68 lines
1.9 KiB
Julia
68 lines
1.9 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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change_pow(s::AutSymbol, n::Int) = reduce(AutSymbol(s.gen, n, s.ex))
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function inv(f::AutSymbol)
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symbol = f.ex.args[1]
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if symbol == :ɛ
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return change_pow(f, f.pow % 2)
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elseif symbol == :σ
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perm = invperm(f.ex.args[2])
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gen = string('σ', [Char(8320 + i) for i in perm]...)
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return AutSymbol(gen, f.pow, :(σ($perm)))
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elseif symbol == :(ϱ) || symbol == :λ
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return AutSymbol(f.gen, -f.pow, f.ex)
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elseif symbol == :IDAutomorphism
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return f
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else
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throw(ArgumentError("Don't know how to invert $f (of type $symbol)"))
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end
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end
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function rmul_AutSymbol(i,j, pow::Int=1)
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gen = string('ϱ',Char(8320+i), Char(8320+j)...)
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return AutSymbol(gen, pow, :(ϱ($i,$j)))
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end
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function lmul_AutSymbol(i,j, pow::Int=1)
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gen = string('λ',Char(8320+i), Char(8320+j)...)
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return AutSymbol(gen, pow, :(λ($i,$j)))
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end
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function flip_AutSymbol(j, pow::Int=1)
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gen = string('ɛ', Char(8320 + j))
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return AutSymbol(gen, pow%2, :(ɛ($j)))
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end
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function symmetric_AutSymbol(perm::Vector{Int}, pow::Int=1)
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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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typealias AutWord GWord{AutSymbol}
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end #end of module AutGroups
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