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src/types.jl
65
src/types.jl
@ -23,8 +23,13 @@ word_type(::Type{<:AbstractFPGroup}) = Word{UInt8}
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# the default (results in free rewriting)
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rewriting(G::AbstractFPGroup) = alphabet(G)
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Base.@propagate_inbounds function (G::AbstractFPGroup)(word::AbstractVector{<:Integer})
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@boundscheck @assert all(l -> 1 <= l <= length(KnuthBendix.alphabet(G)), word)
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Base.@propagate_inbounds function (G::AbstractFPGroup)(
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word::AbstractVector{<:Integer},
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)
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@boundscheck @assert all(
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l -> 1 <= l <= length(KnuthBendix.alphabet(G)),
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word,
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)
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return FPGroupElement(word_type(G)(word), G)
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end
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@ -32,7 +37,8 @@ end
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Base.one(G::AbstractFPGroup) = FPGroupElement(one(word_type(G)), G)
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Base.eltype(::Type{FPG}) where {FPG<:AbstractFPGroup} = FPGroupElement{FPG,word_type(FPG)}
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Base.eltype(::Type{FPG}) where {FPG<:AbstractFPGroup} =
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FPGroupElement{FPG,word_type(FPG)}
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include("iteration.jl")
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@ -43,32 +49,42 @@ function GroupsCore.gens(G::AbstractFPGroup, i::Integer)
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l = alphabet(G)[G.gens[i]]
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return FPGroupElement(word_type(G)([l]), G)
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end
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GroupsCore.gens(G::AbstractFPGroup) = [gens(G, i) for i in 1:GroupsCore.ngens(G)]
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GroupsCore.gens(G::AbstractFPGroup) =
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[gens(G, i) for i in 1:GroupsCore.ngens(G)]
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# TODO: ProductReplacementAlgorithm
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function Base.rand(rng::Random.AbstractRNG, rs::Random.SamplerTrivial{<:AbstractFPGroup})
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function Base.rand(
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rng::Random.AbstractRNG,
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rs::Random.SamplerTrivial{<:AbstractFPGroup},
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)
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l = rand(10:100)
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G = rs[]
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nletters = length(alphabet(G))
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return FPGroupElement(word_type(G)(rand(1:nletters, l)), G)
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end
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Base.isfinite(::AbstractFPGroup) = (@warn "using generic isfinite(::AbstractFPGroup): the returned `false` might be wrong"; false)
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Base.isfinite(::AbstractFPGroup) = (
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@warn "using generic isfinite(::AbstractFPGroup): the returned `false` might be wrong"; false
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)
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## FPGroupElement
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abstract type AbstractFPGroupElement{Gr} <: GroupElement end
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mutable struct FPGroupElement{Gr<:AbstractFPGroup,W<:AbstractWord} <: AbstractFPGroupElement{Gr}
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mutable struct FPGroupElement{Gr<:AbstractFPGroup,W<:AbstractWord} <:
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AbstractFPGroupElement{Gr}
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word::W
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savedhash::UInt
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parent::Gr
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FPGroupElement(word::W, G::AbstractFPGroup, hash::UInt=UInt(0)) where {W<:AbstractWord} =
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new{typeof(G),W}(word, hash, G)
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FPGroupElement(
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word::W,
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G::AbstractFPGroup,
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hash::UInt = UInt(0),
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) where {W<:AbstractWord} = new{typeof(G),W}(word, hash, G)
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FPGroupElement{Gr, W}(word::AbstractWord, G::Gr) where {Gr, W} =
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new{Gr, W}(word, UInt(0), G)
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FPGroupElement{Gr,W}(word::AbstractWord, G::Gr) where {Gr,W} =
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new{Gr,W}(word, UInt(0), G)
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end
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Base.show(io::IO, ::Type{<:FPGroupElement{Gr}}) where {Gr} =
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@ -81,7 +97,7 @@ KnuthBendix.alphabet(g::AbstractFPGroupElement) = alphabet(parent(g))
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function Base.show(io::IO, f::AbstractFPGroupElement)
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f = normalform!(f)
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KnuthBendix.print_repr(io, word(f), alphabet(f))
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return KnuthBendix.print_repr(io, word(f), alphabet(f))
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end
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## GroupElement Interface for FPGroupElement
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@ -100,17 +116,21 @@ function Base.deepcopy_internal(g::FPGroupElement, stackdict::IdDict)
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return FPGroupElement(copy(word(g)), parent(g), g.savedhash)
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end
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function Base.inv(g::GEl) where GEl <: AbstractFPGroupElement
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function Base.inv(g::GEl) where {GEl<:AbstractFPGroupElement}
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G = parent(g)
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return GEl(inv(alphabet(G), word(g)), G)
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end
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function Base.:(*)(g::GEl, h::GEl) where GEl<:AbstractFPGroupElement
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function Base.:(*)(g::GEl, h::GEl) where {GEl<:AbstractFPGroupElement}
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@boundscheck @assert parent(g) === parent(h)
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return GEl(word(g) * word(h), parent(g))
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end
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GroupsCore.isfiniteorder(g::AbstractFPGroupElement) = isone(g) ? true : (@warn "using generic isfiniteorder(::AbstractFPGroupElement): the returned `false` might be wrong"; false)
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GroupsCore.isfiniteorder(g::AbstractFPGroupElement) =
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isone(g) ? true :
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(
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@warn "using generic isfiniteorder(::AbstractFPGroupElement): the returned `false` might be wrong"; false
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)
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# additional methods:
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Base.isone(g::AbstractFPGroupElement) = (normalform!(g); isempty(word(g)))
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@ -129,7 +149,9 @@ struct FreeGroup{T} <: AbstractFPGroup
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end
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function FreeGroup(A::Alphabet)
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@boundscheck @assert all(KnuthBendix.hasinverse(l, A) for l in KnuthBendix.letters(A))
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@boundscheck @assert all(
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KnuthBendix.hasinverse(l, A) for l in KnuthBendix.letters(A)
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)
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ltrs = KnuthBendix.letters(A)
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gens = Vector{eltype(ltrs)}()
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invs = Vector{eltype(ltrs)}()
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@ -149,12 +171,13 @@ function FreeGroup(n::Integer)
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sizehint!(inverses, 2n)
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for i in 1:n
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push!(symbols, Symbol(:f, i), Symbol(:F, i))
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push!(inverses, 2i, 2i-1)
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push!(inverses, 2i, 2i - 1)
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end
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return FreeGroup(symbols[1:2:2n], Alphabet(symbols, inverses))
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end
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Base.show(io::IO, F::FreeGroup) = print(io, "free group on $(ngens(F)) generators")
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Base.show(io::IO, F::FreeGroup) =
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print(io, "free group on $(ngens(F)) generators")
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# mandatory methods:
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KnuthBendix.alphabet(F::FreeGroup) = F.alphabet
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@ -164,7 +187,8 @@ relations(F::FreeGroup) = Pair{eltype(F)}[]
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# these are mathematically correct
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Base.isfinite(::FreeGroup) = false
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GroupsCore.isfiniteorder(g::AbstractFPGroupElement{<:FreeGroup}) = isone(g) ? true : false
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GroupsCore.isfiniteorder(g::AbstractFPGroupElement{<:FreeGroup}) =
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isone(g) ? true : false
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## FP Groups
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@ -185,7 +209,6 @@ function FPGroup(
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ordering = KnuthBendix.LenLex,
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kwargs...,
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) where {GEl<:FPGroupElement}
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O = ordering(alphabet(G))
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for (lhs, rhs) in rels
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@assert parent(lhs) === parent(rhs) === G
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@ -203,7 +226,7 @@ function Base.show(io::IO, G::FPGroup)
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join(io, gens(G), ", ")
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print(io, " | ")
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join(io, relations(G), ", ")
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print(io, "⟩")
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return print(io, "⟩")
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end
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Base.show(io::IO, ::Type{<:FPGroup{T}}) where {T} =
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