@testset "Quick tests" begin
    @testset "SL(2,F₇)" begin
        N = 2
        p = 7
        halfradius = 3
        G = MatrixGroups.SpecialLinearGroup{N}(
            SW.Characters.FiniteFields.GF{p},
        )
        RG, S, sizes = PropertyT.group_algebra(G; halfradius = 3)

        Δ = let RG = RG, S = S
            RG(length(S)) - sum(RG(s) for s in S)
        end

        elt = Δ^2
        unit = Δ
        ub = 0.58578# Inf# 1.5

        @testset "standard formulation" begin
            status, certified, λ_cert = check_positivity(
                elt,
                unit;
                upper_bound = ub,
                halfradius = 2,
                optimizer = scs_optimizer(;
                    eps = 1e-8,
                    max_iters = 20_000,
                    accel = -50,
                    alpha = 1.9,
                ),
            )

            @test status == JuMP.OPTIMAL
            @test certified
            @test λ_cert > 5857 // 10000

            m = PropertyT.sos_problem_dual(elt, unit)
            PropertyT.solve(
                m,
                scs_optimizer(;
                    eps = 1e-8,
                    max_iters = 10_000,
                    accel = -50,
                    alpha = 1.9,
                ),
            )

            @test JuMP.termination_status(m) in
                  (JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL)
            @test JuMP.objective_value(m) ≈
                  PropertyT.IntervalArithmetic.mid(λ_cert) atol = 1e-2
        end

        @testset "Wedderburn decomposition" begin
            P = PG.PermGroup(PG.perm"(1,2)", PG.Perm(circshift(1:N, -1)))
            Σ = Groups.Constructions.WreathProduct(
                PG.PermGroup(PG.perm"(1,2)"),
                P,
            )
            act = PropertyT.action_by_conjugation(G, Σ)

            wd = SW.WedderburnDecomposition(
                Float64,
                Σ,
                act,
                SA.basis(RG),
                SA.Basis{UInt16}(@view SA.basis(RG)[1:sizes[halfradius]]),
            )

            status, certified, λ_cert = check_positivity(
                elt,
                unit,
                wd;
                upper_bound = ub,
                halfradius = 2,
                optimizer = scs_optimizer(;
                    eps = 1e-8,
                    max_iters = 10_000,
                    accel = -50,
                    alpha = 1.9,
                ),
            )

            @test status == JuMP.OPTIMAL
            @test certified
            @test λ_cert > 5857 // 10000
        end
    end
end