112 lines
3.0 KiB
Julia
112 lines
3.0 KiB
Julia
module AutGroups
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using Groups
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using Permutations
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import Base: inv, ^
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import Groups: IdSymbol, change_pow, GWord, ==, hash, reduce!
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export AutSymbol, AutWord, GWord
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export 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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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, :(IdAutomorphism(N)))
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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 == :IdAutomorphism
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return s
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else
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warn("Changing an unknown type of symbol! $s")
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return AutSymbol(s.gen, n, s.ex)
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end
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end
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inv(f::AutSymbol) = change_pow(f, -1*f.pow)
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(^)(s::AutSymbol, n::Integer) = change_pow(s, s.pow*n)
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function rmul_AutSymbol(i,j; pow::Int=1)
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gen = string('ϱ',Char(8320+i), Char(8320+j)...)
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return AutSymbol(gen, pow, :(ϱ($i,$j)))
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end
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function lmul_AutSymbol(i,j; pow::Int=1)
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gen = string('λ',Char(8320+i), Char(8320+j)...)
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return AutSymbol(gen, pow, :(λ($i,$j)))
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end
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function flip_AutSymbol(j; pow::Int=1)
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gen = string('ɛ', Char(8320 + j))
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return AutSymbol(gen, (2+ pow%2)%2, :(ɛ($j)))
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end
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function symmetric_AutSymbol(perm::Vector{Int}; pow::Int=1)
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# if perm == collect(1:length(perm))
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# return one(AutSymbol)
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# end
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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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gen = string('σ', [Char(8320 + i) for i in array(perm)]...)
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return AutSymbol(gen, 1, :(σ($(array(perm)))))
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end
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function getperm(s::AutSymbol)
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if s.ex.args[1] == :σ
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return s.ex.args[2]
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else
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throw(ArgumentError("$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 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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return reduced
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end
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end #end of module AutGroups
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