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remove new_types.jl again
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src/new_types.jl
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src/new_types.jl
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using GroupsCore
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# using Groups
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# import Groups.AbstractFPGroup
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import KnuthBendix
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import KnuthBendix: AbstractWord, Alphabet, Word, RewritingSystem
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import KnuthBendix: alphabet
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using Random
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## "Abstract" definitions
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"""
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AbstractFPGroup
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An Abstract type representing finitely presented groups. Every instance `` must implement
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* `KnuthBendix.alphabet(G::MyFPGroup)`
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* `rewriting(G::MyFPGroup)` : return the rewriting object which must implement
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> `KnuthBendix.rewrite_from_left!(u, v, rewriting(G))`.
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By default `alphabet(G)` is returned, which amounts to free rewriting in `G`.
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* `relations(G::MyFPGroup)` : return a set of defining relations.
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AbstractFPGroup may also override `word_type(::Type{MyFPGroup}) = Word{UInt16}`,
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which controls the word type used for group elements. If a group has more than `255` generators you need to define e.g.
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> `word_type(::Type{MyFPGroup}) = Word{UInt16}`
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"""
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abstract type AbstractFPGroup <: GroupsCore.Group end
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word_type(G::AbstractFPGroup) = word_type(typeof(G))
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# the default:
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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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return FPGroupElement(word_type(G)(word), G)
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end
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function Base.show(io::IO, G::AbstractFPGroup)
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print(io, "⟨")
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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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end
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## Group Interface
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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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include("iteration.jl")
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GroupsCore.ngens(G::AbstractFPGroup) = length(G.gens)
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function GroupsCore.gens(G::AbstractFPGroup, i::Integer)
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@boundscheck 1 <= i <= GroupsCore.ngens(G)
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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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# TODO: ProductReplacementAlgorithm
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function Base.rand(rng::Random.AbstractRNG, rs::Random.SamplerTrivial{<:AbstractFPGroup})
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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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## FPGroupElement
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mutable struct FPGroupElement{G<:AbstractFPGroup,W<:AbstractWord} <: GroupElement
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word::W
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savedhash::UInt
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parent::G
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FPGroupElement(word::W, G::AbstractFPGroup) where {W<:AbstractWord} =
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new{typeof(G),W}(word, UInt(0), G)
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FPGroupElement(word::W, hash::UInt, G::AbstractFPGroup) where {W<:AbstractWord} =
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new{typeof(G),W}(word, hash, G)
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end
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word(f::FPGroupElement) = f.word
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#convenience
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KnuthBendix.alphabet(g::FPGroupElement) = alphabet(parent(g))
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function Base.show(io::IO, f::FPGroupElement)
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f = normalform!(f)
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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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Base.parent(f::FPGroupElement) = f.parent
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GroupsCore.parent_type(::Type{<:FPGroupElement{G}}) where {G} = G
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function Base.:(==)(g::FPGroupElement, h::FPGroupElement)
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@boundscheck @assert parent(g) === parent(h)
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normalform!(g)
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normalform!(h)
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hash(g) != hash(h) && return false
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return word(g) == word(h)
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end
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function Base.deepcopy_internal(g::FPGroupElement, stackdict::IdDict)
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return FPGroupElement(copy(word(g)), g.savedhash, parent(g))
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end
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Base.inv(g::FPGroupElement) = (G = parent(g); FPGroupElement(inv(alphabet(G), word(g)), G))
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function Base.:(*)(g::FPGroupElement, h::FPGroupElement)
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@boundscheck @assert parent(g) === parent(h)
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return FPGroupElement(word(g) * word(h), parent(g))
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end
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GroupsCore.isfiniteorder(g::FPGroupElement) = isone(g) ? true : (@warn "using generic isfiniteorder(::FPGroupElement): the returned `false` might be wrong"; false)
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# additional methods:
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Base.isone(g::FPGroupElement) = (normalform!(g); isempty(word(g)))
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## Free Groups
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struct FreeGroup{T} <: AbstractFPGroup
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gens::Vector{T}
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alphabet::KnuthBendix.Alphabet{T}
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function FreeGroup(gens, A::KnuthBendix.Alphabet) where {W}
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@assert length(gens) == length(unique(gens))
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@assert all(l -> l in KnuthBendix.letters(A), gens)
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return new{eltype(gens)}(gens, A)
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end
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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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return FreeGroup(KnuthBendix.letters(A), A)
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end
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function FreeGroup(n::Integer)
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symbols = Symbol[]
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inverses = Int[]
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sizehint!(symbols, 2n)
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sizehint!(inverses, 2n)
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for i in 1:n
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push!(symbols, Symbol(:f, subscriptify(i)), Symbol(:F, subscriptify(i)))
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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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# mandatory methods:
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KnuthBendix.alphabet(F::FreeGroup) = F.alphabet
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relations(F::FreeGroup) = Pair{eltype(F)}[]
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# GroupsCore interface:
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# these are mathematically correct
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Base.isfinite(::FreeGroup) = false
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GroupsCore.isfiniteorder(g::FPGroupElement{<:FreeGroup}) = isone(g) ? true : false
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## FP Groups
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struct FPGroup{T,R,S} <: AbstractFPGroup
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gens::Vector{T}
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relations::Vector{Pair{S,S}}
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rws::R
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end
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KnuthBendix.alphabet(G::FPGroup) = alphabet(rewriting(G))
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rewriting(G::FPGroup) = G.rws
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relations(G::FPGroup) = G.relations
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function FPGroup(
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G::AbstractFPGroup,
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rels::AbstractVector{<:Pair{GEl,GEl}};
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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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end
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word_rels = [word(lhs) => word(rhs) for (lhs, rhs) in [relations(G); rels]]
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rws = RewritingSystem(word_rels, O)
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KnuthBendix.knuthbendix!(rws; kwargs...)
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return FPGroup(G.gens, rels, rws)
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end
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## GSymbol aka letter of alphabet
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abstract type GSymbol end
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Base.literal_pow(::typeof(^), t::GSymbol, ::Val{-1}) = inv(t)
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subscriptify(i::Integer) = join('₀'+d for d in reverse(digits(i)))
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