diff --git a/superelliptic/superelliptic_class.sage b/superelliptic/superelliptic_class.sage
index 8ecb44f..2a4bc54 100644
--- a/superelliptic/superelliptic_class.sage
+++ b/superelliptic/superelliptic_class.sage
@@ -288,7 +288,7 @@ def reduction_form(C, g):
     g = FxRy(g(x = x1, y=y1))
     for j in range(0, m):
         if j==0:
-            G = Rx(coff(g, 0))
+            G = Fx(coff(g, 0))
             g1 += FxRy(G)
         else:
             G = coff(g, j)
diff --git a/superelliptic/superelliptic_form_class.sage b/superelliptic/superelliptic_form_class.sage
index 4332557..c6bb9b2 100644
--- a/superelliptic/superelliptic_form_class.sage
+++ b/superelliptic/superelliptic_form_class.sage
@@ -37,10 +37,13 @@ class superelliptic_form:
             return str(g) + ' dx'
         return '('+str(g) + ') dx'
 
-    def __rmul__(self, constant):
+    def __rmul__(self, other):
         C = self.curve
+        F = C.base_ring
         omega = self.form
-        return superelliptic_form(C, constant*omega)
+        if other in F:
+            return superelliptic_form(C, other*omega)
+        return superelliptic_form(C, other.function*omega)
     
     def cartier(self):
         '''Computes Cartier operator on the form. Idea: y^m = f(x) -> y^(p^r - 1) = f(x)^M, where r = ord_p(m),
@@ -175,7 +178,7 @@ class superelliptic_form:
         fct = reduction(C, Fxy(y^m*fct))
         return superelliptic_form(C, fct/y^m)
     
-    def int(self):
+    def integral(self):
         '''Computes an "integral" of a form dg. Idea: y^m = f(x) -> y^(p^r - 1) = f(x)^M, where r = ord_p(m),
         M = (p^r - 1)/m. Thus h(x)/y^j dx = h(x) f(x)^(M*j)/y^(p^r * j) dx. Thus int(h(x)/y^j dx) = 1/y^(p^(r-1)*j) int(h(x) f(x)^(M*j) dx).'''
         C = self.curve
diff --git a/superelliptic/superelliptic_function_class.sage b/superelliptic/superelliptic_function_class.sage
index 570fb53..47f50b9 100644
--- a/superelliptic/superelliptic_function_class.sage
+++ b/superelliptic/superelliptic_function_class.sage
@@ -52,12 +52,13 @@ class superelliptic_function:
     
     def __mul__(self, other):
         C = self.curve
-        try:
+        F = C.base_ring
+        if isinstance(other, superelliptic_function):
             g1 = self.function
             g2 = other.function
             g = reduction(C, g1 * g2)
             return superelliptic_function(C, g)
-        except:
+        if isinstance(other, superelliptic_form):
             g1 = self.function
             g2 = other.form
             g = reduction(C, g1 * g2)
diff --git a/superelliptic_drw/regular_form.sage b/superelliptic_drw/regular_form.sage
index 193fd29..9766e67 100644
--- a/superelliptic_drw/regular_form.sage
+++ b/superelliptic_drw/regular_form.sage
@@ -15,7 +15,7 @@ class superelliptic_regular_form:
         C = self.curve
         return self.dx*C.dx + self.dy*C.y.diffn()
     
-    def int(self):
+    def integral(self):
         '''Regular integral. Works only for hyperelliptics.'''
         C = self.curve
         f = C.polynomial
@@ -23,15 +23,18 @@ class superelliptic_regular_form:
             raise ValueError("Works only for hyperelliptics.")
         F = C.base_ring
         Rx.<x> = PolynomialRing(F)
+        Fx = FractionField(Rx)
         Fxy, Rxy, x, y = C.fct_field
         if self.dx == 0*C.x and self.dy == 0*C.x:
             return 0*C.x
         #which = random.choice([0, 1])
-        P = self.dx.function
-        Q = self.dy.function
+        RxRy.<y> = PolynomialRing(Rx)
+        P = RxRy(self.dx.function)
+        Q = RxRy(self.dy.function)
         Py, Px = P.quo_rem(y) #P = y*Py + Px
         Qy, Qx = Q.quo_rem(y)
-        result = superelliptic_function(C, Rx(Px + 1/2*Qy*f.derivative()).integral())
+        Py, Px, Qy, Qx, f = Rx(Py), Rx(Px), Rx(Qy), Rx(Qx), Rx(f)
+        result = superelliptic_function(C, Rx(Px + F(1/2)*Qy*f.derivative()).integral())
         numerator = Rx(2*f*Py + f.derivative()*Qx)
         # Now numerator = 2W' f + W f'. We are looking for W. Then result is W*y.
         W = Rx(0)
diff --git a/superelliptic_drw/superelliptic_drw_auxilliaries.sage b/superelliptic_drw/superelliptic_drw_auxilliaries.sage
index 3f084d4..c6dafc7 100644
--- a/superelliptic_drw/superelliptic_drw_auxilliaries.sage
+++ b/superelliptic_drw/superelliptic_drw_auxilliaries.sage
@@ -5,7 +5,7 @@ def decomposition_g0_pth_power(fct):
         return (fct, 0*C.x)
     '''Decompose fct as g0 + A^p, if possible. Output: (g0, A).'''
     omega = fct.diffn().regular_form()
-    g0 = omega.int()
+    g0 = omega.integral()
     A = (fct - g0).pth_root()
     return (g0, A)
 
@@ -25,7 +25,7 @@ def decomposition_omega0_hpdh(omega):
         return (omega, 0*C.x)
     omega1 = omega.cartier().cartier()
     omega1 = omega1.inv_cartier().inv_cartier()
-    fct = (omega.cartier() - omega1.cartier()).int()
+    fct = (omega.cartier() - omega1.cartier()).integral()
     return (omega1, fct)
 
 def decomposition_omega8_hpdh(omega, prec = 50):
@@ -47,7 +47,7 @@ def decomposition_omega8_hpdh(omega, prec = 50):
     omega_analytic = superelliptic_function(C, omega_analytic)*Cv.diffn()
     omega8 = omega - omega_analytic
     dh = omega.cartier() - omega8.cartier()
-    h = dh.int()
+    h = dh.integral()
     return (omega8, h)
 
 def decomposition_g8_pth_power(fct, prec = 50):
diff --git a/superelliptic_drw/superelliptic_witt.sage b/superelliptic_drw/superelliptic_witt.sage
index 786ac8f..02e8d2f 100644
--- a/superelliptic_drw/superelliptic_witt.sage
+++ b/superelliptic_drw/superelliptic_witt.sage
@@ -135,8 +135,8 @@ def auxilliary_derivative(P):
     C = P.curve
     F = C.base_ring
     Rx.<x> = PolynomialRing(F)
-    P0 = Rx(P0)
-    P1 = Rx(P1)
+    P0 = Rx(P0.numerator())
+    P1 = Rx(P1.numerator())
     if P0 == 0:
         return superelliptic_drw_form(0*C.x, 0*C.dx, P.f)
     M = P0.monomials()[0]
diff --git a/superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage b/superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage
index 9963f4a..59544e1 100644
--- a/superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage
+++ b/superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage
@@ -6,6 +6,8 @@ f = x^3 - x
 C = superelliptic(f, m)
 Rxy.<x, y> = PolynomialRing(F, 2)
 omega = (((2*C.x^18 + 2*C.x^16 + 2*C.x^14 + 2*C.x^10 + 2*C.x^8 + 2*C.x^4 + 2*C.x^2 + 2*C.one)/(C.x^13 + C.x^11 + C.x^9))*C.y) * C.dx
-print(decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1] == omega and decomposition_omega0_omega8(aux.omega)[0].is_regular_on_U0() and decomposition_omega0_omega8(aux.omega)[1].is_regular_on_Uinfty())
+print(decomposition_omega0_omega8(omega)[0] - decomposition_omega0_omega8(omega)[1] == omega and decomposition_omega0_omega8(omega)[0].is_regular_on_U0() and decomposition_omega0_omega8(omega)[1].is_regular_on_Uinfty())
+
 h = ((C.x^10 + C.x^8 + C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)/C.x^6)*C.y
+print(decomposition_g0_g8(h))
 print(decomposition_g0_g8(h)[0] - decomposition_g0_g8(h)[1] + decomposition_g0_g8(h)[2] == h and decomposition_g0_g8(h)[0].function in Rxy and decomposition_g0_g8(h)[1].expansion_at_infty().valuation() >= 0)
\ No newline at end of file
diff --git a/tests.sage b/tests.sage
index 74cb3a1..6dd5760 100644
--- a/tests.sage
+++ b/tests.sage
@@ -9,23 +9,29 @@
 #load('superelliptic/tests/p_rank_test.sage')
 #print("a-number test:")
 #load('superelliptic/tests/a_number_test.sage')
-print("as_cover_test:")
-load('as_covers/tests/as_cover_test.sage')
-print("group_action_matrices_test:")
-load('as_covers/tests/group_action_matrices_test.sage')
-print("dual_element_test:")
-load('as_covers/tests/dual_element_test.sage')
-print("ith_component_test:")
-load('as_covers/tests/ith_component_test.sage')
-print("ith ramification group test:")
-load('as_covers/tests/ith_ramification_gp_test.sage')
-print("uniformizer test:")
-load('as_covers/tests/uniformizer_test.sage')
-print("ramification jumps test:")
-load('as_covers/tests/ramification_jumps_test.sage')
-print("diffn_test:")
-load('as_covers/tests/diffn_test.sage')
-print("Cartier test:")
-load('as_covers/tests/cartier_test.sage')
+#print("as_cover_test:")
+#load('as_covers/tests/as_cover_test.sage')
+#print("group_action_matrices_test:")
+#load('as_covers/tests/group_action_matrices_test.sage')
+#print("dual_element_test:")
+#load('as_covers/tests/dual_element_test.sage')
+#print("ith_component_test:")
+#load('as_covers/tests/ith_component_test.sage')
+#print("ith ramification group test:")
+#load('as_covers/tests/ith_ramification_gp_test.sage')
+#print("uniformizer test:")
+#load('as_covers/tests/uniformizer_test.sage')
+#print("ramification jumps test:")
+#load('as_covers/tests/ramification_jumps_test.sage')
+#print("diffn_test:")
+#load('as_covers/tests/diffn_test.sage')
+#print("Cartier test:")
+#load('as_covers/tests/cartier_test.sage')
 print("Decomposition into g0, g8/ omega0, omega8 test:")
-load('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')
\ No newline at end of file
+load('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')
+print("Auxilliary decomposition test:")
+load('superelliptic_drw/tests/auxilliary_decompositions_test.sage')
+print("Superelliptic de Rham-Witt test:")
+load('superelliptic_drw/tests/superelliptic_drw_tests.sage')
+
+