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Groups.jl/test/AutSigma3.jl

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