110 lines
3.2 KiB
Julia
110 lines
3.2 KiB
Julia
@testset "WreathProducts" begin
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S_3 = PermutationGroup(3)
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R, x = PolynomialRing(QQ, "x")
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F, a = NumberField(x^2 + 1, "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), AbstractAlgebra.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{AddGrp{Generic.ResField{Generic.Poly{Rational{BigInt}}}}, Int64})
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aa = Groups.DirectProductGroupElem([a^0 ,a, a^2])
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@test isa(Groups.WreathProductElem(aa, b), AbstractAlgebra.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{AddGrpElem{Generic.ResF{Generic.Poly{Rational{BigInt}}}}, Int64})
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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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@test B3([a^0 ,a, a^2], perm"(1,2,3)") isa WreathProductElem
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@test B3([a^0 ,a, a^2], perm"(1,2,3)") == B3(aa, b)
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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{AddGrpElem{elem_type(F)}, Int}
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@test parent_type(typeof(B3())) == Groups.WreathProduct{parent_type(typeof(B3.N.group())), Int}
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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 "Basic operations on WreathProductElem" begin
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aa = Groups.DirectProductGroupElem([a^0 ,a, a^2])
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B3 = Groups.WreathProduct(F, 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 == DirectProductGroupElem(AddGrpElem.(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.n[1] = parent(g.n[1])(a)
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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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g.n[1] = a
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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(GF(3), PermutationGroup(4))
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x = B4([0,1,2,0], perm"(1,2,3)(4)")
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@test inv(x) == B4([1,0,2,0], perm"(1,3,2)(4)")
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y = B4([1,0,1,2], perm"(1,4)(2,3)")
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@test inv(y) == B4([1,2,0,2], perm"(1,4)(2,3)")
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@test x*y == B4([0,2,0,2], perm"(1,3,4)(2)")
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@test y*x == B4([1,2,2,2], perm"(1,4,2)(3)")
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@test inv(x)*y == B4([2,1,2,2], perm"(1,2,4)(3)")
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@test y*inv(x) == B4([1,2,1,0], perm"(1,4,3)(2)")
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end
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@testset "Misc" begin
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B3 = Groups.WreathProduct(GF(3), S_3)
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@test order(B3) == 3^3*6
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B3 = Groups.WreathProduct(MultiplicativeGroup(GF(3)), S_3)
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@test order(B3) == 2^3*6
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Wr = WreathProduct(PermutationGroup(2),PermutationGroup(4))
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@test isa([elements(Wr)...], Vector{Groups.WreathProductElem{Generic.perm{Int}, Int}})
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@test order(Wr) == 2^4*factorial(4)
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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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