mirror of
https://github.com/kalmarek/Groups.jl.git
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141 lines
4.7 KiB
Julia
141 lines
4.7 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 = 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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@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 = generators(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 = 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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@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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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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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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