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Major Overhaul: abstract types: Word, GSymbol

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Signed-off-by: kalmar <kalmar@amu.edu.pl>
This commit is contained in:
kalmar 2017-01-17 15:13:54 +01:00
parent d21d10228b
commit d3dc8dce94
1 changed files with 79 additions and 55 deletions
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134
FreeGroups.jl
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@ -1,25 +1,31 @@
module FreeGroups module FreeGroups
export FGSymbol, FGWord, FGAutomorphism export GSymbol, Word, FGSymbol, GWord, FGAutomorphism
import Base: length, ==, show, convert import Base: length, ==, show, convert
import Base: *, ^, convert
immutable FGSymbol abstract GSymbol
abstract Word
immutable FGSymbol <: GSymbol
gen::String gen::String
pow::Int pow::Int
end end
(==)(s::FGSymbol, t::FGSymbol) = s.gen == t.gen && s.pow == t.pow immutable GWord{T<:GSymbol} <:Word
symbols::Vector{T}
immutable FGWord
symbols::Vector{FGSymbol}
end 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 if s.pow == 1
print(io, (s.gen)) print(io, (s.gen))
elseif s.pow == 0 elseif s.pow == 0
@ -30,41 +36,56 @@ function show(io::IO, s::FGSymbol)
end end
FGSymbol(x::String) = FGSymbol(x,1) FGSymbol(x::String) = FGSymbol(x,1)
FGWord() = FGWord(Vector{FGSymbol}()) GWord{T}(s::T) = GWord{T}([s])
FGWord(s::FGSymbol) = FGWord([s])
convert(::Type{FGWord}, s::FGSymbol) = FGWord(s)
convert(::Type{FGSymbol}, y::String) = FGSymbol(y)
import Base: one, inv, reduce, push!, unshift! import Base: one, inv, reduce, push!, unshift!
one(s::FGSymbol) = FGSymbol(s.gen, 0) one(s::FGSymbol) = FGSymbol(s.gen, 0)
one(::Type{FGWord}) = FGWord() one{T}(::Type{GWord{T}}) = GWord(Vector{T}())
one(w::FGWord) = FGWord() one{T}(w::GWord{T}) = one(GWord{T})
inv(s::FGSymbol) = FGSymbol(s.gen, -s.pow) 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 inv{T}(W::GWord{T})
if length(W) == 0
function reduce!(W::FGWord) return W
for i in 1:length(W)-1 else
if W.symbols[i].gen == W.symbols[i+1].gen return prod(reverse([inv(s) for s in W.symbols]))
p1 = W.symbols[i].pow end
p2 = W.symbols[i+1].pow end
W.symbols[i+1] = FGSymbol(W.symbols[i].gen, p1 + p2)
W.symbols[i] = one(W.symbols[i]) reduce!(s::GSymbol) = s
end
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 end
deleteat!(W.symbols, find(x -> x.pow == 0, W.symbols))
return W return W
end 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 if length(W) == 0
print(io, "(id)") print(io, "(id)")
else else
@ -72,12 +93,12 @@ function show(io::IO, W::FGWord)
end end
end; end;
push!(W::FGWord, x...) = push!(W.symbols, x...) push!(W::GWord, x) = push!(W.symbols, x...)
unshift!(W::FGWord, x...) = unshift!(W.symbols, reverse(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 if length(x) > 0
push!(W, x...) push!(W, x)
end end
if reduced if reduced
reduce!(W) reduce!(W)
@ -85,9 +106,9 @@ function r_multiply!(W::FGWord, x...; reduced::Bool=true)
return W return W
end end
function l_multiply!(W::FGWord, x...; reduced::Bool=true) function l_multiply!(W::GWord, x; reduced::Bool=true)
if length(x) > 0 if length(x) > 0
unshift!(W, x...) unshift!(W, x)
end end
if reduced if reduced
reduce!(W) reduce!(W)
@ -95,21 +116,24 @@ function l_multiply!(W::FGWord, x...; reduced::Bool=true)
return W return W
end end
r_multiply(W::FGWord, x...; reduced::Bool=true) = r_multiply(W::GWord, x; reduced::Bool=true) =
r_multiply!(deepcopy(W),x..., reduced=reduced) r_multiply!(deepcopy(W),x, reduced=reduced)
l_multiply(W::FGWord, x...; reduced::Bool=true) = l_multiply(W::GWord, x; reduced::Bool=true) =
l_multiply!(deepcopy(W),x..., reduced=reduced) 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...) function (*)(s::GSymbol, t::GSymbol)
(*)(s::FGSymbol, t::FGSymbol) = FGWord(s)*FGWord(t) W = promote_type(typeof(s), typeof(t))
(*)(W::FGWord, s::FGSymbol) = W*FGWord(s) return GWord{W}([s])*t
(*)(s::FGSymbol, W::FGWord) = FGWord(s)*W 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) (^)(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 if p < 0
return power_by_squaring(inv(x), -p) return power_by_squaring(inv(x), -p)
elseif p == 0 elseif p == 0
@ -136,14 +160,14 @@ function power_by_squaring(x::FGWord, p::Integer)
return reduce!(y) return reduce!(y)
end end
(^)(x::FGWord, n::Integer) = power_by_squaring(x,n) (^)(x::GWord, n::Integer) = power_by_squaring(x,n)
type FGAutomorphism type FGAutomorphism
domain::Vector{FGSymbol} domain::Vector{GSymbol}
image::Vector{FGWord} image::Vector{GWord}
map::Function 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)) || length(domain) == length(unique(domain)) ||
throw(ArgumentError("The elements of $domain are not unique")) throw(ArgumentError("The elements of $domain are not unique"))
length(domain) == length(image) || 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) return v->reduce(*,GroupIdentity, v[idx]^power for (idx, power) in table)
end end
function aut_func_from_word(domain, w::FGWord) function aut_func_from_word(domain, w::GWord)
table = Vector{Tuple{Int, Int}}() table = Vector{Tuple{Int, Int}}()
for s in w.symbols for s in w.symbols
pair = (findfirst([x.gen for x in domain], s.gen), s.pow) 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) return aut_func_from_table(table)
end end
function FGMap(domain::Vector{FGSymbol}, image::Vector{FGWord}) function FGMap(domain::Vector{FGSymbol}, image::Vector{GWord})
function_vector = Vector{Function}() 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]) return v -> Vector{FGWord}([f(v) for f in function_vector])
end end
FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{FGWord}) = FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{GWord}) =
FGAutomorphism(domain, image, FGMap(domain, image)) FGAutomorphism(domain, image, FGMap(domain, image))
FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{FGSymbol}) = FGAutomorphism(domain::Vector{FGSymbol}, image::Vector{FGSymbol}) =
FGAutomorphism(domain, Vector{FGWord}(image)) FGAutomorphism(domain, Vector{GWord}(image))
function FGAutomorphism(domain::Vector, image::Vector) function FGAutomorphism(domain::Vector, image::Vector)
FGAutomorphism(Vector{FGSymbol}(domain), Vector{FGWord}(image)) FGAutomorphism(Vector{FGSymbol}(domain), Vector{GWord}(image))
end end
function FGAutomorphism(domain, image) function FGAutomorphism(domain, image)