mirror of
https://github.com/kalmarek/Groups.jl.git
synced 2024-11-19 14:35:28 +01:00
86 lines
2.4 KiB
Julia
86 lines
2.4 KiB
Julia
@testset "WreathProducts" begin
|
|
S_3 = PermutationGroup(3)
|
|
F, a = FiniteField(2,3,"a")
|
|
b = S_3([2,3,1])
|
|
|
|
@testset "Constructors" begin
|
|
@test isa(Groups.WreathProduct(F, S_3), Nemo.Group)
|
|
@test isa(Groups.WreathProduct(F, S_3), Groups.WreathProduct)
|
|
@test isa(Groups.WreathProduct(F, S_3), Groups.WreathProduct{Nemo.FqNmodFiniteField})
|
|
|
|
aa = Groups.DirectProductGroupElem([a^0 ,a, a^2])
|
|
|
|
@test isa(Groups.WreathProductElem(aa, b), Nemo.GroupElem)
|
|
@test isa(Groups.WreathProductElem(aa, b), Groups.WreathProductElem)
|
|
@test isa(Groups.WreathProductElem(aa, b), Groups.WreathProductElem{typeof(a)})
|
|
|
|
B3 = Groups.WreathProduct(F, S_3)
|
|
|
|
@test B3.N == Groups.DirectProductGroup(F, 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())
|
|
|
|
g = B3(aa, b)
|
|
|
|
@test g.p == b
|
|
@test g.n == aa
|
|
h = deepcopy(g)
|
|
|
|
@test hash(g) == hash(h)
|
|
|
|
g.n[1] = a
|
|
|
|
@test g.n[1] == a
|
|
@test g != h
|
|
|
|
@test hash(g) != hash(h)
|
|
end
|
|
|
|
@testset "Types" begin
|
|
B3 = Groups.WreathProduct(F, S_3)
|
|
|
|
@test elem_type(B3) == Groups.WreathProductElem{elem_type(F)}
|
|
|
|
@test parent_type(typeof(B3())) == Groups.WreathProduct{parent_type(typeof(B3.N.group()))}
|
|
|
|
@test parent(B3()) == Groups.WreathProduct(F,S_3)
|
|
@test parent(B3()) == B3
|
|
end
|
|
|
|
@testset "Group arithmetic" begin
|
|
B3 = Groups.WreathProduct(F, S_3)
|
|
|
|
x = B3(B3.N([1,0,0]), B3.P([2,3,1]))
|
|
y = B3(B3.N([0,1,1]), B3.P([2,1,3]))
|
|
|
|
@test x*y == B3(B3.N([0,0,1]), B3.P([3,2,1]))
|
|
@test y*x == B3(B3.N([0,0,1]), B3.P([1,3,2]))
|
|
|
|
@test inv(x) == B3(B3.N([0,0,1]), B3.P([3,1,2]))
|
|
@test inv(y) == B3(B3.N([1,0,1]), B3.P([2,1,3]))
|
|
|
|
@test inv(x)*y == B3(B3.N([1,1,1]), B3.P([1,3,2]))
|
|
@test y*inv(x) == B3(B3.N([0,1,0]), B3.P([3,2,1]))
|
|
|
|
end
|
|
|
|
@testset "Misc" begin
|
|
B3 = Groups.WreathProduct(FiniteField(2,1,"a")[1], S_3)
|
|
@test order(B3) == 48
|
|
|
|
Wr = WreathProduct(PermutationGroup(2),S_3)
|
|
|
|
@test isa([elements(Wr)...], Vector{Groups.WreathProductElem{Generic.perm{Int64}}})
|
|
|
|
elts = [elements(Wr)...]
|
|
|
|
@test length(elts) == order(Wr)
|
|
@test all([g*inv(g) for g in elts] .== Wr())
|
|
@test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)
|
|
end
|
|
|
|
end
|