kalmar
/
Groups.jl
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This commit is contained in:
Marek Kaluba 2021-12-11 13:55:47 +01:00
parent 70bd59e9b9
commit 7ac7b3aa5b
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1 changed files with 44 additions and 21 deletions
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65
src/types.jl
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@ -23,8 +23,13 @@ word_type(::Type{<:AbstractFPGroup}) = Word{UInt8}
# the default (results in free rewriting)
rewriting(G::AbstractFPGroup) = alphabet(G)
Base.@propagate_inbounds function (G::AbstractFPGroup)(word::AbstractVector{<:Integer})
@boundscheck @assert all(l -> 1 <= l <= length(KnuthBendix.alphabet(G)), word)
Base.@propagate_inbounds function (G::AbstractFPGroup)(
word::AbstractVector{<:Integer},
)
@boundscheck @assert all(
l -> 1 <= l <= length(KnuthBendix.alphabet(G)),
word,
)
return FPGroupElement(word_type(G)(word), G)
end
@ -32,7 +37,8 @@ end
Base.one(G::AbstractFPGroup) = FPGroupElement(one(word_type(G)), G)
Base.eltype(::Type{FPG}) where {FPG<:AbstractFPGroup} = FPGroupElement{FPG,word_type(FPG)}
Base.eltype(::Type{FPG}) where {FPG<:AbstractFPGroup} =
FPGroupElement{FPG,word_type(FPG)}
include("iteration.jl")
@ -43,32 +49,42 @@ function GroupsCore.gens(G::AbstractFPGroup, i::Integer)
l = alphabet(G)[G.gens[i]]
return FPGroupElement(word_type(G)([l]), G)
end
GroupsCore.gens(G::AbstractFPGroup) = [gens(G, i) for i in 1:GroupsCore.ngens(G)]
GroupsCore.gens(G::AbstractFPGroup) =
[gens(G, i) for i in 1:GroupsCore.ngens(G)]
# TODO: ProductReplacementAlgorithm
function Base.rand(rng::Random.AbstractRNG, rs::Random.SamplerTrivial{<:AbstractFPGroup})
function Base.rand(
rng::Random.AbstractRNG,
rs::Random.SamplerTrivial{<:AbstractFPGroup},
)
l = rand(10:100)
G = rs[]
nletters = length(alphabet(G))
return FPGroupElement(word_type(G)(rand(1:nletters, l)), G)
end
Base.isfinite(::AbstractFPGroup) = (@warn "using generic isfinite(::AbstractFPGroup): the returned `false` might be wrong"; false)
Base.isfinite(::AbstractFPGroup) = (
@warn "using generic isfinite(::AbstractFPGroup): the returned `false` might be wrong"; false
)
## FPGroupElement
abstract type AbstractFPGroupElement{Gr} <: GroupElement end
mutable struct FPGroupElement{Gr<:AbstractFPGroup,W<:AbstractWord} <: AbstractFPGroupElement{Gr}
mutable struct FPGroupElement{Gr<:AbstractFPGroup,W<:AbstractWord} <:
AbstractFPGroupElement{Gr}
word::W
savedhash::UInt
parent::Gr
FPGroupElement(word::W, G::AbstractFPGroup, hash::UInt=UInt(0)) where {W<:AbstractWord} =
new{typeof(G),W}(word, hash, G)
FPGroupElement(
word::W,
G::AbstractFPGroup,
hash::UInt = UInt(0),
) where {W<:AbstractWord} = new{typeof(G),W}(word, hash, G)
FPGroupElement{Gr, W}(word::AbstractWord, G::Gr) where {Gr, W} =
new{Gr, W}(word, UInt(0), G)
FPGroupElement{Gr,W}(word::AbstractWord, G::Gr) where {Gr,W} =
new{Gr,W}(word, UInt(0), G)
end
Base.show(io::IO, ::Type{<:FPGroupElement{Gr}}) where {Gr} =
@ -81,7 +97,7 @@ KnuthBendix.alphabet(g::AbstractFPGroupElement) = alphabet(parent(g))
function Base.show(io::IO, f::AbstractFPGroupElement)
f = normalform!(f)
KnuthBendix.print_repr(io, word(f), alphabet(f))
return KnuthBendix.print_repr(io, word(f), alphabet(f))
end
## GroupElement Interface for FPGroupElement
@ -100,17 +116,21 @@ function Base.deepcopy_internal(g::FPGroupElement, stackdict::IdDict)
return FPGroupElement(copy(word(g)), parent(g), g.savedhash)
end
function Base.inv(g::GEl) where GEl <: AbstractFPGroupElement
function Base.inv(g::GEl) where {GEl<:AbstractFPGroupElement}
G = parent(g)
return GEl(inv(alphabet(G), word(g)), G)
end
function Base.:(*)(g::GEl, h::GEl) where GEl<:AbstractFPGroupElement
function Base.:(*)(g::GEl, h::GEl) where {GEl<:AbstractFPGroupElement}
@boundscheck @assert parent(g) === parent(h)
return GEl(word(g) * word(h), parent(g))
end
GroupsCore.isfiniteorder(g::AbstractFPGroupElement) = isone(g) ? true : (@warn "using generic isfiniteorder(::AbstractFPGroupElement): the returned `false` might be wrong"; false)
GroupsCore.isfiniteorder(g::AbstractFPGroupElement) =
isone(g) ? true :
(
@warn "using generic isfiniteorder(::AbstractFPGroupElement): the returned `false` might be wrong"; false
)
# additional methods:
Base.isone(g::AbstractFPGroupElement) = (normalform!(g); isempty(word(g)))
@ -129,7 +149,9 @@ struct FreeGroup{T} <: AbstractFPGroup
end
function FreeGroup(A::Alphabet)
@boundscheck @assert all(KnuthBendix.hasinverse(l, A) for l in KnuthBendix.letters(A))
@boundscheck @assert all(
KnuthBendix.hasinverse(l, A) for l in KnuthBendix.letters(A)
)
ltrs = KnuthBendix.letters(A)
gens = Vector{eltype(ltrs)}()
invs = Vector{eltype(ltrs)}()
@ -149,12 +171,13 @@ function FreeGroup(n::Integer)
sizehint!(inverses, 2n)
for i in 1:n
push!(symbols, Symbol(:f, i), Symbol(:F, i))
push!(inverses, 2i, 2i-1)
push!(inverses, 2i, 2i - 1)
end
return FreeGroup(symbols[1:2:2n], Alphabet(symbols, inverses))
end
Base.show(io::IO, F::FreeGroup) = print(io, "free group on $(ngens(F)) generators")
Base.show(io::IO, F::FreeGroup) =
print(io, "free group on $(ngens(F)) generators")
# mandatory methods:
KnuthBendix.alphabet(F::FreeGroup) = F.alphabet
@ -164,7 +187,8 @@ relations(F::FreeGroup) = Pair{eltype(F)}[]
# these are mathematically correct
Base.isfinite(::FreeGroup) = false
GroupsCore.isfiniteorder(g::AbstractFPGroupElement{<:FreeGroup}) = isone(g) ? true : false
GroupsCore.isfiniteorder(g::AbstractFPGroupElement{<:FreeGroup}) =
isone(g) ? true : false
## FP Groups
@ -185,7 +209,6 @@ function FPGroup(
ordering = KnuthBendix.LenLex,
kwargs...,
) where {GEl<:FPGroupElement}
O = ordering(alphabet(G))
for (lhs, rhs) in rels
@assert parent(lhs) === parent(rhs) === G
@ -203,7 +226,7 @@ function Base.show(io::IO, G::FPGroup)
join(io, gens(G), ", ")
print(io, " | ")
join(io, relations(G), ", ")
print(io, "⟩")
return print(io, "⟩")
end
Base.show(io::IO, ::Type{<:FPGroup{T}}) where {T} =