mirror of
https://github.com/kalmarek/Groups.jl.git
synced 2024-12-25 18:15:29 +01:00
186 lines
5.5 KiB
Julia
186 lines
5.5 KiB
Julia
@testset "Automorphisms" begin
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@testset "Transvections" begin
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@test Groups.Transvection(:ϱ, 1, 2) isa Groups.GSymbol
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@test Groups.Transvection(:ϱ, 1, 2) isa Groups.Transvection
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@test Groups.Transvection(:λ, 1, 2) isa Groups.GSymbol
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@test Groups.Transvection(:λ, 1, 2) isa Groups.Transvection
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t = Groups.Transvection(:ϱ, 1, 2)
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@test inv(t) isa Groups.GSymbol
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@test inv(t) isa Groups.Transvection
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@test t != inv(t)
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s = Groups.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_ = Groups.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 Groups.gersten_alphabet(3) isa Alphabet
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A = Groups.gersten_alphabet(3)
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@test length(A) == 12
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@test sprint(show, Groups.ϱ(1, 2)) == "ϱ₁.₂"
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@test sprint(show, Groups.λ(3, 2)) == "λ₃.₂"
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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 = FreeGroup([:a, :b, :c, :d], A4)
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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 = Groups.Transvection(:ϱ,i,j)
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l = Groups.Transvection(:λ,i,j)
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(t::Groups.Transvection)(v::Tuple) = Groups.evaluate!(v, t)
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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 = Groups.Transvection(:ϱ,i,j)
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l = Groups.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 = Groups.Transvection(:ϱ,i,j)
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l = Groups.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 = Groups.Transvection(:ϱ,i,j)
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l = Groups.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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A = SpecialAutomorphismGroup(F4, maxrules=1000)
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@testset "AutomorphismGroup constructors" begin
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@test A isa Groups.AbstractFPGroup
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@test A isa AutomorphismGroup
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@test alphabet(A) isa Alphabet
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@test Groups.relations(A) isa Vector{<:Pair}
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@test sprint(show, A) == "automorphism group of free group on 4 generators"
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end
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@testset "Automorphisms: hash and evaluate" begin
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@test Groups.domain(gens(A, 1)) == D
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g, h = gens(A, 1), gens(A, 8)
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@test evaluate(g*h) == evaluate(h*g)
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@test (g*h).savedhash == zero(UInt)
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@test sprint(show, typeof(g)) == "Automorphism{FreeGroup{Symbol},…}"
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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 = Groups.domain(g)
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@test evaluate(g) == (x1*x2, x2, x3, x4)
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g = g*inv(gens(A, 4)) # ϱ₂₁
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@test evaluate(g) == (x1*x2, x1^-1, x3, x4)
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g = g*gens(A, 13)
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@test 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 = SpecialAutomorphismGroup(FreeGroup(N))
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S = gens(G)
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@test S isa Vector{<:FPGroupElement{<:AutomorphismGroup{<: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 "Forward evaluate" begin
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N = 3
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F = FreeGroup(N)
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G = SpecialAutomorphismGroup(F)
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a = gens(G, 1) # ϱ₁₂
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f = gens(F)
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@test a(f[1]) == f[1]*f[2]
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@test all(a(f[i]) == f[i] for i in 2:length(f))
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S = let s = gens(G)
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[s; inv.(s)]
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end
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@test all(
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map(first(Groups.wlmetric_ball(S, radius=2))) do g
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lm = Groups.LettersMap(g)
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img = evaluate(g)
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fimg = [F(lm[first(word(s))]) for s in gens(F)]
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succeeded = all(img .== fimg)
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@assert succeeded "forward evaluation of $(word(g)) failed: \n img=$img\n fimg=$(tuple(fimg...))"
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succeeded
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end
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)
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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(alphabet(A)), 10))
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h = A(rand(1:length(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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