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Major Overhaul: abstract types: Word, GSymbol
Signed-off-by: kalmar <kalmar@amu.edu.pl>
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FreeGroups.jl
118
FreeGroups.jl
@ -1,25 +1,31 @@
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module FreeGroups
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export FGSymbol, FGWord, FGAutomorphism
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export GSymbol, Word, FGSymbol, GWord, FGAutomorphism
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import Base: length, ==, show, convert
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import Base: *, ^, convert
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immutable FGSymbol
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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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(==)(s::FGSymbol, t::FGSymbol) = s.gen == t.gen && s.pow == t.pow
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immutable FGWord
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symbols::Vector{FGSymbol}
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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::FGSymbol) = (s.pow == 0 ? 0 : 1)
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length(s::GSymbol) = (s.pow == 0 ? 0 : 1)
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length(W::FGWord) = length(W.symbols)
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(==)(s::FGSymbol, t::FGSymbol) = s.gen == t.gen && s.pow == t.pow
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function show(io::IO, s::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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function show(io::IO, s::GSymbol)
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if s.pow == 1
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print(io, (s.gen))
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elseif s.pow == 0
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@ -30,26 +36,40 @@ function show(io::IO, s::FGSymbol)
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end
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FGSymbol(x::String) = FGSymbol(x,1)
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FGWord() = FGWord(Vector{FGSymbol}())
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FGWord(s::FGSymbol) = FGWord([s])
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convert(::Type{FGWord}, s::FGSymbol) = FGWord(s)
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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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one(s::FGSymbol) = FGSymbol(s.gen, 0)
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one(::Type{FGWord}) = FGWord()
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one(w::FGWord) = FGWord()
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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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inv(W::FGWord) = FGWord(reverse([inv(s) for s in W.symbols]))
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reduce!(s::FGSymbol) = s
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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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else
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return prod(reverse([inv(s) for s in W.symbols]))
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end
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end
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function reduce!(W::FGWord)
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for i in 1:length(W)-1
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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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return W
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end
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reduced = false
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while !reduced
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reduced = true
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for i in 1:length(W.symbols) - 1
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if W.symbols[i].gen == W.symbols[i+1].gen
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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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@ -57,14 +77,15 @@ function reduce!(W::FGWord)
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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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end
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return W
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end
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reduce(W::FGWord) = reduce!(deepcopy(W))
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reduce(W::GWord) = reduce!(deepcopy(W))
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(==)(W::FGWord, Z::FGWord) = reduce(W).symbols == reduce(Z).symbols
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(==)(W::GWord{FGSymbol}, Z::GWord{FGSymbol}) = reduce!(W).symbols == reduce!(Z).symbols
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function show(io::IO, W::FGWord)
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function show(io::IO, W::GWord)
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if length(W) == 0
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print(io, "(id)")
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else
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@ -72,12 +93,12 @@ function show(io::IO, W::FGWord)
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end
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end;
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push!(W::FGWord, x...) = push!(W.symbols, x...)
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unshift!(W::FGWord, x...) = unshift!(W.symbols, reverse(x)...)
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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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function r_multiply!(W::FGWord, x...; reduced::Bool=true)
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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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push!(W, x...)
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push!(W, x)
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end
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if reduced
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reduce!(W)
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@ -85,9 +106,9 @@ function r_multiply!(W::FGWord, x...; reduced::Bool=true)
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return W
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end
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function l_multiply!(W::FGWord, x...; reduced::Bool=true)
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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, x)
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end
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if reduced
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reduce!(W)
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@ -95,21 +116,24 @@ function l_multiply!(W::FGWord, x...; reduced::Bool=true)
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return W
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end
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r_multiply(W::FGWord, x...; reduced::Bool=true) =
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r_multiply!(deepcopy(W),x..., reduced=reduced)
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l_multiply(W::FGWord, x...; reduced::Bool=true) =
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l_multiply!(deepcopy(W),x..., reduced=reduced)
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r_multiply(W::GWord, x; reduced::Bool=true) =
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r_multiply!(deepcopy(W),x, reduced=reduced)
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l_multiply(W::GWord, x; reduced::Bool=true) =
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l_multiply!(deepcopy(W),x, reduced=reduced)
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import Base: *, ^
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(*){T}(W::GWord{T}, Z::GWord{T}) = FreeGroups.r_multiply(W, Z.symbols)
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(*)(W::FGWord, Z::FGWord) = r_multiply(W, Z.symbols...)
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(*)(s::FGSymbol, t::FGSymbol) = FGWord(s)*FGWord(t)
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(*)(W::FGWord, s::FGSymbol) = W*FGWord(s)
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(*)(s::FGSymbol, W::FGWord) = FGWord(s)*W
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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(x::FGWord, p::Integer)
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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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elseif p == 0
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@ -136,14 +160,14 @@ function power_by_squaring(x::FGWord, p::Integer)
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return reduce!(y)
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end
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(^)(x::FGWord, n::Integer) = power_by_squaring(x,n)
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(^)(x::GWord, n::Integer) = power_by_squaring(x,n)
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type FGAutomorphism
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domain::Vector{FGSymbol}
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image::Vector{FGWord}
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domain::Vector{GSymbol}
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image::Vector{GWord}
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map::Function
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function FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{FGWord}, map::Function)
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function FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{GWord}, map::Function)
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length(domain) == length(unique(domain)) ||
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throw(ArgumentError("The elements of $domain are not unique"))
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length(domain) == length(image) ||
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@ -172,7 +196,7 @@ function aut_func_from_table(table::Vector{Tuple{Int,Int}}, GroupIdentity=one(FG
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return v->reduce(*,GroupIdentity, v[idx]^power for (idx, power) in table)
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end
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function aut_func_from_word(domain, w::FGWord)
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function aut_func_from_word(domain, w::GWord)
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table = Vector{Tuple{Int, Int}}()
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for s in w.symbols
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pair = (findfirst([x.gen for x in domain], s.gen), s.pow)
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@ -181,7 +205,7 @@ function aut_func_from_word(domain, w::FGWord)
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return aut_func_from_table(table)
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end
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function FGMap(domain::Vector{FGSymbol}, image::Vector{FGWord})
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function FGMap(domain::Vector{FGSymbol}, image::Vector{GWord})
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function_vector = Vector{Function}()
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@ -192,14 +216,14 @@ function FGMap(domain::Vector{FGSymbol}, image::Vector{FGWord})
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return v -> Vector{FGWord}([f(v) for f in function_vector])
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end
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FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{FGWord}) =
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FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{GWord}) =
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FGAutomorphism(domain, image, FGMap(domain, image))
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FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{FGSymbol}) =
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FGAutomorphism(domain, Vector{FGWord}(image))
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FGAutomorphism(domain, Vector{GWord}(image))
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function FGAutomorphism(domain::Vector, image::Vector)
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FGAutomorphism(Vector{FGSymbol}(domain), Vector{FGWord}(image))
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FGAutomorphism(Vector{FGSymbol}(domain), Vector{GWord}(image))
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end
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function FGAutomorphism(domain, image)
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