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76 lines
2.1 KiB
Julia
76 lines
2.1 KiB
Julia
@testset "Aut(Σ₃.₀)" begin
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genus = 3
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π₁Σ = Groups.SurfaceGroup(genus, 0)
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Groups.PermRightAut(p::Perm) = Groups.PermRightAut(p.d)
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# Groups.PermLeftAut(p::Perm) = Groups.PermLeftAut(p.d)
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autπ₁Σ = let autπ₁Σ = AutomorphismGroup(π₁Σ)
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pauts = let p = perm"(1,3,5)(2,4,6)"
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[Groups.PermRightAut(p^i) for i in 0:2]
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end
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T = eltype(KnuthBendix.letters(alphabet(autπ₁Σ)))
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S = eltype(pauts)
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A = Alphabet(Union{T,S}[KnuthBendix.letters(alphabet(autπ₁Σ)); pauts])
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autG = AutomorphismGroup(
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π₁Σ,
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autπ₁Σ.gens,
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A,
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ntuple(i->inv(gens(π₁Σ, i)), 2Groups.genus(π₁Σ))
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)
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autG
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end
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Al = alphabet(autπ₁Σ)
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S = [gens(autπ₁Σ); inv.(gens(autπ₁Σ))]
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sautFn = let ltrs = KnuthBendix.letters(Al)
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parent(first(ltrs).autFn_word)
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end
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τ = Groups.rotation_element(sautFn)
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@testset "Twists" begin
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A = KnuthBendix.alphabet(sautFn)
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λ = Groups.ΡΛ(:λ, A, 2genus)
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ϱ = Groups.ΡΛ(:ϱ, A, 2genus)
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@test sautFn(Groups.Te_diagonal(λ, ϱ, 1)) ==
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conj(sautFn(Groups.Te_diagonal(λ, ϱ, 2)), τ)
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@test sautFn(Groups.Te_diagonal(λ, ϱ, 3)) == sautFn(Groups.Te(λ, ϱ, 3, 1))
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end
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z = let d = Groups.domain(τ)
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Groups.evaluate(τ^genus)
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end
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@test π₁Σ.(word.(z)) == Groups.domain(first(S))
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d = Groups.domain(first(S))
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p = perm"(1,3,5)(2,4,6)"
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@test Groups.evaluate!(deepcopy(d), τ) == d^inv(p)
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@test Groups.evaluate!(deepcopy(d), τ^2) == d^p
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E, sizes = Groups.wlmetric_ball(S, radius=3)
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@test sizes == [49, 1813, 62971]
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B2 = @view E[1:sizes[2]]
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σ = autπ₁Σ(Word([Al[Groups.PermRightAut(p)]]))
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@test conj(S[7], σ) == S[10]
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@test conj(S[7], σ^2) == S[11]
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@test conj(S[9], σ) == S[12]
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@test conj(S[9], σ^2) == S[8]
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@test conj(S[1], σ) == S[4]
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@test conj(S[1], σ^2) == S[5]
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@test conj(S[3], σ) == S[6]
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@test conj(S[3], σ^2) == S[2]
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B2ᶜ = [conj(b, σ) for b in B2]
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@test B2ᶜ != B2
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@test Set(B2ᶜ) == Set(B2)
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end
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