99 lines
3.0 KiB
Julia
99 lines
3.0 KiB
Julia
@testset "WreathProducts" begin
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S_3 = PermutationGroup(3)
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S_2 = PermutationGroup(2)
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b = perm"(1,2,3)"
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a = perm"(1,2)"
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@testset "Constructors" begin
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@test Groups.WreathProduct(S_2, S_3) isa AbstractAlgebra.Group
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B3 = Groups.WreathProduct(S_2, S_3)
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@test B3 isa Groups.WreathProduct
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@test B3 isa WreathProduct{3, Generic.PermGroup{Int}, Generic.PermGroup{Int}}
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aa = Groups.DirectPowerGroupElem((a^0 ,a, a^2))
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@test Groups.WreathProductElem(aa, b) isa AbstractAlgebra.GroupElem
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x = Groups.WreathProductElem(aa, b)
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@test x isa Groups.WreathProductElem
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@test x isa
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Groups.WreathProductElem{3, Generic.Perm{Int}, Generic.Perm{Int}}
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@test B3.N == Groups.DirectPowerGroup(S_2, 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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w = B3(aa, b)
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@test B3(w) == w
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@test B3(b) == Groups.WreathProductElem(one(B3.N), b)
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@test B3(aa) == Groups.WreathProductElem(aa, one(S_3))
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@test B3((a^0 ,a, a^2), b) isa WreathProductElem
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@test B3((a^0 ,a, a^2), b) == B3(aa, b)
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end
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@testset "Types" begin
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B3 = Groups.WreathProduct(S_2, S_3)
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@test elem_type(B3) == Groups.WreathProductElem{3, Generic.Perm{Int}, Generic.Perm{Int}}
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@test parent_type(typeof(one(B3))) == Groups.WreathProduct{3, parent_type(typeof(one(B3.N.group))), Generic.PermGroup{Int}}
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@test parent(one(B3)) == Groups.WreathProduct(S_2,S_3)
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@test parent(one(B3)) == B3
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end
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@testset "Basic operations on WreathProductElem" begin
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aa = Groups.DirectPowerGroupElem((a^0 ,a, a^2))
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B3 = Groups.WreathProduct(S_2, 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 == DirectPowerGroupElem(aa.elts)
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h = deepcopy(g)
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@test h == g
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@test !(g === h)
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g = B3(Groups.DirectPowerGroupElem((a ,a, a^2)), g.p)
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@test g.n[1] == parent(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 "Group arithmetic" begin
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B4 = Groups.WreathProduct(PermutationGroup(3), PermutationGroup(4))
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id, a, b = perm"(3)", perm"(1,2)(3)", perm"(1,2,3)"
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x = B4((id,a,b,id), perm"(1,2,3)(4)")
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@test inv(x) == B4((inv(b),id, a,id), perm"(1,3,2)(4)")
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y = B4((a,id,a,b), perm"(1,4)(2,3)")
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@test inv(y) == B4((inv(b), a,id, a), perm"(1,4)(2,3)")
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@test x*y == B4((id,id,b*a,b), perm"(1,3,4)(2)")
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@test y*x == B4(( a, b, id,b), perm"(1,4,2)(3)")
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@test inv(x)*y == B4((inv(b)*a,a,a,b), perm"(1,2,4)(3)")
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@test y*inv(x) == B4((a,a,a,id), perm"(1,4,3)(2)")
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@test (x*y)^6 == ((x*y)^2)^3
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end
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@testset "Iteration" begin
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Wr = WreathProduct(PermutationGroup(2),PermutationGroup(4))
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elts = collect(Wr)
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@test elts isa Vector{Groups.WreathProductElem{4, Generic.Perm{Int}, Generic.Perm{Int}}}
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@test order(Wr) == 2^4*factorial(4)
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@test length(elts) == order(Wr)
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@test all((g*inv(g) == one(Wr) 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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