From f8aedc207f163ec97e957ce2ca283f9221e7b4d5 Mon Sep 17 00:00:00 2001 From: kalmarek Date: Wed, 25 Mar 2020 05:00:16 +0100 Subject: [PATCH] make FPGroups more connected to their freepreimages --- src/FPGroups.jl | 66 ++++++++++++++++++++++++++----------------------- src/symbols.jl | 2 ++ 2 files changed, 37 insertions(+), 31 deletions(-) diff --git a/src/FPGroups.jl b/src/FPGroups.jl index e04726a..556ca50 100644 --- a/src/FPGroups.jl +++ b/src/FPGroups.jl @@ -12,14 +12,14 @@ end FPGroupElem = GroupWord{FPSymbol} mutable struct FPGroup <: AbstractFPGroup - gens::Vector{FPSymbol} - rels::Dict{FPGroupElem, FPGroupElem} + gens::Vector{FPSymbol} + rels::Dict{FreeGroupElem, FreeGroupElem} - function FPGroup(gens::Vector{T}, rels::Dict{FPGroupElem, FPGroupElem}) where {T<:GSymbol} - G = new(gens) - G.rels = Dict(G(k) => G(v) for (k,v) in rels) - return G - end + function FPGroup(gens::Vector{T}, rels::Dict{FreeGroupElem, FreeGroupElem}) where {T<:GSymbol} + G = new(gens) + G.rels = Dict(G(k) => G(v) for (k,v) in rels) + return G + end end export FPGroupElem, FPGroup @@ -45,7 +45,7 @@ FPSymbol(s::GSymbol) = FPSymbol(s.id, s.pow) convert(::Type{FPSymbol}, s::FreeSymbol) = FPSymbol(s.id, s.pow) -FPGroup(gens::Vector{FPSymbol}) = FPGroup(gens, Dict{FPGroupElem, FPGroupElem}()) +FPGroup(gens::Vector{FPSymbol}) = FPGroup(gens, Dict{FreeGroupElem, FreeGroupElem}()) FPGroup(a::Vector{String}) = FPGroup([FPSymbol(i) for i in a]) @@ -80,13 +80,13 @@ function (G::FPGroup)(w::GWord) return reduce!(w) end -(G::FPGroup)(s::FPSymbol) = G(FPGroupElem(s)) ############################################################################### # # Basic manipulation # ############################################################################### +(G::FPGroup)(s::GSymbol) = G(FPGroupElem(s)) ############################################################################### # @@ -137,31 +137,35 @@ end # ############################################################################### -function add_rels!(G::FPGroup, newrels::Dict{FPGroupElem,FPGroupElem}) - for w in keys(newrels) - if !(w in keys(G.rels)) - G.rels[w] = G(newrels[w]) - end - end +freepreimage(G::FPGroup) = parent(first(keys(G.rels))) +freepreimage(g::FPGroupElem) = freepreimage(parent(g))(syllables(g)) + +function add_rels!(G::FPGroup, newrels::Dict{FreeGroupElem,FreeGroupElem}) + for w in keys(newrels) + haskey(G.rels, w) && continue + G.rels[w] = newrels[w] + end + return G end function Base.:/(G::FPGroup, newrels::Vector{FPGroupElem}) - for r in newrels - parent(r) == G || throw(DomainError( - "Can not form quotient group: $r is not an element of $G")) - end - H = deepcopy(G) - newrels = Dict(H(r) => one(H) for r in newrels) - add_rels!(H, newrels) - return H + for r in newrels + parent(r) == G || throw(DomainError( + "Can not form quotient group: $r is not an element of $G")) + end + H = deepcopy(G) + F = freepreimage(H) + newrels = Dict(freepreimage(r) => one(F) for r in newrels) + add_rels!(H, newrels) + return H end -function Base.:/(G::FreeGroup, rels::Vector{FreeGroupElem}) - for r in rels - parent(r) == G || throw(DomainError( - "Can not form quotient group: $r is not an element of $G")) - end - H = FPGroup(deepcopy(G)) - H.rels = Dict(H(rel) => one(H) for rel in unique(rels)) - return H +function Base.:/(F::FreeGroup, rels::Vector{FreeGroupElem}) + for r in rels + parent(r) == F || throw(DomainError( + "Can not form quotient group: $r is not an element of $F")) + end + G = FPGroup(FPSymbol.(F.gens)) + G.rels = Dict(rel => one(F) for rel in unique(rels)) + return G end diff --git a/src/symbols.jl b/src/symbols.jl index 3e0c023..7989fdc 100644 --- a/src/symbols.jl +++ b/src/symbols.jl @@ -16,3 +16,5 @@ function (==)(s::GSymbol, t::GSymbol) s.pow == t.pow && s.id == t.id && return true return false end + +Base.convert(::Type{GS}, s::GSymbol) where GS<:GSymbol = GS(s.id, s.pow)