95 lines
2.5 KiB
Julia
95 lines
2.5 KiB
Julia
@testset "FPGroups" begin
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A = Alphabet([:a, :A, :b, :B, :c, :C], [2, 1, 4, 3, 6, 5])
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@test FreeGroup(A) isa FreeGroup
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@test sprint(show, FreeGroup(A)) == "free group on 3 generators"
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F = FreeGroup([:a, :b, :c], Groups.KnuthBendix.LenLex(A))
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@test sprint(show, F) == "free group on 3 generators"
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a, b, c = gens(F)
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@test c * b * a isa FPGroupElement
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# quotient of F:
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G = FPGroup(F, [a * b => b * a, a * c => c * a, b * c => c * b])
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@test G isa FPGroup
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@test sprint(show, G) ==
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"⟨ a b c | \n\t a*b => b*a a*c => c*a b*c => c*b ⟩"
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@test rand(G) isa FPGroupElement
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f = a * c * b
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@test word(f) isa Word{UInt8}
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aG, bG, cG = gens(G)
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@test aG isa FPGroupElement
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@test_throws AssertionError aG == a
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@test word(aG) == word(a)
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g = aG * cG * bG
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@test_throws AssertionError f == g
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@test word(f) == word(g)
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@test word(g) == [1, 5, 3]
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Groups.normalform!(g)
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@test word(g) == [1, 3, 5]
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let g = aG * cG * bG
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# test that we normalize g before printing
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@test sprint(show, g) == "a*b*c"
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end
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# quotient of G
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H = FPGroup(G, [aG^2 => cG, bG * cG => aG]; max_rules = 200)
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h = H(word(g))
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@test h isa FPGroupElement
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@test_throws AssertionError h == g
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@test_throws MethodError h * g
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H′ = FPGroup(G, [aG^2 => cG, bG * cG => aG]; max_rules = 200)
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@test_throws AssertionError one(H) == one(H′)
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Groups.normalform!(h)
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@test h == H([5])
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@test_logs (
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:warn,
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"using generic isfiniteorder(::AbstractFPGroupElement): the returned `false` might be wrong",
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) isfiniteorder(h)
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@test_logs (
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:warn,
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"using generic isfinite(::AbstractFPGroup): the returned `false` might be wrong",
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) isfinite(H)
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Logging.with_logger(Logging.NullLogger()) do
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@testset "GroupsCore conformance: H" begin
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test_Group_interface(H)
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test_GroupElement_interface(rand(H, 2)...)
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end
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end
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@testset "hash/normalform #28" begin
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function cyclic_group(n::Integer)
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A = Alphabet([:a, :A], [2, 1])
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F = FreeGroup(A)
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a, = Groups.gens(F)
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e = one(F)
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Cₙ = FPGroup(F, [a^n => e])
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return Cₙ
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end
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n = 15
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G = cyclic_group(n)
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ball, sizes = Groups.wlmetric_ball(gens(G); radius = n)
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@test first(sizes) == 2
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@test last(sizes) == n
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@test Set(ball) == Set([first(gens(G))^i for i in 0:n-1])
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end
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end
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