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Reshuffling of definitions
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@ -1,29 +1,19 @@
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module FreeGroups
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export GSymbol, Word, FGSymbol, GWord, FGAutomorphism
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export GSymbol, FGSymbol, Word, GWord, FGWord, FGAutomorphism
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import Base: length, ==, show, convert
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import Base: *, ^, convert
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import Base: one, inv, reduce, push!, unshift!
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abstract GSymbol
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abstract Word
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immutable FGSymbol <: GSymbol
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gen::String
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pow::Int
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end
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immutable GWord{T<:GSymbol} <:Word
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symbols::Vector{T}
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end
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length(s::GSymbol) = (s.pow == 0 ? 0 : 1)
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(==)(s::FGSymbol, t::FGSymbol) = s.gen == t.gen && s.pow == t.pow
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function length(W::GWord)
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return sum([abs(s.pow) for s in W.symbols])
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end
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FGSymbol(x::String) = FGSymbol(x,1)
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function show(io::IO, s::GSymbol)
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if s.pow == 1
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@ -35,19 +25,44 @@ function show(io::IO, s::GSymbol)
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end
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end
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FGSymbol(x::String) = FGSymbol(x,1)
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GWord{T}(s::T) = GWord{T}([s])
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convert(::Type{FGSymbol}, y::String) = FGSymbol(y)
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import Base: one, inv, reduce, push!, unshift!
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(==)(s::GSymbol, t::GSymbol) = s.gen == t.gen && s.pow == t.pow
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length(s::GSymbol) = (s.pow == 0 ? 0 : 1)
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one(s::FGSymbol) = FGSymbol(s.gen, 0)
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inv(s::FGSymbol) = FGSymbol(s.gen, -s.pow)
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convert(::Type{FGSymbol}, x::String) = FGSymbol(x)
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reduce!(s::GSymbol) = s
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change_pow(s::FGSymbol, n::Int) = FGSymbol(s.gen, n)
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(^)(x::FGSymbol, n::Integer) = FGSymbol(x.gen, x.pow*n)
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function (*)(s::GSymbol, t::GSymbol)
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W = promote_type(typeof(s), typeof(t))
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return GWord{W}([s])*t
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end
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abstract Word
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immutable GWord{T<:GSymbol} <: Word
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symbols::Vector{T}
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end
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typealias FGWord GWord{FGSymbol}
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GWord{T<:GSymbol}(s::T) = GWord{T}([s])
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FGWord(s::FGSymbol) = FGWord([s])
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# FGWord() = FGWord(Vector{FGSymbol}())
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function length(W::GWord)
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return sum([abs(s.pow) for s in W.symbols])
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end
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one{T}(::Type{GWord{T}}) = GWord(Vector{T}())
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one{T}(w::GWord{T}) = one(GWord{T})
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inv(s::FGSymbol) = FGSymbol(s.gen, -s.pow)
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function inv{T}(W::GWord{T})
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if length(W) == 0
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return W
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@ -56,8 +71,6 @@ function inv{T}(W::GWord{T})
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end
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end
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reduce!(s::GSymbol) = s
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function reduce!(W::GWord{FGSymbol})
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if length(W) < 2
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deleteat!(W.symbols, find(x -> x.pow == 0, W.symbols))
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@ -72,7 +85,7 @@ function reduce!(W::GWord{FGSymbol})
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reduced = false
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p1 = W.symbols[i].pow
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p2 = W.symbols[i+1].pow
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W.symbols[i+1] = FGSymbol(W.symbols[i].gen, p1 + p2)
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W.symbols[i+1] = change_pow(W.symbols[i], p1 + p2)
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W.symbols[i] = one(W.symbols[i])
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end
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end
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@ -91,10 +104,10 @@ function show(io::IO, W::GWord)
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else
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join(io, [string(s) for s in W.symbols], "*")
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end
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end;
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end
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push!(W::GWord, x) = push!(W.symbols, x...)
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unshift!(W::GWord, x) = unshift!(W.symbols, reverse(x)...)
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unshift!(W::GWord, x) = unshift!(W.symbols, x...)
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function r_multiply!(W::GWord, x; reduced::Bool=true)
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if length(x) > 0
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@ -108,7 +121,7 @@ end
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function l_multiply!(W::GWord, x; reduced::Bool=true)
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if length(x) > 0
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unshift!(W, x)
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unshift!(W, reverse(x))
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end
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if reduced
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reduce!(W)
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@ -122,17 +135,9 @@ l_multiply(W::GWord, x; reduced::Bool=true) =
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l_multiply!(deepcopy(W),x, reduced=reduced)
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(*){T}(W::GWord{T}, Z::GWord{T}) = FreeGroups.r_multiply(W, Z.symbols)
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function (*)(s::GSymbol, t::GSymbol)
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W = promote_type(typeof(s), typeof(t))
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return GWord{W}([s])*t
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end
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(*)(W::GWord, s::GSymbol) = W*GWord(s)
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(*)(s::GSymbol, W::GWord) = GWord(s)*W
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(^)(x::FGSymbol, n::Integer) = FGSymbol(x.gen, x.pow*n)
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function power_by_squaring{T}(x::GWord{T}, p::Integer)
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if p < 0
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return power_by_squaring(inv(x), -p)
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