diff --git a/test/1703.09680.jl b/test/1703.09680.jl
index edf0306..6ed0f79 100644
--- a/test/1703.09680.jl
+++ b/test/1703.09680.jl
@@ -1,20 +1,3 @@
-function check_positivity(elt, unit; upper_bound=Inf, halfradius=2, optimizer)
-    @time sos_problem =
-        PropertyT.sos_problem_primal(elt, unit, upper_bound=upper_bound)
-
-    status, _ = PropertyT.solve(sos_problem, optimizer)
-    P = JuMP.value.(sos_problem[:P])
-    Q = real.(sqrt(P))
-    certified, λ_cert = PropertyT.certify_solution(
-        elt,
-        unit,
-        JuMP.objective_value(sos_problem),
-        Q,
-        halfradius=halfradius,
-    )
-    return status, certified, λ_cert
-end
-
 @testset "1703.09680 Examples" begin
 
     @testset "SL(2,Z)" begin
diff --git a/test/1712.07167.jl b/test/1712.07167.jl
index 9a1adcc..be479d9 100644
--- a/test/1712.07167.jl
+++ b/test/1712.07167.jl
@@ -1,27 +1,3 @@
-function check_positivity(elt, unit, wd; upper_bound=Inf, halfradius=2, optimizer)
-    @assert aug(elt) == aug(unit) == 0
-    @time sos_problem, Ps =
-        PropertyT.sos_problem_primal(elt, unit, wd, upper_bound=upper_bound)
-
-    @time status, _ = PropertyT.solve(sos_problem, optimizer)
-
-    Q = let Ps = Ps
-        Qs = [real.(sqrt(JuMP.value.(P))) for P in Ps]
-        PropertyT.reconstruct(Qs, wd)
-    end
-
-    λ = JuMP.value(sos_problem[:λ])
-
-    certified, λ_cert = PropertyT.certify_solution(
-        elt,
-        unit,
-        λ,
-        Q,
-        halfradius=2
-    )
-    return status, certified, λ_cert
-end
-
 @testset "1712.07167 Examples" begin
 
     @testset "SAut(F₃)" begin
diff --git a/test/check_positivity.jl b/test/check_positivity.jl
new file mode 100644
index 0000000..974077b
--- /dev/null
+++ b/test/check_positivity.jl
@@ -0,0 +1,41 @@
+function check_positivity(elt, unit; upper_bound=Inf, halfradius=2, optimizer)
+    @time sos_problem =
+        PropertyT.sos_problem_primal(elt, unit, upper_bound=upper_bound)
+
+    status, _ = PropertyT.solve(sos_problem, optimizer)
+    P = JuMP.value.(sos_problem[:P])
+    Q = real.(sqrt(P))
+    certified, λ_cert = PropertyT.certify_solution(
+        elt,
+        unit,
+        JuMP.objective_value(sos_problem),
+        Q,
+        halfradius=halfradius,
+    )
+    return status, certified, λ_cert
+end
+
+function check_positivity(elt, unit, wd; upper_bound=Inf, halfradius=2, optimizer)
+    @assert aug(elt) == aug(unit) == 0
+    @time sos_problem, Ps =
+        PropertyT.sos_problem_primal(elt, unit, wd, upper_bound=upper_bound)
+
+    @time status, _ = PropertyT.solve(sos_problem, optimizer)
+
+    Q = let Ps = Ps
+        Qs = [real.(sqrt(JuMP.value.(P))) for P in Ps]
+        PropertyT.reconstruct(Qs, wd)
+    end
+
+    λ = JuMP.value(sos_problem[:λ])
+
+    certified, λ_cert = PropertyT.certify_solution(
+        elt,
+        unit,
+        λ,
+        Q,
+        halfradius=halfradius
+    )
+    return status, certified, λ_cert
+end
+
diff --git a/test/quick_tests.jl b/test/quick_tests.jl
new file mode 100644
index 0000000..9a38b5c
--- /dev/null
+++ b/test/quick_tests.jl
@@ -0,0 +1,80 @@
+@testset "Quick tests" begin
+
+    @testset "SL(2,F₇)" begin
+        N = 2
+        p = 7
+        halfradius = 3
+        G = MatrixGroups.SpecialLinearGroup{N}(SymbolicWedderburn.Characters.FiniteFields.GF{p})
+        RG, S, sizes = PropertyT.group_algebra(G, halfradius=3, twisted=true)
+
+        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=cosmo_optimizer(
+                    eps=1e-7,
+                    max_iters=5_000,
+                    accel=50,
+                    alpha=1.95,
+                )
+            )
+
+            @test status == JuMP.OPTIMAL
+            @test certified
+            @test λ_cert > 5857 // 10000
+
+            m = PropertyT.sos_problem_dual(elt, unit)
+            PropertyT.solve(m, cosmo_optimizer(
+                eps=1e-7,
+                max_iters=10_000,
+                accel=50,
+                alpha=1.95,
+            ))
+
+            @test JuMP.termination_status(m) in (JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL)
+            @test JuMP.objective_value(m) ≈ λ_cert atol = 1e-2
+        end
+
+        @testset "Wedderburn decomposition" begin
+            P = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
+            Σ = PropertyT.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
+            act = PropertyT.action_by_conjugation(G, Σ)
+
+            wd = WedderburnDecomposition(
+                Float64,
+                Σ,
+                act,
+                basis(RG),
+                StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[halfradius]]),
+            )
+
+            status, certified, λ_cert = check_positivity(
+                elt,
+                unit,
+                wd,
+                upper_bound=ub,
+                halfradius=2,
+                optimizer=cosmo_optimizer(
+                    eps=1e-7,
+                    max_iters=10_000,
+                    accel=50,
+                    alpha=1.9,
+                ),
+            )
+
+            @test status == JuMP.OPTIMAL
+            @test certified
+            @test λ_cert > 5857 // 10000
+        end
+    end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index cdeac69..7003c1e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,8 +1,6 @@
 using Test
 using LinearAlgebra
 using SparseArrays
-BLAS.set_num_threads(1)
-ENV["OMP_NUM_THREADS"] = 4
 
 using Groups
 using Groups.GroupsCore
@@ -14,15 +12,18 @@ using SymbolicWedderburn.StarAlgebras
 using SymbolicWedderburn.PermutationGroups
 
 include("optimizers.jl")
+include("check_positivity.jl")
+include("quick_tests.jl")
 
-@testset "PropertyT" begin
+if haskey(ENV, "FULL_TEST") || haskey(ENV, "CI")
+    @testset "PropertyT" begin
+        include("constratint_matrices.jl")
+        include("actions.jl")
 
-    include("constratint_matrices.jl")
-    include("actions.jl")
+        include("1703.09680.jl")
+        include("1712.07167.jl")
+        include("1812.03456.jl")
 
-    include("1703.09680.jl")
-    include("1712.07167.jl")
-    include("1812.03456.jl")
-
-    include("graded_adj.jl")
+        include("graded_adj.jl")
+    end
 end