90 lines
2.4 KiB
Julia
90 lines
2.4 KiB
Julia
@testset "DirectPowers" begin
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×(a,b) = Groups.DirectPower(a,b)
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@testset "Constructors" begin
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G = SymmetricGroup(3)
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@test Groups.DirectPowerGroup(G,2) isa AbstractAlgebra.Group
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@test G×G isa AbstractAlgebra.Group
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@test Groups.DirectPowerGroup(G,2) isa Groups.DirectPowerGroup{2, Generic.SymmetricGroup{Int64}}
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@test (G×G)×G == DirectPowerGroup(G, 3)
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@test (G×G)×G == (G×G)×G
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GG = DirectPowerGroup(G,2)
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@test one(G×G) isa GroupElem
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@test (G×G)((one(G), one(G))) isa GroupElem
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@test (G×G)([one(G), one(G)]) isa GroupElem
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@test Groups.DirectPowerGroupElem((one(G), one(G))) == one(G×G)
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@test GG(one(G), one(G)) == one(G×G)
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g = perm"(1,2,3)"
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@test GG(g, g^2) isa GroupElem
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@test GG(g, g^2) isa Groups.DirectPowerGroupElem{2, Generic.Perm{Int64}}
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h = GG(g,g^2)
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@test h == GG(h)
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@test GG(g, g^2) isa GroupElem
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@test GG(g, g^2) isa Groups.DirectPowerGroupElem
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@test_throws MethodError GG(g,g,g)
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@test GG(g,g^2) == h
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@test h[1] == g
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@test h[2] == g^2
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h = GG(g, one(G))
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@test h == GG(g, one(G))
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end
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@testset "Basic arithmetic" begin
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G = SymmetricGroup(3)
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GG = G×G
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i = perm"(1,3)"
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g = perm"(1,2,3)"
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h = GG(g,g^2)
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k = GG(g^3, g^2)
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@test h^2 == GG(g^2,g)
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@test h^6 == one(GG)
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@test h*h == h^2
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@test h*k == GG(g,g)
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@test h*inv(h) == one(G×G)
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w = GG(g,i)*GG(i,g)
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@test w == GG(perm"(1,2)(3)", perm"(2,3)")
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@test w == inv(w)
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@test w^2 == w*w == one(GG)
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end
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@testset "elem/parent_types" begin
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G = SymmetricGroup(3)
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g = perm"(1,2,3)"
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@test elem_type(G×G) == DirectPowerGroupElem{2, elem_type(G)}
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@test elem_type(G×G×G) == DirectPowerGroupElem{3, elem_type(G)}
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@test parent_type(typeof((G×G)(g,g^2))) == Groups.DirectPowerGroup{2, typeof(G)}
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@test parent(DirectPowerGroupElem((g,g^2,g^3))) == DirectPowerGroup(G,3)
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end
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@testset "Misc" begin
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G = SymmetricGroup(3)
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GG = Groups.DirectPowerGroup(G,3)
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@test order(GG) == 216
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@test isa(collect(GG), Vector{Groups.DirectPowerGroupElem{3, elem_type(G)}})
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elts = vec(collect(GG))
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@test length(elts) == 216
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@test all([g*inv(g) == one(GG) for g in elts])
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@test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)
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end
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end
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