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more tests for AutGroup
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@ -262,7 +262,7 @@ end
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function show(io::IO, G::AutGroup)
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print(io, "Automorphism Group of $(G.objectGroup)\n")
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print(io, "Generated by $(join(G.gens, ","))")
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print(io, "Generated by $(gens(G))")
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end
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###############################################################################
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@ -31,11 +31,6 @@ function DirectPower(G::DirectPowerGroup{N}, H::Group) where N
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return DirectPowerGroup(G.group, N+1)
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end
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function DirectPower(R::AbstractAlgebra.Ring, n::Int)
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@warn "Creating DirectPower of the multilplicative group!"
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return DirectPowerGroup(MultiplicativeGroup(R), n)
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end
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struct DirectPowerGroupElem{N, T<:GroupElem} <: GroupElem
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elts::NTuple{N,T}
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end
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@ -188,7 +183,6 @@ end
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###############################################################################
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order(G::DirectPowerGroup{N}) where N = order(G.group)^N
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Base.length(G::DirectPowerGroup) = order(G)
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function iterate(G::DirectPowerGroup{N}) where N
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elts = collect(G.group)
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@ -212,3 +206,4 @@ function iterate(G::DirectPowerGroup{N}, state) where N
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end
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eltype(::Type{DirectPowerGroup{N, G}}) where {N, G} = DirectPowerGroupElem{N, elem_type(G)}
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Base.length(G::DirectPowerGroup) = order(G)
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@ -6,13 +6,17 @@
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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, 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.AutSymbol(perm"(4)"), Groups.AutSymbol)
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@test isa(Groups.AutSymbol(perm"(1,2,3,4)"), 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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@test f isa Groups.GSymbol
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@test f isa Groups.AutSymbol
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@test Groups.AutSymbol(perm"(4)") isa Groups.AutSymbol
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@test Groups.AutSymbol(perm"(1,2,3,4)") isa Groups.AutSymbol
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@test Groups.transvection_R(1,2) isa Groups.AutSymbol
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@test Groups.transvection_R(3,4) isa Groups.AutSymbol
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@test Groups.flip(3) isa Groups.AutSymbol
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@test Groups.id_autsymbol() isa Groups.AutSymbol
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@test inv(Groups.id_autsymbol()) isa Groups.AutSymbol
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@test inv(Groups.id_autsymbol()) == Groups.id_autsymbol()
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end
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a,b,c,d = gens(FreeGroup(4))
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@ -88,35 +92,44 @@
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@test isa(Automorphism{3}(f), Automorphism)
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@test isa(AutGroup(FreeGroup(3)), AbstractAlgebra.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(Groups.gens(A), Vector{Automorphism{1}})
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@test Groups.gens(A) isa Vector{Automorphism{1}}
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@test length(Groups.gens(A)) == 1
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@test length(Groups.gens(Aut(FreeGroup(1)))) == 1
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@test Groups.gens(A) == [A(Groups.flip(1))]
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A = AutGroup(FreeGroup(1), special=true)
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@test length(Groups.gens(A)) == 0
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@test isempty(Groups.gens(A))
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@test Groups.gens(SAut(FreeGroup(1))) == Automorphism{1}[]
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A = AutGroup(FreeGroup(2))
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@test length(Groups.gens(A)) == 7
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Agens = Groups.gens(A)
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@test A(first(Agens)) isa Automorphism
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@test isa(A(Groups.transvection_R(1,2)), Automorphism)
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@test A(Groups.transvection_R(1,2)) isa Automorphism
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@test A(Groups.transvection_R(1,2)) in Agens
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@test isa(A(Groups.transvection_R(2,1)), Automorphism)
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@test A(Groups.transvection_R(2,1)) isa Automorphism
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@test A(Groups.transvection_R(2,1)) in Agens
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@test isa(A(Groups.transvection_R(1,2)), Automorphism)
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@test A(Groups.transvection_R(1,2)) isa Automorphism
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@test A(Groups.transvection_R(1,2)) in Agens
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@test isa(A(Groups.transvection_R(2,1)), Automorphism)
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@test A(Groups.transvection_R(2,1)) isa Automorphism
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@test A(Groups.transvection_R(2,1)) in Agens
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@test isa(A(Groups.flip(1)), Automorphism)
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@test A(Groups.flip(1)) isa Automorphism
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@test A(Groups.flip(1)) in Agens
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@test isa(A(Groups.flip(2)), Automorphism)
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@test A(Groups.flip(2)) isa Automorphism
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@test A(Groups.flip(2)) in Agens
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@test isa(A(Groups.AutSymbol(perm"(1,2)")), Automorphism)
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@test A(Groups.AutSymbol(perm"(1,2)")) isa Automorphism
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@test A(Groups.AutSymbol(perm"(1,2)")) in Agens
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@test A(Groups.id_autsymbol()) isa Automorphism
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end
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A = AutGroup(FreeGroup(4))
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@ -144,8 +157,8 @@
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@test f²^2 == one(A)
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@test !isone(f²)
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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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a = A(Groups.λ(1,2))*Groups.ε(2)
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b = Groups.ε(2)*A(inv(Groups.λ(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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