diff --git a/test_battery.py b/test_battery.py
index b7f80a4..48c85d9 100644
--- a/test_battery.py
+++ b/test_battery.py
@@ -76,7 +76,7 @@ print("Finished battery test", flush=True)
 """
 
 ######### TEST DIFFERENTIAL/INTEGRAL COMMUTATION APLn
-
+"""
 def random_pol(apln):
     n = apln.n
     coef = randint(1,10)
@@ -84,15 +84,16 @@ def random_pol(apln):
     gens = apln.gens()
     return apln.get_term(apln, coef, exp, gens)
 
-n = 4
+n = 5
 s = SimplicialAlgebraplN(n)
 s.inject_variables()
 #cofaces = [x for x in list(powerset(range(n+1)) if len(x) == n]
 
 dp = random_pol(s)*prod(s.gens()[s.n+2:])
+print("dp: ",dp, flush=True)
 p = dp.solve_primitive().reduce()
 fd = sum([((-1)**f)*p.face(f).integral() for f in range(n+1)])
-print("sum([((-1)**f)*p.face(f).integral() for f in range(n+1)])== dq.integral(): ", fd == dp.integral(), flush=True)
+print("sum([((-1)**f)*p.face(f).integral() for f in range(n+1)])== dp.integral(): ", fd == dp.integral(), flush=True)
 
 for f in range(n+1):
     coface = list(range(n+2))
@@ -105,7 +106,45 @@ for f in range(n+1):
     #print(q.face(f).reduce() == p, flush=True)
     print("(-1)**"+str(f)+")*p.face().integral() == dq.integral(): ", ((-1)**f)*dp.integral() == dq.integral(), flush=True)
     #print(p.integral() == dq.integral(), flush=True)
+""" 
+######### TEST DIFFERENTIAL/INTEGRAL COMMUTATION APL(K)
+"""
+def zip_with_constants(a, l):
+    return [(a, i) for i in l]
     
+@parallel(ncpus=Integer(24))
+def check(A,S):
+"""
+
+#S = simplicial_complexes.Sphere(6)
+S = simplicial_complexes.K3Surface()
+S.set_immutable()
+cochainComplex = S.chain_complex(base_ring=QQ).dual()
+A = AlgebraAplK(S)
+for dim in range(4):
+    for i in range(1):
+        v = random_vector(QQ, len(S.n_cells(dim)))
+        print("Lifting random cochain dim ", dim, flush=True)
+        a = A.lift_cochain(A.vector_to_cochain(v,dim))
+        print("Check Apl(K) structure of the lifted element: ",a.check(), flush=True)
+        da = a.differential()
+        Diff = cochainComplex.differential(dim)
+        cda = A.cochain_to_vector(da.integral(),dim+1)
+        equal = Diff*v == cda
+        print("Diff*v == cda.integral()", equal, flush=True)
+        if not equal:
+            raise Exception("the integrals are not equal ", flush=True)
+        
+        for cell in S.n_cells(dim+1):
+            d = da.elements[cell.tuple()]
+            #s = (-1)**(dim*(dim-1)//2) # [FHT, RHT, p.129]
+            di = sum([((-1)**(f))*a.elements[cell.face(f).tuple()].integral() for f in range(cell.dimension()+1)])
+            equal = di == d.integral()
+            if equal:
+                print("di == d.integral(): ", equal, flush=True)
+            else:
+                raise Exception("the integrals are not equal ", flush=True)
+        
 
 
 ######### TEST DIFFERENTIAL/INTEGRAL COMMUTATION WITH RANDOM COCHAINS
@@ -141,4 +180,4 @@ for degree in range(5):
     print("Start parallel DIFF/INTEGRAL at degree " + str(degree), flush=True)
     results = [i[1] for i in check(data)]
 print("Finished battery test", flush=True) 
-"""
+"""
\ No newline at end of file