2017-07-06 09:09:49 +02:00
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###############################################################################
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#
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# FPSymbol/FPGroupElem/FPGroup definition
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#
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###############################################################################
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2017-07-06 09:22:56 +02:00
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@compat struct FPSymbol <: GSymbol
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2017-07-06 09:09:49 +02:00
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str::String
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pow::Int
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end
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2017-07-06 09:22:56 +02:00
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@compat FPGroupElem = GWord{FPSymbol}
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2017-07-06 09:09:49 +02:00
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2017-07-06 09:22:56 +02:00
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@compat mutable struct FPGroup <: AbstractFPGroup
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2017-07-06 09:09:49 +02:00
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gens::Vector{FPSymbol}
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rels::Dict{FPGroupElem, FPGroupElem}
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function FPGroup{T<:GSymbol}(gens::Vector{T}, rels::Dict{FPGroupElem, FPGroupElem})
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G = new(gens)
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G.rels = Dict(G(k) => G(v) for (k,v) in rels)
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return G
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end
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end
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export FPGroupElem, FPGroup
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###############################################################################
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#
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# Type and parent object methods
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#
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###############################################################################
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parent_type(::Type{FPGroupElem}) = FPGroup
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elem_type(::FPGroup) = FPGroupElem
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###############################################################################
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#
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# FPSymbol constructors
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#
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###############################################################################
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FPSymbol(s::String) = FPSymbol(s,1)
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convert(::Type{FPSymbol}, s::FreeSymbol) = FPSymbol(s.str, s.pow)
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FPGroup(gens::Vector{FPSymbol}) = FPGroup(gens, Dict{FPGroupElem, FPGroupElem}())
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FPGroup(a::Vector{String}) = FPGroup([FPSymbol(i) for i in a])
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FPGroup(n::Int, symbol::String="f") = FPGroup(["$symbol$i" for i in 1:n])
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FPGroup(H::FreeGroup) = FPGroup([FPSymbol(s) for s in H.gens])
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###############################################################################
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#
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# Parent object call overloads
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#
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###############################################################################
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function (G::FPGroup)()
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id = FPGroupElem(FPSymbol("", 0))
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id.parent = G
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return id
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end
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function (G::FPGroup)(w::GWord)
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if length(w) == 0
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return G()
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end
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if eltype(w.symbols) == FreeSymbol
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w = FPGroupElem(w.symbols)
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end
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if eltype(w.symbols) == FPSymbol
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for s in w.symbols
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i = findfirst(g -> g.str == s.str, G.gens)
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i == 0 && throw("Symbol $s does not belong to $G.")
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s.pow % G.gens[i].pow == 0 || throw("Symbol $s doesn't belong to $G.")
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end
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end
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w.parent = G
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return reduce!(w)
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end
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(G::FPGroup)(s::FPSymbol) = G(FPGroupElem(s))
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###############################################################################
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#
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# Basic manipulation
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#
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###############################################################################
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hash(s::FPSymbol, h::UInt) = hash(s.str, hash(s.pow, hash(FPSymbol, h)))
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change_pow(s::FPSymbol, n::Int) = FPSymbol(s.str, n)
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length(s::FPSymbol) = abs(s.pow)
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###############################################################################
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#
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# String I/O
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#
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###############################################################################
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function show(io::IO, G::FPGroup)
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print(io, "FPgroup on $(length(G.gens)) generators: ")
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print(io, "⟨ ", join(G.gens, ", "), " | ", join(G.rels, ", "), " ⟩.")
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end
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###############################################################################
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#
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# Comparison
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#
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###############################################################################
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function (==)(s::FPSymbol, t::FPSymbol)
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isone(s) && isone(t) && return true
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s.str == t.str || return false
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s.pow == t.pow || return false
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return true
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end
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###############################################################################
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#
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# Inversion
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#
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###############################################################################
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inv(s::FPSymbol) = change_pow(s, -s.pow)
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###############################################################################
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#
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# Binary operations
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#
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###############################################################################
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(*)(W::FPGroupElem, Z::FPGroupElem) = r_multiply(W, Z.symbols)
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(*)(W::FPGroupElem, s::FPSymbol) = r_multiply(W, [s])
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(*)(s::FPSymbol, W::FPGroupElem) = l_multiply(W, [s])
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function reduce!(W::FPGroupElem)
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if length(W) < 2
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deleteat!(W.symbols, find(x -> x.pow == 0, W.symbols))
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else
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reduced = false
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while !reduced
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reduced = free_reduce!(W) || replace_all!(W, parent(W).rels)
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end
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end
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W.savedhash = hash(W.symbols, hash(typeof(W)))
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W.modified = false
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return W
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end
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###############################################################################
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#
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# Misc
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#
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###############################################################################
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function add_rels!(G::FPGroup, newrels::Dict{FPGroupElem,FPGroupElem})
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for w in keys(newrels)
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if !(w in keys(G.rels))
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G.rels[w] = G(newrels[w])
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end
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end
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end
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function /(G::FPGroup, newrels::Vector{FPGroupElem})
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for r in rels
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parent(r) == G || throw("Can not form quotient group: $r is not an element of $G")
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end
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H = deepcopy(G)
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newrels = Dict(H(r) => H() for r in newrels)
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add_rels!(H, newrels)
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return H
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end
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function /(G::FreeGroup, rels::Vector{FreeGroupElem})
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for r in rels
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parent(r) == G || throw("Can not form quotient group: $r is not an element of $G")
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end
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H = FPGroup(G)
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H.rels = Dict(H(rel) => H() for rel in unique(rels))
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return H
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end
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