mirror of
https://github.com/kalmarek/Groups.jl.git
synced 2024-12-25 18:15:29 +01:00
90 lines
2.4 KiB
Julia
90 lines
2.4 KiB
Julia
@testset "DirectPowers" begin
|
||
|
||
×(a,b) = Groups.DirectPower(a,b)
|
||
|
||
@testset "Constructors" begin
|
||
G = SymmetricGroup(3)
|
||
|
||
@test Groups.DirectPowerGroup(G,2) isa AbstractAlgebra.Group
|
||
@test G×G isa AbstractAlgebra.Group
|
||
@test Groups.DirectPowerGroup(G,2) isa Groups.DirectPowerGroup{2, Generic.SymmetricGroup{Int64}}
|
||
|
||
@test (G×G)×G == DirectPowerGroup(G, 3)
|
||
@test (G×G)×G == (G×G)×G
|
||
|
||
GG = DirectPowerGroup(G,2)
|
||
@test one(G×G) isa GroupElem
|
||
@test (G×G)((one(G), one(G))) isa GroupElem
|
||
@test (G×G)([one(G), one(G)]) isa GroupElem
|
||
|
||
@test Groups.DirectPowerGroupElem((one(G), one(G))) == one(G×G)
|
||
@test GG(one(G), one(G)) == one(G×G)
|
||
|
||
g = perm"(1,2,3)"
|
||
|
||
@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.DirectPowerGroupElem
|
||
|
||
@test_throws MethodError GG(g,g,g)
|
||
@test GG(g,g^2) == h
|
||
|
||
@test h[1] == g
|
||
@test h[2] == g^2
|
||
h = GG(g, one(G))
|
||
@test h == GG(g, one(G))
|
||
end
|
||
|
||
@testset "Basic arithmetic" begin
|
||
G = SymmetricGroup(3)
|
||
GG = G×G
|
||
i = perm"(1,3)"
|
||
g = perm"(1,2,3)"
|
||
|
||
h = GG(g,g^2)
|
||
k = GG(g^3, g^2)
|
||
|
||
@test h^2 == GG(g^2,g)
|
||
@test h^6 == one(GG)
|
||
|
||
@test h*h == h^2
|
||
@test h*k == GG(g,g)
|
||
|
||
@test h*inv(h) == one(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 == one(GG)
|
||
end
|
||
|
||
@testset "elem/parent_types" begin
|
||
G = SymmetricGroup(3)
|
||
g = perm"(1,2,3)"
|
||
|
||
@test elem_type(G×G) == DirectPowerGroupElem{2, elem_type(G)}
|
||
@test elem_type(G×G×G) == DirectPowerGroupElem{3, elem_type(G)}
|
||
@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)
|
||
end
|
||
|
||
@testset "Misc" begin
|
||
G = SymmetricGroup(3)
|
||
GG = Groups.DirectPowerGroup(G,3)
|
||
@test order(GG) == 216
|
||
|
||
@test isa(collect(GG), Vector{Groups.DirectPowerGroupElem{3, elem_type(G)}})
|
||
elts = vec(collect(GG))
|
||
|
||
@test length(elts) == 216
|
||
@test all([g*inv(g) == one(GG) for g in elts])
|
||
@test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)
|
||
end
|
||
end
|