mirror of
https://github.com/kalmarek/Groups.jl.git
synced 2024-11-19 06:30:29 +01:00
84 lines
2.3 KiB
Julia
84 lines
2.3 KiB
Julia
@testset "DirectProducts" begin
|
||
using Nemo
|
||
|
||
G = PermutationGroup(3)
|
||
g = G([2,3,1])
|
||
F, a = FiniteField(2,3,"a")
|
||
|
||
@testset "Constructors" begin
|
||
@test isa(Groups.DirectProductGroup(G,2), Nemo.Group)
|
||
@test isa(G×G, Nemo.Group)
|
||
@test isa(Groups.DirectProductGroup(G,2), Groups.DirectProductGroup{Generic.PermGroup{Int64}})
|
||
|
||
GG = Groups.DirectProductGroup(G,2)
|
||
|
||
@test GG == Groups.DirectProductGroup(G,2)
|
||
|
||
@test Groups.DirectProductGroupElem([G(), G()]) == GG()
|
||
@test GG(G(), G()) == GG()
|
||
|
||
@test isa(GG([g, g^2]), GroupElem)
|
||
@test isa(GG([g, g^2]), Groups.DirectProductGroupElem{Generic.perm{Int64}})
|
||
|
||
h = GG([g,g^2])
|
||
|
||
@test h == GG(h)
|
||
|
||
@test isa(GG(g, g^2), GroupElem)
|
||
@test isa(GG(g, g^2), Groups.DirectProductGroupElem)
|
||
|
||
@test_throws String GG(g,g,g)
|
||
@test GG(g,g^2) == h
|
||
|
||
@test size(h) == (2,)
|
||
@test h[1] == g
|
||
@test h[2] == g^2
|
||
h[2] = G()
|
||
@test h == GG(g, G())
|
||
end
|
||
|
||
GG = Groups.DirectProductGroup(G,2)
|
||
FF = Groups.DirectProductGroup(F,2)
|
||
|
||
@testset "Types" begin
|
||
@test elem_type(GG) == Groups.DirectProductGroupElem{elem_type(G)}
|
||
@test elem_type(FF) == Groups.DirectProductGroupElem{elem_type(F)}
|
||
@test parent_type(typeof(GG(g,g^2))) == Groups.DirectProductGroup{typeof(G)}
|
||
@test parent_type(typeof(FF(a,a^2))) == Groups.DirectProductGroup{typeof(F)}
|
||
|
||
@test isa(FF([0,1]), GroupElem)
|
||
@test isa(FF([0,1]), Groups.DirectProductGroupElem)
|
||
@test isa(FF([0,1]), Groups.DirectProductGroupElem{elem_type(F)})
|
||
@test_throws MethodError FF(1,0)
|
||
end
|
||
|
||
@testset "Group arithmetic" begin
|
||
g = G([2,3,1])
|
||
h = GG([g,g^2])
|
||
|
||
@test h^2 == GG(g^2,g)
|
||
@test h^6 == GG()
|
||
|
||
@test h*h == h^2
|
||
|
||
@test h*inv(h) == GG()
|
||
|
||
@test FF([0,a])*FF([a,1]) == FF(a,1+a)
|
||
x, y = FF([1,a]), FF([a^2,1])
|
||
@test x*y == FF([a^2+1, a+1])
|
||
@test inv(x) == FF([1,a])
|
||
end
|
||
|
||
@testset "Misc" begin
|
||
@test order(GG) == 36
|
||
@test order(FF) == 64
|
||
|
||
@test isa([elements(GG)...], Vector{Groups.DirectProductGroupElem{elem_type(G)}})
|
||
elts = [elements(GG)...]
|
||
|
||
@test length(elts) == 36
|
||
@test all([g*inv(g) for g in elts] .== GG())
|
||
@test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)
|
||
end
|
||
end
|