Groups.jl/test/matrix_groups.jl

using Groups.MatrixGroups

@testset "Matrix Groups" begin
    @testset "SL(n, ℤ)" begin
        SL3Z = SpecialLinearGroup{3}(Int8)

        S = gens(SL3Z); union!(S, inv.(S))

        E, 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]
        _, sizes = Groups.wlmetric_ball_serial(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(w)*r

        @test length(word(x)) == 5
        @test size(x) == (3,3)
        @test eltype(x) == Int8

        @test contains(sprint(print, SL3Z), "special linear group of 3×3")
        @test contains(sprint(show, MIME"text/plain"(), x), "SL{3,Int8} matrix:")
        @test sprint(print, x) isa String

        @test length(word(x)) == 3
    end

    @testset "Sp(6, ℤ)" begin
        Sp6 = MatrixGroups.SymplecticGroup{6}(Int8)

        @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

        @test contains(sprint(print, Sp6), "group of 6×6 symplectic matrices")

        x = gens(Sp6, 1)
        x *= inv(x) * gens(Sp6, 2)

        @test length(word(x)) == 3
        @test size(x) == (6,6)
        @test eltype(x) == Int8

        @test contains(sprint(show, MIME"text/plain"(), x), "6×6 symplectic matrix:")
        @test sprint(print, x) isa String

        @test length(word(x)) == 1

        for g in gens(Sp6)
            @test MatrixGroups.issymplectic(MatrixGroups.matrix_repr(g))
        end
    end
end