mirror of
https://github.com/kalmarek/Groups.jl.git
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86 lines
2.4 KiB
Julia
86 lines
2.4 KiB
Julia
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@testset "WreathProducts" begin
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S_3 = PermutationGroup(3)
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F, a = FiniteField(2,3,"a")
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b = S_3([2,3,1])
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@testset "Constructors" begin
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@test isa(Groups.WreathProduct(F, S_3), Nemo.Group)
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@test isa(Groups.WreathProduct(F, S_3), Groups.WreathProduct)
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@test isa(Groups.WreathProduct(F, S_3), Groups.WreathProduct{Nemo.FqNmodFiniteField})
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aa = Groups.DirectProductGroupElem([a^0 ,a, a^2])
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@test isa(Groups.WreathProductElem(aa, b), Nemo.GroupElem)
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@test isa(Groups.WreathProductElem(aa, b), Groups.WreathProductElem)
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@test isa(Groups.WreathProductElem(aa, b), Groups.WreathProductElem{typeof(a)})
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B3 = Groups.WreathProduct(F, S_3)
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@test B3.N == Groups.DirectProductGroup(F, 3)
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@test B3.P == S_3
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@test B3(aa, b) == Groups.WreathProductElem(aa, b)
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@test B3(b) == Groups.WreathProductElem(B3.N(), b)
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@test B3(aa) == Groups.WreathProductElem(aa, S_3())
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g = B3(aa, b)
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@test g.p == b
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@test g.n == aa
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h = deepcopy(g)
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@test hash(g) == hash(h)
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g.n[1] = a
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@test g.n[1] == a
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@test g != h
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@test hash(g) != hash(h)
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end
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@testset "Types" begin
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B3 = Groups.WreathProduct(F, S_3)
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@test elem_type(B3) == Groups.WreathProductElem{elem_type(F)}
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@test parent_type(typeof(B3())) == Groups.WreathProduct{parent_type(typeof(B3.N.group()))}
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@test parent(B3()) == Groups.WreathProduct(F,S_3)
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@test parent(B3()) == B3
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end
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@testset "Group arithmetic" begin
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B3 = Groups.WreathProduct(F, S_3)
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x = B3(B3.N([1,0,0]), B3.P([2,3,1]))
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y = B3(B3.N([0,1,1]), B3.P([2,1,3]))
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@test x*y == B3(B3.N([0,0,1]), B3.P([3,2,1]))
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@test y*x == B3(B3.N([0,0,1]), B3.P([1,3,2]))
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@test inv(x) == B3(B3.N([0,0,1]), B3.P([3,1,2]))
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@test inv(y) == B3(B3.N([1,0,1]), B3.P([2,1,3]))
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@test inv(x)*y == B3(B3.N([1,1,1]), B3.P([1,3,2]))
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@test y*inv(x) == B3(B3.N([0,1,0]), B3.P([3,2,1]))
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end
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@testset "Misc" begin
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B3 = Groups.WreathProduct(FiniteField(2,1,"a")[1], S_3)
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@test order(B3) == 48
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Wr = WreathProduct(PermutationGroup(2),S_3)
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@test isa([elements(Wr)...], Vector{Groups.WreathProductElem{Nemo.perm}})
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elts = [elements(Wr)...]
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@test length(elts) == order(Wr)
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@test all([g*inv(g) for g in elts] .== Wr())
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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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