72 lines
1.8 KiB
Julia
72 lines
1.8 KiB
Julia
function test_homomorphism(hom)
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F = hom.source
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@test isone(hom(one(F)))
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@test all(inv(hom(g)) == hom(inv(g)) for g in gens(F))
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@test all(isone(hom(g) * hom(inv(g))) for g in gens(F))
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@test all(hom(g * h) == hom(g) * hom(h) for g in gens(F) for h in gens(F))
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@test all(
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hom(inv(g * h)) == inv(hom(g * h)) == hom(inv(h)) * hom(inv(g)) for
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g in gens(F) for h in gens(F)
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)
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end
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@testset "Homomorphisms" begin
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F₂ = FreeGroup(2)
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g,h = gens(F₂)
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ℤ² = FPGroup(F₂, [g*h => h*g])
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let hom = Groups.Homomorphism((i, G, H) -> Groups.word_type(H)([i]), F₂, ℤ²)
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@test hom(word(g)) == word(g)
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@test hom(word(g*h*inv(g))) == [1,3,2]
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@test hom(g*h*inv(g)) == hom(h)
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@test isone(hom(g*h*inv(g)*inv(h)))
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@test contains(sprint(print, hom), "Homomorphism")
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test_homomorphism(hom)
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end
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SAutF3 = SpecialAutomorphismGroup(FreeGroup(3))
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SL3Z = MatrixGroups.SpecialLinearGroup{3}(Int8)
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let hom = Groups.Homomorphism(
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Groups._abelianize,
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SAutF3,
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SL3Z,
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)
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A = alphabet(SAutF3)
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g = SAutF3([A[Groups.ϱ(1,2)]])
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h = SAutF3([A[Groups.λ(1,2)]])^-1
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@test !isone(g) && !isone(hom(g))
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@test !isone(h) && !isone(hom(h))
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@test !isone(g*h) && isone(hom(g*h))
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test_homomorphism(hom)
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end
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@testset "Correctness of autπ₁Σ → SpN" begin
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GENUS = 3
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π₁Σ = Groups.SurfaceGroup(GENUS, 0)
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autπ₁Σ = AutomorphismGroup(π₁Σ)
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SpN = MatrixGroups.SymplecticGroup{2GENUS}(Int8)
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hom = Groups.Homomorphism(
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Groups._abelianize,
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autπ₁Σ,
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SpN,
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check = false,
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)
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test_homomorphism(hom)
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end
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end
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