mirror of
https://github.com/kalmarek/Groups.jl.git
synced 2024-11-19 14:35:28 +01:00
120 lines
3.5 KiB
Julia
120 lines
3.5 KiB
Julia
using Groups.MatrixGroups
|
||
|
||
@testset "Matrix Groups" begin
|
||
@testset "SL(n, ℤ)" begin
|
||
SL3Z = SpecialLinearGroup{3}(Int8)
|
||
|
||
S = gens(SL3Z)
|
||
union!(S, inv.(S))
|
||
|
||
_, sizes = Groups.wlmetric_ball(S; radius = 4)
|
||
|
||
@test sizes == [13, 121, 883, 5455]
|
||
|
||
E(i, j) = SL3Z([A[MatrixGroups.ElementaryMatrix{3}(i, j, Int8(1))]])
|
||
|
||
A = alphabet(SL3Z)
|
||
w = E(1, 2)
|
||
r = E(2, 3)^-3
|
||
s = E(1, 3)^2 * E(3, 2)^-1
|
||
|
||
S = [w, r, s]
|
||
S = unique([S; inv.(S)])
|
||
_, sizes = Groups.wlmetric_ball(S; radius = 4)
|
||
@test sizes == [7, 33, 141, 561]
|
||
|
||
Logging.with_logger(Logging.NullLogger()) do
|
||
@testset "GroupsCore conformance" begin
|
||
test_Group_interface(SL3Z)
|
||
g = SL3Z(rand(1:length(alphabet(SL3Z)), 10))
|
||
h = SL3Z(rand(1:length(alphabet(SL3Z)), 10))
|
||
|
||
test_GroupElement_interface(g, h)
|
||
end
|
||
end
|
||
|
||
x = w * inv(SL3Z(word(w)[end:end])) * r
|
||
|
||
@test length(word(x)) == length(word(r))
|
||
@test size(x) == (3, 3)
|
||
@test eltype(x) == Int8
|
||
|
||
@test contains(sprint(show, SL3Z), "SL{3,Int8}")
|
||
@test contains(
|
||
sprint(show, MIME"text/plain"(), SL3Z),
|
||
"special linear group",
|
||
)
|
||
@test contains(sprint(show, MIME"text/plain"(), x), "∈ SL{3,Int8}")
|
||
@test sprint(print, x) isa String
|
||
|
||
@test length(word(x)) == 3
|
||
end
|
||
|
||
@testset "Sp(6, ℤ)" begin
|
||
Sp6 = MatrixGroups.SymplecticGroup{6}(Int8)
|
||
|
||
Logging.with_logger(Logging.NullLogger()) do
|
||
@testset "GroupsCore conformance" begin
|
||
test_Group_interface(Sp6)
|
||
g = Sp6(rand(1:length(alphabet(Sp6)), 10))
|
||
h = Sp6(rand(1:length(alphabet(Sp6)), 10))
|
||
|
||
test_GroupElement_interface(g, h)
|
||
end
|
||
end
|
||
|
||
x = gens(Sp6, 1) * gens(Sp6, 2)^2
|
||
x *= inv(gens(Sp6, 2)^2) * gens(Sp6, 3)
|
||
|
||
@test length(word(x)) == 2
|
||
@test size(x) == (6, 6)
|
||
@test eltype(x) == Int8
|
||
|
||
@test contains(sprint(show, Sp6), "Sp{6,Int8}")
|
||
@test contains(
|
||
sprint(show, MIME"text/plain"(), Sp6),
|
||
"group of 6×6 symplectic matrices",
|
||
)
|
||
@test contains(sprint(show, MIME"text/plain"(), x), "∈ Sp{6,Int8}")
|
||
@test sprint(print, x) isa String
|
||
|
||
@test length(word(x)) == 2
|
||
|
||
for g in gens(Sp6)
|
||
@test MatrixGroups.issymplectic(MatrixGroups.matrix(g))
|
||
end
|
||
end
|
||
|
||
@testset "General matrix group" begin
|
||
Sp6 = MatrixGroups.SymplecticGroup{6}(Int8)
|
||
G = Groups.MatrixGroup{6}(Matrix{Int16}.(gens(Sp6)))
|
||
|
||
Logging.with_logger(Logging.NullLogger()) do
|
||
@testset "GroupsCore conformance" begin
|
||
test_Group_interface(G)
|
||
g = G(rand(1:length(alphabet(G)), 10))
|
||
h = G(rand(1:length(alphabet(G)), 10))
|
||
|
||
test_GroupElement_interface(g, h)
|
||
end
|
||
end
|
||
|
||
x = gens(G, 1) * gens(G, 2)^3
|
||
x *= gens(G, 2)^-3
|
||
|
||
@test length(word(x)) == 1
|
||
@test size(x) == (6, 6)
|
||
@test eltype(x) == Int16
|
||
|
||
@test contains(sprint(show, G), "H ⩽ GL{6,Int16}")
|
||
@test contains(
|
||
sprint(show, MIME"text/plain"(), G),
|
||
"subgroup of 6×6 invertible matrices",
|
||
)
|
||
@test contains(sprint(show, MIME"text/plain"(), x), "∈ H ⩽ GL{6,Int16}")
|
||
@test sprint(print, x) isa String
|
||
|
||
@test length(word(x)) == 1
|
||
end
|
||
end
|