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fix tests
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@ -1,73 +1,93 @@
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@testset "DirectProducts" begin
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@testset "DirectPowers" begin
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×(a,b) = Groups.pow(a,b)
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×(a,b) = Groups.DirectPower(a,b)
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@testset "Constructors" begin
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G = PermutationGroup(3)
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g = G([2,3,1])
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@test Groups.DirectProductGroup(G,2) isa AbstractAlgebra.Group
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@test Groups.DirectPowerGroup(G,2) isa AbstractAlgebra.Group
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@test G×G isa AbstractAlgebra.Group
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@test Groups.DirectProductGroup(G,2) isa Groups.DirectProductGroup{Generic.PermGroup{Int64}}
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@test Groups.DirectPowerGroup(G,2) isa Groups.DirectPowerGroup{2, Generic.PermGroup{Int64}}
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@test (G×G)×G == DirectProductGroup(G, 3)
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@test (G×G)×G == DirectPowerGroup(G, 3)
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@test (G×G)×G == (G×G)×G
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F = GF(13)
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FF = F×F
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@test FF×F == F×FF
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GG = DirectPowerGroup(G,2)
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@test (G×G)() isa GroupElem
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@test (G×G)((G(), G())) isa GroupElem
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@test (G×G)([G(), G()]) isa GroupElem
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GG = DirectProductGroup(G,2)
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@test Groups.DirectProductGroupElem([G(), G()]) == (G×G)()
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@test Groups.DirectPowerGroupElem((G(), G())) == (G×G)()
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@test GG(G(), G()) == (G×G)()
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@test GG([g, g^2]) isa GroupElem
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@test GG([g, g^2]) isa Groups.DirectProductGroupElem{Generic.perm{Int64}}
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g = perm"(1,2,3)"
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h = GG([g,g^2])
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@test GG(g, g^2) isa GroupElem
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@test GG(g, g^2) isa Groups.DirectPowerGroupElem{2, Generic.perm{Int64}}
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h = GG(g,g^2)
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@test h == GG(h)
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@test GG(g, g^2) isa GroupElem
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@test GG(g, g^2) isa Groups.DirectProductGroupElem
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@test GG(g, g^2) isa Groups.DirectPowerGroupElem
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@test_throws DomainError GG(g,g,g)
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@test_throws MethodError GG(g,g,g)
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@test GG(g,g^2) == h
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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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h = GG(g, G())
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@test h == GG(g, G())
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end
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@testset "Basic arithmetic" begin
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G = PermutationGroup(3)
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g = G([2,3,1])
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h = (G×G)([g,g^2])
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GG = G×G
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i = perm"(1,3)"
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g = perm"(1,2,3)"
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h = GG(g,g^2)
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k = GG(g^3, g^2)
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@test h^2 == (G×G)(g^2,g)
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@test h^6 == (G×G)()
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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*k == GG(g,g)
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@test h*inv(h) == (G×G)()
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w = GG(g,i)*GG(i,g)
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@test w == GG(perm"(1,2)(3)", perm"(2,3)")
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@test w == inv(w)
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@test w^2 == w*w == GG()
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end
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@testset "elem/parent_types" begin
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G = PermutationGroup(3)
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g = G([2,3,1])
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g = perm"(1,2,3)"
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@test elem_type(G×G) == DirectProductGroupElem{elem_type(G)}
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@test parent_type(typeof((G×G)(g,g^2))) == Groups.DirectProductGroup{typeof(G)}
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@test parent((G×G)(g,g^2)) == DirectProductGroup(G,2)
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@test elem_type(G×G) == DirectPowerGroupElem{2, elem_type(G)}
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@test elem_type(G×G×G) == DirectPowerGroupElem{3, elem_type(G)}
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@test parent_type(typeof((G×G)(g,g^2))) == Groups.DirectPowerGroup{2, typeof(G)}
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@test parent(DirectPowerGroupElem((g,g^2,g^3))) == DirectPowerGroup(G,3)
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F = AdditiveGroup(GF(13))
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@test elem_type(F×F) == DirectProductGroupElem{Groups.AddGrpElem{AbstractAlgebra.gfelem{Int}}}
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@test parent_type(typeof((F×F)(1,5))) == Groups.DirectProductGroup{Groups.AddGrp{AbstractAlgebra.GFField{Int}}}
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parent((F×F)(1,5)) == DirectProductGroup(F,2)
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@test elem_type(F×F) ==
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DirectPowerGroupElem{2, Groups.AddGrpElem{AbstractAlgebra.gfelem{Int}}}
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@test parent_type(typeof((F×F)(1,5))) ==
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Groups.DirectPowerGroup{2, Groups.AddGrp{AbstractAlgebra.GFField{Int}}}
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parent((F×F)(1,5)) == DirectPowerGroup(F,2)
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F = MultiplicativeGroup(GF(13))
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@test elem_type(F×F) ==
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DirectPowerGroupElem{2, Groups.MltGrpElem{AbstractAlgebra.gfelem{Int}}}
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@test parent_type(typeof((F×F)(1,5))) ==
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Groups.DirectPowerGroup{2, Groups.MltGrp{AbstractAlgebra.GFField{Int}}}
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parent((F×F)(1,5)) == DirectPowerGroup(F,2)
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end
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@testset "Additive/Multiplicative groups" begin
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@ -76,9 +96,6 @@
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F, a = NumberField(x^3 + x + 1, "a")
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G = PermutationGroup(3)
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GG = Groups.DirectProductGroup(G,2)
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FF = Groups.DirectProductGroup(F,2)
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@testset "MltGrp basic functionality" begin
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Gr = MltGrp(F)
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@test Gr(a) isa MltGrpElem
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@ -104,22 +121,22 @@
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R, x = PolynomialRing(QQ, "x")
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F, a = NumberField(x^3 + x + 1, "a")
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FF = Groups.DirectProductGroup(MltGrp(F),2)
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FF = Groups.DirectPowerGroup(MltGrp(F),2)
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@test FF([a,1]) isa GroupElem
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@test FF([a,1]) isa DirectProductGroupElem
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@test FF([a,1]) isa DirectProductGroupElem{MltGrpElem{elem_type(F)}}
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@test FF([a,1]) isa DirectPowerGroupElem
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@test FF([a,1]) isa DirectPowerGroupElem{2, MltGrpElem{elem_type(F)}}
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@test_throws DomainError FF(1,0)
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@test_throws DomainError FF([0,1])
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@test_throws DomainError FF([1,0])
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@test MltGrp(F) isa AbstractAlgebra.Group
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@test MltGrp(F) isa MultiplicativeGroup
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@test DirectProductGroup(MltGrp(F), 2) isa AbstractAlgebra.Group
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@test DirectProductGroup(MltGrp(F), 2) isa DirectProductGroup{MltGrp{typeof(F)}}
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@test DirectPowerGroup(MltGrp(F), 2) isa AbstractAlgebra.Group
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@test DirectPowerGroup(MltGrp(F), 2) isa DirectPowerGroup{2, MltGrp{typeof(F)}}
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F, a = NumberField(x^3 + x + 1, "a")
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FF = DirectProductGroup(MltGrp(F), 2)
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FF = DirectPowerGroup(MltGrp(F), 2)
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@test FF(a,a+1) == FF([a,a+1])
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@test FF([1,a+1])*FF([a,a]) == FF(a,a^2+a)
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@ -138,14 +155,14 @@
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# Additive Group
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@test AddGrp(F) isa AbstractAlgebra.Group
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@test AddGrp(F) isa AdditiveGroup
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@test DirectProductGroup(AddGrp(F), 2) isa AbstractAlgebra.Group
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@test DirectProductGroup(AddGrp(F), 2) isa DirectProductGroup{AddGrp{typeof(F)}}
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@test DirectPowerGroup(AddGrp(F), 2) isa AbstractAlgebra.Group
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@test DirectPowerGroup(AddGrp(F), 2) isa DirectPowerGroup{2, AddGrp{typeof(F)}}
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FF = DirectProductGroup(AdditiveGroup(F), 2)
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FF = DirectPowerGroup(AdditiveGroup(F), 2)
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@test FF([0,a]) isa AbstractAlgebra.GroupElem
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@test FF(F(0),a) isa DirectProductGroupElem
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@test FF(0,0) isa DirectProductGroupElem{AddGrpElem{elem_type(F)}}
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@test FF(F(0),a) isa DirectPowerGroupElem
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@test FF(0,0) isa DirectPowerGroupElem{2, AddGrpElem{elem_type(F)}}
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@test FF(F(1),a+1) == FF([1,a+1])
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@ -161,31 +178,31 @@
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@testset "Misc" begin
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F = GF(5)
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FF = DirectProductGroup(AdditiveGroup(F),2)
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FF = DirectPowerGroup(AdditiveGroup(F),2)
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@test order(FF) == 25
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elts = vec(collect(elements(FF)))
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elts = vec(collect(FF))
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@test length(elts) == 25
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@test all([g*inv(g) == FF() 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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FF = DirectProductGroup(MultiplicativeGroup(F), 3)
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FF = DirectPowerGroup(MultiplicativeGroup(F), 3)
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@test order(FF) == 64
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elts = vec(collect(elements(FF)))
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elts = vec(collect(FF))
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@test length(elts) == 64
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@test all([g*inv(g) == FF() 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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G = PermutationGroup(3)
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GG = Groups.DirectProductGroup(G,2)
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@test order(GG) == 36
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GG = Groups.DirectPowerGroup(G,3)
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@test order(GG) == 216
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@test isa([elements(GG)...], Vector{Groups.DirectProductGroupElem{elem_type(G)}})
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elts = vec(collect(elements(GG)))
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@test isa(collect(GG), Vector{Groups.DirectPowerGroupElem{3, elem_type(G)}})
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elts = vec(collect(GG))
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@test length(elts) == 36
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@test length(elts) == 216
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@test all([g*inv(g) == GG() 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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@ -1,104 +1,102 @@
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@testset "WreathProducts" begin
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S_3 = PermutationGroup(3)
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S_2 = PermutationGroup(2)
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b = S_3([2,3,1])
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a = S_2([2,1])
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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 isa(Groups.WreathProduct(S_2, S_3), AbstractAlgebra.Group)
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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{AbstractAlgebra.Generic.PermGroup{Int}, Int}
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@test B3 isa WreathProduct{3, AbstractAlgebra.Generic.PermGroup{Int}, Int}
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aa = Groups.DirectProductGroupElem([a^0 ,a, a^2])
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aa = Groups.DirectPowerGroupElem((a^0 ,a, a^2))
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@test isa(Groups.WreathProductElem(aa, b), AbstractAlgebra.GroupElem)
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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 Groups.WreathProductElem{AbstractAlgebra.Generic.perm{Int}, Int}
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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.DirectProductGroup(S_2, 3)
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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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@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), b) isa WreathProductElem
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@test B3([a^0 ,a, a^2], perm"(1,2,3)") == B3(aa, b)
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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{perm{Int}, Int}
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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{parent_type(typeof(B3.N.group())), 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.DirectProductGroupElem([a^0 ,a, a^2])
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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 == DirectProductGroupElem(aa.elts)
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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.n[1] = parent(g.n[1])(a)
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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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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(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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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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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 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 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 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 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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B3 = Groups.WreathProduct(AdditiveGroup(GF(3)), S_3)
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@test order(B3) == 3^3*6
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@test collect(B3) isa Vector{
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WreathProductElem{3, AddGrpElem{AbstractAlgebra.gfelem{Int}}, Int}}
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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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B3 = Groups.WreathProduct(MultiplicativeGroup(GF(3)), S_3)
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@test order(B3) == 2^3*6
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@test collect(B3) isa Vector{
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WreathProductElem{3, MltGrpElem{AbstractAlgebra.gfelem{Int}}, Int}}
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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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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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