186 lines
6.0 KiB
Julia
186 lines
6.0 KiB
Julia
@testset "Automorphisms" begin
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using Nemo
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G = PermutationGroup(4)
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@testset "AutSymbol" begin
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@test_throws MethodError Groups.AutSymbol("a")
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@test_throws MethodError Groups.AutSymbol("a", 1)
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f = Groups.AutSymbol("a", 1, :(a()))
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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(G([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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end
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a,b,c,d = Nemo.gens(FreeGroup(4))
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domain = [a,b,c,d]
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@testset "flip_autsymbol correctness" begin
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@test Groups.flip_autsymbol(1)(domain) == [a^-1, b,c,d]
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@test Groups.flip_autsymbol(2)(domain) == [a, b^-1,c,d]
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@test Groups.flip_autsymbol(3)(domain) == [a, b,c^-1,d]
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@test Groups.flip_autsymbol(4)(domain) == [a, b,c,d^-1]
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@test inv(Groups.flip_autsymbol(1))(domain) == [a^-1, b,c,d]
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@test inv(Groups.flip_autsymbol(2))(domain) == [a, b^-1,c,d]
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@test inv(Groups.flip_autsymbol(3))(domain) == [a, b,c^-1,d]
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@test inv(Groups.flip_autsymbol(4))(domain) == [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(G([1,2,3,4]))
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@test σ(domain) == domain
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@test inv(σ)(domain) == domain
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σ = Groups.perm_autsymbol(G([2,3,4,1]))
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@test σ(domain) == [b, c, d, a]
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@test inv(σ)(domain) == [d, a, b, c]
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σ = Groups.perm_autsymbol(G([2,1,4,3]))
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@test σ(domain) == [b, a, d, c]
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@test inv(σ)(domain) == [b, a, d, c]
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σ = Groups.perm_autsymbol(G([2,3,1,4]))
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@test σ(domain) == [b,c,a,d]
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@test inv(σ)(domain) == [c,a,b,d]
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end
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@testset "rmul/lmul_autsymbol 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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@test r(domain) == [a*b,b,c,d]
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@test inv(r)(domain) == [a*b^-1,b,c,d]
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@test l(domain) == [b*a,b,c,d]
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@test inv(l)(domain) == [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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@test r(domain) == [a,b,c*a,d]
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@test inv(r)(domain) == [a,b,c*a^-1,d]
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@test l(domain) == [a,b,a*c,d]
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@test inv(l)(domain) == [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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@test r(domain) == [a,b,c,d*c]
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@test inv(r)(domain) == [a,b,c,d*c^-1]
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@test l(domain) == [a,b,c,c*d]
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@test inv(l)(domain) == [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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@test r(domain) == [a,b*d,c,d]
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@test inv(r)(domain) == [a,b*d^-1,c,d]
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@test l(domain) == [a,d*b,c,d]
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@test inv(l)(domain) == [a,d^-1*b,c,d]
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end
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@testset "AutGroup/AutGroupElem constructors" begin
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f = Groups.AutSymbol("a", 1, :(a()))
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@test isa(AutGroupElem(f), Groups.GWord)
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@test isa(AutGroupElem(f), AutGroupElem)
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@test isa(AutGroup(FreeGroup(3)), Nemo.Group)
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@test isa(AutGroup(FreeGroup(1)), Groups.AbstractFPGroup)
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A = AutGroup(FreeGroup(1))
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@test isa(Nemo.gens(A), Vector{AutGroupElem})
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@test length(Nemo.gens(A)) == 1
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A = AutGroup(FreeGroup(1), special=true)
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@test length(Nemo.gens(A)) == 0
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A = AutGroup(FreeGroup(2))
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@test length(Nemo.gens(A)) == 7
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gens = Nemo.gens(A)
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@test isa(A(Groups.rmul_autsymbol(1,2)), AutGroupElem)
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@test A(Groups.rmul_autsymbol(1,2)) in gens
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@test isa(A(Groups.rmul_autsymbol(2,1)), AutGroupElem)
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@test A(Groups.rmul_autsymbol(2,1)) in gens
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@test isa(A(Groups.lmul_autsymbol(1,2)), AutGroupElem)
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@test A(Groups.lmul_autsymbol(1,2)) in gens
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@test isa(A(Groups.lmul_autsymbol(2,1)), AutGroupElem)
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@test A(Groups.lmul_autsymbol(2,1)) in gens
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@test isa(A(Groups.flip_autsymbol(1)), AutGroupElem)
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@test A(Groups.flip_autsymbol(1)) in gens
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@test isa(A(Groups.flip_autsymbol(2)), AutGroupElem)
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@test A(Groups.flip_autsymbol(2)) in gens
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@test isa(A(Groups.perm_autsymbol(PermutationGroup(2)([2,1]))),
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AutGroupElem)
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@test A(Groups.perm_autsymbol(PermutationGroup(2)([2,1]))) in gens
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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(G([2,3,4,1]))
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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(G([2,1,4,3]))
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@test isa(inv(f), Groups.AutSymbol)
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@test_throws DomainError f^-1
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@test_throws MethodError f*f
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@test A(f)^-1 == A(inv(f))
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end
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@testset "reductions/arithmetic" begin
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f = Groups.perm_autsymbol(G([2,3,4,1]))
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f² = Groups.r_multiply(A(f), [f], reduced=false)
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@test Groups.simplify_perms!(f²) == false
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@test f²^2 == A()
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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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@test a*b == b*a
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@test a^3 * b^3 == A()
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g,h = Nemo.gens(A)[[1,8]]
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domain = Nemo.gens(A.objectGroup)
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@test (g*h)(domain) == (h*g)(domain)
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@test (g*h).savedhash != (h*g).savedhash
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a = g*h
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b = h*g
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@test hash(a) == hash(b)
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@test a.savedhash == b.savedhash
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@test length(unique([a,b])) == 1
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@test length(unique([g*h, h*g])) == 1
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end
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@testset "specific Aut(F4) tests" begin
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N = 4
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G = AutGroup(FreeGroup(N))
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S = G.gens
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@test isa(S, Vector{Groups.AutSymbol})
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S = [G(s) for s in unique(S)]
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@test isa(S, Vector{AutGroupElem})
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@test S == Nemo.gens(G)
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@test length(S) == 51
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S_inv = [S..., [inv(s) for s in S]...]
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@test length(unique(S_inv)) == 75
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G = AutGroup(FreeGroup(N), special=true)
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S = Nemo.gens(G)
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S_inv = [G(), S..., [inv(s) for s in S]...]
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S_inv = unique(S_inv)
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B_2 = [i*j for (i,j) in Base.product(S_inv, S_inv)]
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@test length(B_2) == 2401
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@test length(unique(B_2)) == 1777
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end
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end
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