mirror of
https://github.com/kalmarek/Groups.jl.git
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210 lines
6.1 KiB
Julia
210 lines
6.1 KiB
Julia
@testset "DirectPowers" begin
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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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@test Groups.DirectPowerGroup(G,2) isa AbstractAlgebra.Group
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@test G×G isa AbstractAlgebra.Group
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@test Groups.DirectPowerGroup(G,2) isa Groups.DirectPowerGroup{2, Generic.PermGroup{Int64}}
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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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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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@test Groups.DirectPowerGroupElem((G(), G())) == (G×G)()
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@test GG(G(), G()) == (G×G)()
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g = perm"(1,2,3)"
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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.DirectPowerGroupElem
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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 = 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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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 == 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 = perm"(1,2,3)"
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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) ==
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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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R, x = PolynomialRing(QQ, "x")
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F, a = NumberField(x^3 + x + 1, "a")
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G = PermutationGroup(3)
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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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g = Gr(a)
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@test deepcopy(g) isa MltGrpElem
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@test inv(g) == Gr(a^-1)
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@test Gr() == Gr(1)
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@test inv(g)*g == Gr()
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end
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@testset "AddGrp basic functionality" begin
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Gr = AddGrp(F)
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@test Gr(a) isa AddGrpElem
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g = Gr(a)
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@test deepcopy(g) isa AddGrpElem
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@test inv(g) == Gr(-a)
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@test Gr() == Gr(0)
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@test inv(g)*g == Gr()
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end
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end
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@testset "Direct Product of Multiplicative Groups" begin
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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.DirectPowerGroup(MltGrp(F),2)
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@test FF([a,1]) isa GroupElem
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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 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 = 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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x, y = FF([1,a]), FF([a^2,1])
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@test x*y == FF([a^2, a])
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@test inv(x) == FF([1,-a^2-1])
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@test parent(x) == FF
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end
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@testset "Direct Product of Additive Groups" begin
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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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# 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 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 = 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 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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@test FF([F(1),a+1])*FF([a,a]) == FF(1+a,2a+1)
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x, y = FF([1,a]), FF([a^2,1])
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@test x*y == FF(a^2+1, a+1)
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@test inv(x) == FF([F(-1),-a])
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@test parent(x) == FF
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end
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@testset "Misc" begin
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F = GF(5)
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FF = DirectPowerGroup(AdditiveGroup(F),2)
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@test order(FF) == 25
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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 = DirectPowerGroup(MultiplicativeGroup(F), 3)
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@test order(FF) == 64
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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.DirectPowerGroup(G,3)
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@test order(GG) == 216
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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) == 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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end
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