84 lines
2.3 KiB
Julia
84 lines
2.3 KiB
Julia
@testset "DirectProducts" begin
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using Nemo
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G = PermutationGroup(3)
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g = G([2,3,1])
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F, a = FiniteField(2,3,"a")
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@testset "Constructors" begin
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@test isa(Groups.DirectProductGroup(G,2), Nemo.Group)
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@test isa(G×G, Nemo.Group)
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@test isa(Groups.DirectProductGroup(G,2), Groups.DirectProductGroup{Nemo.PermGroup})
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GG = Groups.DirectProductGroup(G,2)
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@test GG == Groups.DirectProductGroup(G,2)
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@test Groups.DirectProductGroupElem([G(), G()]) == GG()
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@test GG(G(), G()) == GG()
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@test isa(GG([g, g^2]), GroupElem)
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@test isa(GG([g, g^2]), Groups.DirectProductGroupElem{Nemo.perm})
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h = GG([g,g^2])
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@test h == GG(h)
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@test isa(GG(g, g^2), GroupElem)
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@test isa(GG(g, g^2), Groups.DirectProductGroupElem)
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@test_throws String GG(g,g,g)
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@test GG(g,g^2) == h
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@test size(h) == (2,)
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@test h[1] == g
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@test h[2] == g^2
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h[2] = G()
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@test h == GG(g, G())
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end
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GG = Groups.DirectProductGroup(G,2)
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FF = Groups.DirectProductGroup(F,2)
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@testset "Types" begin
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@test elem_type(GG) == Groups.DirectProductGroupElem{elem_type(G)}
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@test elem_type(FF) == Groups.DirectProductGroupElem{elem_type(F)}
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@test parent_type(typeof(GG(g,g^2))) == Groups.DirectProductGroup{typeof(G)}
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@test parent_type(typeof(FF(a,a^2))) == Groups.DirectProductGroup{typeof(F)}
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@test isa(FF([0,1]), GroupElem)
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@test isa(FF([0,1]), Groups.DirectProductGroupElem)
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@test isa(FF([0,1]), Groups.DirectProductGroupElem{elem_type(F)})
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@test_throws MethodError FF(1,0)
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end
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@testset "Group arithmetic" begin
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g = G([2,3,1])
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h = GG([g,g^2])
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@test h^2 == GG(g^2,g)
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@test h^6 == GG()
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@test h*h == h^2
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@test h*inv(h) == GG()
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@test FF([0,a])*FF([a,1]) == FF(a,1+a)
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x, y = FF([1,a]), FF([a^2,1])
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@test x*y == FF([a^2+1, a+1])
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@test inv(x) == FF([1,a])
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end
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@testset "Misc" begin
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@test order(GG) == 36
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@test order(FF) == 64
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@test isa([elements(GG)...], Vector{Groups.DirectProductGroupElem{elem_type(G)}})
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elts = [elements(GG)...]
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@test length(elts) == 36
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@test all([g*inv(g) for g in elts] .== GG())
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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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