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Reshuffling of definitions

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kalmar 2017-01-17 17:54:30 +01:00
parent 4cb85478d8
commit c858b77b8c
1 changed files with 40 additions and 35 deletions
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75
FreeGroups.jl
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@ -1,29 +1,19 @@
module FreeGroups
export GSymbol, Word, FGSymbol, GWord, FGAutomorphism
export GSymbol, FGSymbol, Word, GWord, FGWord, FGAutomorphism
import Base: length, ==, show, convert
import Base: *, ^, convert
import Base: one, inv, reduce, push!, unshift!
abstract GSymbol
abstract Word
immutable FGSymbol <: GSymbol
gen::String
pow::Int
end
immutable GWord{T<:GSymbol} <:Word
symbols::Vector{T}
end
length(s::GSymbol) = (s.pow == 0 ? 0 : 1)
(==)(s::FGSymbol, t::FGSymbol) = s.gen == t.gen && s.pow == t.pow
function length(W::GWord)
return sum([abs(s.pow) for s in W.symbols])
end
FGSymbol(x::String) = FGSymbol(x,1)
function show(io::IO, s::GSymbol)
if s.pow == 1
@ -35,19 +25,44 @@ function show(io::IO, s::GSymbol)
end
end
FGSymbol(x::String) = FGSymbol(x,1)
GWord{T}(s::T) = GWord{T}([s])
convert(::Type{FGSymbol}, y::String) = FGSymbol(y)
import Base: one, inv, reduce, push!, unshift!
(==)(s::GSymbol, t::GSymbol) = s.gen == t.gen && s.pow == t.pow
length(s::GSymbol) = (s.pow == 0 ? 0 : 1)
one(s::FGSymbol) = FGSymbol(s.gen, 0)
inv(s::FGSymbol) = FGSymbol(s.gen, -s.pow)
convert(::Type{FGSymbol}, x::String) = FGSymbol(x)
reduce!(s::GSymbol) = s
change_pow(s::FGSymbol, n::Int) = FGSymbol(s.gen, n)
(^)(x::FGSymbol, n::Integer) = FGSymbol(x.gen, x.pow*n)
function (*)(s::GSymbol, t::GSymbol)
W = promote_type(typeof(s), typeof(t))
return GWord{W}([s])*t
end
abstract Word
immutable GWord{T<:GSymbol} <: Word
symbols::Vector{T}
end
typealias FGWord GWord{FGSymbol}
GWord{T<:GSymbol}(s::T) = GWord{T}([s])
FGWord(s::FGSymbol) = FGWord([s])
# FGWord() = FGWord(Vector{FGSymbol}())
function length(W::GWord)
return sum([abs(s.pow) for s in W.symbols])
end
one{T}(::Type{GWord{T}}) = GWord(Vector{T}())
one{T}(w::GWord{T}) = one(GWord{T})
inv(s::FGSymbol) = FGSymbol(s.gen, -s.pow)
function inv{T}(W::GWord{T})
if length(W) == 0
return W
@ -56,8 +71,6 @@ function inv{T}(W::GWord{T})
end
end
reduce!(s::GSymbol) = s
function reduce!(W::GWord{FGSymbol})
if length(W) < 2
deleteat!(W.symbols, find(x -> x.pow == 0, W.symbols))
@ -72,7 +85,7 @@ function reduce!(W::GWord{FGSymbol})
reduced = false
p1 = W.symbols[i].pow
p2 = W.symbols[i+1].pow
W.symbols[i+1] = FGSymbol(W.symbols[i].gen, p1 + p2)
W.symbols[i+1] = change_pow(W.symbols[i], p1 + p2)
W.symbols[i] = one(W.symbols[i])
end
end
@ -91,10 +104,10 @@ function show(io::IO, W::GWord)
else
join(io, [string(s) for s in W.symbols], "*")
end
end;
end
push!(W::GWord, x) = push!(W.symbols, x...)
unshift!(W::GWord, x) = unshift!(W.symbols, reverse(x)...)
unshift!(W::GWord, x) = unshift!(W.symbols, x...)
function r_multiply!(W::GWord, x; reduced::Bool=true)
if length(x) > 0
@ -108,7 +121,7 @@ end
function l_multiply!(W::GWord, x; reduced::Bool=true)
if length(x) > 0
unshift!(W, x)
unshift!(W, reverse(x))
end
if reduced
reduce!(W)
@ -122,17 +135,9 @@ l_multiply(W::GWord, x; reduced::Bool=true) =
l_multiply!(deepcopy(W),x, reduced=reduced)
(*){T}(W::GWord{T}, Z::GWord{T}) = FreeGroups.r_multiply(W, Z.symbols)
function (*)(s::GSymbol, t::GSymbol)
W = promote_type(typeof(s), typeof(t))
return GWord{W}([s])*t
end
(*)(W::GWord, s::GSymbol) = W*GWord(s)
(*)(s::GSymbol, W::GWord) = GWord(s)*W
(^)(x::FGSymbol, n::Integer) = FGSymbol(x.gen, x.pow*n)
function power_by_squaring{T}(x::GWord{T}, p::Integer)
if p < 0
return power_by_squaring(inv(x), -p)