mirror of
https://github.com/kalmarek/Groups.jl.git
synced 2024-12-03 01:46:28 +01:00
fix tests
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@ -70,7 +70,6 @@
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@test l(deepcopy(D)) == (a, b, c, c*d)
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@test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d)
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i,j = 2,4
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r = Groups.rmul_autsymbol(i,j)
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l = Groups.lmul_autsymbol(i,j)
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@ -81,19 +80,20 @@
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end
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@testset "AutGroup/Automorphism constructors" begin
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f = Groups.AutSymbol("a", 1, Groups.FlipAut(1))
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@test isa(Automorphism{3}(f), Groups.GWord)
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@test isa(Automorphism{3}(f), Automorphism)
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@test isa(AutGroup(FreeGroup(3)), Group)
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@test isa(AutGroup(FreeGroup(3)), AbstractAlgebra.Group)
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@test isa(AutGroup(FreeGroup(1)), Groups.AbstractFPGroup)
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A = AutGroup(FreeGroup(1))
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@test isa(gens(A), Vector{Automorphism{1}})
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@test length(gens(A)) == 1
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@test isa(Groups.gens(A), Vector{Automorphism{1}})
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@test length(Groups.gens(A)) == 1
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A = AutGroup(FreeGroup(1), special=true)
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@test length(gens(A)) == 0
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@test length(Groups.gens(A)) == 0
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A = AutGroup(FreeGroup(2))
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@test length(gens(A)) == 7
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gens = gens(A)
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@test length(Groups.gens(A)) == 7
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gens = Groups.gens(A)
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@test isa(A(Groups.rmul_autsymbol(1,2)), Automorphism)
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@test A(Groups.rmul_autsymbol(1,2)) in gens
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@ -146,15 +146,17 @@
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b = Groups.flip_autsymbol(2)*A(inv(Groups.rmul_autsymbol(1,2)))
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@test a*b == b*a
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@test a^3 * b^3 == A()
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g,h = gens(A)[[1,8]] # (g, h) = (ϱ₁₂, ϱ₃₂)
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g,h = Groups.gens(A)[[1,8]] # (g, h) = (ϱ₁₂, ϱ₃₂)
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@test Groups.domain(A) == NTuple{4, FreeGroupElem}(gens(A.objectGroup))
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@test (g*h)(Groups.domain(A)) == (h*g)(Groups.domain(A))
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@test (g*h).savedhash != (h*g).savedhash
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@test (g*h).savedhash == zero(UInt)
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@test (h*g).savedhash == zero(UInt)
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a = g*h
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b = h*g
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@test hash(a) == hash(b)
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@test hash(a) != zero(UInt)
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@test hash(b) == hash(a)
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@test a.savedhash == b.savedhash
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@test length(unique([a,b])) == 1
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@test length(unique([g*h, h*g])) == 1
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@ -228,6 +230,9 @@
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@test Groups.linear_repr(ϱ₁₂^-1) == M
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@test Groups.linear_repr(λ₁₂^-1) == M
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@test Groups.linear_repr(ϱ₁₂*λ₁₂^-1) == eye(N)
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@test Groups.linear_repr(λ₁₂^-1*ϱ₁₂) == eye(N)
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M = eye(N)
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M[2,2] = -1
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ε₂ = G(Groups.flip_autsymbol(2))
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@ -235,7 +240,8 @@
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@test Groups.linear_repr(ε₂) == M
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@test Groups.linear_repr(ε₂^2) == eye(N)
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M = [0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]
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M = [0 1 0; 0 0 1; 1 0 0]
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σ = G(Groups.perm_autsymbol([2,3,1]))
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@test Groups.linear_repr(σ) == M
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@test Groups.linear_repr(σ^3) == eye(3)
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@ -1,32 +1,36 @@
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@testset "DirectProducts" begin
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G = PermutationGroup(3)
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g = G([2,3,1])
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F, a = FiniteField(2,3,"a")
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@testset "Constructors" begin
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@test isa(Groups.DirectProductGroup(G,2), AbstractArray.Group)
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@test isa(G×G, AbstractAlgebra.Group)
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@test isa(Groups.DirectProductGroup(G,2), Groups.DirectProductGroup{Generic.PermGroup{Int64}})
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G = PermutationGroup(3)
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g = G([2,3,1])
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GG = Groups.DirectProductGroup(G,2)
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@test Groups.DirectProductGroup(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 GG == Groups.DirectProductGroup(G,2)
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@test (G×G)×G == DirectProductGroup(G, 3)
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@test (G×G)×G == (G×G)×G
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@test Groups.DirectProductGroupElem([G(), G()]) == GG()
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@test GG(G(), G()) == GG()
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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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@test isa(GG([g, g^2]), GroupElem)
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@test isa(GG([g, g^2]), Groups.DirectProductGroupElem{Generic.perm{Int64}})
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GG = DirectProductGroup(G,2)
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@test Groups.DirectProductGroupElem([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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h = GG([g,g^2])
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@test h == GG(h)
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@test isa(GG(g, g^2), GroupElem)
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@test isa(GG(g, g^2), Groups.DirectProductGroupElem)
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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_throws String GG(g,g,g)
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@test_throws DomainError GG(g,g,g)
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@test GG(g,g^2) == h
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@test size(h) == (2,)
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@ -34,46 +38,153 @@
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@test h[2] == g^2
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h[2] = G()
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@test h == GG(g, G())
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end
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GG = Groups.DirectProductGroup(G,2)
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FF = Groups.DirectProductGroup(F,2)
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@testset "Types" begin
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@test elem_type(GG) == Groups.DirectProductGroupElem{elem_type(G)}
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@test elem_type(FF) == Groups.DirectProductGroupElem{elem_type(F)}
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@test parent_type(typeof(GG(g,g^2))) == Groups.DirectProductGroup{typeof(G)}
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@test parent_type(typeof(FF(a,a^2))) == Groups.DirectProductGroup{typeof(F)}
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@test isa(FF([0,1]), GroupElem)
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@test isa(FF([0,1]), Groups.DirectProductGroupElem)
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@test isa(FF([0,1]), Groups.DirectProductGroupElem{elem_type(F)})
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@test_throws MethodError FF(1,0)
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end
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@testset "Group arithmetic" begin
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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 = GG([g,g^2])
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h = (G×G)([g,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^2 == (G×G)(g^2,g)
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@test h^6 == (G×G)()
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@test h*h == h^2
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@test h*inv(h) == GG()
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@test h*inv(h) == (G×G)()
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end
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@test FF([0,a])*FF([a,1]) == FF(a,1+a)
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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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@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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F = GF(13)
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@test elem_type(F×F) == DirectProductGroupElem{Groups.AddGrpElem{elem_type(F)}}
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@test parent_type(typeof((F×F)(1,5))) == Groups.DirectProductGroup{AddGrp{typeof(F)}}
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parent((F×F)(1,5)) == DirectProductGroup(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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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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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.DirectProductGroup(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_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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F, a = NumberField(x^3 + x + 1, "a")
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FF = DirectProductGroup(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+1, a+1])
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@test inv(x) == FF([1,a])
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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 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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FF = DirectProductGroup(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(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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@test order(GG) == 36
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F = GF(5)
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FF = DirectProductGroup(F,2)
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@test order(FF) == 25
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elts = vec(collect(elements(FF)))
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@test length(elts) == 25
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@test all([g*inv(g) for g in elts] .== FF())
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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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@test order(FF) == 64
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elts = vec(collect(elements(FF)))
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@test length(elts) == 64
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@test all([g*inv(g) for g in elts] .== FF())
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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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@test isa([elements(GG)...], Vector{Groups.DirectProductGroupElem{elem_type(G)}})
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elts = [elements(GG)...]
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elts = vec(collect(elements(GG)))
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@test length(elts) == 36
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@test all([g*inv(g) for g in elts] .== GG())
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@ -41,7 +41,7 @@ end
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end
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@testset "FreeGroup" begin
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@test isa(FreeGroup(["s", "t"]), Group)
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@test isa(FreeGroup(["s", "t"]), AbstractAlgebra.Group)
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G = FreeGroup(["s", "t"])
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@testset "elements constructors" begin
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@ -1,18 +1,19 @@
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@testset "WreathProducts" begin
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S_3 = PermutationGroup(3)
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F, a = FiniteField(2,3,"a")
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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{AbstractAlgebra.FqNmodFiniteField})
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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{typeof(a)})
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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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@ -23,26 +24,15 @@
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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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g = B3(aa, b)
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@test B3([a^0 ,a, a^2], perm"(1,2,3)") isa WreathProductElem
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@test g.p == b
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@test g.n == aa
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h = deepcopy(g)
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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] == a
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@test g != h
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@test hash(g) != hash(h)
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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{elem_type(F), Int}
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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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@ -50,30 +40,64 @@
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@test parent(B3()) == B3
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end
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@testset "Group arithmetic" begin
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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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x = B3(B3.N([1,0,0]), B3.P([2,3,1]))
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y = B3(B3.N([0,1,1]), B3.P([2,1,3]))
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@test g.p == b
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@test g.n == DirectProductGroupElem(AddGrpElem.(aa.elts))
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@test x*y == B3(B3.N([0,0,1]), B3.P([3,2,1]))
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@test y*x == B3(B3.N([0,0,1]), B3.P([1,3,2]))
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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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@test inv(x) == B3(B3.N([0,0,1]), B3.P([3,1,2]))
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@test inv(y) == B3(B3.N([1,0,1]), B3.P([2,1,3]))
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g.n[1] = parent(g.n[1])(a)
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@test inv(x)*y == B3(B3.N([1,1,1]), B3.P([1,3,2]))
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@test y*inv(x) == B3(B3.N([0,1,0]), B3.P([3,2,1]))
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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)
|
||||
@test g != h
|
||||
|
||||
@test hash(g) != hash(h)
|
||||
end
|
||||
|
||||
|
||||
@testset "Group arithmetic" begin
|
||||
B4 = Groups.WreathProduct(GF(3), PermutationGroup(4))
|
||||
|
||||
x = B4([0,1,2,0], perm"(1,2,3)(4)")
|
||||
@test inv(x) == B4([1,0,2,0], perm"(1,3,2)(4)")
|
||||
|
||||
y = B4([1,0,1,2], perm"(1,4)(2,3)")
|
||||
@test inv(y) == B4([1,2,0,2], perm"(1,4)(2,3)")
|
||||
|
||||
@test x*y == B4([0,2,0,2], perm"(1,3,4)(2)")
|
||||
|
||||
@test y*x == B4([1,2,2,2], perm"(1,4,2)(3)")
|
||||
|
||||
|
||||
@test inv(x)*y == B4([2,1,2,2], perm"(1,2,4)(3)")
|
||||
|
||||
@test y*inv(x) == B4([1,2,1,0], perm"(1,4,3)(2)")
|
||||
|
||||
end
|
||||
|
||||
@testset "Misc" begin
|
||||
B3 = Groups.WreathProduct(FiniteField(2,1,"a")[1], S_3)
|
||||
@test order(B3) == 48
|
||||
B3 = Groups.WreathProduct(GF(3), S_3)
|
||||
@test order(B3) == 3^3*6
|
||||
|
||||
Wr = WreathProduct(PermutationGroup(2),S_3)
|
||||
B3 = Groups.WreathProduct(MultiplicativeGroup(GF(3)), S_3)
|
||||
@test order(B3) == 2^3*6
|
||||
|
||||
Wr = WreathProduct(PermutationGroup(2),PermutationGroup(4))
|
||||
|
||||
@test isa([elements(Wr)...], Vector{Groups.WreathProductElem{Generic.perm{Int}, Int}})
|
||||
@test order(Wr) == 2^4*factorial(4)
|
||||
|
||||
elts = [elements(Wr)...]
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user