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