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update AutGroup-tests
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@ -5,7 +5,7 @@
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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 = AutSymbol("a", 1, :(a()), v -> v)
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f = Groups.AutSymbol("a", 1, :(a()), v -> v)
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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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@ -83,58 +83,94 @@
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end
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@testset "AutGroup/AutGroupElem constructors" begin
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f = AutSymbol("a", 1, :(a()), v -> v)
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@test isa(GWord(f), GWord)
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@test isa(GWord(f), AutGroupElem)
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f = Groups.AutSymbol("a", 1, :(a()), v -> v)
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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)), Group)
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@test isa(AutGroup(FreeGroup(1)), FPGroup)
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@test isa(AutGroup(FreeGroup(3)), Nemo.Group)
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@test isa(AutGroup(FreeGroup(1)), Groups.FPGroup)
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A = AutGroup(FreeGroup(1))
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@test isa(f*f, AutWord)
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@test isa(f^2, AutWord)
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@test isa(f^-1, AutWord)
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@test isa(generators(A), Vector{AutGroupElem})
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@test length(generators(A)) == 1
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A = AutGroup(FreeGroup(1), special=true)
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@test length(generators(A)) == 0
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A = AutGroup(FreeGroup(2))
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@test length(generators(A)) == 7
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gens = generators(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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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 == generators(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, outer=true)
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S = generators(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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#
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# @testset "eltary functions" begin
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# f = perm_autsymbol([2,1,4,3])
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# @test isa(inv(f), AutSymbol)
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# @test isa(f^-1, AutWord)
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# @test f^-1 == GWord(inv(f))
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# @test inv(f) == f
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# end
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#
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# @testset "reductions/arithmetic" begin
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# f = perm_autsymbol([2,1,4,3])
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# f² = Groups.r_multiply(AutWord(f), [f], reduced=false)
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# @test Groups.simplify_perms!(f²) == false
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# @test f² == one(typeof(f*f))
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#
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# a = rmul_autsymbol(1,2)*flip_autsymbol(2)
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# b = flip_autsymbol(2)*inv(rmul_autsymbol(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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# end
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#
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# @testset "specific Aut(𝔽₄) tests" begin
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# N = 4
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# import Combinatorics.nthperm
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# SymmetricGroup(n) = [nthperm(collect(1:n), k) for k in 1:factorial(n)]
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# indexing = [[i,j] for i in 1:N for j in 1:N if i≠j]
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#
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# σs = [perm_autsymbol(perm) for perm in SymmetricGroup(N)[2:end]];
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# ϱs = [rmul_autsymbol(i,j) for (i,j) in indexing]
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# λs = [lmul_autsymbol(i,j) for (i,j) in indexing]
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# ɛs = [flip_autsymbol(i) for i in 1:N];
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#
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# S = vcat(ϱs, λs, σs, ɛs)
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# S = vcat(S, [inv(s) for s in S])
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# @test isa(S, Vector{AutSymbol})
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# @test length(S) == 102
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# @test length(unique(S)) == 75
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# S₁ = [GWord(s) for s in unique(S)]
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# @test isa(S₁, Vector{AutWord})
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# p = prod(S₁)
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# @test length(p) == 53
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# end
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end
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