mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-12-25 18:25:30 +01:00
Splitted into Groups.jl package
This commit is contained in:
parent
56b63058e3
commit
e69f5d13b6
@ -1,25 +0,0 @@
|
||||
module FreeGroups
|
||||
|
||||
using Groups
|
||||
|
||||
import Base: inv, convert
|
||||
|
||||
export FGSymbol, IDSymbol
|
||||
|
||||
immutable FGSymbol <: GSymbol
|
||||
gen::String
|
||||
pow::Int
|
||||
end
|
||||
|
||||
IDSymbol(::Type{FGSymbol}) = FGSymbol("(id)", 0)
|
||||
FGSymbol(x::String) = FGSymbol(x,1)
|
||||
|
||||
inv(s::FGSymbol) = FGSymbol(s.gen, -s.pow)
|
||||
convert(::Type{FGSymbol}, x::String) = FGSymbol(x)
|
||||
change_pow(s::FGSymbol, n::Int) = reduce(FGSymbol(s.gen, n))
|
||||
|
||||
typealias FGWord GWord{FGSymbol}
|
||||
|
||||
FGWord(s::FGSymbol) = FGWord([s])
|
||||
|
||||
end #end of module FreeGroups
|
||||
173
Groups.jl
173
Groups.jl
@ -1,173 +0,0 @@
|
||||
module Groups
|
||||
|
||||
import Base: length, ==, hash, show
|
||||
import Base: one, inv, reduce, *, ^
|
||||
|
||||
export GSymbol, GWord
|
||||
|
||||
export IdSymbol, change_pow
|
||||
|
||||
abstract GSymbol
|
||||
|
||||
function show(io::IO, s::GSymbol)
|
||||
if s.pow == 0
|
||||
print(io, "(id)")
|
||||
elseif s.pow == 1
|
||||
print(io, s.gen)
|
||||
else
|
||||
print(io, (s.gen)*"^$(s.pow)")
|
||||
end
|
||||
end
|
||||
|
||||
length(s::GSymbol) = (s.pow == 0 ? 0 : 1)
|
||||
|
||||
IdSymbol(T::Type{GSymbol}) = throw(ArgumentError("Define IdSymbol(::Type{$T}) which is the identity element for Your type!"))
|
||||
|
||||
one{T<:GSymbol}(::Type{T}) = IdSymbol(T)
|
||||
one(s::GSymbol) = one(typeof(s))
|
||||
|
||||
(*){T<:GSymbol}(s::T, t::T) = return GWord{T}([s])*t
|
||||
|
||||
change_pow(s::GSymbol, n::Int) = throw(ArgumentError("Define change_pow function for $(typeof(s))!"))
|
||||
|
||||
|
||||
abstract Word
|
||||
|
||||
type GWord{T<:GSymbol} <: Word
|
||||
symbols::Vector{T}
|
||||
savedhash::UInt
|
||||
modified::Bool
|
||||
|
||||
function GWord(symbols::Vector{T})
|
||||
return new(symbols, hash(symbols), false)
|
||||
end
|
||||
end
|
||||
|
||||
GWord{T<:GSymbol}(s::T) = GWord{T}([s])
|
||||
|
||||
IDWord{T<:GSymbol}(::Type{T}) = GWord(one(T))
|
||||
IDWord{T<:GSymbol}(W::GWord{T}) = IDWord(T)
|
||||
|
||||
function length(W::GWord)
|
||||
return sum([abs(s.pow) for s in W.symbols])
|
||||
end
|
||||
|
||||
one{T}(::Type{GWord{T}}) = IDWord(T)
|
||||
one{T}(w::GWord{T}) = one(GWord{T})
|
||||
|
||||
function inv{T}(W::GWord{T})
|
||||
if length(W) == 0
|
||||
return W
|
||||
else
|
||||
return freegroup_reduce!(GWord{T}(reverse([inv(s) for s in W.symbols])))
|
||||
end
|
||||
end
|
||||
|
||||
function join_free_symbols!(W::GWord)
|
||||
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] = change_pow(W.symbols[i], p1 + p2)
|
||||
W.symbols[i] = one(W.symbols[i])
|
||||
end
|
||||
end
|
||||
return reduced
|
||||
end
|
||||
|
||||
function freegroup_reduce!{T}(W::GWord{T})
|
||||
if length(W) < 2
|
||||
deleteat!(W.symbols, find(x -> x.pow == 0, W.symbols))
|
||||
else
|
||||
reduced = false
|
||||
while !reduced
|
||||
reduced = join_free_symbols!(W)
|
||||
deleteat!(W.symbols, find(x -> x.pow == 0, W.symbols))
|
||||
end
|
||||
end
|
||||
|
||||
W.modified = false
|
||||
W.savedhash = hash(W.symbols,hash(typeof(W)))
|
||||
return W
|
||||
end
|
||||
|
||||
freegroup_reduce(W::GWord) = freegroup_reduce!(deepcopy(W))
|
||||
|
||||
hash{T}(W::GWord{T}) = (W.modified && freegroup_reduce!(W); W.savedhash)
|
||||
|
||||
function (==){T}(W::GWord{T}, Z::GWord{T})
|
||||
W.modified && freegroup_reduce!(W) # reduce could actually clear the flag and recalculate the hash
|
||||
Z.modified && freegroup_reduce!(Z)
|
||||
return W.savedhash == Z.savedhash && W.symbols == Z.symbols
|
||||
end
|
||||
|
||||
function show(io::IO, W::GWord)
|
||||
if length(W) == 0
|
||||
print(io, "(id)")
|
||||
else
|
||||
join(io, [string(s) for s in W.symbols], "*")
|
||||
end
|
||||
end
|
||||
|
||||
function r_multiply!(W::GWord, x; reduced::Bool=true)
|
||||
if length(x) > 0
|
||||
push!(W.symbols, x...)
|
||||
end
|
||||
if reduced
|
||||
freegroup_reduce!(W)
|
||||
end
|
||||
return W
|
||||
end
|
||||
|
||||
function l_multiply!(W::GWord, x; reduced::Bool=true)
|
||||
if length(x) > 0
|
||||
unshift!(W.symbols, reverse(x)...)
|
||||
end
|
||||
if reduced
|
||||
freegroup_reduce!(W)
|
||||
end
|
||||
return W
|
||||
end
|
||||
|
||||
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)
|
||||
|
||||
(*){T}(W::GWord{T}, Z::GWord{T}) = r_multiply(W, Z.symbols)
|
||||
(*)(W::GWord, s::GSymbol) = W*GWord(s)
|
||||
(*)(s::GSymbol, W::GWord) = GWord(s)*W
|
||||
|
||||
function power_by_squaring{T}(x::GWord{T}, p::Integer)
|
||||
if p < 0
|
||||
return power_by_squaring(inv(x), -p)
|
||||
elseif p == 0
|
||||
return one(x)
|
||||
elseif p == 1
|
||||
return deepcopy(x)
|
||||
elseif p == 2
|
||||
return x*x
|
||||
end
|
||||
t = trailing_zeros(p) + 1
|
||||
p >>= t
|
||||
while (t -= 1) > 0
|
||||
x *= x
|
||||
end
|
||||
y = x
|
||||
while p > 0
|
||||
t = trailing_zeros(p) + 1
|
||||
p >>= t
|
||||
while (t -= 1) >= 0
|
||||
x *= x
|
||||
end
|
||||
y *= x
|
||||
end
|
||||
return freegroup_reduce!(y)
|
||||
end
|
||||
|
||||
(^)(x::GWord, n::Integer) = power_by_squaring(x,n)
|
||||
|
||||
|
||||
end
|
||||
Loading…
Reference in New Issue
Block a user