94 lines
2.4 KiB
Julia
94 lines
2.4 KiB
Julia
function Base.inv(W::T) where T<:GWord
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length(W) == 0 && return W
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G = parent(W)
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w = T([inv(s) for s in Iterators.reverse(syllables(W))])
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return setparent!(w, G)
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end
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###############################################################################
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#
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# Binary operators
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#
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function Base.push!(w::GWord{T}, s::T) where T <: GSymbol
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push!(syllables(w), s)
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return w
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end
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function Base.pushfirst!(w::GWord{T}, s::T) where T <: GSymbol
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pushfirst!(syllables(w), s)
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return w
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end
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function Base.append!(w::T, v::T) where T <: GWord
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append!(syllables(w), syllables(v))
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return w
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end
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function Base.prepend!(w::T, v::T) where T <: GWord
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prepend!(syllables(w), syllables(v))
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return w
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end
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Base.append!(w::T, v::T, others::Vararg{T,N}) where {N,T <: GWord} =
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append!(append!(w, v), others...)
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function rmul!(out::T, x::T, y::T) where T<: GWord
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if out === x
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out = deepcopy(out)
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return freereduce!(append!(out, y))
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elseif out === y
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out = deepcopy(out)
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return freereduce!(prepend!(out, x))
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else
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slenx = syllablelength(x)
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sleny = syllablelength(y)
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resize!(syllables(out), slenx+sleny)
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syllables(out)[1:slenx] .= syllables(x)
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syllables(out)[slenx+1:slenx+sleny] .= syllables(y)
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return freereduce!(out)
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end
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end
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rmul!(out::T, v::T) where T<:GWord = freereduce!(append!(out, v))
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lmul!(out::T, v::T) where T<:GWord = freereduce!(prepend!(out, v))
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lmul!(out::T, x::T, y::T) where T <: GWord = rmul!(out, y, x)
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AbstractAlgebra.mul!(out::T, x::T, y::T) where T <: GWord = rmul!(out, x, y)
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(*)(W::GW, Z::GW) where GW <: GWord = rmul!(deepcopy(W), W, Z)
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(*)(W::GWord, s::GSymbol) = freereduce!(push!(deepcopy(W), s))
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(*)(s::GSymbol, W::GWord) = freereduce!(pushfirst!(deepcopy(W), s))
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function power_by_squaring(W::GWord, p::Integer)
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if p < 0
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return power_by_squaring(inv(W), -p)
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elseif p == 0
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return one(W)
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elseif p == 1
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return W
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elseif p == 2
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return W*W
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end
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W = deepcopy(W)
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t = trailing_zeros(p) + 1
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p >>= t
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while (t -= 1) > 0
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append!(W, W)
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end
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Z = deepcopy(W)
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while p > 0
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t = trailing_zeros(p) + 1
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p >>= t
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while (t -= 1) >= 0
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append!(W, W)
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end
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append!(Z, W)
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end
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return freereduce!(Z)
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end
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(^)(x::GWord, n::Integer) = power_by_squaring(x,n)
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