fix tests
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ac4ee69fc6
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7d95338e33
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@ -8,72 +8,73 @@
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f = Groups.AutSymbol(:a, 1, Groups.FlipAut(2))
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@test isa(f, Groups.GSymbol)
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@test isa(f, Groups.AutSymbol)
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@test isa(Groups.perm_autsymbol(Int8.([1,2,3,4])), Groups.AutSymbol)
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@test isa(Groups.rmul_autsymbol(1,2), Groups.AutSymbol)
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@test isa(Groups.lmul_autsymbol(3,4), Groups.AutSymbol)
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@test isa(Groups.flip_autsymbol(3), Groups.AutSymbol)
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@test isa(Groups.AutSymbol(perm"(4)"), Groups.AutSymbol)
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@test isa(Groups.AutSymbol([2,3,4,1]), Groups.AutSymbol)
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@test isa(Groups.transvection_R(1,2), Groups.AutSymbol)
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@test isa(Groups.transvection_R(3,4), Groups.AutSymbol)
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@test isa(Groups.flip(3), Groups.AutSymbol)
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end
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a,b,c,d = gens(FreeGroup(4))
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D = NTuple{4,FreeGroupElem}([a,b,c,d])
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@testset "flip_autsymbol correctness" begin
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@test Groups.flip_autsymbol(1)(deepcopy(D)) == (a^-1, b,c,d)
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@test Groups.flip_autsymbol(2)(deepcopy(D)) == (a, b^-1,c,d)
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@test Groups.flip_autsymbol(3)(deepcopy(D)) == (a, b,c^-1,d)
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@test Groups.flip_autsymbol(4)(deepcopy(D)) == (a, b,c,d^-1)
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@test inv(Groups.flip_autsymbol(1))(deepcopy(D)) == (a^-1, b,c,d)
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@test inv(Groups.flip_autsymbol(2))(deepcopy(D)) == (a, b^-1,c,d)
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@test inv(Groups.flip_autsymbol(3))(deepcopy(D)) == (a, b,c^-1,d)
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@test inv(Groups.flip_autsymbol(4))(deepcopy(D)) == (a, b,c,d^-1)
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@testset "flip correctness" begin
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@test Groups.flip(1)(deepcopy(D)) == (a^-1, b,c,d)
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@test Groups.flip(2)(deepcopy(D)) == (a, b^-1,c,d)
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@test Groups.flip(3)(deepcopy(D)) == (a, b,c^-1,d)
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@test Groups.flip(4)(deepcopy(D)) == (a, b,c,d^-1)
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@test inv(Groups.flip(1))(deepcopy(D)) == (a^-1, b,c,d)
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@test inv(Groups.flip(2))(deepcopy(D)) == (a, b^-1,c,d)
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@test inv(Groups.flip(3))(deepcopy(D)) == (a, b,c^-1,d)
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@test inv(Groups.flip(4))(deepcopy(D)) == (a, b,c,d^-1)
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end
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@testset "perm_autsymbol correctness" begin
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σ = Groups.perm_autsymbol([1,2,3,4])
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@testset "perm correctness" begin
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σ = Groups.AutSymbol(perm"(4)")
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@test σ(deepcopy(D)) == deepcopy(D)
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@test inv(σ)(deepcopy(D)) == deepcopy(D)
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σ = Groups.perm_autsymbol([2,3,4,1])
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σ = Groups.AutSymbol(perm"(1,2,3,4)")
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@test σ(deepcopy(D)) == (b, c, d, a)
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@test inv(σ)(deepcopy(D)) == (d, a, b, c)
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σ = Groups.perm_autsymbol([2,1,4,3])
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σ = Groups.AutSymbol(perm"(1,2)(4,3)")
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@test σ(deepcopy(D)) == (b, a, d, c)
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@test inv(σ)(deepcopy(D)) == (b, a, d, c)
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σ = Groups.perm_autsymbol([2,3,1,4])
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σ = Groups.AutSymbol(perm"(1,2,3)(4)")
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@test σ(deepcopy(D)) == (b, c, a, d)
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@test inv(σ)(deepcopy(D)) == (c, a, b, d)
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end
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@testset "rmul/lmul_autsymbol correctness" begin
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@testset "rmul/transvection_R correctness" begin
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i,j = 1,2
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r = Groups.rmul_autsymbol(i,j)
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l = Groups.lmul_autsymbol(i,j)
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r = Groups.transvection_R(i,j)
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l = Groups.transvection_L(i,j)
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@test r(deepcopy(D)) == (a*b, b, c, d)
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@test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d)
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@test l(deepcopy(D)) == (b*a, b, c, d)
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@test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d)
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i,j = 3,1
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r = Groups.rmul_autsymbol(i,j)
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l = Groups.lmul_autsymbol(i,j)
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r = Groups.transvection_R(i,j)
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l = Groups.transvection_L(i,j)
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@test r(deepcopy(D)) == (a, b, c*a, d)
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@test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d)
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@test l(deepcopy(D)) == (a, b, a*c, d)
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@test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d)
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i,j = 4,3
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r = Groups.rmul_autsymbol(i,j)
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l = Groups.lmul_autsymbol(i,j)
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r = Groups.transvection_R(i,j)
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l = Groups.transvection_L(i,j)
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@test r(deepcopy(D)) == (a, b, c, d*c)
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@test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1)
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@test l(deepcopy(D)) == (a, b, c, c*d)
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@test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d)
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i,j = 2,4
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r = Groups.rmul_autsymbol(i,j)
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l = Groups.lmul_autsymbol(i,j)
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r = Groups.transvection_R(i,j)
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l = Groups.transvection_L(i,j)
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@test r(deepcopy(D)) == (a, b*d, c, d)
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@test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d)
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@test l(deepcopy(D)) == (a, d*b, c, d)
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@ -94,40 +95,40 @@
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@test length(Groups.gens(A)) == 0
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A = AutGroup(FreeGroup(2))
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@test length(Groups.gens(A)) == 7
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gens = Groups.gens(A)
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Agens = Groups.gens(A)
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@test isa(A(Groups.rmul_autsymbol(1,2)), Automorphism)
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@test A(Groups.rmul_autsymbol(1,2)) in gens
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@test isa(A(Groups.transvection_R(1,2)), Automorphism)
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@test A(Groups.transvection_R(1,2)) in Agens
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@test isa(A(Groups.rmul_autsymbol(2,1)), Automorphism)
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@test A(Groups.rmul_autsymbol(2,1)) in gens
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@test isa(A(Groups.transvection_R(2,1)), Automorphism)
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@test A(Groups.transvection_R(2,1)) in Agens
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@test isa(A(Groups.lmul_autsymbol(1,2)), Automorphism)
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@test A(Groups.lmul_autsymbol(1,2)) in gens
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@test isa(A(Groups.transvection_R(1,2)), Automorphism)
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@test A(Groups.transvection_R(1,2)) in Agens
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@test isa(A(Groups.lmul_autsymbol(2,1)), Automorphism)
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@test A(Groups.lmul_autsymbol(2,1)) in gens
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@test isa(A(Groups.transvection_R(2,1)), Automorphism)
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@test A(Groups.transvection_R(2,1)) in Agens
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@test isa(A(Groups.flip_autsymbol(1)), Automorphism)
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@test A(Groups.flip_autsymbol(1)) in gens
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@test isa(A(Groups.flip(1)), Automorphism)
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@test A(Groups.flip(1)) in Agens
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@test isa(A(Groups.flip_autsymbol(2)), Automorphism)
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@test A(Groups.flip_autsymbol(2)) in gens
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@test isa(A(Groups.flip(2)), Automorphism)
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@test A(Groups.flip(2)) in Agens
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@test isa(A(Groups.perm_autsymbol([2,1])), Automorphism)
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@test A(Groups.perm_autsymbol([2,1])) in gens
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@test isa(A(Groups.AutSymbol(perm"(1,2)")), Automorphism)
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@test A(Groups.AutSymbol(perm"(1,2)")) in Agens
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end
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A = AutGroup(FreeGroup(4))
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@testset "eltary functions" begin
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f = Groups.perm_autsymbol([2,3,4,1])
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f = Groups.AutSymbol(perm"(1,2,3,4)")
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@test (Groups.change_pow(f, 2)).pow == 1
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@test (Groups.change_pow(f, -2)).pow == 1
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@test (inv(f)).pow == 1
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f = Groups.perm_autsymbol([2,1,4,3])
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f = Groups.AutSymbol(perm"(1,2)(3,4)")
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@test isa(inv(f), Groups.AutSymbol)
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@test_throws MethodError f*f
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@ -136,14 +137,15 @@
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end
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@testset "reductions/arithmetic" begin
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f = Groups.perm_autsymbol([2,3,4,1])
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f = Groups.AutSymbol(perm"(1,2,3,4)")
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f² = Groups.r_multiply(A(f), [f], reduced=false)
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@test Groups.simplifyperms!(f²) == false
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f² = append!(A(f), [f])
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@test Groups.simplifyperms!(Bool, f²) == false
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@test f²^2 == one(A)
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@test !isone(f²)
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a = A(Groups.rmul_autsymbol(1,2))*Groups.flip_autsymbol(2)
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b = Groups.flip_autsymbol(2)*A(inv(Groups.rmul_autsymbol(1,2)))
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a = A(Groups.transvection_L(1,2))*Groups.flip(2)
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b = Groups.flip(2)*A(inv(Groups.transvection_L(1,2)))
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@test a*b == b*a
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@test a^3 * b^3 == one(A)
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g,h = Groups.gens(A)[[1,8]] # (g, h) = (ϱ₁₂, ϱ₃₂)
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@ -164,27 +166,22 @@
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# Not so simple arithmetic: applying starting on the left:
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# ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄
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g = A(Groups.rmul_autsymbol(1,2))
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g = A(Groups.transvection_R(1,2))
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x1, x2, x3, x4 = Groups.domain(A)
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@test g(Groups.domain(A)) == (x1*x2, x2, x3, x4)
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g = g*inv(A(Groups.rmul_autsymbol(2,1)))
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g = g*inv(A(Groups.transvection_R(2,1)))
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@test g(Groups.domain(A)) == (x1*x2, x1^-1, x3, x4)
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g = g*A(Groups.lmul_autsymbol(1,2))
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g = g*A(Groups.transvection_L(1,2))
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@test g(Groups.domain(A)) == (x2, x1^-1, x3, x4)
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g = g*A(Groups.flip_autsymbol(2))
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g = g*A(Groups.flip(2))
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@test g(Groups.domain(A)) == (x2, x1, x3, x4)
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@test g(Groups.domain(A)) == A(Groups.perm_autsymbol([2,1,3,4]))(Groups.domain(A))
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@test g(Groups.domain(A)) == A(Groups.AutSymbol(perm"(1,2)(4)"))(Groups.domain(A))
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@test g == A(Groups.perm_autsymbol([2,1,3,4]))
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@test g == A(Groups.AutSymbol(perm"(1,2)(4)"))
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g_im = g(Groups.domain(A))
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@test length(g_im[1]) == 5
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@test length(g_im[2]) == 3
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@test length(g_im[3]) == 1
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@test length(g_im[4]) == 1
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@test length.(Groups.reduce!.(g_im)) == (1,1,1,1)
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@test length.(g_im) == (1,1,1,1)
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end
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@testset "specific Aut(F4) tests" begin
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@ -219,8 +216,8 @@
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M = Matrix{Int}(I, N, N)
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M[1,2] = 1
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ϱ₁₂ = G(Groups.rmul_autsymbol(1,2))
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λ₁₂ = G(Groups.rmul_autsymbol(1,2))
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ϱ₁₂ = G(Groups.transvection_R(1,2))
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λ₁₂ = G(Groups.transvection_R(1,2))
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@test Groups.linear_repr(ϱ₁₂) == M
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@test Groups.linear_repr(λ₁₂) == M
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@ -235,14 +232,14 @@
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M = Matrix{Int}(I, N, N)
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M[2,2] = -1
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ε₂ = G(Groups.flip_autsymbol(2))
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ε₂ = G(Groups.flip(2))
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@test Groups.linear_repr(ε₂) == M
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@test Groups.linear_repr(ε₂^2) == Matrix{Int}(I, N, N)
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M = [0 1 0; 0 0 1; 1 0 0]
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σ = G(Groups.perm_autsymbol([2,3,1]))
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σ = G(Groups.AutSymbol(perm"(1,2,3)"))
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@test Groups.linear_repr(σ) == M
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@test Groups.linear_repr(σ^3) == Matrix{Int}(I, 3, 3)
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@test Groups.linear_repr(σ)^3 == Matrix{Int}(I, 3, 3)
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@ -1,15 +1,18 @@
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@testset "FPGroups definitions" begin
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F = FreeGroup(["a", "b", "c"])
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a,b,c = gens(F)
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a,b,c = Groups.gens(F)
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R = [a^2, a*b*a, c*b*a]
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@test F/R isa FPGroup
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@test F isa FreeGroup
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G = F/R
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A,B,C = gens(G)
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A,B,C = Groups.gens(G)
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@test A^2 == one(G)
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@test A*B*A*A == A
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@test A*A*B*A == B*A
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@test Groups.reduce!(A^2) == one(G)
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@test Groups.reduce!(A*B*A*A) == A
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@test Groups.reduce!(A*A*B*A) == A
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@test Groups.freepreimage(G) == F
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@test Groups.freepreimage(B^2) == b^2
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@test G/[B^2, C*B*C] isa FPGroup
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end
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@ -55,23 +55,18 @@ end
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@testset "internal arithmetic" begin
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@test Vector{Groups.FreeGroupElem}([s,t]) == [Groups.GroupWord(s), Groups.GroupWord(t)]
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@test (s*s).symbols == (s^2).symbols
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@test hash([t^1,s^1]) == hash([t^2*inv(t),s*inv(s)*s])
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t_symb = Groups.FreeSymbol(:t)
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tt = deepcopy(t)
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@test string(Groups.r_multiply!(tt,[inv(t_symb)]; reduced=true)) ==
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"(id)"
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@test string(Groups.rmul!(tt, tt, inv(t_symb))) == "(id)"
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tt = deepcopy(t)
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@test string(Groups.r_multiply!(tt,[inv(t_symb)]; reduced=false)) ==
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"t*t^-1"
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@test string(append!(tt, [inv(t_symb)])) == "t*t^-1"
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tt = deepcopy(t)
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@test string(Groups.l_multiply!(tt,[inv(t_symb)]; reduced=true)) ==
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"(id)"
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@test string(Groups.lmul!(tt, tt, inv(t_symb))) == "(id)"
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tt = deepcopy(t)
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@test string(Groups.l_multiply!(tt,[inv(t_symb)]; reduced=false)) ==
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"t^-1*t"
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@test string(prepend!(tt, [inv(t_symb)])) == "t^-1*t"
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end
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@testset "reductions" begin
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@ -79,7 +74,7 @@ end
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@test length((one(G)*one(G)).symbols) == 0
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@test one(G) == one(G)*one(G)
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w = deepcopy(s)
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push!(w.symbols, (s^-1).symbols[1])
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push!(Groups.syllables(w), (s^-1).symbols[1])
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@test Groups.reduce!(w) == one(parent(w))
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o = (t*s)^3
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@test o == t*s*t*s*t*s
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@ -116,23 +111,23 @@ end
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@test Groups.issubsymbol(inv(b), Groups.change_pow(b,-2)) == true
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c = s*t*s^-1*t^-1
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@test findfirst(c, s^-1*t^-1) == 3
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@test findnext(c*s^-1, s^-1*t^-1,3) == 3
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@test findnext(c*s^-1*t^-1, s^-1*t^-1,4) == 5
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@test findfirst(c*t, c) == 0
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@test findfirst(s^-1*t^-1, c) == 3
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@test findnext(s^-1*t^-1, c*s^-1,3) == 3
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@test findnext(s^-1*t^-1, c*s^-1*t^-1,4) == 5
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@test findfirst(c, c*t) === nothing
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w = s*t*s^-1
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subst = Dict{FreeGroupElem, FreeGroupElem}(w => s^1, s*t^-1 => t^4)
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@test Groups.replace(c, 1, s*t, one(G)) == s^-1*t^-1
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@test Groups.replace(c, 1, w, subst[w]) == s*t^-1
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@test Groups.replace(s*c*t^-1, 1, w, subst[w]) == s^2*t^-2
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@test Groups.replace(t*c*t, 2, w, subst[w]) == t*s
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@test Groups.replace_all(s*c*s*c*s, subst) == s*t^4*s*t^4*s
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@test Groups.replace(c, s*t=>one(G)) == s^-1*t^-1
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@test Groups.replace(c, w=>subst[w]) == s*t^-1
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@test Groups.replace(s*c*t^-1, w=>subst[w]) == s^2*t^-2
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@test Groups.replace(t*c*t, w=>subst[w]) == t*s
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@test Groups.replace(s*c*s*c*s, subst) == s*t^4*s*t^4*s
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G = FreeGroup(["x", "y"])
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x,y = gens(G)
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@test Groups.replace(x*y^9, 2, y^2, y) == x*y^8
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@test Groups.replace(x^3, 1, x^2, y) == x*y
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@test Groups.replace(y*x^3*y, 2, x^2, y) == y*x*y^2
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@test Groups.replace(x*y^9, y^2=>y) == x*y^5
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@test Groups.replace(x^3, x^2=>y) == x*y
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@test Groups.replace(y*x^3*y, x^2=>y) == y*x*y^2
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end
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end
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