diff --git a/.github/workflows/TagBot.yml b/.github/workflows/TagBot.yml index d77d3a0..f49313b 100644 --- a/.github/workflows/TagBot.yml +++ b/.github/workflows/TagBot.yml @@ -1,11 +1,15 @@ name: TagBot on: - schedule: - - cron: 0 * * * * + issue_comment: + types: + - created + workflow_dispatch: jobs: TagBot: + if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot' runs-on: ubuntu-latest steps: - uses: JuliaRegistries/TagBot@v1 with: token: ${{ secrets.GITHUB_TOKEN }} + ssh: ${{ secrets.DOCUMENTER_KEY }} diff --git a/.github/workflows/runtests.yml b/.github/workflows/runtests.yml index e4c950e..6ccb8a7 100644 --- a/.github/workflows/runtests.yml +++ b/.github/workflows/runtests.yml @@ -14,7 +14,7 @@ jobs: matrix: version: - '1.3' - - '1.5' + - '1' - 'nightly' os: - ubuntu-latest diff --git a/Project.toml b/Project.toml index b7fe35a..cd77d3f 100644 --- a/Project.toml +++ b/Project.toml @@ -4,26 +4,24 @@ authors = ["Marek Kaluba "] version = "0.6.0" [deps] -AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d" GroupsCore = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120" KnuthBendix = "c2604015-7b3d-4a30-8a26-9074551ec60a" -LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" OrderedCollections = "bac558e1-5e72-5ebc-8fee-abe8a469f55d" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" ThreadsX = "ac1d9e8a-700a-412c-b207-f0111f4b6c0d" [compat] -AbstractAlgebra = "^0.13.0, ^0.14.0, ^0.15.0" +AbstractAlgebra = "0.15, 0.16" GroupsCore = "^0.3" -KnuthBendix = "^0.2.0" +KnuthBendix = "^0.2.1" OrderedCollections = "1" ThreadsX = "^0.1.0" -julia = "1.3, 1.4, 1.5" +julia = "1.3, 1.4, 1.5, 1.6" [extras] +AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d" BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" -PermutationGroups = "8bc5a954-2dfc-11e9-10e6-cd969bffa420" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [targets] -test = ["Test", "BenchmarkTools", "PermutationGroups"] +test = ["Test", "BenchmarkTools", "AbstractAlgebra"] diff --git a/README.md b/README.md index fe6af31..79523ed 100644 --- a/README.md +++ b/README.md @@ -1,7 +1,153 @@ # Groups -[![Build Status](https://travis-ci.org/kalmarek/Groups.jl.svg?branch=master)](https://travis-ci.org/kalmarek/Groups.jl) +[![CI](https://github.com/kalmarek/Groups.jl/actions/workflows/runtests.yml/badge.svg)](https://github.com/kalmarek/Groups.jl/actions/workflows/runtests.yml) [![codecov](https://codecov.io/gh/kalmarek/Groups.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/kalmarek/Groups.jl) -A very rudimentary implementation of finitely-presented groups (syllable representation). Relatively complete are only [automorphism groups of free groups](https://github.com/kalmarek/Groups.jl/blob/master/src/AutGroup.jl) and [wreath products](https://github.com/kalmarek/Groups.jl/blob/master/src/WreathProducts.jl) (which are not finitely-presented, but based on the standard normal form). +An implementation of finitely-presented groups together with normalization (using Knuth-Bendix procedure). -Have a look into `test` directory for eample use. +The package implements `AbstractFPGroup` with three concrete types: `FreeGroup`, `FPGroup` and `AutomorphismGroup`. Here's an example usage: + +```julia +julia> using Groups, GroupsCore + +julia> A = Alphabet([:a, :A, :b, :B, :c, :C], [2, 1, 4, 3, 6, 5]) +Alphabet of Symbol: + 1. :a = (:A)⁻¹ + 2. :A = (:a)⁻¹ + 3. :b = (:B)⁻¹ + 4. :B = (:b)⁻¹ + 5. :c = (:C)⁻¹ + 6. :C = (:c)⁻¹ + +julia> F = FreeGroup(A) +free group on 3 generators + +julia> a,b,c = gens(F) +3-element Vector{FPGroupElement{FreeGroup{Symbol}, KnuthBendix.Word{UInt8}}}: + a + b + c + +julia> a*inv(a) +(empty word) + +julia> (a*b)^2 +a*b*a*b + +julia> commutator(a, b) +A*B*a*b + +julia> x = a*b; y = inv(b)*a; + +julia> x*y +a^2 + +``` +Let's create a quotient of the free group above: +```julia +julia> ε = one(F); + +julia> G = FPGroup(F, [a^2 => ε, b^3=> ε, (a*b)^7=>ε, (a*b*a*inv(b))^6 => ε, commutator(a, c) => ε, commutator(b, c) => ε ]) +┌ Warning: Maximum number of rules (100) reached. The rewriting system may not be confluent. +│ You may retry `knuthbendix` with a larger `maxrules` kwarg. +└ @ KnuthBendix ~/.julia/packages/KnuthBendix/i93Np/src/kbs.jl:6 +⟨a, b, c | a^2 => (empty word), b^3 => (empty word), a*b*a*b*a*b*a*b*a*b*a*b*a*b => (empty word), a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B => (empty word), A*C*a*c => (empty word), B*C*b*c => (empty word)⟩ + +``` +As you can see from the warning, the Knuth-Bendix procedure has not completed successfully. This means that we only are able to approximate the word problem in `G`, i.e. if the equality (`==`) of two group elements may return `false` even if group elements are equal. Let us try with a larger maximal number of rules in the underlying rewriting system. + +```julia +julia> G = FPGroup(F, [a^2 => ε, b^3=> ε, (a*b)^7=>ε, (a*b*a*inv(b))^6 => ε, commutator(a, c) => ε, commutator(b, c) => ε ], maxrules=500) +⟨a, b, c | a^2 => (empty word), b^3 => (empty word), a*b*a*b*a*b*a*b*a*b*a*b*a*b => (empty word), a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B => (empty word), A*C*a*c => (empty word), B*C*b*c => (empty word)⟩ + +``` +This time there was no warning, i.e. Knuth-Bendix completion was successful and we may treat the equality (`==`) as true mathematical equality. Note that `G` is the direct product of `ℤ = ⟨ c ⟩` and a quotient of van Dyck `(2,3,7)`-group. Let's create a random word and reduce it as an element of `G`. +```julia +julia> using Random; Random.seed!(1); w = Groups.Word(rand(1:length(A), 16)) +KnuthBendix.Word{UInt16}: 4·6·1·1·1·6·5·1·5·2·3·6·2·4·2·6 + +julia> F(w) # freely reduced w +B*C*a^4*c*A*b*C*A*B*A*C + +julia> G(w) # w as an element of G +B*a*b*a*B*a*C^2 + +julia> F(w) # freely reduced w +B*C*a^4*c*A*b*C*A*B*A*C + +julia> word(ans) # the underlying word in A +KnuthBendix.Word{UInt8}: 4·6·1·1·1·1·5·2·3·6·2·4·2·6 + +julia> G(w) # w as an element of G +B*a*b*a*B*a*C^2 + +julia> word(ans) # the underlying word in A +KnuthBendix.Word{UInt8}: 4·1·3·1·4·1·6·6 + +``` +As we can see the underlying words change according to where they are reduced. +Note that a word `w` (of type `Word <: AbstractWord`) is just a sequence of numbers -- pointers to letters of an `Alphabet`. Without the alphabet `w` has no meaning. + +### Automorphism Groups + +Relatively complete is the support for the automorphisms of free groups, as given by Gersten presentation: +```julia +julia> saut = SpecialAutomorphismGroup(F, maxrules=100) +┌ Warning: Maximum number of rules (100) reached. The rewriting system may not be confluent. +│ You may retry `knuthbendix` with a larger `maxrules` kwarg. +└ @ KnuthBendix ~/.julia/packages/KnuthBendix/i93Np/src/kbs.jl:6 +automorphism group of free group on 3 generators + +julia> S = gens(saut) +12-element Vector{Automorphism{FreeGroup{Symbol},…}}: + ϱ₁.₂ + ϱ₁.₃ + ϱ₂.₁ + ϱ₂.₃ + ϱ₃.₁ + ϱ₃.₂ + λ₁.₂ + λ₁.₃ + λ₂.₁ + λ₂.₃ + λ₃.₁ + λ₃.₂ + +julia> x, y, z = S[1], S[12], S[6]; + +julia> f = x*y*inv(z) +ϱ₁.₂*λ₃.₂*ϱ₃.₂^-1 + +julia> g = inv(z)*y*x +ϱ₃.₂^-1*ϱ₁.₂*λ₃.₂ + +julia> word(f), word(g) +(KnuthBendix.Word{UInt8}: 1·12·18, KnuthBendix.Word{UInt8}: 18·1·12) + +``` +Even though Knuth-Bendix did not finish successfully in automorphism groups we have another ace in our sleeve to solve the word problem: evaluation. +Lets have a look at the images of generators under those automorphisms: +```julia +julia> evaluate(f) # or to be more verbose... +(a*b, b, b*c*B) + +julia> Groups.domain(g) +(a, b, c) + +julia> Groups.evaluate!(Groups.domain(g), g) +(a*b, b, b*c*B) + +``` +Since these automorphism map the standard generating set to the same new generating set, they should be considered as equal! And indeed they are: +```julia +julia> f == g +true +``` +This is what is happening behind the scenes: + 1. words are reduced using a rewriting system + 2. if resulting words are equal `true` is returned + 3. if they are not equal `Groups.equality_data` is computed for each argument (here: the images of generators) and the result of comparison is returned. + +Moreover we try to amortize the cost of computing those images. That is a hash of `equality_daata` is lazily stored in each group element and used as needed. Essentially only if `true` is returned, but comparison of words returns `false` recomputation of images is needed (to guard against hash collisions). + +---- +This package was developed for computations in [1712.07167](https://arxiv.org/abs/1712.07167) and in [1812.03456](https://arxiv.org/abs/1812.03456). If you happen to use this package please cite either of them. 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 $(length(G.gens)) generators: ") - join(io, G.gens, ", ") -end diff --git a/src/Groups.jl b/src/Groups.jl index f5ab027..c2f5594 100644 --- a/src/Groups.jl +++ b/src/Groups.jl @@ -1,144 +1,24 @@ module Groups using GroupsCore -using LinearAlgebra using ThreadsX - -import AbstractAlgebra import KnuthBendix +import KnuthBendix: AbstractWord, Alphabet, Word +import KnuthBendix: alphabet +import Random -export gens, FreeGroup, Aut, SAut - -include("types.jl") - -include("FreeGroup.jl") -include("FPGroups.jl") -include("AutGroup.jl") - -include("symbols.jl") -include("words.jl") -include("hashing.jl") -include("freereduce.jl") -include("arithmetic.jl") -include("findreplace.jl") - -module New import OrderedCollections: OrderedSet -include("new_types.jl") -include("new_hashing.jl") +export Alphabet, AutomorphismGroup, FreeGroup, FreeGroup, FPGroup, FPGroupElement, SpecialAutomorphismGroup +export alphabet, evaluate, word + +include("types.jl") +include("hashing.jl") include("normalform.jl") -include("new_autgroups.jl") +include("autgroups.jl") include("groups/sautFn.jl") include("groups/mcg.jl") -end # module New - -############################################################################### -# -# String I/O -# - -function Base.show(io::IO, W::GWord) - if length(W) == 0 - print(io, "(id)") - else - join(io, (string(s) for s in syllables(W)), "*") - end -end - -function Base.show(io::IO, s::T) where {T<:GSymbol} - if s.pow == 1 - print(io, string(s.id)) - else - print(io, "$(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/new_autgroups.jl b/src/autgroups.jl similarity index 89% rename from src/new_autgroups.jl rename to src/autgroups.jl index 4147cbf..d214005 100644 --- a/src/new_autgroups.jl +++ b/src/autgroups.jl @@ -84,17 +84,6 @@ Base.show(io::IO, ::Type{<:FPGroupElement{<:AutomorphismGroup{T}}}) where {T} = Base.show(io::IO, A::AutomorphismGroup) = print(io, "automorphism group of ", object(A)) - -function Base.show(io::IO, ::MIME"text/plain", a::FPGroupElement{<:AutomorphismGroup}) - println(io, " ┌ $(a):") - im = evaluate(a) - d = domain(a) - for (x, imx) in zip(d, im[1:end-1]) - println(io, " │ $x ↦ $imx") - end - print(io, " └ $(last(d)) ↦ $(last(im))") -end - ## Automorphism Evaluation domain(f::FPGroupElement{<:AutomorphismGroup}) = deepcopy(parent(f).domain) @@ -116,4 +105,3 @@ function evaluate!( end evaluate!(t::NTuple{N, T}, s::GSymbol, A, tmp=one(first(t))) where {N, T} = throw("you need to implement `evaluate!(::$(typeof(t)), ::$(typeof(s)), ::Alphabet, tmp=one(first(t)))`") - 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/groups/sautFn.jl b/src/groups/sautFn.jl index e6a22d9..c47612f 100644 --- a/src/groups/sautFn.jl +++ b/src/groups/sautFn.jl @@ -3,7 +3,7 @@ include("gersten_relations.jl") function SpecialAutomorphismGroup(F::FreeGroup; ordering = KnuthBendix.LenLex, kwargs...) - n = length(KnuthBendix.alphabet(F)) ÷ 2 + n = length(alphabet(F)) ÷ 2 A, rels = gersten_relations(n, commutative = false) S = KnuthBendix.letters(A)[1:2(n^2-n)] @@ -15,6 +15,6 @@ end KnuthBendix.alphabet(G::AutomorphismGroup{<:FreeGroup}) = alphabet(rewriting(G)) function relations(G::AutomorphismGroup{<:FreeGroup}) - n = length(KnuthBendix.alphabet(object(G))) ÷ 2 + n = length(alphabet(object(G))) ÷ 2 return last(gersten_relations(n, commutative = false)) end diff --git a/src/groups/transvections.jl b/src/groups/transvections.jl index 17b0d89..e405359 100644 --- a/src/groups/transvections.jl +++ b/src/groups/transvections.jl @@ -31,12 +31,11 @@ end function Base.show(io::IO, t::Transvection) id = if t.id === :ϱ - "ϱ" + 'ϱ' else # if t.id === :λ - "λ" + 'λ' end - # print(io, id, Groups.subscriptify(t.i), ".", Groups.subscriptify(t.j)) - print(io, id, "_", t.i, ",", t.j) + print(io, id, subscriptify(t.i), '.', subscriptify(t.j)) t.inv && print(io, "^-1") end diff --git a/src/hashing.jl b/src/hashing.jl index b9fd17f..b8d7e4b 100644 --- a/src/hashing.jl +++ b/src/hashing.jl @@ -1,34 +1,46 @@ -############################################################################### -# -# hashing, deepcopy and == -# +## Hashing -function hash_internal(W::GWord) - reduce!(W) - h = hasparent(W) ? hash(parent(W)) : zero(UInt) - return hash(syllables(W), hash(typeof(W), h)) -end +equality_data(g::FPGroupElement) = (normalform!(g); word(g)) -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 +bitget(h::UInt, n::Int) = Bool((h & (1 << n)) >> n) +bitclear(h::UInt, n::Int) = h & ~(1 << n) +bitset(h::UInt, n::Int) = h | (1 << n) +bitset(h::UInt, v::Bool, n::Int) = v ? bitset(h, n) : bitclear(h, n) -# 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) +# We store hash of a word in field `savedhash` to use it as cheap proxy to +# determine non-equal words. Additionally bits of `savehash` store boolean +# information as follows +# * `savedhash & 1` (the first bit): is word in normal form? +# * `savedhash & 2` (the second bit): is the hash valid? +const __BITFLAGS_MASK = ~(~(UInt(0)) << 2) + +isnormalform(g::FPGroupElement) = bitget(g.savedhash, 0) +_isvalidhash(g::FPGroupElement) = bitget(g.savedhash, 1) + +_setnormalform(h::UInt, v::Bool) = bitset(h, v, 0) +_setvalidhash(h::UInt, v::Bool) = bitset(h, v, 1) + +_setnormalform!(g::FPGroupElement, v::Bool) = g.savedhash = _setnormalform(g.savedhash, v) +_setvalidhash!(g::FPGroupElement, v::Bool) = g.savedhash = _setvalidhash(g.savedhash, v) + +# To update hash use this internal method, possibly only after computing the +# normal form of `g`: +function _update_savedhash!(g::FPGroupElement, data) + h = hash(data, hash(parent(g))) + h = (h << count_ones(__BITFLAGS_MASK)) | (__BITFLAGS_MASK & g.savedhash) + g.savedhash = _setvalidhash(h, true) 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) +function Base.hash(g::FPGroupElement, h::UInt) + _isvalidhash(g) || _update_savedhash!(g, equality_data(g)) + return hash(g.savedhash >> count_ones(__BITFLAGS_MASK), h) +end + +function Base.copyto!(res::FPGroupElement, g::FPGroupElement) + @assert parent(res) === parent(g) + resize!(word(res), length(word(g))) + copyto!(word(res), word(g)) + res.savedhash = g.savedhash + return res end diff --git a/src/new_hashing.jl b/src/new_hashing.jl deleted file mode 100644 index b8d7e4b..0000000 --- a/src/new_hashing.jl +++ /dev/null @@ -1,46 +0,0 @@ -## Hashing - -equality_data(g::FPGroupElement) = (normalform!(g); word(g)) - -bitget(h::UInt, n::Int) = Bool((h & (1 << n)) >> n) -bitclear(h::UInt, n::Int) = h & ~(1 << n) -bitset(h::UInt, n::Int) = h | (1 << n) -bitset(h::UInt, v::Bool, n::Int) = v ? bitset(h, n) : bitclear(h, n) - -# We store hash of a word in field `savedhash` to use it as cheap proxy to -# determine non-equal words. Additionally bits of `savehash` store boolean -# information as follows -# * `savedhash & 1` (the first bit): is word in normal form? -# * `savedhash & 2` (the second bit): is the hash valid? -const __BITFLAGS_MASK = ~(~(UInt(0)) << 2) - -isnormalform(g::FPGroupElement) = bitget(g.savedhash, 0) -_isvalidhash(g::FPGroupElement) = bitget(g.savedhash, 1) - -_setnormalform(h::UInt, v::Bool) = bitset(h, v, 0) -_setvalidhash(h::UInt, v::Bool) = bitset(h, v, 1) - -_setnormalform!(g::FPGroupElement, v::Bool) = g.savedhash = _setnormalform(g.savedhash, v) -_setvalidhash!(g::FPGroupElement, v::Bool) = g.savedhash = _setvalidhash(g.savedhash, v) - -# To update hash use this internal method, possibly only after computing the -# normal form of `g`: -function _update_savedhash!(g::FPGroupElement, data) - h = hash(data, hash(parent(g))) - h = (h << count_ones(__BITFLAGS_MASK)) | (__BITFLAGS_MASK & g.savedhash) - g.savedhash = _setvalidhash(h, true) - return g -end - -function Base.hash(g::FPGroupElement, h::UInt) - _isvalidhash(g) || _update_savedhash!(g, equality_data(g)) - return hash(g.savedhash >> count_ones(__BITFLAGS_MASK), h) -end - -function Base.copyto!(res::FPGroupElement, g::FPGroupElement) - @assert parent(res) === parent(g) - resize!(word(res), length(word(g))) - copyto!(word(res), word(g)) - res.savedhash = g.savedhash - return res -end diff --git a/src/normalform.jl b/src/normalform.jl index a8213f6..f1d67ff 100644 --- a/src/normalform.jl +++ b/src/normalform.jl @@ -42,8 +42,5 @@ Defaults to the rewriting in the free group. """ @inline function normalform!(res::AbstractWord, g::FPGroupElement) isone(res) && isnormalform(g) && return append!(res, word(g)) - if isnormalform(g) && inv(alphabet(g), last(out)) != first(word(g)) - return append!(res, word(g)) - end return KnuthBendix.rewrite_from_left!(res, word(g), rewriting(parent(g))) 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 index 316554a..bed9221 100644 --- a/src/types.jl +++ b/src/types.jl @@ -1,50 +1,210 @@ +## "Abstract" definitions + +""" + AbstractFPGroup + +An Abstract type representing finitely presented groups. Every instance `` must implement + * `KnuthBendix.alphabet(G::MyFPGroup)` + * `rewriting(G::MyFPGroup)` : return the rewriting object which must implement + > `KnuthBendix.rewrite_from_left!(u, v, rewriting(G))`. +By default `alphabet(G)` is returned, which amounts to free rewriting in `G`. + * `relations(G::MyFPGroup)` : return a set of defining relations. + +AbstractFPGroup may also override `word_type(::Type{MyFPGroup}) = Word{UInt16}`, +which controls the word type used for group elements. If a group has more than `255` generators you need to define e.g. +> `word_type(::Type{MyFPGroup}) = Word{UInt16}` +""" 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 +word_type(G::AbstractFPGroup) = word_type(typeof(G)) +# the default: +word_type(::Type{<:AbstractFPGroup}) = Word{UInt8} + +# the default (results in free rewriting) +rewriting(G::AbstractFPGroup) = alphabet(G) + +Base.@propagate_inbounds function (G::AbstractFPGroup)(word::AbstractVector{<:Integer}) + @boundscheck @assert all(l -> 1 <= l <= length(KnuthBendix.alphabet(G)), word) + return FPGroupElement(word_type(G)(word), G) 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 +## Group Interface -abstract type GWord{T<:GSymbol} <: GroupsCore.GroupElement end +Base.one(G::AbstractFPGroup) = FPGroupElement(one(word_type(G)), G) -""" - 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. +Base.eltype(::Type{FPG}) where {FPG<:AbstractFPGroup} = FPGroupElement{FPG,word_type(FPG)} -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. -""" +include("iteration.jl") -mutable struct GroupWord{T} <: GWord{T} - symbols::Vector{T} - modified::Bool +GroupsCore.ngens(G::AbstractFPGroup) = length(G.gens) + +function GroupsCore.gens(G::AbstractFPGroup, i::Integer) + @boundscheck 1 <= i <= GroupsCore.ngens(G) + l = alphabet(G)[G.gens[i]] + return FPGroupElement(word_type(G)([l]), G) +end +GroupsCore.gens(G::AbstractFPGroup) = [gens(G, i) for i in 1:GroupsCore.ngens(G)] + +# TODO: ProductReplacementAlgorithm +function Base.rand(rng::Random.AbstractRNG, rs::Random.SamplerTrivial{<:AbstractFPGroup}) + l = rand(10:100) + G = rs[] + nletters = length(alphabet(G)) + return FPGroupElement(word_type(G)(rand(1:nletters, l)), G) +end + +Base.isfinite(::AbstractFPGroup) = (@warn "using generic isfinite(::AbstractFPGroup): the returned `false` might be wrong"; false) + +## FPGroupElement + +mutable struct FPGroupElement{G<:AbstractFPGroup,W<:AbstractWord} <: GroupElement + word::W savedhash::UInt - parent::Group + parent::G - 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) + FPGroupElement(word::W, G::AbstractFPGroup) where {W<:AbstractWord} = + new{typeof(G),W}(word, UInt(0), G) + + FPGroupElement(word::W, hash::UInt, G::AbstractFPGroup) where {W<:AbstractWord} = + new{typeof(G),W}(word, hash, G) +end + +word(f::FPGroupElement) = f.word + +#convenience +KnuthBendix.alphabet(g::FPGroupElement) = alphabet(parent(g)) + +function Base.show(io::IO, f::FPGroupElement) + f = normalform!(f) + KnuthBendix.print_repr(io, word(f), alphabet(f)) +end + +## GroupElement Interface for FPGroupElement + +Base.parent(f::FPGroupElement) = f.parent +GroupsCore.parent_type(::Type{<:FPGroupElement{G}}) where {G} = G + +function Base.:(==)(g::FPGroupElement, h::FPGroupElement) + @boundscheck @assert parent(g) === parent(h) + normalform!(g) + normalform!(h) + hash(g) != hash(h) && return false + return word(g) == word(h) +end + +function Base.deepcopy_internal(g::FPGroupElement, stackdict::IdDict) + return FPGroupElement(copy(word(g)), g.savedhash, parent(g)) +end + +Base.inv(g::FPGroupElement) = (G = parent(g); FPGroupElement(inv(alphabet(G), word(g)), G)) + +function Base.:(*)(g::FPGroupElement, h::FPGroupElement) + @boundscheck @assert parent(g) === parent(h) + return FPGroupElement(word(g) * word(h), parent(g)) +end + +GroupsCore.isfiniteorder(g::FPGroupElement) = isone(g) ? true : (@warn "using generic isfiniteorder(::FPGroupElement): the returned `false` might be wrong"; false) + +# additional methods: +Base.isone(g::FPGroupElement) = (normalform!(g); isempty(word(g))) + +## Free Groups + +struct FreeGroup{T} <: AbstractFPGroup + gens::Vector{T} + alphabet::KnuthBendix.Alphabet{T} + + function FreeGroup(gens, A::KnuthBendix.Alphabet) where {W} + @assert length(gens) == length(unique(gens)) + @assert all(l -> l in KnuthBendix.letters(A), gens) + return new{eltype(gens)}(gens, A) + end +end + +function FreeGroup(A::Alphabet) + @boundscheck @assert all(KnuthBendix.hasinverse(l, A) for l in KnuthBendix.letters(A)) + ltrs = KnuthBendix.letters(A) + gens = Vector{eltype(ltrs)}() + invs = Vector{eltype(ltrs)}() + for l in ltrs + l ∈ invs && continue + push!(gens, l) + push!(invs, inv(A, l)) + end + + return FreeGroup(gens, A) +end + +function FreeGroup(n::Integer) + symbols = Symbol[] + inverses = Int[] + sizehint!(symbols, 2n) + sizehint!(inverses, 2n) + for i in 1:n + push!(symbols, Symbol(:f, i), Symbol(:F, i)) + push!(inverses, 2i, 2i-1) + end + return FreeGroup(symbols[1:2:2n], Alphabet(symbols, inverses)) +end + +Base.show(io::IO, F::FreeGroup) = print(io, "free group on $(ngens(F)) generators") + +# mandatory methods: +KnuthBendix.alphabet(F::FreeGroup) = F.alphabet +relations(F::FreeGroup) = Pair{eltype(F)}[] + +# GroupsCore interface: +# these are mathematically correct +Base.isfinite(::FreeGroup) = false + +GroupsCore.isfiniteorder(g::FPGroupElement{<:FreeGroup}) = isone(g) ? true : false + +## FP Groups + +struct FPGroup{T,R,S} <: AbstractFPGroup + gens::Vector{T} + relations::Vector{Pair{S,S}} + rws::R +end + +KnuthBendix.alphabet(G::FPGroup) = alphabet(rewriting(G)) +rewriting(G::FPGroup) = G.rws + +relations(G::FPGroup) = G.relations + +function FPGroup( + G::AbstractFPGroup, + rels::AbstractVector{<:Pair{GEl,GEl}}; + ordering = KnuthBendix.LenLex, + kwargs..., +) where {GEl<:FPGroupElement} + + O = ordering(alphabet(G)) + for (lhs, rhs) in rels + @assert parent(lhs) === parent(rhs) === G + end + word_rels = [word(lhs) => word(rhs) for (lhs, rhs) in [relations(G); rels]] + rws = KnuthBendix.RewritingSystem(word_rels, O) + + KnuthBendix.knuthbendix!(rws; kwargs...) + + return FPGroup(G.gens, rels, rws) +end + +function Base.show(io::IO, G::FPGroup) + print(io, "⟨") + join(io, gens(G), ", ") + print(io, " | ") + join(io, relations(G), ", ") + print(io, "⟩") +end + +## GSymbol aka letter of alphabet + +abstract type GSymbol end +Base.literal_pow(::typeof(^), t::GSymbol, ::Val{-1}) = inv(t) + +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 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/AutFn.jl b/test/AutFn.jl index ecd469e..a33dc65 100644 --- a/test/AutFn.jl +++ b/test/AutFn.jl @@ -2,27 +2,30 @@ @testset "Transvections" begin - @test New.Transvection(:ϱ, 1, 2) isa New.GSymbol - @test New.Transvection(:ϱ, 1, 2) isa New.Transvection - @test New.Transvection(:λ, 1, 2) isa New.GSymbol - @test New.Transvection(:λ, 1, 2) isa New.Transvection - t = New.Transvection(:ϱ, 1, 2) - @test inv(t) isa New.GSymbol - @test inv(t) isa New.Transvection + @test Groups.Transvection(:ϱ, 1, 2) isa Groups.GSymbol + @test Groups.Transvection(:ϱ, 1, 2) isa Groups.Transvection + @test Groups.Transvection(:λ, 1, 2) isa Groups.GSymbol + @test Groups.Transvection(:λ, 1, 2) isa Groups.Transvection + t = Groups.Transvection(:ϱ, 1, 2) + @test inv(t) isa Groups.GSymbol + @test inv(t) isa Groups.Transvection @test t != inv(t) - s = New.Transvection(:ϱ, 1, 2) + s = Groups.Transvection(:ϱ, 1, 2) @test t == s @test hash(t) == hash(s) - s_ = New.Transvection(:ϱ, 1, 3) + s_ = Groups.Transvection(:ϱ, 1, 3) @test s_ != s @test hash(s_) != hash(s) - @test New.gersten_alphabet(3) isa Alphabet - A = New.gersten_alphabet(3) + @test Groups.gersten_alphabet(3) isa Alphabet + A = Groups.gersten_alphabet(3) @test length(A) == 12 + + @test sprint(show, Groups.ϱ(1, 2)) == "ϱ₁.₂" + @test sprint(show, Groups.λ(3, 2)) == "λ₃.₂" end A4 = Alphabet( @@ -35,18 +38,16 @@ [ 2, 1, 4, 3, 6, 5, 8, 7,10, 9] ) - F4 = New.FreeGroup([:a, :b, :c, :d], A4) - A = New.SpecialAutomorphismGroup(F4, maxrules=1000) - + F4 = FreeGroup([:a, :b, :c, :d], A4) a,b,c,d = gens(F4) D = ntuple(i->gens(F4, i), 4) @testset "Transvection action correctness" begin i,j = 1,2 - r = New.Transvection(:ϱ,i,j) - l = New.Transvection(:λ,i,j) + r = Groups.Transvection(:ϱ,i,j) + l = Groups.Transvection(:λ,i,j) - (t::New.Transvection)(v::Tuple) = New.evaluate!(v, t, A4) + (t::Groups.Transvection)(v::Tuple) = Groups.evaluate!(v, t, A4) @test r(deepcopy(D)) == (a*b, b, c, d) @test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d) @@ -54,45 +55,49 @@ @test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d) i,j = 3,1 - r = New.Transvection(:ϱ,i,j) - l = New.Transvection(:λ,i,j) + r = Groups.Transvection(:ϱ,i,j) + l = Groups.Transvection(:λ,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 = New.Transvection(:ϱ,i,j) - l = New.Transvection(:λ,i,j) + r = Groups.Transvection(:ϱ,i,j) + l = Groups.Transvection(:λ,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 = New.Transvection(:ϱ,i,j) - l = New.Transvection(:λ,i,j) + r = Groups.Transvection(:ϱ,i,j) + l = Groups.Transvection(:λ,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 "AutomorphismGroup constructors" begin - @test A isa New.AbstractFPGroup - @test A isa New.AutomorphismGroup - @test KnuthBendix.alphabet(A) isa Alphabet - @test New.relations(A) isa Vector{<:Pair} + A = SpecialAutomorphismGroup(F4, maxrules=1000) + @testset "AutomorphismGroup constructors" begin + @test A isa Groups.AbstractFPGroup + @test A isa AutomorphismGroup + @test alphabet(A) isa Alphabet + @test Groups.relations(A) isa Vector{<:Pair} + @test sprint(show, A) == "automorphism group of free group on 4 generators" end @testset "Automorphisms: hash and evaluate" begin - @test New.domain(gens(A, 1)) == D + @test Groups.domain(gens(A, 1)) == D g, h = gens(A, 1), gens(A, 8) - @test New.evaluate(g*h) == New.evaluate(h*g) + @test evaluate(g*h) == evaluate(h*g) @test (g*h).savedhash == zero(UInt) + @test sprint(show, typeof(g)) == "Automorphism{FreeGroup{Symbol},…}" + a = g*h b = h*g @test hash(a) != zero(UInt) @@ -106,22 +111,22 @@ # ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄ g = gens(A, 1) - x1, x2, x3, x4 = New.domain(g) - @test New.evaluate(g) == (x1*x2, x2, x3, x4) + x1, x2, x3, x4 = Groups.domain(g) + @test evaluate(g) == (x1*x2, x2, x3, x4) g = g*inv(gens(A, 4)) # ϱ₂₁ - @test New.evaluate(g) == (x1*x2, x1^-1, x3, x4) + @test evaluate(g) == (x1*x2, x1^-1, x3, x4) g = g*gens(A, 13) - @test New.evaluate(g) == (x2, x1^-1, x3, x4) + @test evaluate(g) == (x2, x1^-1, x3, x4) end @testset "Automorphisms: SAut(F₄)" begin N = 4 - G = New.SpecialAutomorphismGroup(New.FreeGroup(N)) + G = SpecialAutomorphismGroup(FreeGroup(N)) S = gens(G) - @test S isa Vector{<:New.FPGroupElement{<:New.AutomorphismGroup{<:New.FreeGroup}}} + @test S isa Vector{<:FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}} @test length(S) == 2*N*(N-1) @test length(unique(S)) == length(S) @@ -141,8 +146,8 @@ @testset "GroupsCore conformance" begin test_Group_interface(A) - g = A(rand(1:length(KnuthBendix.alphabet(A)), 10)) - h = A(rand(1:length(KnuthBendix.alphabet(A)), 10)) + g = A(rand(1:length(alphabet(A)), 10)) + h = A(rand(1:length(alphabet(A)), 10)) test_GroupElement_interface(g, h) end @@ -152,7 +157,7 @@ end # using Random # using GroupsCore # -# A = New.SpecialAutomorphismGroup(New.FreeGroup(4), maxrules=2000, ordering=KnuthBendix.RecursivePathOrder) +# A = New.SpecialAutomorphismGroup(FreeGroup(4), maxrules=2000, ordering=KnuthBendix.RecursivePathOrder) # # # for seed in 1:1000 # let seed = 68 @@ -163,22 +168,22 @@ end # @info "seed=$seed" g h # @time isone(g*inv(g)) # @time isone(inv(g)*g) -# @info "" length(New.word(New.normalform!(g*inv(g)))) length(New.word(New.normalform!(inv(g)*g))) +# @info "" length(word(New.normalform!(g*inv(g)))) length(word(New.normalform!(inv(g)*g))) # a = commutator(g, h, g) # b = conj(inv(g), h) * conj(conj(g, h), g) # -# @info length(New.word(a)) -# @info length(New.word(b)) +# @info length(word(a)) +# @info length(word(b)) # # w = a*inv(b) -# @info length(New.word(w)) +# @info length(word(w)) # New.normalform!(w) -# @info length(New.word(w)) +# @info length(word(w)) # # # # -# # @time ima = New.evaluate(a) -# # @time imb = New.evaluate(b) +# # @time ima = evaluate(a) +# # @time imb = evaluate(b) # # @info "" a b ima imb # # @time a == b # end 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/benchmarks.jl b/test/benchmarks.jl index 0505cda..4a6db1f 100644 --- a/test/benchmarks.jl +++ b/test/benchmarks.jl @@ -6,7 +6,7 @@ using Groups.New function wl_ball(F; radius::Integer) g, state = iterate(F) - while length(New.word(g)) <= radius + while length(word(g)) <= radius res = iterate(F, state) isnothing(res) && break g, state = res @@ -20,7 +20,7 @@ end N = 4 @testset "iteration: FreeGroup" begin - FN = New.FreeGroup(N) + FN = FreeGroup(N) R = 8 let G = FN @@ -46,7 +46,7 @@ end @testset "iteration: SAut(F_n)" begin R = 4 - FN = New.FreeGroup(N) + FN = FreeGroup(N) SAutFN = New.SpecialAutomorphismGroup(FN) let G = SAutFN diff --git a/test/fp_groups.jl b/test/fp_groups.jl index 19fc9f4..89d83b5 100644 --- a/test/fp_groups.jl +++ b/test/fp_groups.jl @@ -1,44 +1,54 @@ @testset "FPGroups" begin A = Alphabet([:a, :A, :b, :B, :c, :C], [2,1,4,3,6,5]) - F = New.FreeGroup([:a, :b, :c], A) + @test FreeGroup(A) isa FreeGroup + @test sprint(show, FreeGroup(A)) == "free group on 3 generators" + + F = FreeGroup([:a, :b, :c], A) + @test sprint(show, F) == "free group on 3 generators" a,b,c = gens(F) - @test c*b*a isa New.FPGroupElement + @test c*b*a isa FPGroupElement # quotient of F: - G = New.FPGroup(F, [a*b=>b*a, a*c=>c*a, b*c=>c*b]) + G = FPGroup(F, [a*b=>b*a, a*c=>c*a, b*c=>c*b]) - @test G isa New.FPGroup - @test rand(G) isa New.FPGroupElement + @test G isa FPGroup + @test sprint(show, G) == "⟨a, b, c | a*b => b*a, a*c => c*a, b*c => c*b⟩" + @test rand(G) isa FPGroupElement f = a*c*b - @test New.word(f) isa Word{UInt8} + @test word(f) isa Word{UInt8} aG,bG,cG = gens(G) - @test aG isa New.FPGroupElement + @test aG isa FPGroupElement @test_throws AssertionError aG == a - @test New.word(aG) == New.word(a) + @test word(aG) == word(a) g = aG*cG*bG @test_throws AssertionError f == g - @test New.word(f) == New.word(g) - @test New.word(g) == [1, 5, 3] - New.normalform!(g) - @test New.word(g) == [1, 3, 5] + @test word(f) == word(g) + @test word(g) == [1, 5, 3] + Groups.normalform!(g) + @test word(g) == [1, 3, 5] + + let g = aG*cG*bG + # test that we normalize g before printing + @test sprint(show, g) == "a*b*c" + end # quotient of G - H = New.FPGroup(G, [aG^2=>cG, bG*cG=>aG], maxrules=200) + H = FPGroup(G, [aG^2=>cG, bG*cG=>aG], maxrules=200) - h = H(New.word(g)) + h = H(word(g)) - @test h isa New.FPGroupElement + @test h isa FPGroupElement @test_throws AssertionError h == g @test_throws AssertionError h*g - New.normalform!(h) + Groups.normalform!(h) @test h == H([5]) @testset "GroupsCore conformance: H" begin diff --git a/test/free_groups.jl b/test/free_groups.jl index 181c789..ced86a8 100644 --- a/test/free_groups.jl +++ b/test/free_groups.jl @@ -1,12 +1,12 @@ -@testset "New.FreeGroup" begin +@testset "FreeGroup" begin A3 = Alphabet([:a, :b, :c, :A, :B, :C], [4,5,6,1,2,3]) - F3 = New.FreeGroup([:a, :b, :c], A3) - @test F3 isa New.FreeGroup + F3 = FreeGroup([:a, :b, :c], A3) + @test F3 isa FreeGroup @test gens(F3) isa Vector - @test eltype(F3) <: New.FPGroupElement{<:New.FreeGroup} + @test eltype(F3) <: FPGroupElement{<:FreeGroup} w = F3([1,2,3,4]) W = inv(w) @@ -15,7 +15,7 @@ @test isone(w*W) - @test New.alphabet(w) == A3 + @test alphabet(w) == A3 @testset "generic iteration" begin w, s = iterate(F3) @@ -43,7 +43,7 @@ @testset "wl_ball" begin function wl_ball(F; radius::Integer) g, state = iterate(F) - while length(New.word(g)) <= radius + while length(word(g)) <= radius res = iterate(F, state) isnothing(res) && break g, state = res @@ -55,11 +55,11 @@ E4 = wl_ball(F3, radius=4) @test length(E4) == 937 - @test New.word(last(E4)) == Word([6])^4 + @test word(last(E4)) == Word([6])^4 E8, t, _ = @timed wl_ball(F3, radius=8) @test length(E8) == 585937 - @test New.word(last(E8)) == Word([6])^8 + @test word(last(E8)) == Word([6])^8 @test t/10^9 < 1 end diff --git a/test/runtests.jl b/test/runtests.jl index c7633d5..e69bce8 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -2,43 +2,32 @@ using Test import AbstractAlgebra using Groups -include("symmetric.jl") -using LinearAlgebra +import KnuthBendix: Word + +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") - include("AutSigma_41.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)