From 26781bad5cc3194fa87b87d807d47bf13027ab55 Mon Sep 17 00:00:00 2001 From: Marek Kaluba Date: Mon, 21 Jun 2021 18:16:04 +0200 Subject: [PATCH] remove the old implementation --- src/AutGroup.jl | 346 ---------------------------------------- src/FPGroups.jl | 135 ---------------- src/FreeGroup.jl | 73 --------- src/Groups.jl | 129 +-------------- src/arithmetic.jl | 93 ----------- src/findreplace.jl | 183 --------------------- src/freereduce.jl | 49 ------ src/hashing.jl | 34 ---- src/symbols.jl | 23 --- src/types.jl | 50 ------ src/wl_ball.jl | 62 +++++++ src/words.jl | 43 ----- test/AutGroup-tests.jl | 288 --------------------------------- test/FPGroup-tests.jl | 18 --- test/FreeGroup-tests.jl | 188 ---------------------- test/runtests.jl | 52 +++--- test/symmetric.jl | 31 ---- 17 files changed, 85 insertions(+), 1712 deletions(-) delete mode 100644 src/AutGroup.jl delete mode 100644 src/FPGroups.jl delete mode 100644 src/FreeGroup.jl delete mode 100644 src/arithmetic.jl delete mode 100644 src/findreplace.jl delete mode 100644 src/freereduce.jl delete mode 100644 src/hashing.jl delete mode 100644 src/symbols.jl delete mode 100644 src/types.jl create mode 100644 src/wl_ball.jl delete mode 100644 src/words.jl delete mode 100644 test/AutGroup-tests.jl delete mode 100644 test/FPGroup-tests.jl delete mode 100644 test/FreeGroup-tests.jl delete mode 100644 test/symmetric.jl diff --git a/src/AutGroup.jl b/src/AutGroup.jl deleted file mode 100644 index 901a616..0000000 --- a/src/AutGroup.jl +++ /dev/null @@ -1,346 +0,0 @@ -export Automorphism, AutGroup, Aut, SAut - -############################################################################### -# -# AutSymbol/ AutGroup / Automorphism -# - -struct RTransvect - i::Int8 - j::Int8 -end - -struct LTransvect - i::Int8 - j::Int8 -end - -struct FlipAut - i::Int8 -end - -struct PermAut - perm::AbstractAlgebra.Generic.Perm{Int8} -end - -struct Identity end - -struct AutSymbol <: GSymbol - id::Symbol - pow::Int8 - fn::Union{LTransvect, RTransvect, PermAut, FlipAut, Identity} -end - -# taken from ValidatedNumerics, under under the MIT "Expat" License: -# https://github.com/JuliaIntervals/ValidatedNumerics.jl/blob/master/LICENSE.md -function subscriptify(n::Integer) - subscript_0 = Int(0x2080) # Char(0x2080) -> subscript 0 - return join([Char(subscript_0 + i) for i in reverse(digits(n))], "") -end - -function id_autsymbol() - return AutSymbol(Symbol("(id)"), 0, Identity()) -end - -function transvection_R(i::Integer, j::Integer, pow::Integer=1) - if 0 < i < 10 && 0 < j < 10 - id = Symbol(:ϱ, subscriptify(i), subscriptify(j)) - else - id = Symbol(:ϱ, subscriptify(i), "." ,subscriptify(j)) - end - return AutSymbol(id, pow, RTransvect(i, j)) -end - -function transvection_L(i::Integer, j::Integer, pow::Integer=1) - if 0 < i < 10 && 0 < j < 10 - id = Symbol(:λ, subscriptify(i), subscriptify(j)) - else - id = Symbol(:λ, subscriptify(i), "." ,subscriptify(j)) - end - return AutSymbol(id, pow, LTransvect(i, j)) -end - -function flip(i::Integer, pow::Integer=1) - iseven(pow) && return id_autsymbol() - id = Symbol(:ɛ, subscriptify(i)) - return AutSymbol(id, 1, FlipAut(i)) -end - -function AutSymbol(p::AbstractAlgebra.Generic.Perm, pow::Integer=1) - if pow != 1 - p = p^pow - end - - if any(p.d[i] != i for i in eachindex(p.d)) - id = Symbol(:σ, "₍", join([subscriptify(i) for i in p.d],""), "₎") - return AutSymbol(id, 1, PermAut(p)) - end - return id_autsymbol() -end - -ϱ(i::Integer, j::Integer, pow::Integer=1) = transvection_R(i, j, pow) -λ(i::Integer, j::Integer, pow::Integer=1) = transvection_L(i, j, pow) -ε(i::Integer, pow::Integer=1) = flip(i, pow) -σ(v::AbstractAlgebra.Generic.Perm, pow::Integer=1) = AutSymbol(v, pow) - -function change_pow(s::AutSymbol, n::Integer) - iszero(n) && id_autsymbol() - - symbol = s.fn - if symbol isa FlipAut - return flip(symbol.i, n) - elseif symbol isa PermAut - return AutSymbol(symbol.perm, n) - elseif symbol isa RTransvect - return transvection_R(symbol.i, symbol.j, n) - elseif symbol isa LTransvect - return transvection_L(symbol.i, symbol.j, n) - elseif symbol isa Identity - return id_autsymbol() - else - throw(DomainError("Unknown type of AutSymbol: $s")) - end -end - -############################################################################### -# -# AutGroup / Automorphism -# - -mutable struct AutGroup{N} <: AbstractFPGroup - objectGroup::FreeGroup - gens::Vector{AutSymbol} -end - -mutable struct Automorphism{N} <: GWord{AutSymbol} - symbols::Vector{AutSymbol} - modified::Bool - savedhash::UInt - parent::AutGroup{N} - - function Automorphism{N}(f::Vector{AutSymbol}) where {N} - return new{N}(f, true, zero(UInt)) - end -end - -Base.eltype(::Type{AutGroup{N}}) where N = Automorphism{N} -GroupsCore.parent_type(::Type{Automorphism{N}}) where N = AutGroup{N} - -function AutGroup(G::FreeGroup; special=false) - S = AutSymbol[] - n = length(gens(G)) - n == 0 && return AutGroup{n}(G, S) - - indexing = [[i,j] for i in 1:n for j in 1:n if i≠j] - - rmuls = [ϱ(i,j) for (i,j) in indexing] - lmuls = [λ(i,j) for (i,j) in indexing] - - append!(S, [rmuls; lmuls]) - - if !special - flips = [ε(i) for i in 1:n] - syms = [σ(p) for p in AbstractAlgebra.SymmetricGroup(Int8(n))][2:end] - - append!(S, [flips; syms]) - end - return AutGroup{n}(G, S) -end - -Aut(G::Group) = AutGroup(G) -SAut(G::Group) = AutGroup(G, special=true) - -Automorphism{N}(s::AutSymbol) where N = Automorphism{N}(AutSymbol[s]) - -function (G::AutGroup{N})(f::AutSymbol) where N - g = Automorphism{N}([f]) - setparent!(g, G) - return g -end - -(G::AutGroup{N})(g::Automorphism{N}) where N = (setparent!(g, G); g) - -############################################################################### -# -# AutSymbol defining functions && evaluation -# NOTE: all automorphisms operate on a tuple of FreeWords INPLACE! -# - -function (ϱ::RTransvect)(v, pow::Integer=1) - rmul!(v[ϱ.i], v[ϱ.j]^pow) - return v -end - -function (λ::LTransvect)(v, pow::Integer=1) - lmul!(v[λ.i], v[λ.j]^pow) - return v -end - -function (σ::PermAut)(v, pow::Integer=1) - w = deepcopy(v) - s = (σ.perm^pow).d - @inbounds for k in eachindex(v) - v[k].symbols = w[s[k]].symbols - end - return v -end - -function (ɛ::FlipAut)(v, pow::Integer=1) - @inbounds if isodd(pow) - v[ɛ.i].symbols = inv(v[ɛ.i]).symbols - end - return v -end - -(::Identity)(v, pow::Integer=1) = v - -############################################################################### -# -# Functional call overloads for evaluation of AutSymbol and Automorphism -# - -(s::AutSymbol)(v::NTuple{N, T}) where {N, T} = s.fn(v, s.pow)::NTuple{N, T} - -function (f::Automorphism{N})(v::NTuple{N, T}) where {N, T} - for s in syllables(f) - v = s(v)::NTuple{N, T} - end - return v -end - -function domain(G::AutGroup{N}) where N - F = G.objectGroup - return ntuple(i->F(F.gens[i]), N) -end - -evaluate(f::Automorphism) = f(domain(parent(f))) - -############################################################################### -# -# hashing && equality -# - -function hash_internal( - g::Automorphism, - h::UInt = 0x7d28276b01874b19; # hash(Automorphism) - # alternatively: 0xcbf29ce484222325 from FNV-1a algorithm - images = compute_images(g), - prime = 0x00000100000001b3, # prime from FNV-1a algorithm -) - return foldl((h,x) -> hash(x, h)*prime, images, init = hash(parent(g), h)) -end - -function compute_images(g::Automorphism) - images = evaluate(g) - for im in images - reduce!(im) - end - return images -end - -function Base.:(==)(g::Automorphism{N}, h::Automorphism{N}) where N - syllables(g) == syllables(h) && return true - img_computed, imh_computed = false, false - - if ismodified(g) - img = compute_images(g) # sets modified bit - hash(g; images=img) - img_computed = true - end - - if ismodified(h) - imh = compute_images(h) # sets modified bit - hash(h; images=imh) - imh_computed = true - end - - @assert !ismodified(g) && !ismodified(h) - # cheap - # if hashes differ, images must have differed as well - hash(g) != hash(h) && return false - - # hashes equal, hence either equal elements, or a hash conflict - begin - if !img_computed - img_task = Threads.@spawn img = compute_images(g) - # img = compute_images(g) - end - if !imh_computed - imh_task = Threads.@spawn imh = compute_images(h) - # imh = compute_images(h) - end - !img_computed && fetch(img_task) - !imh_computed && fetch(imh_task) - end - - img != imh && @warn "hash collision in == :" g h - return img == imh -end - -############################################################################### -# -# String I/O -# - -function Base.show(io::IO, G::AutGroup) - print(io, "Automorphism Group of $(G.objectGroup)\n") - print(io, "Generated by $(gens(G))") -end - -############################################################################### -# -# Reduction -# - -getperm(s::AutSymbol) = s.fn.perm^s.pow - -function simplifyperms!(::Type{Bool}, w::Automorphism{N}) where N - reduced = true - for i in 1:syllablelength(w)-1 - s, ns = syllables(w)[i], syllables(w)[i+1] - if isone(s) - continue - elseif s.fn isa PermAut && ns.fn isa PermAut - reduced = false - setmodified!(w) - syllables(w)[i+1] = AutSymbol(getperm(s)*getperm(ns)) - syllables(w)[i] = change_pow(s, 0) - end - end - filter!(!isone, syllables(w)) - return reduced -end - -function reduce!(w::Automorphism) - reduced = false - while !reduced - reduced = simplifyperms!(Bool, w) && freereduce!(Bool, w) - end - return w -end - -############################################################################### -# -# Abelianization (natural Representation to GL(N,Z)) -# - -abelianize(A::Automorphism{N}) where N = image(A, abelianize; n=N) - -# homomorphism definition -abelianize(; n::Integer=1) = Matrix{Int}(I, n, n) -abelianize(a::AutSymbol; n::Int=1) = abelianize(a.fn, n, a.pow) - -function abelianize(a::Union{RTransvect, LTransvect}, n::Int, pow) - x = Matrix{Int}(I, n, n) - x[a.i,a.j] = pow - return x -end - -function abelianize(a::FlipAut, n::Int, pow) - x = Matrix{Int}(I, n, n) - x[a.i,a.i] = -1 - return x -end - -abelianize(a::PermAut, n::Integer, pow) = Matrix{Int}(I, n, n)[(a.perm^pow).d, :] -abelianize(a::Identity, n::Integer, pow) = abelianize(;n=n) diff --git a/src/FPGroups.jl b/src/FPGroups.jl deleted file mode 100644 index d7c909c..0000000 --- a/src/FPGroups.jl +++ /dev/null @@ -1,135 +0,0 @@ -############################################################################### -# -# FPSymbol/FPGroupElem/FPGroup definition -# -############################################################################### - -struct FPSymbol <: GSymbol - id::Symbol - pow::Int -end - -FPGroupElem = GroupWord{FPSymbol} - -mutable struct FPGroup <: AbstractFPGroup - gens::Vector{FPSymbol} - rels::Dict{FreeGroupElem, FreeGroupElem} - - 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 - -############################################################################### -# -# Type and parent object methods -# - -Base.eltype(::Type{FPGroup}) = FPGroupElem -GroupsCore.parent_type(::Type{FPGroupElem}) = FPGroup - -############################################################################### -# -# FPSymbol constructors -# - -FPSymbol(s::Symbol) = FPSymbol(s, 1) -FPSymbol(s::String) = FPSymbol(Symbol(s)) -FPSymbol(s::GSymbol) = FPSymbol(s.id, s.pow) - -FPGroup(n::Int, symbol::String="f") = FPGroup([Symbol(symbol,i) for i in 1:n]) -FPGroup(a::AbstractVector) = FPGroup([FPSymbol(i) for i in a]) -FPGroup(gens::Vector{FPSymbol}) = FPGroup(gens, Dict{FreeGroupElem, FreeGroupElem}()) - -FPGroup(H::FreeGroup) = FPGroup([FPSymbol(s) for s in H.gens]) - -############################################################################### -# -# Parent object call overloads -# - -function (G::FPGroup)(w::GWord) - if isempty(w) - return one(G) - end - - @boundscheck for s in syllables(w) - i = findfirst(g -> g.id == s.id, G.gens) - i == 0 && throw(DomainError("Symbol $s does not belong to $G.")) - s.pow % G.gens[i].pow != 0 && throw( - DomainError("Symbol $s doesn't belong to $G.")) - end - - w = FPGroupElem(FPSymbol.(syllables(w))) - setparent!(w, G) - return reduce!(w) -end - -(G::FPGroup)(s::GSymbol) = G(FPGroupElem(s)) - -############################################################################### -# -# String I/O -# - -function Base.show(io::IO, G::FPGroup) - print(io, "FPgroup on $(length(G.gens)) generators ") - strrels = join(G.rels, ", ") - if length(strrels) > 200 - print(io, "⟨ ", join(G.gens, ", "), " | $(length(G.rels)) relation(s) ⟩.") - else - print(io, "⟨ ", join(G.gens, ", "), " | ", join(G.rels, ", "), " ⟩.") - end -end - -function reduce!(W::FPGroupElem) - reduced = false - while !reduced - W = replace(W, parent(W).rels) - reduced = freereduce!(Bool, W) - end - return W -end - -############################################################################### -# -# Misc -# -############################################################################### - -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) - F = freepreimage(H) - newrels = Dict(freepreimage(r) => one(F) for r in newrels) - add_rels!(H, newrels) - return H -end - -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/FreeGroup.jl b/src/FreeGroup.jl deleted file mode 100644 index de1fab5..0000000 --- a/src/FreeGroup.jl +++ /dev/null @@ -1,73 +0,0 @@ -############################################################################### -# -# FreeSymbol/FreeGroupElem/FreeGroup definition -# - -struct FreeSymbol <: GSymbol - id::Symbol - pow::Int -end - -FreeGroupElem = GroupWord{FreeSymbol} - -mutable struct FreeGroup <: AbstractFPGroup - gens::Vector{FreeSymbol} - - function FreeGroup(gens::AbstractVector{T}) where {T<:GSymbol} - G = new(gens) - G.gens = gens - return G - end -end - -export FreeGroupElem, FreeGroup - -############################################################################### -# -# Type and parent object methods -# - -Base.eltype(::Type{FreeGroup}) = FreeGroupElem -GroupsCore.parent_type(::Type{FreeGroupElem}) = FreeGroup - -############################################################################### -# -# FreeSymbol constructors -# - -FreeSymbol(s::Symbol) = FreeSymbol(s,1) -FreeSymbol(s::AbstractString) = FreeSymbol(Symbol(s)) -FreeSymbol(s::GSymbol) = FreeSymbol(s.id, s.pow) - -FreeGroup(n::Int, symbol::String="f") = FreeGroup([Symbol(symbol,i) for i in 1:n]) -FreeGroup(a::AbstractVector) = FreeGroup(FreeSymbol.(a)) - -############################################################################### -# -# Parent object call overloads -# - -function (G::FreeGroup)(w::GroupWord{FreeSymbol}) - for s in syllables(w) - i = findfirst(g -> g.id == s.id, G.gens) - isnothing(i) && throw(DomainError( - "Symbol $s does not belong to $G.")) - s.pow % G.gens[i].pow == 0 || throw(DomainError( - "Symbol $s doesn't belong to $G.")) - end - setparent!(w, G) - return reduce!(w) -end - -(G::FreeGroup)(s::GSymbol) = G(FreeGroupElem(s)) -(G::FreeGroup)(v::AbstractVector{<:GSymbol}) = G(FreeGroupElem(FreeSymbol.(v))) - -############################################################################### -# -# String I/O -# - -function Base.show(io::IO, G::FreeGroup) - print(io, "Free group on $(length(G.gens)) generators: ") - join(io, G.gens, ", ") -end diff --git a/src/Groups.jl b/src/Groups.jl index 596e127..9edff49 100644 --- a/src/Groups.jl +++ b/src/Groups.jl @@ -1,30 +1,12 @@ module Groups using GroupsCore -using LinearAlgebra using ThreadsX - -import AbstractAlgebra import KnuthBendix +import OrderedCollections: OrderedSet export gens, FreeGroup, Aut, SAut -include("types.jl") - -include("FreeGroup.jl") -include("FPGroups.jl") -include("AutGroup.jl") - -include("symbols.jl") -include("words.jl") -include("hashing.jl") -include("freereduce.jl") -include("arithmetic.jl") -include("findreplace.jl") - -module New -import OrderedCollections: OrderedSet - include("new_types.jl") include("new_hashing.jl") include("normalform.jl") @@ -32,112 +14,5 @@ include("new_autgroups.jl") include("groups/sautFn.jl") -end # module New - -############################################################################### -# -# String I/O -# - -function Base.show(io::IO, W::GWord) - if length(W) == 0 - print(io, "(id)") - else - join(io, (string(s) for s in syllables(W)), "*") - end -end - -function Base.show(io::IO, s::T) where {T<:GSymbol} - if s.pow == 1 - print(io, string(s.id)) - else - print(io, "$(s.id)^$(s.pow)") - end -end - -############################################################################### -# -# Misc -# - -GroupsCore.gens(G::AbstractFPGroup) = G.(G.gens) - -""" - wlmetric_ball(S::AbstractVector{<:GroupElem} - [, center=one(first(S)); radius=2, op=*]) -Compute metric ball as a list of elements of non-decreasing length, given the -word-length metric on the group generated by `S`. The ball is centered at `center` -(by default: the identity element). `radius` and `op` keywords specify the -radius and multiplication operation to be used. -""" -function wlmetric_ball_serial(S::AbstractVector{T}; radius = 2, op = *) where {T} - @assert radius > 0 - old = unique!([one(first(S)), S...]) - sizes = [1, length(old)] - for i in 2:radius - new = collect(op(o, s) for o in @view(old[sizes[end-1]:end]) for s in S) - append!(old, new) - resize!(new, 0) - old = unique!(old) - push!(sizes, length(old)) - end - return old, sizes[2:end] -end - -function wlmetric_ball_thr(S::AbstractVector{T}; radius = 2, op = *) where {T} - @assert radius > 0 - old = unique!([one(first(S)), S...]) - sizes = [1, length(old)] - for r in 2:radius - begin - new = - ThreadsX.collect(op(o, s) for o in @view(old[sizes[end-1]:end]) for s in S) - ThreadsX.foreach(hash, new) - end - append!(old, new) - resize!(new, 0) - old = ThreadsX.unique(old) - push!(sizes, length(old)) - end - return old, sizes[2:end] -end - -function wlmetric_ball_serial(S::AbstractVector{T}, center::T; radius = 2, op = *) where {T} - E, sizes = wlmetric_ball_serial(S, radius = radius, op = op) - isone(center) && return E, sizes - return c .* E, sizes -end - -function wlmetric_ball_thr(S::AbstractVector{T}, center::T; radius = 2, op = *) where {T} - E, sizes = wlmetric_ball_thr(S, radius = radius, op = op) - isone(center) && return E, sizes - return c .* E, sizes -end - -function wlmetric_ball( - S::AbstractVector{T}, - center::T = one(first(S)); - radius = 2, - op = *, - threading = true, -) where {T} - threading && return wlmetric_ball_thr(S, center, radius = radius, op = op) - return wlmetric_ball_serial(S, center, radius = radius, op = op) -end - -""" - image(w::GWord, homomorphism; kwargs...) -Evaluate homomorphism `homomorphism` on a group word (element) `w`. -`homomorphism` needs to implement -> `hom(w; kwargs...)`, -where `hom(;kwargs...)` returns the value at the identity element. -""" -function image(w::GWord, hom; kwargs...) - return reduce( - *, - (hom(s; kwargs...) for s in syllables(w)), - init = hom(; kwargs...), - ) -end - +include("wl_ball.jl") end # of module Groups diff --git a/src/arithmetic.jl b/src/arithmetic.jl deleted file mode 100644 index 59ac04a..0000000 --- a/src/arithmetic.jl +++ /dev/null @@ -1,93 +0,0 @@ -function Base.inv(W::T) where T<:GWord - length(W) == 0 && return one(W) - G = parent(W) - w = T([inv(s) for s in Iterators.reverse(syllables(W))]) - return setparent!(w, G) -end - -############################################################################### -# -# Binary operators -# - -function Base.push!(w::GWord{T}, s::T) where T <: GSymbol - push!(syllables(w), s) - return w -end - -function Base.pushfirst!(w::GWord{T}, s::T) where T <: GSymbol - pushfirst!(syllables(w), s) - return w -end - -function Base.append!(w::T, v::T) where T <: GWord - append!(syllables(w), syllables(v)) - return w -end - -function Base.prepend!(w::T, v::T) where T <: GWord - prepend!(syllables(w), syllables(v)) - return w -end - -Base.append!(w::T, v::T, others::Vararg{T,N}) where {N,T <: GWord} = - append!(append!(w, v), others...) - -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 - -rmul!(out::T, v::T) where T<:GWord = freereduce!(append!(out, v)) -lmul!(out::T, v::T) where T<:GWord = freereduce!(prepend!(out, v)) - -lmul!(out::T, x::T, y::T) where T <: GWord = rmul!(out, y, x) - -GroupsCore.mul!(out::T, x::T, y::T) where T <: GWord = rmul!(out, x, y) - -Base.:(*)(W::GW, Z::GW) where GW <: GWord = rmul!(deepcopy(W), W, Z) -Base.:(*)(W::GWord, s::GSymbol) = freereduce!(push!(deepcopy(W), s)) -Base.:(*)(s::GSymbol, W::GWord) = freereduce!(pushfirst!(deepcopy(W), s)) - -function Base.power_by_squaring(W::GWord, p::Integer) - if p < 0 - return Base.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 - -Base.:(^)(x::GWord, n::Integer) = Base.power_by_squaring(x,n) diff --git a/src/findreplace.jl b/src/findreplace.jl deleted file mode 100644 index fe59ee4..0000000 --- a/src/findreplace.jl +++ /dev/null @@ -1,183 +0,0 @@ -############################################################################### -# -# Replacement of symbols / sub-words -# - -issubsymbol(s::GSymbol, t::GSymbol) = - s.id == t.id && (0 ≤ s.pow ≤ t.pow || 0 ≥ s.pow ≥ t.pow) - -function issubsymbol(s::FreeSymbol, w::GWord, sindex::Integer) - @boundscheck 1 ≤ sindex ≤ syllablelength(w) || throw(BoundsError(w, sindex)) - return issubsymbol(s, syllables(w)[sindex]) -end - -function issubword(z::GWord, w::GWord, sindex::Integer) - isempty(z) && return true - @boundscheck 1 ≤ sindex ≤ syllablelength(w) || throw(BoundsError(w, sindex)) - n = syllablelength(z) - n == 1 && return issubsymbol(first(syllables(z)), syllables(w)[sindex]) - - lastindex = sindex + n - 1 - lastindex > syllablelength(w) && return false - - issubsymbol(first(z), syllables(w)[sindex]) || return false - issubsymbol(syllables(z)[end], syllables(w)[lastindex]) || return false - for (zidx, widx) in zip(2:n-1, sindex+1:lastindex-1) - syllables(z)[zidx] == syllables(w)[widx] || return false - end - return true -end - -""" - -Find the first syllable index k>=i such that Z < syllables(W)[k:k+syllablelength(Z)-1] -""" -function Base.findnext(subword::GWord, word::GWord, start::Integer) - @boundscheck 1 ≤ start ≤ syllablelength(word) || throw(BoundsError(word, start)) - isempty(subword) && return start - stop = syllablelength(word) - syllablelength(subword) +1 - - for idx in start:1:stop - issubword(subword, word, idx) && return idx - end - return nothing -end - -function Base.findnext(s::FreeSymbol, word::GWord, start::Integer) - @boundscheck 1 ≤ start ≤ syllablelength(word) || throw(BoundsError(word, start)) - isone(s) && return start - stop = syllablelength(word) - - for idx in start:1:stop - issubsymbol(s, word, idx) && return idx - end - return nothing -end - -function Base.findprev(subword::GWord, word::GWord, start::Integer) - @boundscheck 1 ≤ start ≤ syllablelength(word) || throw(BoundsError(word, start)) - isempty(subword) && return start - stop = 1 - - for idx in start:-1:1 - issubword(subword, word, idx) && return idx - end - return nothing -end - -function Base.findprev(s::FreeSymbol, word::GWord, start::Integer) - @boundscheck 1 ≤ start ≤ syllablelength(word) || throw(BoundsError(word, start)) - isone(s) && return start - stop = 1 - - for idx in start:-1:stop - issubsymbol(s, word, idx) && return idx - end - return nothing -end - -Base.findfirst(subword::GWord, word::GWord) = findnext(subword, word, 1) -Base.findlast(subword::GWord, word::GWord) = - findprev(subword, word, syllablelength(word)-syllablelength(subword)+1) - -function Base.replace!(out::GW, W::GW, lhs_rhs::Pair{GS, T}; count::Integer=typemax(Int)) where - {GS<:GSymbol, T<:GWord, GW<:GWord} - (count == 0 || isempty(W)) && return W - count < 0 && throw(DomainError(count, "`count` must be non-negative.")) - - lhs, rhs = lhs_rhs - - sW = syllables(W) - sW_idx = 1 - r = something(findnext(lhs, W, sW_idx), 0) - - sout = syllables(out) - resize!(sout, 0) - sizehint!(sout, syllablelength(W)) - - c = 0 - - while !iszero(r) - append!(sout, view(sW, sW_idx:r-1)) - a, b = divrem(sW[r].pow, lhs.pow) - - if b != 0 - push!(sout, change_pow(sW[r], b)) - end - - append!(sout, repeat(syllables(rhs), a)) - - sW_idx = r+1 - sW_idx > syllablelength(W) && break - - r = something(findnext(lhs, W, sW_idx), 0) - c += 1 - c == count && break - end - append!(sout, sW[sW_idx:end]) - return freereduce!(out) -end - -function Base.replace!(out::GW, W::GW, lhs_rhs::Pair{T, T}; count::Integer=typemax(Int)) where - {GW<:GWord, T <: GWord} - (count == 0 || isempty(W)) && return W - count < 0 && throw(DomainError(count, "`count` must be non-negative.")) - - lhs, rhs = lhs_rhs - lhs_slen = syllablelength(lhs) - lhs_slen == 1 && return replace!(out, W, first(syllables(lhs))=>rhs; count=count) - - sW = syllables(W) - sW_idx = 1 - r = something(findnext(lhs, W, sW_idx), 0) - - sout = syllables(out) - resize!(sout, 0) - sizehint!(sout, syllablelength(W)) - - c = 0 - - while !iszero(r) - append!(sout, view(sW, sW_idx:r-1)) - - exp = sW[r].pow - first(syllables(lhs)).pow - if exp != 0 - push!(sout, change_pow(sW[r], exp)) - end - - append!(sout, syllables(rhs)) - - exp = sW[r+lhs_slen-1].pow - last(syllables(lhs)).pow - if exp != 0 - push!(sout, change_pow(sW[r+lhs_slen-1], exp)) - end - - sW_idx = r+lhs_slen - sW_idx > syllablelength(W) && break - - r = something(findnext(lhs, W, sW_idx), 0) - c += 1 - c == count && break - end - - # copy the rest - append!(sout, sW[sW_idx:end]) - return freereduce!(out) -end - -function Base.replace(W::GW, lhs_rhs::Pair{T, T}; count::Integer=typemax(Int)) where - {GW<:GWord, T <: GWord} - return replace!(one(W), W, lhs_rhs; count=count) -end - -function Base.replace(W::GW, subst_dict::Dict{T,T}) where {GW<:GWord, T<:GWord} - out = W - for toreplace in reverse!(sort!(collect(keys(subst_dict)), by=length)) - replacement = subst_dict[toreplace] - if length(toreplace) > length(out) - continue - end - out = replace(out, toreplace=>replacement) - end - return out -end diff --git a/src/freereduce.jl b/src/freereduce.jl deleted file mode 100644 index 017f829..0000000 --- a/src/freereduce.jl +++ /dev/null @@ -1,49 +0,0 @@ -############################################################################### -# -# Naive reduction -# - -function freereduce!(::Type{Bool}, w::GWord) - if syllablelength(w) == 1 - filter!(!isone, syllables(w)) - return syllablelength(w) == 1 - end - - reduced = true - @inbounds for i in 1:syllablelength(w)-1 - s, ns = syllables(w)[i], syllables(w)[i+1] - if isone(s) - continue - elseif s.id === ns.id - reduced = false - p1 = s.pow - p2 = ns.pow - - syllables(w)[i+1] = change_pow(s, p1 + p2) - syllables(w)[i] = change_pow(s, 0) - end - end - if !reduced - filter!(!isone, syllables(w)) - setmodified!(w) - end - return reduced -end - -function freereduce!(w::GWord) - reduced = false - while !reduced - reduced = freereduce!(Bool, w) - end - return w -end - -reduce!(w::GWord) = freereduce!(w) - -""" - reduce(w::GWord) -performs reduction/simplification of a group element (word in generators). -The default reduction is the reduction in the free group reduction. -More specific procedures should be dispatched on `GWord`s type parameter. -""" -Base.reduce(w::GWord) = reduce!(deepcopy(w)) diff --git a/src/hashing.jl b/src/hashing.jl deleted file mode 100644 index b9fd17f..0000000 --- a/src/hashing.jl +++ /dev/null @@ -1,34 +0,0 @@ -############################################################################### -# -# hashing, deepcopy and == -# - -function hash_internal(W::GWord) - reduce!(W) - h = hasparent(W) ? hash(parent(W)) : zero(UInt) - return hash(syllables(W), hash(typeof(W), h)) -end - -function Base.hash(W::GWord, h::UInt=UInt(0); kwargs...) - if ismodified(W) - savehash!(W, hash_internal(W; kwargs...)) - unsetmodified!(W) - end - return xor(savedhash(W), h) -end - -# WARNING: Due to specialised (constant) hash function of GWords this one is actually necessary! -function Base.deepcopy_internal(W::T, dict::IdDict) where T<:GWord - G = parent(W) - g = T(deepcopy(syllables(W))) - setparent!(g, G) - return g -end - -function Base.:(==)(W::T, Z::T) where T <: GWord - hash(W) != hash(Z) && return false # distinguishes parent and parentless words - if hasparent(W) && hasparent(Z) - parent(W) != parent(Z) && return false - end - return syllables(W) == syllables(Z) -end diff --git a/src/symbols.jl b/src/symbols.jl deleted file mode 100644 index e964df8..0000000 --- a/src/symbols.jl +++ /dev/null @@ -1,23 +0,0 @@ -change_pow(s::S, n::Integer) where S<:GSymbol = S(s.id, n) - -function Base.iterate(s::GS, i=1) where GS<:GSymbol - return i <= abs(s.pow) ? (change_pow(s, sign(s.pow)), i+1) : nothing -end -Base.size(s::GSymbol) = (abs(s.pow), ) -Base.length(s::GSymbol) = first(size(s)) - -Base.eltype(s::GS) where GS<:GSymbol = GS - -Base.isone(s::GSymbol) = iszero(s.pow) -Base.literal_pow(::typeof(^), s::Groups.GSymbol, ::Val{-1}) = inv(s) -Base.inv(s::GSymbol) = change_pow(s, -s.pow) -Base.hash(s::S, h::UInt) where S<:GSymbol = hash(s.id, hash(s.pow, hash(S, h))) - -function Base.:(==)(s::GSymbol, t::GSymbol) - isone(s) && isone(t) && return true - 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) -Base.convert(::Type{GS}, s::GS) where GS<:GSymbol = s diff --git a/src/types.jl b/src/types.jl deleted file mode 100644 index 316554a..0000000 --- a/src/types.jl +++ /dev/null @@ -1,50 +0,0 @@ -abstract type AbstractFPGroup <: GroupsCore.Group end - -function Base.one(G::Gr) where Gr <: AbstractFPGroup - El = eltype(G) - id = El(eltype(El)[]) - id.parent = G - return id -end - -""" - GSymbol -Represents a syllable. Abstract type which all group symbols of -`AbstractFPGroups` should subtype. Each concrete subtype should implement fields: - * `id` which is the `Symbol` representation/identification of a symbol - * `pow` which is the (multiplicative) exponent of a symbol. -""" -abstract type GSymbol end - -abstract type GWord{T<:GSymbol} <: GroupsCore.GroupElement end - -""" - W::GroupWord{T} <: GWord{T<:GSymbol} <:GroupElem -Basic representation of element of a finitely presented group. -* `syllables(W)` return particular group syllables which multiplied constitute `W` -group as a word in generators. -* `parent(W)` return the parent group. - -As the reduction (inside the parent group) of word to normal form may be time -consuming, we provide a shortcut that is useful in practice: -`savehash!(W, h)` and `ismodified(W)` functions. -When computing `hash(W)`, a reduction to normal form is performed and a -persistent hash is stored inside `W`, setting `ismodified(W)` flag to `false`. -This hash can be accessed by `savedhash(W)`. -Future comparisons of `W` try not to perform reduction and use the stored hash as shortcut. Only when hashes collide reduction is performed. Whenever word `W` is -changed, `ismodified(W)` returns `false` and stored hash is invalidated. -""" - -mutable struct GroupWord{T} <: GWord{T} - symbols::Vector{T} - modified::Bool - savedhash::UInt - parent::Group - - function GroupWord{T}(symbols::AbstractVector{<:GSymbol}) where T - return new{T}(symbols, true, zero(UInt)) - end - GroupWord(v::AbstractVector{T}) where T<:GSymbol = GroupWord{T}(v) - GroupWord{T}(s::GSymbol) where T<:GSymbol = GroupWord{T}(T[s]) - GroupWord(s::T) where T<:GSymbol = GroupWord{T}(s) -end diff --git a/src/wl_ball.jl b/src/wl_ball.jl new file mode 100644 index 0000000..f7f4e12 --- /dev/null +++ b/src/wl_ball.jl @@ -0,0 +1,62 @@ +""" + wlmetric_ball(S::AbstractVector{<:GroupElem} + [, center=one(first(S)); radius=2, op=*]) +Compute metric ball as a list of elements of non-decreasing length, given the +word-length metric on the group generated by `S`. The ball is centered at `center` +(by default: the identity element). `radius` and `op` keywords specify the +radius and multiplication operation to be used. +""" +function wlmetric_ball_serial(S::AbstractVector{T}; radius = 2, op = *) where {T} + @assert radius > 0 + old = unique!([one(first(S)), S...]) + sizes = [1, length(old)] + for i in 2:radius + new = collect(op(o, s) for o in @view(old[sizes[end-1]:end]) for s in S) + append!(old, new) + resize!(new, 0) + old = unique!(old) + push!(sizes, length(old)) + end + return old, sizes[2:end] +end + +function wlmetric_ball_thr(S::AbstractVector{T}; radius = 2, op = *) where {T} + @assert radius > 0 + old = unique!([one(first(S)), S...]) + sizes = [1, length(old)] + for r in 2:radius + begin + new = + ThreadsX.collect(op(o, s) for o in @view(old[sizes[end-1]:end]) for s in S) + ThreadsX.foreach(hash, new) + end + append!(old, new) + resize!(new, 0) + old = ThreadsX.unique(old) + push!(sizes, length(old)) + end + return old, sizes[2:end] +end + +function wlmetric_ball_serial(S::AbstractVector{T}, center::T; radius = 2, op = *) where {T} + E, sizes = wlmetric_ball_serial(S, radius = radius, op = op) + isone(center) && return E, sizes + return c .* E, sizes +end + +function wlmetric_ball_thr(S::AbstractVector{T}, center::T; radius = 2, op = *) where {T} + E, sizes = wlmetric_ball_thr(S, radius = radius, op = op) + isone(center) && return E, sizes + return c .* E, sizes +end + +function wlmetric_ball( + S::AbstractVector{T}, + center::T = one(first(S)); + radius = 2, + op = *, + threading = true, +) where {T} + threading && return wlmetric_ball_thr(S, center, radius = radius, op = op) + return wlmetric_ball_serial(S, center, radius = radius, op = op) +end diff --git a/src/words.jl b/src/words.jl deleted file mode 100644 index 976ffca..0000000 --- a/src/words.jl +++ /dev/null @@ -1,43 +0,0 @@ -syllablelength(w::GWord) = length(w.symbols) -syllables(w::GWord) = w.symbols -ismodified(w::GWord) = w.modified -setmodified!(w::GWord) = (w.modified = true; w) -unsetmodified!(w::GWord) = (w.modified = false; w) -savehash!(w::GWord, h::UInt) = (w.savedhash = h; w) -savedhash(w::GWord) = w.savedhash -Base.parent(w::GWord) = w.parent -hasparent(w::GWord) = isdefined(w, :parent) -setparent!(w::GWord, G::AbstractFPGroup) = (w.parent = G; w) - -Base.isempty(w::GWord) = isempty(syllables(w)) -Base.isone(w::GWord) = (freereduce!(w); isempty(w)) -Base.one(w::GWord) = one(parent(w)) - -function Base.iterate(w::GWord, state=(syllable=1, pow=1)) - state.syllable > syllablelength(w) && return nothing - next = iterate(syllables(w)[state.syllable], state.pow) - next === nothing && return iterate(w, (syllable=state.syllable+1, pow=1)) - return first(next), (syllable=state.syllable, pow=last(next)) -end - -Base.eltype(::Type{<:GWord{T}}) where T = T -Base.length(w::GWord) = isempty(w) ? 0 : sum(length, syllables(w)) -Base.size(w::GWord) = (length(w),) -Base.lastindex(w::GWord) = length(w) - -Base.@propagate_inbounds function Base.getindex(w::GWord, i::Integer) - csum = 0 - idx = 0 - @boundscheck 0 < i <= length(w) || throw(BoundsError(w, i)) - while csum < i - idx += 1 - csum += length(syllables(w)[idx]) - end - return first(syllables(w)[idx]) -end - -Base.@propagate_inbounds Base.getindex(w::GWord, itr) = [w[i] for i in itr] - -# no setindex! for syllable based words - -Base.convert(::Type{GW}, s::GSymbol) where GW <: GWord = GW(s) diff --git a/test/AutGroup-tests.jl b/test/AutGroup-tests.jl deleted file mode 100644 index 52a4631..0000000 --- a/test/AutGroup-tests.jl +++ /dev/null @@ -1,288 +0,0 @@ -import AbstractAlgebra.@perm_str - -@testset "Automorphisms" begin - - G = AbstractAlgebra.SymmetricGroup(Int8(4)) - - @testset "AutSymbol" begin - @test_throws MethodError Groups.AutSymbol(:a) - @test_throws MethodError Groups.AutSymbol(:a, 1) - f = Groups.AutSymbol(:a, 1, Groups.FlipAut(2)) - @test f isa Groups.GSymbol - @test f isa Groups.AutSymbol - @test Groups.AutSymbol(perm"(4)") isa Groups.AutSymbol - @test Groups.AutSymbol(perm"(1,2,3,4)") isa Groups.AutSymbol - @test Groups.transvection_R(1,2) isa Groups.AutSymbol - @test Groups.transvection_R(3,4) isa Groups.AutSymbol - @test Groups.flip(3) isa Groups.AutSymbol - - @test Groups.id_autsymbol() isa Groups.AutSymbol - @test inv(Groups.id_autsymbol()) isa Groups.AutSymbol - x = Groups.id_autsymbol() - @test inv(x) == Groups.id_autsymbol() - end - - a,b,c,d = gens(FreeGroup(4)) - D = NTuple{4,FreeGroupElem}([a,b,c,d]) - - @testset "flip correctness" begin - @test Groups.flip(1)(deepcopy(D)) == (a^-1, b,c,d) - @test Groups.flip(2)(deepcopy(D)) == (a, b^-1,c,d) - @test Groups.flip(3)(deepcopy(D)) == (a, b,c^-1,d) - @test Groups.flip(4)(deepcopy(D)) == (a, b,c,d^-1) - @test inv(Groups.flip(1))(deepcopy(D)) == (a^-1, b,c,d) - @test inv(Groups.flip(2))(deepcopy(D)) == (a, b^-1,c,d) - @test inv(Groups.flip(3))(deepcopy(D)) == (a, b,c^-1,d) - @test inv(Groups.flip(4))(deepcopy(D)) == (a, b,c,d^-1) - end - - @testset "perm correctness" begin - σ = Groups.AutSymbol(perm"(4)") - @test σ(deepcopy(D)) == deepcopy(D) - @test inv(σ)(deepcopy(D)) == deepcopy(D) - - σ = Groups.AutSymbol(perm"(1,2,3,4)") - @test σ(deepcopy(D)) == (b, c, d, a) - @test inv(σ)(deepcopy(D)) == (d, a, b, c) - - σ = Groups.AutSymbol(perm"(1,2)(4,3)") - @test σ(deepcopy(D)) == (b, a, d, c) - @test inv(σ)(deepcopy(D)) == (b, a, d, c) - - σ = Groups.AutSymbol(perm"(1,2,3)(4)") - @test σ(deepcopy(D)) == (b, c, a, d) - @test inv(σ)(deepcopy(D)) == (c, a, b, d) - end - - @testset "rmul/transvection_R correctness" begin - i,j = 1,2 - r = Groups.transvection_R(i,j) - l = Groups.transvection_L(i,j) - @test r(deepcopy(D)) == (a*b, b, c, d) - @test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d) - @test l(deepcopy(D)) == (b*a, b, c, d) - @test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d) - - i,j = 3,1 - r = Groups.transvection_R(i,j) - l = Groups.transvection_L(i,j) - @test r(deepcopy(D)) == (a, b, c*a, d) - @test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d) - @test l(deepcopy(D)) == (a, b, a*c, d) - @test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d) - - i,j = 4,3 - r = Groups.transvection_R(i,j) - l = Groups.transvection_L(i,j) - @test r(deepcopy(D)) == (a, b, c, d*c) - @test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1) - @test l(deepcopy(D)) == (a, b, c, c*d) - @test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d) - - i,j = 2,4 - r = Groups.transvection_R(i,j) - l = Groups.transvection_L(i,j) - @test r(deepcopy(D)) == (a, b*d, c, d) - @test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d) - @test l(deepcopy(D)) == (a, d*b, c, d) - @test inv(l)(deepcopy(D)) == (a, d^-1*b,c, d) - end - - @testset "AutGroup/Automorphism constructors" begin - - f = Groups.AutSymbol(:a, 1, Groups.FlipAut(1)) - @test isa(Automorphism{3}(f), Groups.GWord) - @test isa(Automorphism{3}(f), Automorphism) - @test isa(AutGroup(FreeGroup(3)), GroupsCore.Group) - @test isa(AutGroup(FreeGroup(1)), Groups.AbstractFPGroup) - - A = AutGroup(FreeGroup(1)) - @test Groups.gens(A) isa Vector{Automorphism{1}} - @test length(Groups.gens(A)) == 1 - @test length(Groups.gens(Aut(FreeGroup(1)))) == 1 - @test Groups.gens(A) == [A(Groups.flip(1))] - - A = AutGroup(FreeGroup(1), special=true) - @test isempty(Groups.gens(A)) - @test Groups.gens(SAut(FreeGroup(1))) == Automorphism{1}[] - - A = AutGroup(FreeGroup(2)) - @test length(Groups.gens(A)) == 7 - Agens = Groups.gens(A) - @test A(first(Agens)) isa Automorphism - - @test A(Groups.transvection_R(1,2)) isa Automorphism - @test A(Groups.transvection_R(1,2)) in Agens - - @test A(Groups.transvection_R(2,1)) isa Automorphism - @test A(Groups.transvection_R(2,1)) in Agens - - @test A(Groups.transvection_R(1,2)) isa Automorphism - @test A(Groups.transvection_R(1,2)) in Agens - - @test A(Groups.transvection_R(2,1)) isa Automorphism - @test A(Groups.transvection_R(2,1)) in Agens - - @test A(Groups.flip(1)) isa Automorphism - @test A(Groups.flip(1)) in Agens - - @test A(Groups.flip(2)) isa Automorphism - @test A(Groups.flip(2)) in Agens - - @test A(Groups.AutSymbol(perm"(1,2)")) isa Automorphism - @test A(Groups.AutSymbol(perm"(1,2)")) in Agens - - @test A(Groups.id_autsymbol()) isa Automorphism - end - - A = AutGroup(FreeGroup(4)) - - @testset "eltary functions" begin - - f = Groups.AutSymbol(perm"(1,2,3,4)") - @test (Groups.change_pow(f, 2)).pow == 1 - @test (Groups.change_pow(f, -2)).pow == 1 - @test (inv(f)).pow == 1 - - g = Groups.AutSymbol(perm"(1,2)(3,4)") - @test isa(inv(g), Groups.AutSymbol) - - @test_throws MethodError g*f - - @test A(g)^-1 == A(inv(g)) - - h = Groups.transvection_R(1,2) - - @test collect(A(g)*A(h)) == [g, h] - @test collect(A(h)^2) == [h, h] - end - - @testset "reductions/arithmetic" begin - f = Groups.AutSymbol(perm"(1,2,3,4)") - - f² = push!(A(f), f) - @test Groups.simplifyperms!(Bool, f²) == false - @test f²^2 == one(A) - @test !isone(f²) - - a = A(Groups.λ(1,2))*Groups.ε(2) - b = Groups.ε(2)*A(inv(Groups.λ(1,2))) - @test a*b == b*a - @test a^3 * b^3 == one(A) - g,h = Groups.gens(A)[[1,8]] # (g, h) = (ϱ₁₂, ϱ₃₂) - - @test Groups.domain(A) == NTuple{4, FreeGroupElem}(gens(A.objectGroup)) - - @test (g*h)(Groups.domain(A)) == (h*g)(Groups.domain(A)) - @test (g*h).savedhash == zero(UInt) - @test (h*g).savedhash == zero(UInt) - a = g*h - b = h*g - @test hash(a) != zero(UInt) - @test hash(b) == hash(a) - @test a.savedhash == b.savedhash - @test length(unique([a,b])) == 1 - @test length(unique([g*h, h*g])) == 1 - - # Not so simple arithmetic: applying starting on the left: - # ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄ - - g = A(Groups.transvection_R(1,2)) - x1, x2, x3, x4 = Groups.domain(A) - @test g(Groups.domain(A)) == (x1*x2, x2, x3, x4) - g = g*inv(A(Groups.transvection_R(2,1))) - @test g(Groups.domain(A)) == (x1*x2, x1^-1, x3, x4) - g = g*A(Groups.transvection_L(1,2)) - @test g(Groups.domain(A)) == (x2, x1^-1, x3, x4) - g = g*A(Groups.flip(2)) - @test g(Groups.domain(A)) == (x2, x1, x3, x4) - - @test g(Groups.domain(A)) == A(Groups.AutSymbol(perm"(1,2)(4)"))(Groups.domain(A)) - - @test g == A(Groups.AutSymbol(perm"(1,2)(4)")) - - g_im = g(Groups.domain(A)) - @test length.(g_im) == (1,1,1,1) - - g = A(Groups.σ(perm"(1,2)(4)")) - h = A(Groups.σ(perm"(2,3,4)")) - @test g*h isa Groups.Automorphism{4} - f = g*h - Groups - @test Groups.syllablelength(f) == 2 - @test Groups.reduce!(f) isa Groups.Automorphism{4} - @test Groups.syllablelength(f) == 1 - end - - @testset "specific Aut(F4) tests" begin - N = 4 - G = AutGroup(FreeGroup(N)) - S = G.gens - @test isa(S, Vector{Groups.AutSymbol}) - S = [G(s) for s in unique(S)] - @test isa(S, Vector{Automorphism{N}}) - @test S == gens(G) - @test length(S) == 51 - S_inv = [S..., [inv(s) for s in S]...] - @test length(unique(S_inv)) == 75 - - G = AutGroup(FreeGroup(N), special=true) - S = gens(G) - S_inv = [one(G), S..., [inv(s) for s in S]...] - S_inv = unique(S_inv) - B_2 = [i*j for (i,j) in Base.product(S_inv, S_inv)] - @test length(B_2) == 2401 - @test length(unique(B_2)) == 1777 - end - - @testset "abelianization homomorphism" begin - N = 4 - G = AutGroup(FreeGroup(N)) - S = unique([gens(G); inv.(gens(G))]) - R = 3 - - @test Groups.abelianize(one(G)) isa Matrix{Int} - @test Groups.abelianize(one(G)) == Matrix{Int}(I, N, N) - - M = Matrix{Int}(I, N, N) - M[1,2] = 1 - ϱ₁₂ = G(Groups.ϱ(1,2)) - λ₁₂ = G(Groups.λ(1,2)) - - @test Groups.abelianize(ϱ₁₂) == M - @test Groups.abelianize(λ₁₂) == M - - M[1,2] = -1 - - @test Groups.abelianize(ϱ₁₂^-1) == M - @test Groups.abelianize(λ₁₂^-1) == M - - @test Groups.abelianize(ϱ₁₂*λ₁₂^-1) == Matrix{Int}(I, N, N) - @test Groups.abelianize(λ₁₂^-1*ϱ₁₂) == Matrix{Int}(I, N, N) - - M = Matrix{Int}(I, N, N) - M[2,2] = -1 - ε₂ = G(Groups.flip(2)) - - @test Groups.abelianize(ε₂) == M - @test Groups.abelianize(ε₂^2) == Matrix{Int}(I, N, N) - - M = [0 1 0 0; 0 0 0 1; 0 0 1 0; 1 0 0 0] - - σ = G(Groups.AutSymbol(perm"(1,2,4)")) - @test Groups.abelianize(σ) == M - @test Groups.abelianize(σ^3) == Matrix{Int}(I, N, N) - @test Groups.abelianize(σ)^3 == Matrix{Int}(I, N, N) - - @test Groups.abelianize(G(Groups.id_autsymbol())) == Matrix{Int}(I, N, N) - - function test_homomorphism(S, r) - for elts in Iterators.product([[g for g in S] for _ in 1:r]...) - prod(Groups.abelianize.(elts)) == Groups.abelianize(prod(elts)) || error("linear representaton test failed at $elts") - end - return 0 - end - - @test test_homomorphism(S, R) == 0 - end -end diff --git a/test/FPGroup-tests.jl b/test/FPGroup-tests.jl deleted file mode 100644 index ddf29e9..0000000 --- a/test/FPGroup-tests.jl +++ /dev/null @@ -1,18 +0,0 @@ -@testset "FPGroups definitions" begin - F = FreeGroup(["a", "b", "c"]) - a,b,c = Groups.gens(F) - R = [a^2, a*b*a, c*b*a] - @test F/R isa FPGroup - @test F isa FreeGroup - G = F/R - A,B,C = Groups.gens(G) - - @test Groups.reduce!(A^2) == one(G) - @test Groups.reduce!(A*B*A*A) == A - @test Groups.reduce!(A*A*B*A) == A - - @test Groups.freepreimage(G) == F - @test Groups.freepreimage(B^2) == b^2 - - @test G/[B^2, C*B*C] isa FPGroup -end diff --git a/test/FreeGroup-tests.jl b/test/FreeGroup-tests.jl deleted file mode 100644 index 12c2c42..0000000 --- a/test/FreeGroup-tests.jl +++ /dev/null @@ -1,188 +0,0 @@ -@testset "Groups.FreeSymbols" begin - s = Groups.FreeSymbol(:s) - t = Groups.FreeSymbol(:t) - - @testset "constructors" begin - @test isa(Groups.FreeSymbol(:aaaaaaaaaaaaaaaa), Groups.GSymbol) - @test Groups.FreeSymbol(:abc).pow == 1 - @test isa(s, Groups.FreeSymbol) - @test isa(t, Groups.FreeSymbol) - end - @testset "eltary functions" begin - @test length(s) == 1 - @test Groups.change_pow(s, 0) == Groups.change_pow(t, 0) - @test length(Groups.change_pow(s, 0)) == 0 - @test inv(s).pow == -1 - @test Groups.FreeSymbol(:s, 3) == Groups.change_pow(s, 3) - @test Groups.FreeSymbol(:s, 3) != Groups.FreeSymbol(:t, 3) - @test Groups.change_pow(inv(s), -3) == inv(Groups.change_pow(s, 3)) - end - @testset "powers" begin - s⁴ = Groups.change_pow(s,4) - @test s⁴.pow == 4 - @test Groups.change_pow(s, 4) == Groups.FreeSymbol(:s, 4) - end -end - -@testset "FreeGroupSymbols manipulation" begin - s = Groups.FreeSymbol("s") - t = Groups.FreeSymbol(:t, -2) - - @test isa(Groups.GroupWord(s), Groups.GWord{Groups.FreeSymbol}) - @test isa(Groups.GroupWord(s), FreeGroupElem) - @test isa(FreeGroupElem(s), Groups.GWord) - @test isa(convert(FreeGroupElem, s), Groups.GWord) - @test isa(convert(FreeGroupElem, s), FreeGroupElem) - @test isa(Vector{FreeGroupElem}([s,t]), Vector{FreeGroupElem}) - @test length(FreeGroupElem(s)) == 1 - @test length(FreeGroupElem(t)) == 2 - @test Groups.FreeSymbol(:s, 1) != Groups.FreeSymbol(:s, 2) - @test Groups.FreeSymbol(:s, 1) != Groups.FreeSymbol(:t, 1) - @test collect(Groups.FreeSymbol(:s, 2)) == [i for i in Groups.FreeSymbol(:s, 2)] == [s, s] -end - -@testset "FreeGroup" begin - @test isa(FreeGroup(["s", "t"]), GroupsCore.Group) - G = FreeGroup(["s", "t"]) - s, t = gens(G) - - @testset "elements constructors" begin - @test isa(one(G), FreeGroupElem) - @test eltype(G.gens) == Groups.FreeSymbol - @test length(G.gens) == 2 - @test eltype(gens(G)) == FreeGroupElem - @test length(gens(G)) == 2 - - tt, ss = Groups.FreeSymbol(:t), Groups.FreeSymbol(:s) - @test Groups.GroupWord([tt, inv(tt)]) isa FreeGroupElem - - @test collect(s*t) == Groups.syllables(s*t) - @test collect(t^2) == [tt, tt] - ttinv = Groups.FreeSymbol(:t, -1) - w = t^-2*s^3*t^2 - @test collect(w) == [inv(tt), inv(tt), ss, ss, ss, tt, tt] - @test w[1] == inv(tt) - @test w[2] == inv(tt) - @test w[3] == ss - @test w[3:5] == [ss, ss, ss] - @test w[end] == tt - - @test collect(ttinv) == [ttinv] - - @test isone(t^0) - @test !isone(t^1) - end - - @testset "internal arithmetic" begin - - @test (s*s).symbols == (s^2).symbols - @test hash([t^1,s^1]) == hash([t^2*inv(t),s*inv(s)*s]) - - t_symb = Groups.FreeSymbol(:t) - tt = deepcopy(t) - @test string(Groups.rmul!(tt, tt, inv(tt))) == "(id)" - tt = deepcopy(t) - @test string(Groups.lmul!(tt, tt, inv(tt))) == "(id)" - - w = deepcopy(t) - @test length(Groups.rmul!(w, t)) == 2 - @test length(Groups.lmul!(w, inv(t))) == 1 - w = GroupsCore.mul!(w, w, s) - @test length(w) == 2 - @test length(Groups.lmul!(w, inv(s))) == 3 - - tt = deepcopy(t) - push!(tt, inv(t_symb)) - @test string(tt) == "t*t^-1" - tt = deepcopy(t) - pushfirst!(tt, inv(t_symb)) - @test string(tt) == "t^-1*t" - - tt = deepcopy(t) - append!(tt, inv(t)) - @test string(tt) == "t*t^-1" - - tt = deepcopy(t) - prepend!(tt, inv(t)) - @test string(tt) == "t^-1*t" - - tt = deepcopy(t) - append!(tt, s, inv(t)) - @test string(tt) == "t*s*t^-1" - - o = one(t) - o_inv = inv(o) - @test o == o_inv - @test o !== o_inv - Groups.rmul!(o, t) - @test o != o_inv - end - - @testset "reductions" begin - @test length(one(G).symbols) == 0 - @test length((one(G)*one(G)).symbols) == 0 - @test one(G) == one(G)*one(G) - w = deepcopy(s) - push!(Groups.syllables(w), (s^-1).symbols[1]) - @test Groups.reduce!(w) == one(parent(w)) - o = (t*s)^3 - @test o == t*s*t*s*t*s - p = (t*s)^-3 - @test p == s^-1*t^-1*s^-1*t^-1*s^-1*t^-1 - @test o*p == one(parent(o*p)) - w = FreeGroupElem([o.symbols..., p.symbols...]) - w.parent = G - @test Groups.syllables(Groups.reduce(w)) == Vector{Groups.FreeSymbol}([]) - end - - @testset "Group operations" begin - @test parent(s) == G - @test parent(s) === parent(deepcopy(s)) - @test isa(s*t, FreeGroupElem) - @test parent(s*t) == parent(s^2) - @test s*s == s^2 - @test inv(s*s) == inv(s^2) - @test inv(s)^2 == inv(s^2) - @test inv(s)*inv(s) == inv(s^2) - @test inv(s*t) == inv(t)*inv(s) - w = s*t*s^-1 - @test inv(w) == s*t^-1*s^-1 - @test (t*s*t^-1)^10 == t*s^10*t^-1 - @test (t*s*t^-1)^-10 == t*s^-10*t^-1 - end - - @testset "replacements" begin - a = Groups.FreeSymbol(:a) - b = Groups.FreeSymbol(:b) - @test Groups.issubsymbol(a, Groups.change_pow(a,2)) == true - @test Groups.issubsymbol(a, Groups.change_pow(a,-2)) == false - @test Groups.issubsymbol(b, Groups.change_pow(a,-2)) == false - @test Groups.issubsymbol(inv(b), Groups.change_pow(b,-2)) == true - - c = s*t*s^-1*t^-1 - @test findfirst(s^-1*t^-1, c) == 3 - @test findnext(s^-1*t^-1, c*s^-1,3) == 3 - @test findnext(s^-1*t^-1, c*s^-1*t^-1, 4) == 5 - @test findfirst(c, c*t) === nothing - - @test findlast(s^-1*t^-1, c) == 3 - @test findprev(s, s*t*s*t, 4) == 3 - @test findprev(s*t, s*t*s*t, 2) == 1 - @test findprev(Groups.FreeSymbol(:t, 2), c, 4) === nothing - - w = s*t*s^-1 - subst = Dict{FreeGroupElem, FreeGroupElem}(w => s^1, s*t^-1 => t^4) - @test Groups.replace(c, s*t=>one(G)) == s^-1*t^-1 - @test Groups.replace(c, w=>subst[w]) == s*t^-1 - @test Groups.replace(s*c*t^-1, w=>subst[w]) == s^2*t^-2 - @test Groups.replace(t*c*t, w=>subst[w]) == t*s - @test Groups.replace(s*c*s*c*s, subst) == s*t^4*s*t^4*s - - G = FreeGroup(["x", "y"]) - x,y = gens(G) - - @test Groups.replace(x*y^9, y^2=>y) == x*y^5 - @test Groups.replace(x^3, x^2=>y) == x*y - @test Groups.replace(y*x^3*y, x^2=>y) == y*x*y^2 - end -end diff --git a/test/runtests.jl b/test/runtests.jl index 7755670..5b689c8 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -2,42 +2,32 @@ using Test import AbstractAlgebra using Groups -include("symmetric.jl") -using LinearAlgebra +using KnuthBendix + +using GroupsCore +include(joinpath(pathof(GroupsCore), "..", "..", "test", "conformance_test.jl")) @testset "Groups" begin - @testset "wlmetric_ball" begin - M = AbstractAlgebra.MatrixAlgebra(AbstractAlgebra.zz, 3) - w = one(M); w[1,2] = 1; - r = one(M); r[2,3] = -3; - s = one(M); s[1,3] = 2; s[3,2] = -1; + @testset "wlmetric_ball" begin + M = AbstractAlgebra.MatrixAlgebra(AbstractAlgebra.zz, 3) + w = one(M); w[1,2] = 1; + r = one(M); r[2,3] = -3; + s = one(M); s[1,3] = 2; s[3,2] = -1; - S = [w,r,s]; S = unique([S; inv.(S)]); - _, sizes = Groups.wlmetric_ball(S, radius=4); - @test sizes == [7, 33, 141, 561] - _, sizes = Groups.wlmetric_ball_serial(S, radius=4); - @test sizes == [7, 33, 141, 561] - end + S = [w,r,s]; S = unique([S; inv.(S)]); + _, sizes = Groups.wlmetric_ball(S, radius=4); + @test sizes == [7, 33, 141, 561] + _, sizes = Groups.wlmetric_ball_serial(S, radius=4); + @test sizes == [7, 33, 141, 561] + end - include("FreeGroup-tests.jl") - include("AutGroup-tests.jl") - include("FPGroup-tests.jl") + include("free_groups.jl") + include("fp_groups.jl") - @testset "New FPGroups" begin - using Groups.New - using KnuthBendix + include("AutFn.jl") - using GroupsCore - include(joinpath(pathof(GroupsCore), "..", "..", "test", "conformance_test.jl")) - - include("free_groups.jl") - include("fp_groups.jl") - - include("AutFn.jl") - - if !haskey(ENV, "CI") - include("benchmarks.jl") - end - end + # if !haskey(ENV, "CI") + # include("benchmarks.jl") + # end end diff --git a/test/symmetric.jl b/test/symmetric.jl deleted file mode 100644 index f4ea750..0000000 --- a/test/symmetric.jl +++ /dev/null @@ -1,31 +0,0 @@ -import AbstractAlgebra -using GroupsCore - -# disambiguation -GroupsCore.order( - ::Type{I}, - G::AbstractAlgebra.Generic.SymmetricGroup, -) where {I<:Integer} = I(factorial(G.n)) - -# disambiguation -GroupsCore.order( - ::Type{I}, - g::AbstractAlgebra.Generic.Perm, -) where {I<:Integer} = - I(foldl(lcm, length(c) for c in AbstractAlgebra.cycles(g))) - -# correct the AA length: -Base.length(G::AbstractAlgebra.Generic.SymmetricGroup) = order(Int, G) - -# genuinely new methods: -Base.IteratorSize(::Type{<:AbstractAlgebra.AbstractPermutationGroup}) = Base.HasLength() - -function GroupsCore.gens(G::AbstractAlgebra.Generic.SymmetricGroup{I}) where {I} - a, b = one(G), one(G) - circshift!(a.d, b.d, -1) - b.d[1], b.d[2] = 2, 1 - return [a, b] -end - -Base.deepcopy_internal(g::AbstractAlgebra.Generic.Perm, ::IdDict) = - AbstractAlgebra.Generic.Perm(deepcopy(g.d), false)