mirror of
https://github.com/kalmarek/Groups.jl.git
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155 lines
4.1 KiB
Julia
155 lines
4.1 KiB
Julia
using Permutations
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import Base: convert
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export AutSymbol, AutWord, rmul_AutSymbol, lmul_AutSymbol, flip_AutSymbol, symmetric_AutSymbol
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immutable AutSymbol <: GSymbol
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gen::String
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pow::Int
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ex::Expr
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fmap::Function
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imap::Function
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end
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function (f::AutSymbol){T}(v::Vector{GWord{T}})
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if f.pow > 0
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map = f.fmap
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else
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map = f.imap
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end
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for i in 1:abs(f.pow)
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v::Vector{GWord{T}} = map(v)
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end
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return v
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end
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(==)(s::AutSymbol, t::AutSymbol) = s.gen == t.gen && s.pow == t.pow
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hash(s::AutSymbol, h::UInt) = hash(s.gen, hash(s.pow, hash(:AutSymbol, h)))
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IdSymbol(::Type{AutSymbol}) = AutSymbol("(id)", 0, :(Id(N)), v -> Vector{GWord}(v), v -> Vector{GWord}(v))
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function change_pow(s::AutSymbol, n::Int)
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if n == 0
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return one(s)
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end
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symbol = s.ex.args[1]
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if symbol == :ɛ
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return flip_AutSymbol(s.ex.args[2], pow=n)
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elseif symbol == :σ
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return symmetric_AutSymbol(s.ex.args[2], pow=n)
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elseif symbol == :ϱ
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return rmul_AutSymbol(s.ex.args[2], s.ex.args[3], pow=n)
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elseif symbol == :λ
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return lmul_AutSymbol(s.ex.args[2], s.ex.args[3], pow=n)
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elseif symbol == :Id
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return s
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else
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warn("Changing an unknown type of symbol! $s")
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return AutSymbol(s.gen, n, s.ex, s.fmap, s.imap)
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end
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end
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inv(f::AutSymbol) = change_pow(f, -f.pow)
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function ϱ(i,j)
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# @assert i ≠ j
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return v -> [(k!=i ? GWord(v[k]) : v[i]*v[j]) for k in eachindex(v)]
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end
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function ϱ_inv(i,j)
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# @assert i ≠ j
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return v -> [(k!=i ? GWord(v[k]) : v[i]*v[j]^-1) for k in eachindex(v)]
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end
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function λ(i,j)
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# @assert i ≠ j
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return v -> ([(k!=i ? GWord(v[k]) : v[j]*v[i]) for k in eachindex(v)])
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end
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function λ_inv(i,j)
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# @assert i ≠ j
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return v -> ([(k!=i ? GWord(v[k]) : v[j]^-1*v[i]) for k in eachindex(v)])
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end
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ɛ(i) = v -> [(k!=i ? GWord(v[k]) : v[k]^-1) for k in eachindex(v)]
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function σ(perm)
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# @assert sort(perm) == collect(1:length(perm))
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return v -> [GWord(v[perm[k]]) for k in eachindex(v)]
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end
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function rmul_AutSymbol(i,j; pow::Int=1)
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gen = string('ϱ',Char(8320+i), Char(8320+j)...)
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return AutSymbol(gen, pow, :(ϱ($i,$j)), ϱ(i,j), ϱ_inv(i,j))
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end
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function lmul_AutSymbol(i,j; pow::Int=1)
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gen = string('λ',Char(8320+i), Char(8320+j)...)
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return AutSymbol(gen, pow, :(λ($i,$j)), λ(i,j), λ_inv(i,j))
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end
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function flip_AutSymbol(j; pow::Int=1)
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gen = string('ɛ', Char(8320 + j))
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return AutSymbol(gen, (2+ pow%2)%2, :(ɛ($j)), ɛ(j), ɛ(j))
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end
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function symmetric_AutSymbol(perm::Vector{Int}; pow::Int=1)
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perm = Permutation(perm)
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ord = order(perm)
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pow = pow % ord
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perm = perm^pow
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p = array(perm)
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if p == collect(1:length(p))
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return one(AutSymbol)
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else
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gen = string('σ', [Char(8320 + i) for i in p]...)
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return AutSymbol(gen, 1, :(σ($p)), σ(p), σ(array(inv(perm))))
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end
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end
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function getperm(s::AutSymbol)
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if s.ex.args[1] == :σ
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return s.ex.args[2]
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else
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throw(ArgumentError("$s is not a permutation automorphism!"))
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end
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end
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typealias AutWord GWord{AutSymbol}
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function (F::AutWord)(v)
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for f in F.symbols
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v = f(v)
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end
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return v
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end
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convert(::Type{AutWord}, s::AutSymbol) = GWord(s)
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function simplify_perms!(W::AutWord)
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reduced = true
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for i in 1:length(W.symbols) - 1
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current = W.symbols[i]
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if current.ex.args[1] == :σ
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if current.pow != 1
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current = symmetric_AutSymbol(perm(current), pow=current.pow)
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end
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next_s = W.symbols[i+1]
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if next_s.ex.args[1] == :σ
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reduced = false
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if next_s.pow != 1
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next_s = symmetric_AutSymbol(perm(next_s), pow=next_s.pow)
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end
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p1 = Permutation(getperm(current))
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p2 = Permutation(getperm(next_s))
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W.symbols[i] = one(AutSymbol)
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W.symbols[i+1] = symmetric_AutSymbol(array(p1*p2))
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end
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end
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end
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deleteat!(W.symbols, find(x -> x.pow == 0, W.symbols))
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return reduced
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end
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