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126 lines
3.9 KiB
Julia
126 lines
3.9 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, AbstractAlgebra.Generic.PermGroup{Int}, 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, AbstractAlgebra.Generic.perm{Int}, 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(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), 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, perm{Int}, Int}
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@test parent_type(typeof(B3())) == Groups.WreathProduct{3, parent_type(typeof(B3.N.group())), Int}
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@test parent(B3()) == Groups.WreathProduct(S_2,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.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(AdditiveGroup(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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@test (x*y)^6 == ((x*y)^2)^3
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end
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@testset "Iteration" begin
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B3_a = Groups.WreathProduct(AdditiveGroup(GF(3)), S_3)
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@test order(B3_a) == 3^3*6
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@test collect(B3_a) isa Vector{
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WreathProductElem{3, AddGrpElem{AbstractAlgebra.gfelem{Int}}, Int}}
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B3_m = Groups.WreathProduct(MultiplicativeGroup(GF(3)), S_3)
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@test order(B3_m) == 2^3*6
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@test collect(B3_m) isa Vector{
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WreathProductElem{3, MltGrpElem{AbstractAlgebra.gfelem{Int}}, Int}}
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@test length(Set([B3_a, B3_m, B3_a])) == 2
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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}, 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) == 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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@testset "Misc" begin
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B3_a = Groups.WreathProduct(AdditiveGroup(GF(3)), S_3)
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@test string(B3_a) == "Wreath Product of The additive group of Finite field F_3 by Permutation group over 3 elements"
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@test string(B3_a(perm"(1,3)")) == "([0,0,0]≀(1,3))"
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B3_m = Groups.WreathProduct(MultiplicativeGroup(GF(3)), S_3)
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@test string(B3_m) == "Wreath Product of The multiplicative group of Finite field F_3 by Permutation group over 3 elements"
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@test string(B3_m(perm"(1,3)")) == "([1,1,1]≀(1,3))"
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end
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end
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