kalmar
/
Groups.jl
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Marek Kaluba 2021-05-16 23:22:33 +02:00
parent 84bfbd7408
commit 75b7d9fab3
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7 changed files with 47 additions and 53 deletions
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1
Project.toml
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@ -7,6 +7,7 @@ version = "0.5.2"
AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
GroupsCore = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
KnuthBendix = "c2604015-7b3d-4a30-8a26-9074551ec60a"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
ThreadsX = "ac1d9e8a-700a-412c-b207-f0111f4b6c0d"

6
src/iteration.jl
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@ -1,4 +1,4 @@
mutable struct FPIterState{GEl, T}
mutable struct FPIterState{GEl,T}
elts::OrderedSet{GEl}
u::GEl
v::GEl
@ -42,12 +42,12 @@ function Base.iterate(G::AbstractFPGroup, state)
end
if res in iter
return iterate(G, (iter, elt, gen_idx+1))
return iterate(G, (iter, elt, gen_idx + 1))
else
w = deepcopy(res)
@assert isnormalform(w)
push!(iter, w)
return w, (iter, elt, gen_idx+1)
return w, (iter, elt, gen_idx + 1)
end
end

25
src/new_autgroups.jl
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@ -4,7 +4,7 @@ function KnuthBendix.Alphabet(S::AbstractVector{<:GSymbol})
return Alphabet(S, inversions)
end
struct AutomorphismGroup{G<:Group, T, R, S} <: AbstractFPGroup
struct AutomorphismGroup{G<:Group,T,R,S} <: AbstractFPGroup
group::G
gens::Vector{T}
rws::R
@ -13,29 +13,28 @@ end
object(G::AutomorphismGroup) = G.group
function SpecialAutomorphismGroup(F::FreeGroup;
ordering=KnuthBendix.LenLex, kwargs...)
function SpecialAutomorphismGroup(F::FreeGroup; ordering = KnuthBendix.LenLex, kwargs...)
n = length(KnuthBendix.alphabet(F))÷2
A, rels = gersten_relations(n, commutative=false)
S = KnuthBendix.letters(A)[1:2(n^2 - n)]
n = length(KnuthBendix.alphabet(F)) ÷ 2
A, rels = gersten_relations(n, commutative = false)
S = KnuthBendix.letters(A)[1:2(n^2-n)]
rws = KnuthBendix.RewritingSystem(rels, ordering(A))
KnuthBendix.knuthbendix!(rws; kwargs...)
return AutomorphismGroup(F, S, rws, ntuple(i->gens(F, i), n))
return AutomorphismGroup(F, S, rws, ntuple(i -> gens(F, i), n))
end
KnuthBendix.alphabet(G::AutomorphismGroup{<:FreeGroup}) = alphabet(rewriting(G))
rewriting(G::AutomorphismGroup) = G.rws
function relations(G::AutomorphismGroup)
n = length(KnuthBendix.alphabet(object(G)))÷2
return last(gersten_relations(n, commutative=false))
n = length(KnuthBendix.alphabet(object(G))) ÷ 2
return last(gersten_relations(n, commutative = false))
end
equality_data(f::FPGroupElement{<:AutomorphismGroup}) = normalform!.(evaluate(f))
function Base.:(==)(g::A, h::A) where A<:FPGroupElement{<:AutomorphismGroup}
function Base.:(==)(g::A, h::A) where {A<:FPGroupElement{<:AutomorphismGroup}}
@assert parent(g) === parent(h)
if _isvalidhash(g) && _isvalidhash(h)
@ -81,15 +80,15 @@ end
# eye-candy
Base.show(io::IO, ::Type{<:FPGroupElement{<:AutomorphismGroup{T}}}) where T <: FreeGroup = print(io, "Automorphism{$T}")
Base.show(io::IO, ::Type{<:FPGroupElement{<:AutomorphismGroup{T}}}) where {T<:FreeGroup} =
print(io, "Automorphism{$T,…}")
## Automorphism Evaluation
domain(f::FPGroupElement{<:AutomorphismGroup}) = deepcopy(parent(f).domain)
# tuple(gens(object(parent(f)))...)
evaluate(f::FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}) =
evaluate!(domain(f), f)
evaluate(f::FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}) = evaluate!(domain(f), f)
function evaluate!(
t::NTuple{N,T},

8
src/new_hashing.jl
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@ -20,10 +20,8 @@ _isvalidhash(g::FPGroupElement) = bitget(g.savedhash, 1)
_setnormalform(h::UInt, v::Bool) = bitset(h, v, 0)
_setvalidhash(h::UInt, v::Bool) = bitset(h, v, 1)
_setnormalform!(g::FPGroupElement, v::Bool) =
g.savedhash = _setnormalform(g.savedhash, v)
_setvalidhash!(g::FPGroupElement, v::Bool) =
g.savedhash = _setvalidhash(g.savedhash, v)
_setnormalform!(g::FPGroupElement, v::Bool) = g.savedhash = _setnormalform(g.savedhash, v)
_setvalidhash!(g::FPGroupElement, v::Bool) = g.savedhash = _setvalidhash(g.savedhash, v)
# To update hash use this internal method, possibly only after computing the
# normal form of `g`:
@ -36,7 +34,7 @@ end
function Base.hash(g::FPGroupElement, h::UInt)
_isvalidhash(g) || _update_savedhash!(g, equality_data(g))
return hash(g.savedhash >> count_ones(__BITFLAGS_MASK) , h)
return hash(g.savedhash >> count_ones(__BITFLAGS_MASK), h)
end
function Base.copyto!(res::FPGroupElement, g::FPGroupElement)

6
src/new_transvections.jl
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@ -6,16 +6,16 @@ struct Transvection <: GSymbol
ij::UInt8
inv::Bool
function Transvection(id::Symbol, i::Integer, j::Integer, inv=false)
function Transvection(id::Symbol, i::Integer, j::Integer, inv = false)
@assert id in (:ϱ, :λ)
return new(id, _indices(UInt8(i),UInt8(j)), inv)
return new(id, _indices(UInt8(i), UInt8(j)), inv)
end
end
ϱ(i, j) = Transvection(:ϱ, i, j)
λ(i, j) = Transvection(:λ, i, j)
_indices(ij::UInt8) = (ij & 0xf0)>>4, (ij & 0x0f)
_indices(ij::UInt8) = (ij & 0xf0) >> 4, (ij & 0x0f)
function _indices(i::UInt8, j::UInt8)
@boundscheck @assert i < typemax(i) ÷ 2

52
src/new_types.jl
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@ -29,10 +29,11 @@ word_type(G::AbstractFPGroup) = word_type(typeof(G))
# the default:
word_type(::Type{<:AbstractFPGroup}) = Word{UInt16}
# the default (results in free rewriting)
rewriting(G::AbstractFPGroup) = alphabet(G)
function (G::AbstractFPGroup)(word::AbstractVector{<:Integer})
@boundscheck @assert all(l -> 1<= l <=length(KnuthBendix.alphabet(G)), word)
@boundscheck @assert all(l -> 1 <= l <= length(KnuthBendix.alphabet(G)), word)
return FPGroupElement(word_type(G)(word), G)
end
@ -40,25 +41,21 @@ 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")
GroupsCore.ngens(G::AbstractFPGroup) = length(G.gens)
function GroupsCore.gens(G::AbstractFPGroup, i::Integer)
@boundscheck 1<=i<=GroupsCore.ngens(G)
@boundscheck 1 <= i <= GroupsCore.ngens(G)
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)]
# 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))
@ -67,16 +64,16 @@ end
## FPGroupElement
mutable struct FPGroupElement{G<:AbstractFPGroup, W<:AbstractWord} <: GroupElement
mutable struct FPGroupElement{G<:AbstractFPGroup,W<:AbstractWord} <: GroupElement
word::W
savedhash::UInt
parent::G
FPGroupElement(word::W, G::AbstractFPGroup) where W<:AbstractWord =
new{typeof(G), W}(word, UInt(0), G)
FPGroupElement(word::W, G::AbstractFPGroup) where {W<:AbstractWord} =
new{typeof(G),W}(word, UInt(0), G)
FPGroupElement(word::W, hash::UInt, G::AbstractFPGroup) where W<:AbstractWord =
new{typeof(G), W}(word, hash, G)
FPGroupElement(word::W, hash::UInt, G::AbstractFPGroup) where {W<:AbstractWord} =
new{typeof(G),W}(word, hash, G)
end
word(f::FPGroupElement) = f.word
@ -92,7 +89,7 @@ end
## GroupElement Interface for FPGroupElement
Base.parent(f::FPGroupElement) = f.parent
GroupsCore.parent_type(::Type{<:FPGroupElement{G}}) where G = G
GroupsCore.parent_type(::Type{<:FPGroupElement{G}}) where {G} = G
function Base.:(==)(g::FPGroupElement, h::FPGroupElement)
@boundscheck @assert parent(g) === parent(h)
@ -106,12 +103,11 @@ function Base.deepcopy_internal(g::FPGroupElement, stackdict::IdDict)
return FPGroupElement(copy(word(g)), g.savedhash, parent(g))
end
Base.inv(g::FPGroupElement) =
(G = parent(g); FPGroupElement(inv(alphabet(G), word(g)), G))
Base.inv(g::FPGroupElement) = (G = parent(g); FPGroupElement(inv(alphabet(G), word(g)), G))
function Base.:(*)(g::FPGroupElement, h::FPGroupElement)
@boundscheck @assert parent(g) === parent(h)
return FPGroupElement(word(g)*word(h), parent(g))
return FPGroupElement(word(g) * word(h), parent(g))
end
GroupsCore.isfiniteorder(g::FPGroupElement) = isone(g) ? true : throw("Not Implemented")
@ -125,16 +121,15 @@ struct FreeGroup{T} <: AbstractFPGroup
gens::Vector{T}
alphabet::KnuthBendix.Alphabet{T}
function FreeGroup(gens, A::KnuthBendix.Alphabet) where W
function FreeGroup(gens, A::KnuthBendix.Alphabet) where {W}
@assert length(gens) == length(unique(gens))
@assert all(l->l in KnuthBendix.letters(A), gens)
@assert all(l -> l in KnuthBendix.letters(A), gens)
return new{eltype(gens)}(gens, A)
end
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))
return FreeGroup(KnuthBendix.letters(A), A)
end
@ -146,9 +141,9 @@ relations(F::FreeGroup) = Pair{eltype(F)}[]
## FP Groups
struct FPGroup{T, R, S} <: AbstractFPGroup
struct FPGroup{T,R,S} <: AbstractFPGroup
gens::Vector{T}
relations::Vector{Pair{S, S}}
relations::Vector{Pair{S,S}}
rws::R
end
@ -159,15 +154,16 @@ relations(G::FPGroup) = G.relations
function FPGroup(
G::AbstractFPGroup,
rels::AbstractVector{<:Pair{GEl, GEl}};
ordering=KnuthBendix.LenLex,
kwargs...) where GEl<:FPGroupElement
rels::AbstractVector{<:Pair{GEl,GEl}};
ordering = KnuthBendix.LenLex,
kwargs...,
) where {GEl<:FPGroupElement}
O = ordering(alphabet(G))
for (lhs, rhs) in rels
@assert parent(lhs) === parent(rhs) === G
end
word_rels = [word(lhs)=>word(rhs) for (lhs, rhs) in [relations(G); rels]]
word_rels = [word(lhs) => word(rhs) for (lhs, rhs) in [relations(G); rels]]
rws = RewritingSystem(word_rels, O)
KnuthBendix.knuthbendix!(rws; kwargs...)
@ -177,7 +173,7 @@ end
function Base.show(io::IO, G::FPGroup)
print(io, "⟨")
Base.print_array(io, reshape(gens(G), (1, New.ngens(G))))
Base.print_array(io, reshape(gens(G), (1, ngens(G))))
print(io, " | ")
Base.print_array(io, relations(G))
print(io, "⟩")

2
src/normalform.jl
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@ -21,7 +21,7 @@ end
normalform!(res::GEl, g::GEl) where GEl<:FPGroupElement
Compute the normal fom of `g`, storing it in `res`.
"""
function normalform!(res::GEl, g::GEl) where GEl<:FPGroupElement
function normalform!(res::GEl, g::GEl) where {GEl<:FPGroupElement}
@boundscheck @assert parent(res) === parent(g)
if isnormalform(g)
copyto!(res, g)