|
||||
X[rand(G)] += rand(1:3)
|
||||
Y[rand(G)] -= rand(1:3)
|
||||
end
|
||||
|
||||
@test X*Y ==
|
||||
RG2(X)*RG2(Y) ==
|
||||
|
||||
@test X*Y ==
|
||||
RG2(X)*RG2(Y) ==
|
||||
GroupRings.mul!(Z, X, Y)
|
||||
|
||||
|
||||
@test Z.coeffs == GroupRings.GRmul!(W.coeffs, X.coeffs, Y.coeffs, RG.pm) == W.coeffs
|
||||
@test (2*X*Y).coeffs ==
|
||||
@test (2*X*Y).coeffs ==
|
||||
GroupRings.fmac!(W.coeffs, X.coeffs, Y.coeffs, RG.pm) ==
|
||||
GroupRings.mul!(2, X*Y).coeffs
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
@testset "SumOfSquares in group rings" begin
|
||||
∗ = star
|
||||
|
||||
|
||||
G = FreeGroup(["g", "h", "k", "l"])
|
||||
S = G.(G.gens)
|
||||
S = [S; inv.(S)]
|
||||
|
||||
|
||||
ID = G()
|
||||
RADIUS=3
|
||||
@time E_R, sizes = Groups.generate_balls(S, ID, radius=2*RADIUS);
|
||||
@ -254,14 +268,14 @@ using SparseArrays
|
||||
E_rdict = GroupRings.reverse_dict(E_R)
|
||||
pm = GroupRings.create_pm(E_R, E_rdict, sizes[RADIUS]; twisted=true);
|
||||
RG = GroupRing(G, E_R, E_rdict, pm)
|
||||
|
||||
|
||||
g = RG.basis[2]
|
||||
h = RG.basis[3]
|
||||
k = RG.basis[4]
|
||||
l = RG.basis[5]
|
||||
G = (1-RG(g))
|
||||
@test G^2 == 2 - RG(g) - ∗(RG(g))
|
||||
|
||||
|
||||
G = (1-RG(g))
|
||||
H = (1-RG(h))
|
||||
K = (1-RG(k))
|
||||
@ -271,59 +285,59 @@ using SparseArrays
|
||||
|
||||
X = (2 - ∗(RG(g)) - RG(h))
|
||||
Y = (2 - ∗(RG(g*h)) - RG(k))
|
||||
|
||||
|
||||
@test -(2 - RG(g*h) - ∗(RG(g*h))) + 2G^2 + 2H^2 == X^2
|
||||
@test (2 - RG(g*h) - ∗(RG(g*h))) == GH^2
|
||||
@test -(2 - RG(g*h*k) - ∗(RG(g*h*k))) + 2GH^2 + 2K^2 == Y^2
|
||||
@test -(2 - RG(g*h*k) - ∗(RG(g*h*k))) +
|
||||
2(GH^2 - 2G^2 - 2H^2) +
|
||||
4G^2 + 4H^2 + 2K^2 ==
|
||||
@test -(2 - RG(g*h*k) - ∗(RG(g*h*k))) +
|
||||
2(GH^2 - 2G^2 - 2H^2) +
|
||||
4G^2 + 4H^2 + 2K^2 ==
|
||||
Y^2
|
||||
|
||||
|
||||
@test GH^2 - 2G^2 - 2H^2 == - X^2
|
||||
@test -(2 - RG(g*h*k) - ∗(RG(g*h*k))) + 4G^2 + 4H^2 + 2K^2 == 2X^2 + Y^2
|
||||
|
||||
|
||||
@test GH^2 == 2G^2 + 2H^2 - (2 - ∗(RG(g)) - RG(h))^2
|
||||
@test KL^2 == 2K^2 + 2L^2 - (2 - ∗(RG(k)) - RG(l))^2
|
||||
|
||||
@test KL^2 == 2K^2 + 2L^2 - (2 - ∗(RG(k)) - RG(l))^2
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) + 2*GH^2 + 2*KL^2 ==
|
||||
(2 - ∗(RG(g*h)) - RG(k*l))^2
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
2(2G^2 + 2H^2 - (2 - ∗(RG(g)) - RG(h))^2) +
|
||||
2(2K^2 + 2L^2 - (2 - ∗(RG(k)) - RG(l))^2) ==
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
2(2G^2 + 2H^2 - (2 - ∗(RG(g)) - RG(h))^2) +
|
||||
2(2K^2 + 2L^2 - (2 - ∗(RG(k)) - RG(l))^2) ==
|
||||
(2 - ∗(RG(g*h)) - RG(k*l))^2
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
2(2G^2 + 2H^2) +
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
2(2G^2 + 2H^2) +
|
||||
2(2K^2 + 2L^2) ==
|
||||
(2 - ∗(RG(g*h)) - RG(k*l))^2 +
|
||||
2(2 - ∗(RG(g)) - RG(h))^2 +
|
||||
(2 - ∗(RG(g*h)) - RG(k*l))^2 +
|
||||
2(2 - ∗(RG(g)) - RG(h))^2 +
|
||||
2(2 - ∗(RG(k)) - RG(l))^2
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
2(2 - ∗(RG(g*h*k)) - RG(g*h*k)) + 2L^2 ==
|
||||
(2 - ∗(RG(g*h*k)) - RG(l))^2
|
||||
|
||||
@test 2 - ∗(RG(g*h*k)) - RG(g*h*k) ==
|
||||
|
||||
@test 2 - ∗(RG(g*h*k)) - RG(g*h*k) ==
|
||||
2GH^2 + 2K^2 - (2 - ∗(RG(g*h)) - RG(k))^2
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
2(2GH^2 + 2K^2 - (2 - ∗(RG(g*h)) - RG(k))^2) + 2L^2 ==
|
||||
(2 - ∗(RG(g*h*k)) - RG(l))^2
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
2(2GH^2 + 2K^2) + 2L^2 ==
|
||||
(2 - ∗(RG(g*h*k)) - RG(l))^2 +
|
||||
(2 - ∗(RG(g*h*k)) - RG(l))^2 +
|
||||
2(2 - ∗(RG(g*h)) - RG(k))^2
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
8G^2 + 8H^2 + 4K^2 + 2L^2 ==
|
||||
(2 - ∗(RG(g*h*k)) - RG(l))^2 + 2(2 - ∗(RG(g*h)) - RG(k))^2 + 4(2 - ∗(RG(g)) - RG(h))^2
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
|
||||
2GH^2 + 2KL^2 == (2 - ∗(RG(g*h)) - RG(k*l))^2
|
||||
|
||||
|
||||
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) + 2(2G^2 + 2H^2) + 2(2K^2 + 2L^2) ==
|
||||
(2 - ∗(RG(g*h)) - RG(k*l))^2 + 2(2 - ∗(RG(k)) - RG(l))^2 + 2(2 - ∗(RG(g)) - RG(h))^2
|
||||
end
|
||||
|
||||
Loading…
Reference in New Issue
Block a user