add tests for automorphisms and iteration benchmarks
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@ -20,6 +20,7 @@ julia = "1.3, 1.4, 1.5"
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[extras]
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Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
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[targets]
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test = ["Test"]
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test = ["Test", "BenchmarkTools"]
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@ -0,0 +1,184 @@
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@testset "Automorphisms" begin
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@testset "Transvections" begin
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@test New.Transvection(:ϱ, 1, 2) isa New.GSymbol
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@test New.Transvection(:ϱ, 1, 2) isa New.Transvection
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@test New.Transvection(:λ, 1, 2) isa New.GSymbol
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@test New.Transvection(:λ, 1, 2) isa New.Transvection
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t = New.Transvection(:ϱ, 1, 2)
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@test inv(t) isa New.GSymbol
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@test inv(t) isa New.Transvection
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@test t != inv(t)
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s = New.Transvection(:ϱ, 1, 2)
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@test t == s
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@test hash(t) == hash(s)
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s_ = New.Transvection(:ϱ, 1, 3)
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@test s_ != s
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@test hash(s_) != hash(s)
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@test New.gersten_alphabet(3) isa Alphabet
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A = New.gersten_alphabet(3)
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@test length(A) == 12
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end
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A4 = Alphabet(
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[:a,:A,:b,:B,:c,:C,:d,:D],
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[ 2, 1, 4, 3, 6, 5, 8, 7]
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)
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A5 = Alphabet(
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[:a,:A,:b,:B,:c,:C,:d,:D,:e,:E],
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[ 2, 1, 4, 3, 6, 5, 8, 7,10, 9]
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)
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F4 = New.FreeGroup([:a, :b, :c, :d], A4)
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A = New.SpecialAutomorphismGroup(F4, maxrules=1000)
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a,b,c,d = gens(F4)
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D = ntuple(i->gens(F4, i), 4)
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@testset "Transvection action correctness" begin
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i,j = 1,2
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r = New.Transvection(:ϱ,i,j)
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l = New.Transvection(:λ,i,j)
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(t::New.Transvection)(v::Tuple) = New.evaluate!(v, t, A4)
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@test r(deepcopy(D)) == (a*b, b, c, d)
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@test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d)
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@test l(deepcopy(D)) == (b*a, b, c, d)
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@test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d)
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i,j = 3,1
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r = New.Transvection(:ϱ,i,j)
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l = New.Transvection(:λ,i,j)
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@test r(deepcopy(D)) == (a, b, c*a, d)
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@test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d)
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@test l(deepcopy(D)) == (a, b, a*c, d)
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@test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d)
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i,j = 4,3
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r = New.Transvection(:ϱ,i,j)
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l = New.Transvection(:λ,i,j)
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@test r(deepcopy(D)) == (a, b, c, d*c)
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@test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1)
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@test l(deepcopy(D)) == (a, b, c, c*d)
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@test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d)
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i,j = 2,4
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r = New.Transvection(:ϱ,i,j)
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l = New.Transvection(:λ,i,j)
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@test r(deepcopy(D)) == (a, b*d, c, d)
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@test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d)
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@test l(deepcopy(D)) == (a, d*b, c, d)
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@test inv(l)(deepcopy(D)) == (a, d^-1*b,c, d)
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end
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@testset "AutomorphismGroup constructors" begin
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@test A isa New.AbstractFPGroup
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@test A isa New.AutomorphismGroup
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@test KnuthBendix.alphabet(A) isa Alphabet
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@test New.relations(A) isa Vector{<:Pair}
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end
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@testset "Automorphisms: hash and evaluate" begin
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@test New.domain(gens(A, 1)) == D
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g, h = gens(A, 1), gens(A, 8)
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@test New.evaluate(g*h) == New.evaluate(h*g)
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@test (g*h).savedhash == zero(UInt)
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a = g*h
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b = h*g
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@test hash(a) != zero(UInt)
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@test hash(a) == hash(b)
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@test a.savedhash == b.savedhash
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@test length(unique([a,b])) == 1
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@test length(unique([g*h, h*g])) == 1
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# Not so simple arithmetic: applying starting on the left:
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# ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄
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g = gens(A, 1)
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x1, x2, x3, x4 = New.domain(g)
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@test New.evaluate(g) == (x1*x2, x2, x3, x4)
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g = g*inv(gens(A, 4)) # ϱ₂₁
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@test New.evaluate(g) == (x1*x2, x1^-1, x3, x4)
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g = g*gens(A, 13)
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@test New.evaluate(g) == (x2, x1^-1, x3, x4)
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end
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@testset "Automorphisms: SAut(F₄)" begin
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N = 4
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G = New.SpecialAutomorphismGroup(New.FreeGroup(N))
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S = gens(G)
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@test S isa Vector{<:New.FPGroupElement{<:New.AutomorphismGroup{<:New.FreeGroup}}}
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@test length(S) == 2*N*(N-1)
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@test length(unique(S)) == length(S)
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S_sym = [S; inv.(S)]
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@test length(S_sym) == length(unique(S_sym))
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pushfirst!(S_sym, one(G))
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B_2 = [i*j for (i,j) in Base.product(S_sym, S_sym)]
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@test length(B_2) == 2401
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@test length(unique(B_2)) == 1777
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@test all(g->isone(inv(g)*g), B_2)
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@test all(g->isone(g*inv(g)), B_2)
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end
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@testset "GroupsCore conformance" begin
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test_Group_interface(A)
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g = A(rand(1:length(KnuthBendix.alphabet(A)), 10))
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h = A(rand(1:length(KnuthBendix.alphabet(A)), 10))
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test_GroupElement_interface(g, h)
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end
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end
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# using Random
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# using GroupsCore
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#
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# A = New.SpecialAutomorphismGroup(New.FreeGroup(4), maxrules=2000, ordering=KnuthBendix.RecursivePathOrder)
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#
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# # for seed in 1:1000
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# let seed = 68
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# N = 14
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# Random.seed!(seed)
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# g = A(rand(1:length(KnuthBendix.alphabet(A)), N))
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# h = A(rand(1:length(KnuthBendix.alphabet(A)), N))
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# @info "seed=$seed" g h
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# @time isone(g*inv(g))
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# @time isone(inv(g)*g)
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# @info "" length(New.word(New.normalform!(g*inv(g)))) length(New.word(New.normalform!(inv(g)*g)))
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# a = commutator(g, h, g)
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# b = conj(inv(g), h) * conj(conj(g, h), g)
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#
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# @info length(New.word(a))
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# @info length(New.word(b))
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#
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# w = a*inv(b)
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# @info length(New.word(w))
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# New.normalform!(w)
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# @info length(New.word(w))
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#
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#
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# #
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# # @time ima = New.evaluate(a)
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# # @time imb = New.evaluate(b)
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# # @info "" a b ima imb
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# # @time a == b
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# end
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@ -0,0 +1,72 @@
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using BenchmarkTools
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using Test
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using Groups
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using Groups.New
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function wl_ball(F; radius::Integer)
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g, state = iterate(F)
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while length(New.word(g)) <= radius
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res = iterate(F, state)
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isnothing(res) && break
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g, state = res
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end
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elts = collect(state.seen)
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elts = resize!(elts, length(elts)-1)
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return elts
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end
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@testset "Benchmarks" begin
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N = 4
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@testset "iteration: FreeGroup" begin
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FN = New.FreeGroup(N)
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R = 8
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let G = FN
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S = unique([gens(G); inv.(gens(G))])
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sizes1 = last(Groups.wlmetric_ball(S, radius=R, threading=false))
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sizes2 = last(Groups.wlmetric_ball(S, radius=R, threading=true))
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l = length(wl_ball(G, radius=R))
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@test sizes1 == sizes2
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@test last(sizes1) == l
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@info "Ball of radius $R in $(parent(first(S)))" sizes=sizes1
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@info "serial"
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@time Groups.wlmetric_ball(S, radius=R, threading=false)
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@info "threaded"
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@time Groups.wlmetric_ball(S, radius=R, threading=true)
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@info "iteration"
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@time wl_ball(G, radius=R)
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end
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end
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@testset "iteration: SAut(F_n)" begin
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R = 4
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FN = New.FreeGroup(N)
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SAutFN = New.SpecialAutomorphismGroup(FN)
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let G = SAutFN
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S = unique([gens(G); inv.(gens(G))])
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sizes1 = last(Groups.wlmetric_ball(S, radius=R, threading=false))
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sizes2 = last(Groups.wlmetric_ball(S, radius=R, threading=true))
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l = length(wl_ball(G, radius=R))
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@test sizes1 == sizes2
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@test last(sizes1) == l
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@info "Ball of radius $R in $(parent(first(S)))" sizes=sizes1
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@info "serial"
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@time Groups.wlmetric_ball(S, radius=R, threading=false)
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@info "threaded"
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@time Groups.wlmetric_ball(S, radius=R, threading=true)
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@info "iteration"
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@time wl_ball(G, radius=R)
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end
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end
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end
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@ -33,12 +33,11 @@
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return w
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end
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@time k = test_iteration(F3, 10)
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k = test_iteration(F3, 10)
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@test k == a*b^-1
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k = test_iteration(F3, 1000)
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@test k == (a^2)*c^2*a^-1
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@time k = test_iteration(F3, 1000)
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@test k == (a^2)*c^2*a^-1
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end
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@testset "wl_ball" begin
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@ -58,9 +57,10 @@
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@test length(E4) == 937
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@test New.word(last(E4)) == Word([6])^4
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@time E8 = wl_ball(F3, radius=8)
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E8, t, _ = @timed wl_ball(F3, radius=8)
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@test length(E8) == 585937
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@test New.word(last(E8)) == Word([6])^8
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@test t/10^9 < 1
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end
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@testset "GroupsCore conformance" begin
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@ -33,5 +33,7 @@ using LinearAlgebra
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include("free_groups.jl")
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include("fp_groups.jl")
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include("automorphisms.jl")
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include("benchmarks.jl")
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end
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end
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