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@ -7,6 +7,7 @@ version = "0.5.2"
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AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
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DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
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GroupsCore = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
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KnuthBendix = "c2604015-7b3d-4a30-8a26-9074551ec60a"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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ThreadsX = "ac1d9e8a-700a-412c-b207-f0111f4b6c0d"
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@ -1,4 +1,4 @@
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mutable struct FPIterState{GEl, T}
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mutable struct FPIterState{GEl,T}
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elts::OrderedSet{GEl}
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u::GEl
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v::GEl
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@ -42,12 +42,12 @@ function Base.iterate(G::AbstractFPGroup, state)
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end
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if res in iter
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return iterate(G, (iter, elt, gen_idx+1))
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return iterate(G, (iter, elt, gen_idx + 1))
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else
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w = deepcopy(res)
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@assert isnormalform(w)
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push!(iter, w)
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return w, (iter, elt, gen_idx+1)
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return w, (iter, elt, gen_idx + 1)
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end
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end
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@ -4,7 +4,7 @@ function KnuthBendix.Alphabet(S::AbstractVector{<:GSymbol})
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return Alphabet(S, inversions)
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end
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struct AutomorphismGroup{G<:Group, T, R, S} <: AbstractFPGroup
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struct AutomorphismGroup{G<:Group,T,R,S} <: AbstractFPGroup
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group::G
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gens::Vector{T}
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rws::R
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@ -13,29 +13,28 @@ end
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object(G::AutomorphismGroup) = G.group
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function SpecialAutomorphismGroup(F::FreeGroup;
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ordering=KnuthBendix.LenLex, kwargs...)
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function SpecialAutomorphismGroup(F::FreeGroup; ordering = KnuthBendix.LenLex, kwargs...)
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n = length(KnuthBendix.alphabet(F))÷2
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A, rels = gersten_relations(n, commutative=false)
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S = KnuthBendix.letters(A)[1:2(n^2 - n)]
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n = length(KnuthBendix.alphabet(F)) ÷ 2
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A, rels = gersten_relations(n, commutative = false)
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S = KnuthBendix.letters(A)[1:2(n^2-n)]
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rws = KnuthBendix.RewritingSystem(rels, ordering(A))
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KnuthBendix.knuthbendix!(rws; kwargs...)
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return AutomorphismGroup(F, S, rws, ntuple(i->gens(F, i), n))
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return AutomorphismGroup(F, S, rws, ntuple(i -> gens(F, i), n))
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end
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KnuthBendix.alphabet(G::AutomorphismGroup{<:FreeGroup}) = alphabet(rewriting(G))
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rewriting(G::AutomorphismGroup) = G.rws
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function relations(G::AutomorphismGroup)
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n = length(KnuthBendix.alphabet(object(G)))÷2
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return last(gersten_relations(n, commutative=false))
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n = length(KnuthBendix.alphabet(object(G))) ÷ 2
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return last(gersten_relations(n, commutative = false))
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end
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equality_data(f::FPGroupElement{<:AutomorphismGroup}) = normalform!.(evaluate(f))
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function Base.:(==)(g::A, h::A) where A<:FPGroupElement{<:AutomorphismGroup}
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function Base.:(==)(g::A, h::A) where {A<:FPGroupElement{<:AutomorphismGroup}}
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@assert parent(g) === parent(h)
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if _isvalidhash(g) && _isvalidhash(h)
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@ -81,15 +80,15 @@ end
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# eye-candy
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Base.show(io::IO, ::Type{<:FPGroupElement{<:AutomorphismGroup{T}}}) where T <: FreeGroup = print(io, "Automorphism{$T}")
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Base.show(io::IO, ::Type{<:FPGroupElement{<:AutomorphismGroup{T}}}) where {T<:FreeGroup} =
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print(io, "Automorphism{$T,…}")
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## Automorphism Evaluation
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domain(f::FPGroupElement{<:AutomorphismGroup}) = deepcopy(parent(f).domain)
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# tuple(gens(object(parent(f)))...)
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evaluate(f::FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}) =
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evaluate!(domain(f), f)
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evaluate(f::FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}) = evaluate!(domain(f), f)
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function evaluate!(
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t::NTuple{N,T},
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@ -20,10 +20,8 @@ _isvalidhash(g::FPGroupElement) = bitget(g.savedhash, 1)
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_setnormalform(h::UInt, v::Bool) = bitset(h, v, 0)
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_setvalidhash(h::UInt, v::Bool) = bitset(h, v, 1)
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_setnormalform!(g::FPGroupElement, v::Bool) =
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g.savedhash = _setnormalform(g.savedhash, v)
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_setvalidhash!(g::FPGroupElement, v::Bool) =
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g.savedhash = _setvalidhash(g.savedhash, v)
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_setnormalform!(g::FPGroupElement, v::Bool) = g.savedhash = _setnormalform(g.savedhash, v)
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_setvalidhash!(g::FPGroupElement, v::Bool) = g.savedhash = _setvalidhash(g.savedhash, v)
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# To update hash use this internal method, possibly only after computing the
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# normal form of `g`:
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@ -36,7 +34,7 @@ end
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function Base.hash(g::FPGroupElement, h::UInt)
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_isvalidhash(g) || _update_savedhash!(g, equality_data(g))
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return hash(g.savedhash >> count_ones(__BITFLAGS_MASK) , h)
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return hash(g.savedhash >> count_ones(__BITFLAGS_MASK), h)
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end
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function Base.copyto!(res::FPGroupElement, g::FPGroupElement)
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@ -6,16 +6,16 @@ struct Transvection <: GSymbol
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ij::UInt8
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inv::Bool
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function Transvection(id::Symbol, i::Integer, j::Integer, inv=false)
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function Transvection(id::Symbol, i::Integer, j::Integer, inv = false)
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@assert id in (:ϱ, :λ)
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return new(id, _indices(UInt8(i),UInt8(j)), inv)
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return new(id, _indices(UInt8(i), UInt8(j)), inv)
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end
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end
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ϱ(i, j) = Transvection(:ϱ, i, j)
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λ(i, j) = Transvection(:λ, i, j)
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_indices(ij::UInt8) = (ij & 0xf0)>>4, (ij & 0x0f)
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_indices(ij::UInt8) = (ij & 0xf0) >> 4, (ij & 0x0f)
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function _indices(i::UInt8, j::UInt8)
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@boundscheck @assert i < typemax(i) ÷ 2
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@ -29,10 +29,11 @@ word_type(G::AbstractFPGroup) = word_type(typeof(G))
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# the default:
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word_type(::Type{<:AbstractFPGroup}) = Word{UInt16}
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# the default (results in free rewriting)
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rewriting(G::AbstractFPGroup) = alphabet(G)
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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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@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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@ -40,25 +41,21 @@ 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} =
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FPGroupElement{FPG, word_type(FPG)}
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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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@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(
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rng::Random.AbstractRNG,
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rs::Random.SamplerTrivial{<:AbstractFPGroup},
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)
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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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@ -67,16 +64,16 @@ end
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## FPGroupElement
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mutable struct FPGroupElement{G<:AbstractFPGroup, W<:AbstractWord} <: GroupElement
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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, 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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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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@ -92,7 +89,7 @@ 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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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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@ -106,12 +103,11 @@ 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) =
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(G = parent(g); FPGroupElement(inv(alphabet(G), word(g)), G))
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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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return FPGroupElement(word(g) * word(h), parent(g))
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end
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GroupsCore.isfiniteorder(g::FPGroupElement) = isone(g) ? true : throw("Not Implemented")
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@ -125,16 +121,15 @@ 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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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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@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)
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for l in KnuthBendix.letters(A))
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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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@ -146,9 +141,9 @@ relations(F::FreeGroup) = Pair{eltype(F)}[]
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## FP Groups
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struct FPGroup{T, R, S} <: AbstractFPGroup
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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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relations::Vector{Pair{S,S}}
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rws::R
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end
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@ -159,15 +154,16 @@ 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...) where GEl<:FPGroupElement
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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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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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@ -177,7 +173,7 @@ end
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function Base.show(io::IO, G::FPGroup)
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print(io, "⟨")
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Base.print_array(io, reshape(gens(G), (1, New.ngens(G))))
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Base.print_array(io, reshape(gens(G), (1, ngens(G))))
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print(io, " | ")
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Base.print_array(io, relations(G))
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print(io, "⟩")
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@ -21,7 +21,7 @@ end
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normalform!(res::GEl, g::GEl) where GEl<:FPGroupElement
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Compute the normal fom of `g`, storing it in `res`.
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"""
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function normalform!(res::GEl, g::GEl) where GEl<:FPGroupElement
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function normalform!(res::GEl, g::GEl) where {GEl<:FPGroupElement}
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@boundscheck @assert parent(res) === parent(g)
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if isnormalform(g)
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copyto!(res, g)
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