mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-13 22:05:27 +01:00
112 lines
3.0 KiB
Julia
112 lines
3.0 KiB
Julia
module AutGroups
|
||
|
||
using Groups
|
||
using Permutations
|
||
|
||
import Base: inv, ^
|
||
import Groups: IdSymbol, change_pow, GWord, ==, hash, reduce!
|
||
|
||
export AutSymbol, AutWord, GWord
|
||
export rmul_AutSymbol, lmul_AutSymbol, flip_AutSymbol, symmetric_AutSymbol
|
||
|
||
immutable AutSymbol <: GSymbol
|
||
gen::String
|
||
pow::Int
|
||
ex::Expr
|
||
end
|
||
|
||
(==)(s::AutSymbol, t::AutSymbol) = s.gen == t.gen && s.pow == t.pow
|
||
hash(s::AutSymbol, h::UInt) = hash(s.gen, hash(s.pow, hash(:AutSymbol, h)))
|
||
|
||
IdSymbol(::Type{AutSymbol}) = AutSymbol("(id)", 0, :(IdAutomorphism(N)))
|
||
|
||
function change_pow(s::AutSymbol, n::Int)
|
||
|
||
if n == 0
|
||
return one(s)
|
||
end
|
||
|
||
symbol = s.ex.args[1]
|
||
if symbol == :ɛ
|
||
return flip_AutSymbol(s.ex.args[2], pow=n)
|
||
elseif symbol == :σ
|
||
return symmetric_AutSymbol(s.ex.args[2], pow=n)
|
||
elseif symbol == :ϱ
|
||
return rmul_AutSymbol(s.ex.args[2], s.ex.args[3], pow=n)
|
||
elseif symbol == :λ
|
||
return lmul_AutSymbol(s.ex.args[2], s.ex.args[3], pow=n)
|
||
elseif symbol == :IdAutomorphism
|
||
return s
|
||
else
|
||
warn("Changing an unknown type of symbol! $s")
|
||
return AutSymbol(s.gen, n, s.ex)
|
||
end
|
||
end
|
||
|
||
inv(f::AutSymbol) = change_pow(f, -1*f.pow)
|
||
(^)(s::AutSymbol, n::Integer) = change_pow(s, s.pow*n)
|
||
|
||
function rmul_AutSymbol(i,j; pow::Int=1)
|
||
gen = string('ϱ',Char(8320+i), Char(8320+j)...)
|
||
return AutSymbol(gen, pow, :(ϱ($i,$j)))
|
||
end
|
||
|
||
function lmul_AutSymbol(i,j; pow::Int=1)
|
||
gen = string('λ',Char(8320+i), Char(8320+j)...)
|
||
return AutSymbol(gen, pow, :(λ($i,$j)))
|
||
end
|
||
|
||
function flip_AutSymbol(j; pow::Int=1)
|
||
gen = string('ɛ', Char(8320 + j))
|
||
return AutSymbol(gen, (2+ pow%2)%2, :(ɛ($j)))
|
||
end
|
||
|
||
function symmetric_AutSymbol(perm::Vector{Int}; pow::Int=1)
|
||
# if perm == collect(1:length(perm))
|
||
# return one(AutSymbol)
|
||
# end
|
||
perm = Permutation(perm)
|
||
ord = order(perm)
|
||
pow = pow % ord
|
||
perm = perm^pow
|
||
gen = string('σ', [Char(8320 + i) for i in array(perm)]...)
|
||
return AutSymbol(gen, 1, :(σ($(array(perm)))))
|
||
end
|
||
|
||
function getperm(s::AutSymbol)
|
||
if s.ex.args[1] == :σ
|
||
return s.ex.args[2]
|
||
else
|
||
throw(ArgumentError("$s is not a permutation automorphism!"))
|
||
end
|
||
end
|
||
|
||
|
||
|
||
typealias AutWord GWord{AutSymbol}
|
||
|
||
function simplify_perms!(W::AutWord)
|
||
reduced = true
|
||
for i in 1:length(W.symbols) - 1
|
||
current = W.symbols[i]
|
||
if current.ex.args[1] == :σ
|
||
if current.pow != 1
|
||
current = symmetric_AutSymbol(perm(current), pow=current.pow)
|
||
end
|
||
next_s = W.symbols[i+1]
|
||
if next_s.ex.args[1] == :σ
|
||
reduced = false
|
||
if next_s.pow != 1
|
||
next_s = symmetric_AutSymbol(perm(next_s), pow=next_s.pow)
|
||
end
|
||
p1 = Permutation(getperm(current))
|
||
p2 = Permutation(getperm(next_s))
|
||
W.symbols[i] = one(AutSymbol)
|
||
W.symbols[i+1] = symmetric_AutSymbol(array(p1*p2))
|
||
end
|
||
end
|
||
end
|
||
return reduced
|
||
end
|
||
end #end of module AutGroups
|