1
0
mirror of https://github.com/kalmarek/Groups.jl.git synced 2024-12-25 18:15:29 +01:00
Groups.jl/test/DirectPower-tests.jl

90 lines
2.4 KiB
Julia
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

@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