diff --git a/test_battery.py b/test_battery.py
index a55eaa9..6c69cbb 100644
--- a/test_battery.py
+++ b/test_battery.py
@@ -11,6 +11,107 @@ load("minimalModel_parallel.py")
 #smodel = load("sullivan_model_K3_deg3.sobj")
 #smorphism = load("model_morphism_K3_deg3.sobj")
 
+
+######### TEST INTEGRAND/INTEGRAL APLn
+"""
+N=10
+for dim in range(10):
+    print("Start test at dimension ", dim, flush=True)
+    s = SimplicialAlgebraplN(dim)
+    for i in range(N):
+        value = randint(-20,20); 
+        p = s.integrand(value);
+        #print(p); 
+        equal = p.integral() == value
+        if not equal:
+            raise Exception("The integral is not equal")
+        else:
+            None
+            #print("ok", flush=True)
+print("Test finished")
+"""
+######### TEST SOLVE PRIMITIVE WITH RANDOM COCHAINS
+"""
+S = simplicial_complexes.Sphere(4)
+#S = simplicial_complexes.K3Surface()
+S.set_immutable()
+A = AlgebraAplK(S)
+cochainComplex = S.chain_complex(base_ring=QQ).dual()
+N = 4
+for dim in range(1,4):
+    for r in range(N): 
+        print("Working on dimension ", dim, flush=True)
+        v = random_vector(QQ, len(S.n_cells(dim)))
+        print("Lifting random cochain", flush=True)
+        a = A.lift_cochain(A.vector_to_cochain(v,dim))
+        print("Checking Apl(K) structure", flush=True)
+        a.check()
+        #if a.check():
+        #    print("lift ok", flush=True)
+        da = a.differential()
+        print("Checking Apl(K) structure of the differential", flush=True)
+        da.check()
+        #if da.check():
+        #    print("da ok", flush=True)
+        #p_basis = da._get_primitive_basis()
+        print("Solving primitive", flush=True)
+        b = da.solve_primitive()
+        print("Checking Apl(K) structure of the solution found", flush=True)
+        b.check()
+        #if b.check():
+        #    print("solve_primitive ok", flush=True)
+        print(b.differential()==da)
+        print("Test INTEGRAL/DIFFERENTIAL COMMUTATION", flush=True)
+        Diff = cochainComplex.differential(dim)
+        cb = A.cochain_to_vector(b.integral(), dim)
+        cda = A.cochain_to_vector(da.integral(), dim + 1)
+        equal = Diff*cb == cda
+        if not equal:
+            raise ValueError("the cochains are not equal at degree " + str(degree))
+        else:
+            print("OK", flush=True)
+
+"""
+def zip_with_constants(a, b, c, l):
+    return [(a, b, c, i) for i in l]
+    
+@parallel(ncpus=Integer(24))
+def check_solve_primitive(A, dim, Diff, v):
+    #print("Lift random cochain to Apl(K)", flush=True)
+    a = A.lift_cochain(A.vector_to_cochain(v,dim))
+    #print("Checking Apl(K) structure of the random element ", flush=True)
+    a.check()
+    #print(a.check(), flush=True)
+    da = a.differential()
+    b = da.solve_primitive()
+    print("Checking Apl(K) structure of the primitive element ", flush=True)
+    b.check()
+    print("Checking b.differential()==da ", flush=True)
+    equal = b.differential()==da
+    if not equal:
+         raise ValueError("the differential is not equal")
+         return -1
+    cb = A.cochain_to_vector(b.integral(), dim)
+    cda = A.cochain_to_vector(da.integral(), dim + 1)
+    equal = Diff*cb == cda
+    if not equal:
+        raise ValueError("the cochains are not equal at degree " + str(dim))
+    return 0    
+
+#S = simplicial_complexes.Sphere(3)
+S = simplicial_complexes.K3Surface()
+S.set_immutable()
+A = AlgebraAplK(S)
+cochainComplex = S.chain_complex(base_ring=QQ).dual()
+N = 96
+for dim in range(1,4):
+    Diff = cochainComplex.differential(dim)
+    random_cochains = [random_vector(QQ, len(S.n_cells(dim))) for i in range(N)]
+    data = zip_with_constants(A, dim, Diff, random_cochains)
+    print("Start parallel tests at dimension " + str(dim), flush=True)
+    results = [i[1] for i in check_solve_primitive(data)]
+
+print("Test finished", flush=True)
 ######### RUN MINIMAL MODEL ALGORITHM
 """
 [sullivan_model, model_morphism, cohomology_correspondence] = minimal_model(S, max_depth=12000, max_dim=3)
@@ -109,6 +210,7 @@ for f in range(n+1):
 """ 
 ######### TEST DIFFERENTIAL/INTEGRAL COMMUTATION APL(K)
 
+"""
 def zip_with_constants(a,s,c, l):
     return [(a,s,c, i) for i in l]
     
@@ -139,20 +241,20 @@ def check_dif_int(A, S, cochainComplex, v):
             return -1
     return 0
 
-S = simplicial_complexes.Sphere(7)
+S = simplicial_complexes.Sphere(5)
 #S = simplicial_complexes.K3Surface()
 S.set_immutable()
 A = AlgebraAplK(S)
 cochainComplex = S.chain_complex(base_ring=QQ).dual()
 N = 1
-for dim in range(5):
+for dim in range(7):
     l = [random_vector(QQ, len(S.n_cells(dim))) for i in range(N)]
     data = zip_with_constants(A, S, cochainComplex, l)
     print("Start parallel test at dimension " + str(dim), flush=True)
     results = [i[1] for i in check_dif_int(data)]
 
 print("Test finished", flush=True)
-
+"""
 ######### TEST DIFFERENTIAL/INTEGRAL COMMUTATION WITH RANDOM COCHAINS
 """
 def zip_with_constants(a, b, c, l):