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60 lines
1.4 KiB
Julia
60 lines
1.4 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], 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) == "⟨a, b, c | 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], maxrules=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 AssertionError h*g
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Groups.normalform!(h)
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@test h == H([5])
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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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