From d3dc8dce946569abadc49e64b9ba789ea2722daf Mon Sep 17 00:00:00 2001 From: kalmar Date: Tue, 17 Jan 2017 15:13:54 +0100 Subject: [PATCH] Major Overhaul: abstract types: Word, GSymbol Signed-off-by: kalmar --- FreeGroups.jl | 134 +++++++++++++++++++++++++++++--------------------- 1 file changed, 79 insertions(+), 55 deletions(-) diff --git a/FreeGroups.jl b/FreeGroups.jl index da6ac77..07a076d 100644 --- a/FreeGroups.jl +++ b/FreeGroups.jl @@ -1,25 +1,31 @@ module FreeGroups -export FGSymbol, FGWord, FGAutomorphism +export GSymbol, Word, FGSymbol, GWord, FGAutomorphism import Base: length, ==, show, convert +import Base: *, ^, convert -immutable FGSymbol +abstract GSymbol +abstract Word + +immutable FGSymbol <: GSymbol gen::String pow::Int end -(==)(s::FGSymbol, t::FGSymbol) = s.gen == t.gen && s.pow == t.pow - -immutable FGWord - symbols::Vector{FGSymbol} +immutable GWord{T<:GSymbol} <:Word + symbols::Vector{T} end -length(s::FGSymbol) = (s.pow == 0 ? 0 : 1) +length(s::GSymbol) = (s.pow == 0 ? 0 : 1) -length(W::FGWord) = length(W.symbols) +(==)(s::FGSymbol, t::FGSymbol) = s.gen == t.gen && s.pow == t.pow -function show(io::IO, s::FGSymbol) +function length(W::GWord) + return sum([abs(s.pow) for s in W.symbols]) +end + +function show(io::IO, s::GSymbol) if s.pow == 1 print(io, (s.gen)) elseif s.pow == 0 @@ -30,41 +36,56 @@ function show(io::IO, s::FGSymbol) end FGSymbol(x::String) = FGSymbol(x,1) -FGWord() = FGWord(Vector{FGSymbol}()) -FGWord(s::FGSymbol) = FGWord([s]) - -convert(::Type{FGWord}, s::FGSymbol) = FGWord(s) +GWord{T}(s::T) = GWord{T}([s]) +convert(::Type{FGSymbol}, y::String) = FGSymbol(y) import Base: one, inv, reduce, push!, unshift! one(s::FGSymbol) = FGSymbol(s.gen, 0) -one(::Type{FGWord}) = FGWord() -one(w::FGWord) = FGWord() +one{T}(::Type{GWord{T}}) = GWord(Vector{T}()) +one{T}(w::GWord{T}) = one(GWord{T}) inv(s::FGSymbol) = FGSymbol(s.gen, -s.pow) -inv(W::FGWord) = FGWord(reverse([inv(s) for s in W.symbols])) -reduce!(s::FGSymbol) = s - -function reduce!(W::FGWord) - for i in 1:length(W)-1 - if W.symbols[i].gen == W.symbols[i+1].gen - 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] = one(W.symbols[i]) - end +function inv{T}(W::GWord{T}) + if length(W) == 0 + return W + else + return prod(reverse([inv(s) for s in W.symbols])) + 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)) + return W + end + + reduced = false + while !reduced + reduced = true + for i in 1:length(W.symbols) - 1 + if W.symbols[i].gen == W.symbols[i+1].gen + 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] = one(W.symbols[i]) + end + end + deleteat!(W.symbols, find(x -> x.pow == 0, W.symbols)) end - deleteat!(W.symbols, find(x -> x.pow == 0, W.symbols)) return W end -reduce(W::FGWord) = reduce!(deepcopy(W)) +reduce(W::GWord) = reduce!(deepcopy(W)) -(==)(W::FGWord, Z::FGWord) = reduce(W).symbols == reduce(Z).symbols +(==)(W::GWord{FGSymbol}, Z::GWord{FGSymbol}) = reduce!(W).symbols == reduce!(Z).symbols -function show(io::IO, W::FGWord) +function show(io::IO, W::GWord) if length(W) == 0 print(io, "(id)") else @@ -72,12 +93,12 @@ function show(io::IO, W::FGWord) end end; -push!(W::FGWord, x...) = push!(W.symbols, x...) -unshift!(W::FGWord, x...) = unshift!(W.symbols, reverse(x)...) +push!(W::GWord, x) = push!(W.symbols, x...) +unshift!(W::GWord, x) = unshift!(W.symbols, reverse(x)...) -function r_multiply!(W::FGWord, x...; reduced::Bool=true) +function r_multiply!(W::GWord, x; reduced::Bool=true) if length(x) > 0 - push!(W, x...) + push!(W, x) end if reduced reduce!(W) @@ -85,9 +106,9 @@ function r_multiply!(W::FGWord, x...; reduced::Bool=true) return W end -function l_multiply!(W::FGWord, x...; reduced::Bool=true) +function l_multiply!(W::GWord, x; reduced::Bool=true) if length(x) > 0 - unshift!(W, x...) + unshift!(W, x) end if reduced reduce!(W) @@ -95,21 +116,24 @@ function l_multiply!(W::FGWord, x...; reduced::Bool=true) return W end -r_multiply(W::FGWord, x...; reduced::Bool=true) = - r_multiply!(deepcopy(W),x..., reduced=reduced) -l_multiply(W::FGWord, x...; reduced::Bool=true) = - l_multiply!(deepcopy(W),x..., reduced=reduced) +r_multiply(W::GWord, x; reduced::Bool=true) = + r_multiply!(deepcopy(W),x, reduced=reduced) +l_multiply(W::GWord, x; reduced::Bool=true) = + l_multiply!(deepcopy(W),x, reduced=reduced) -import Base: *, ^ +(*){T}(W::GWord{T}, Z::GWord{T}) = FreeGroups.r_multiply(W, Z.symbols) -(*)(W::FGWord, Z::FGWord) = r_multiply(W, Z.symbols...) -(*)(s::FGSymbol, t::FGSymbol) = FGWord(s)*FGWord(t) -(*)(W::FGWord, s::FGSymbol) = W*FGWord(s) -(*)(s::FGSymbol, W::FGWord) = FGWord(s)*W +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(x::FGWord, p::Integer) +function power_by_squaring{T}(x::GWord{T}, p::Integer) if p < 0 return power_by_squaring(inv(x), -p) elseif p == 0 @@ -136,14 +160,14 @@ function power_by_squaring(x::FGWord, p::Integer) return reduce!(y) end -(^)(x::FGWord, n::Integer) = power_by_squaring(x,n) +(^)(x::GWord, n::Integer) = power_by_squaring(x,n) type FGAutomorphism - domain::Vector{FGSymbol} - image::Vector{FGWord} + domain::Vector{GSymbol} + image::Vector{GWord} map::Function - function FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{FGWord}, map::Function) + function FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{GWord}, map::Function) length(domain) == length(unique(domain)) || throw(ArgumentError("The elements of $domain are not unique")) length(domain) == length(image) || @@ -172,7 +196,7 @@ function aut_func_from_table(table::Vector{Tuple{Int,Int}}, GroupIdentity=one(FG return v->reduce(*,GroupIdentity, v[idx]^power for (idx, power) in table) end -function aut_func_from_word(domain, w::FGWord) +function aut_func_from_word(domain, w::GWord) table = Vector{Tuple{Int, Int}}() for s in w.symbols pair = (findfirst([x.gen for x in domain], s.gen), s.pow) @@ -181,7 +205,7 @@ function aut_func_from_word(domain, w::FGWord) return aut_func_from_table(table) end -function FGMap(domain::Vector{FGSymbol}, image::Vector{FGWord}) +function FGMap(domain::Vector{FGSymbol}, image::Vector{GWord}) function_vector = Vector{Function}() @@ -192,14 +216,14 @@ function FGMap(domain::Vector{FGSymbol}, image::Vector{FGWord}) return v -> Vector{FGWord}([f(v) for f in function_vector]) end -FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{FGWord}) = +FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{GWord}) = FGAutomorphism(domain, image, FGMap(domain, image)) FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{FGSymbol}) = - FGAutomorphism(domain, Vector{FGWord}(image)) + FGAutomorphism(domain, Vector{GWord}(image)) function FGAutomorphism(domain::Vector, image::Vector) - FGAutomorphism(Vector{FGSymbol}(domain), Vector{FGWord}(image)) + FGAutomorphism(Vector{FGSymbol}(domain), Vector{GWord}(image)) end function FGAutomorphism(domain, image)