fix tests

test/DirectProd-tests.jl

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

test/WreathProd-tests.jl

@@ -1,105 +1,103 @@
 @testset "WreathProducts" begin
    S_3 = PermutationGroup(3)
    S_2 = PermutationGroup(2)
-   b = S_3([2,3,1])
+   b = perm"(1,2,3)"
-   a = S_2([2,1])
+   a = perm"(1,2)"
 
    @testset "Constructors" begin
-      @test isa(Groups.WreathProduct(S_2, S_3), AbstractAlgebra.Group)
+      @test Groups.WreathProduct(S_2, S_3) isa AbstractAlgebra.Group
       B3 = Groups.WreathProduct(S_2, S_3)
       @test B3 isa Groups.WreathProduct
-      @test B3 isa WreathProduct{AbstractAlgebra.Generic.PermGroup{Int}, Int}
+      @test B3 isa WreathProduct{3, AbstractAlgebra.Generic.PermGroup{Int}, Int}
 
-      aa = Groups.DirectProductGroupElem([a^0 ,a, a^2])
+      aa = Groups.DirectPowerGroupElem((a^0 ,a, a^2))
 
-      @test isa(Groups.WreathProductElem(aa, b), AbstractAlgebra.GroupElem)
+      @test Groups.WreathProductElem(aa, b) isa AbstractAlgebra.GroupElem
       x = Groups.WreathProductElem(aa, b)
       @test x isa Groups.WreathProductElem
-      @test x isa Groups.WreathProductElem{AbstractAlgebra.Generic.perm{Int}, Int}
+      @test x isa 
+         Groups.WreathProductElem{3, AbstractAlgebra.Generic.perm{Int}, Int}
 
-      @test B3.N == Groups.DirectProductGroup(S_2, 3)
+      @test B3.N == Groups.DirectPowerGroup(S_2, 3)
       @test B3.P == S_3
 
       @test B3(aa, b) == Groups.WreathProductElem(aa, b)
       @test B3(b) == Groups.WreathProductElem(B3.N(), b)
       @test B3(aa) == Groups.WreathProductElem(aa, S_3())
 
-      @test B3([a^0 ,a, a^2], perm"(1,2,3)") isa WreathProductElem
+      @test B3((a^0 ,a, a^2), b) isa WreathProductElem
 
-      @test B3([a^0 ,a, a^2], perm"(1,2,3)") == B3(aa, b)
+      @test B3((a^0 ,a, a^2), b) == B3(aa, b)
    end
 
    @testset "Types" begin
       B3 = Groups.WreathProduct(S_2, S_3)
 
-      @test elem_type(B3) == Groups.WreathProductElem{perm{Int}, Int}
+      @test elem_type(B3) == Groups.WreathProductElem{3, perm{Int}, Int}
 
-      @test parent_type(typeof(B3())) == Groups.WreathProduct{parent_type(typeof(B3.N.group())), Int}
+      @test parent_type(typeof(B3())) == Groups.WreathProduct{3, parent_type(typeof(B3.N.group())), Int}
 
       @test parent(B3()) == Groups.WreathProduct(S_2,S_3)
       @test parent(B3()) == B3
    end
 
    @testset "Basic operations on WreathProductElem" begin
-      aa = Groups.DirectProductGroupElem([a^0 ,a, a^2])
+      aa = Groups.DirectPowerGroupElem((a^0 ,a, a^2))
       B3 = Groups.WreathProduct(S_2, S_3)
       g = B3(aa, b)
 
       @test g.p == b
-      @test g.n == DirectProductGroupElem(aa.elts)
+      @test g.n == DirectPowerGroupElem(aa.elts)
 
       h = deepcopy(g)
       @test h == g
       @test !(g === h)
 
-      g.n[1] = parent(g.n[1])(a)
+      g = B3(Groups.DirectPowerGroupElem((a ,a, a^2)), g.p)
 
       @test g.n[1] == parent(g.n[1])(a)
       @test g != h
 
       @test hash(g) != hash(h)
-
-      g.n[1] = a
-      @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(AdditiveGroup(GF(3)), PermutationGroup(4))
 
-      x = B4([0,1,2,0], perm"(1,2,3)(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)")
+      @test inv(x) == B4((1,0,2,0), perm"(1,3,2)(4)")
 
-      y = B4([1,0,1,2], perm"(1,4)(2,3)")
+      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 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 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 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 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)")
+      @test y*inv(x) == B4((1,2,1,0), perm"(1,4,3)(2)")
 
    end
 
    @testset "Misc" begin
-      B3 = Groups.WreathProduct(GF(3), S_3)
+      B3 = Groups.WreathProduct(AdditiveGroup(GF(3)), S_3)
       @test order(B3) == 3^3*6
+      @test collect(B3) isa Vector{
+      WreathProductElem{3, AddGrpElem{AbstractAlgebra.gfelem{Int}}, Int}}
 
-      # B3 = Groups.WreathProduct(MultiplicativeGroup(GF(3)), S_3)
+      B3 = Groups.WreathProduct(MultiplicativeGroup(GF(3)), S_3)
-      # @test order(B3) == 2^3*6
+      @test order(B3) == 2^3*6
+      @test collect(B3) isa Vector{
+      WreathProductElem{3, MltGrpElem{AbstractAlgebra.gfelem{Int}}, Int}}
 
       Wr = WreathProduct(PermutationGroup(2),PermutationGroup(4))
 
-      @test isa([elements(Wr)...], Vector{Groups.WreathProductElem{Generic.perm{Int}, Int}})
+      elts = collect(Wr)
+      @test elts isa Vector{Groups.WreathProductElem{4, Generic.perm{Int}, Int}}
       @test order(Wr) == 2^4*factorial(4)      
 
-      elts = [elements(Wr)...]
-
       @test length(elts) == order(Wr)
       @test all([g*inv(g) == Wr() for g in elts])
       @test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)