1
0
mirror of https://github.com/kalmarek/Groups.jl.git synced 2024-12-25 02:05:30 +01:00

add new_transvections for Aut(F_n)

This commit is contained in:
Marek Kaluba 2021-05-16 22:47:20 +02:00
parent f4858fba14
commit 5da33782aa
No known key found for this signature in database
GPG Key ID: 8BF1A3855328FC15
4 changed files with 95 additions and 37 deletions

View File

@ -23,13 +23,13 @@ include("arithmetic.jl")
include("findreplace.jl")
module New
import Groups: AutSymbol, GSymbol, λ, ϱ, RTransvect, LTransvect
using DataStructures
include("new_types.jl")
include("new_hashing.jl")
include("normalform.jl")
include("new_transvections.jl")
include("gersten_relations.jl")
include("new_autgroups.jl")

View File

@ -1,12 +1,9 @@
function gersten_alphabet(n::Integer; commutative::Bool = true)
indexing = [[i, j] for i in 1:n for j in 1:n if i j]
rmuls = [ϱ(i, j) for (i, j) in indexing]
indexing = [(i, j) for i in 1:n for j in 1:n if i j]
S = [ϱ(i, j) for (i, j) in indexing]
S = if commutative
Vector{AutSymbol}(rmuls)
else
lmuls = [λ(i, j) for (i, j) in indexing]
AutSymbol[rmuls; lmuls]
if !commutative
append!(S, [λ(i, j) for (i, j) in indexing])
end
return Alphabet(S)

View File

@ -89,37 +89,13 @@ domain(f::FPGroupElement{<:AutomorphismGroup}) = deepcopy(parent(f).domain)
evaluate(f::FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}) =
evaluate!(domain(f), f)
function evaluate!(t::NTuple{N, T}, f::FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}) where {T<:FPGroupElement, N}
function evaluate!(
t::NTuple{N,T},
f::FPGroupElement{<:AutomorphismGroup{<:FreeGroup}},
) where {T<:FPGroupElement,N}
A = alphabet(f)
for idx in word(f)
t = evaluate!(t, A[idx])::NTuple{N, T}
t = evaluate!(t, A[idx], alphabet(object(parent(f))))::NTuple{N,T}
end
return t
end
function evaluate!(v::NTuple{N, T}, s::AutSymbol) where {N, T}
@assert s.pow in (-1, 1)
return evaluate!(v, s.fn, isone(s.pow))::NTuple{N, T}
end
function evaluate!(v, ϱ::RTransvect, flag)
if flag
append!(New.word(v[ϱ.i]), New.word(v[ϱ.j] ))
else
append!(New.word(v[ϱ.i]), New.word(v[ϱ.j]^-1))
end
_setnormalform!(v[ϱ.i], false)
_setvalidhash!(v[ϱ.i], false)
return v
end
function evaluate!(v, λ::LTransvect, flag)
if flag
prepend!(New.word(v[λ.i]), New.word(v[λ.j] ))
else
prepend!(New.word(v[λ.i]), New.word(v[λ.j]^-1))
end
_setnormalform!(v[λ.i], false)
_setvalidhash!(v[λ.i], false)
return v
end

85
src/new_transvections.jl Normal file
View File

@ -0,0 +1,85 @@
abstract type GSymbol end
Base.literal_pow(::typeof(^), t::GSymbol, ::Val{-1}) = inv(t)
struct Transvection <: GSymbol
id::Symbol
ij::UInt8
inv::Bool
function Transvection(id::Symbol, i::Integer, j::Integer, inv=false)
@assert id in (:ϱ, )
return new(id, _indices(UInt8(i),UInt8(j)), inv)
end
end
ϱ(i, j) = Transvection(:ϱ, i, j)
λ(i, j) = Transvection(, i, j)
_indices(ij::UInt8) = (ij & 0xf0)>>4, (ij & 0x0f)
function _indices(i::UInt8, j::UInt8)
@boundscheck @assert i < typemax(i) ÷ 2
@boundscheck @assert j < typemax(j) ÷ 2
sizeof
return (i << 4) + j
end
indices(t::Transvection) = Int.(_indices(t.ij))
function Base.getproperty(t::Transvection, s::Symbol)
s === :i && return first(indices(t))
s === :j && return last(indices(t))
return Core.getfield(t, s)
end
function Base.show(io::IO, t::Transvection)
id = if t.id === :ϱ
"ϱ"
else # if t.id === :λ
"λ"
end
# print(io, id, Groups.subscriptify(t.i), ".", Groups.subscriptify(t.j))
print(io, id, "_", t.i, ",", t.j)
t.inv && print(io, "^-1")
end
Base.inv(t::Transvection) = Transvection(t.id, _indices(t.ij)..., !t.inv)
Base.:(==)(t::Transvection, s::Transvection) =
t.id === s.id && t.ij == s.ij && t.inv == s.inv
Base.hash(t::Transvection, h::UInt) = hash(t.id, hash(t.ij, hash(t.inv, h)))
function evaluate!(v::Tuple, t::Transvection, A::Alphabet)
i, j = indices(t)
@assert i length(v) && j length(v)
@inbounds begin
if t.id === :ϱ
if !t.inv
append!(word(v[i]), word(v[j]))
else
# append!(word(v[i]), inv(A, word(v[j])))
for l in Iterators.reverse(word(v[j]))
push!(word(v[i]), inv(A, l))
end
end
else # if t.id === :λ
if !t.inv
# prepend!(word(v[i]), word(v[j]))
for l in Iterators.reverse(word(v[j]))
pushfirst!(word(v[i]), l)
end
else
# prepend!(word(v[i]), inv(A, word(v[j])))
for l in word(v[j])
pushfirst!(word(v[i]), inv(A, l))
end
end
end
_setnormalform!(v[i], false)
_setvalidhash!(v[i], false)
end
return v
end