mirror of
https://github.com/kalmarek/Groups.jl.git
synced 2024-12-26 02:20:30 +01:00
separate arithmetic
This commit is contained in:
parent
e84152a9cf
commit
afa0988ebc
@ -20,6 +20,7 @@ include("fallbacks.jl")
|
|||||||
include("words.jl")
|
include("words.jl")
|
||||||
include("hashing.jl")
|
include("hashing.jl")
|
||||||
include("freereduce.jl")
|
include("freereduce.jl")
|
||||||
|
include("arithmetic.jl")
|
||||||
|
|
||||||
include("FreeGroup.jl")
|
include("FreeGroup.jl")
|
||||||
include("FPGroups.jl")
|
include("FPGroups.jl")
|
||||||
@ -62,102 +63,6 @@ function show(io::IO, s::T) where {T<:GSymbol}
|
|||||||
print(io, string((s.id))*"^$(s.pow)")
|
print(io, string((s.id))*"^$(s.pow)")
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
|
|
||||||
###############################################################################
|
|
||||||
#
|
|
||||||
# Binary operators
|
|
||||||
#
|
|
||||||
###############################################################################
|
|
||||||
|
|
||||||
function Base.append!(w::GWord{T}, v::AbstractVector{T}) where T
|
|
||||||
append!(syllables(w), v)
|
|
||||||
return w
|
|
||||||
end
|
|
||||||
|
|
||||||
function Base.prepend!(w::GWord{T}, v::AbstractVector{T}) where T
|
|
||||||
prepend!(syllables(w), v)
|
|
||||||
return w
|
|
||||||
end
|
|
||||||
|
|
||||||
Base.append!(w::T, v::T) where T <: GWord = append!(w, syllables(v))
|
|
||||||
Base.prepend!(w::T, v::T) where T <: GWord = prepend!(w, syllables(v))
|
|
||||||
|
|
||||||
for (mul, f) in ((:rmul!, :push!), (:lmul!, :pushfirst!))
|
|
||||||
@eval begin
|
|
||||||
function $mul(out::T, w::T, s::GSymbol) where T <:GWord
|
|
||||||
$f(syllables(out), s)
|
|
||||||
return freereduce!(out)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
function rmul!(out::T, x::T, y::T) where T<: GWord
|
|
||||||
if out === x
|
|
||||||
out = deepcopy(out)
|
|
||||||
return freereduce!(append!(out, y))
|
|
||||||
elseif out === y
|
|
||||||
out = deepcopy(out)
|
|
||||||
return freereduce!(prepend!(out, x))
|
|
||||||
else
|
|
||||||
slenx = syllablelength(x)
|
|
||||||
sleny = syllablelength(y)
|
|
||||||
resize!(syllables(out), slenx+sleny)
|
|
||||||
syllables(out)[1:slenx] .= syllables(x)
|
|
||||||
syllables(out)[slenx+1:slenx+sleny] .= syllables(y)
|
|
||||||
return freereduce!(out)
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
lmul!(out::T, x::T, y::T) where T <: GWord = rmul!(out, y, x)
|
|
||||||
|
|
||||||
function AbstractAlgebra.mul!(out::T, x::T, y::T) where T <: GWord
|
|
||||||
return rmul!(out, x, y)
|
|
||||||
end
|
|
||||||
|
|
||||||
(*)(W::GW, Z::GW) where GW <: GWord = rmul!(deepcopy(W), W, Z)
|
|
||||||
(*)(W::GWord, s::GSymbol) = rmul!(deepcopy(W), W, s)
|
|
||||||
(*)(s::GSymbol, W::GWord) = lmul!(deepcopy(W), W, s)
|
|
||||||
|
|
||||||
function power_by_squaring(W::GWord, p::Integer)
|
|
||||||
if p < 0
|
|
||||||
return power_by_squaring(inv(W), -p)
|
|
||||||
elseif p == 0
|
|
||||||
return one(parent(W))
|
|
||||||
elseif p == 1
|
|
||||||
return W
|
|
||||||
elseif p == 2
|
|
||||||
return W*W
|
|
||||||
end
|
|
||||||
W = deepcopy(W)
|
|
||||||
t = trailing_zeros(p) + 1
|
|
||||||
p >>= t
|
|
||||||
while (t -= 1) > 0
|
|
||||||
append!(W, W)
|
|
||||||
end
|
|
||||||
Z = deepcopy(W)
|
|
||||||
while p > 0
|
|
||||||
t = trailing_zeros(p) + 1
|
|
||||||
p >>= t
|
|
||||||
while (t -= 1) >= 0
|
|
||||||
append!(W, W)
|
|
||||||
end
|
|
||||||
append!(Z, W)
|
|
||||||
end
|
|
||||||
|
|
||||||
return freereduce!(Z)
|
|
||||||
end
|
|
||||||
|
|
||||||
(^)(x::GWord, n::Integer) = power_by_squaring(x,n)
|
|
||||||
|
|
||||||
###############################################################################
|
|
||||||
#
|
|
||||||
# Inversion
|
|
||||||
#
|
|
||||||
###############################################################################
|
|
||||||
|
|
||||||
function inv(W::T) where T<:GWord
|
|
||||||
if length(W) == 0
|
|
||||||
return W
|
|
||||||
else
|
else
|
||||||
G = parent(W)
|
G = parent(W)
|
||||||
w = T([inv(s) for s in Iterators.reverse(syllables(W))])
|
w = T([inv(s) for s in Iterators.reverse(syllables(W))])
|
||||||
|
|||||||
93
src/arithmetic.jl
Normal file
93
src/arithmetic.jl
Normal file
@ -0,0 +1,93 @@
|
|||||||
|
function Base.inv(W::T) where T<:GWord
|
||||||
|
length(W) == 0 && return W
|
||||||
|
G = parent(W)
|
||||||
|
w = T([inv(s) for s in Iterators.reverse(syllables(W))])
|
||||||
|
return setparent!(w, G)
|
||||||
|
end
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
#
|
||||||
|
# Binary operators
|
||||||
|
#
|
||||||
|
|
||||||
|
function Base.append!(w::GWord{T}, v::AbstractVector{T}) where T
|
||||||
|
append!(syllables(w), v)
|
||||||
|
return w
|
||||||
|
end
|
||||||
|
|
||||||
|
function Base.prepend!(w::GWord{T}, v::AbstractVector{T}) where T
|
||||||
|
prepend!(syllables(w), v)
|
||||||
|
return w
|
||||||
|
end
|
||||||
|
|
||||||
|
Base.append!(w::T, v::T) where T <: GWord = append!(w, syllables(v))
|
||||||
|
Base.prepend!(w::T, v::T) where T <: GWord = prepend!(w, syllables(v))
|
||||||
|
|
||||||
|
for (mul, f) in ((:rmul!, :push!), (:lmul!, :pushfirst!))
|
||||||
|
@eval begin
|
||||||
|
function $mul(out::T, w::T, s::GSymbol) where T <:GWord
|
||||||
|
resize!(syllables(out), syllablelength(w))
|
||||||
|
syllables(out) .= syllables(w)
|
||||||
|
$f(syllables(out), s)
|
||||||
|
return freereduce!(out)
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function rmul!(out::T, x::T, y::T) where T<: GWord
|
||||||
|
if out === x
|
||||||
|
out = deepcopy(out)
|
||||||
|
return freereduce!(append!(out, y))
|
||||||
|
elseif out === y
|
||||||
|
out = deepcopy(out)
|
||||||
|
return freereduce!(prepend!(out, x))
|
||||||
|
else
|
||||||
|
slenx = syllablelength(x)
|
||||||
|
sleny = syllablelength(y)
|
||||||
|
resize!(syllables(out), slenx+sleny)
|
||||||
|
syllables(out)[1:slenx] .= syllables(x)
|
||||||
|
syllables(out)[slenx+1:slenx+sleny] .= syllables(y)
|
||||||
|
return freereduce!(out)
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
lmul!(out::T, x::T, y::T) where T <: GWord = rmul!(out, y, x)
|
||||||
|
|
||||||
|
function AbstractAlgebra.mul!(out::T, x::T, y::T) where T <: GWord
|
||||||
|
return rmul!(out, x, y)
|
||||||
|
end
|
||||||
|
|
||||||
|
(*)(W::GW, Z::GW) where GW <: GWord = rmul!(deepcopy(W), W, Z)
|
||||||
|
(*)(W::GWord, s::GSymbol) = rmul!(deepcopy(W), W, s)
|
||||||
|
(*)(s::GSymbol, W::GWord) = lmul!(deepcopy(W), W, s)
|
||||||
|
|
||||||
|
function power_by_squaring(W::GWord, p::Integer)
|
||||||
|
if p < 0
|
||||||
|
return power_by_squaring(inv(W), -p)
|
||||||
|
elseif p == 0
|
||||||
|
return one(W)
|
||||||
|
elseif p == 1
|
||||||
|
return W
|
||||||
|
elseif p == 2
|
||||||
|
return W*W
|
||||||
|
end
|
||||||
|
W = deepcopy(W)
|
||||||
|
t = trailing_zeros(p) + 1
|
||||||
|
p >>= t
|
||||||
|
while (t -= 1) > 0
|
||||||
|
append!(W, W)
|
||||||
|
end
|
||||||
|
Z = deepcopy(W)
|
||||||
|
while p > 0
|
||||||
|
t = trailing_zeros(p) + 1
|
||||||
|
p >>= t
|
||||||
|
while (t -= 1) >= 0
|
||||||
|
append!(W, W)
|
||||||
|
end
|
||||||
|
append!(Z, W)
|
||||||
|
end
|
||||||
|
|
||||||
|
return freereduce!(Z)
|
||||||
|
end
|
||||||
|
|
||||||
|
(^)(x::GWord, n::Integer) = power_by_squaring(x,n)
|
||||||
Loading…
Reference in New Issue
Block a user