diff --git a/src/tea3/pretty_print.py b/src/tea3/pretty_print.py
index 5fa6706..2959a13 100644
--- a/src/tea3/pretty_print.py
+++ b/src/tea3/pretty_print.py
@@ -1,38 +1,20 @@
-### print
-
-def monomial_to_str(exp, names):
-    factors = []
-    for i, e in enumerate(exp):
-        if e == 0:
-            continue
-        name = names[i]
-        if e == 1:
-            factors.append(name)
-        else:
-            factors.append(f"{name}^{e}")
-    return "*".join(factors) if factors else "1"
-
-
 def pretty_print(poly):
     ring = poly.parent()
-    names = ring.variable_names()
 
     R_terms = []
     r_terms = []
     x_terms = []
     mixed_terms = []
-    has_const = False
 
-    for exp, coeff in poly.dict().items():
-        if coeff == 0:
+    has_const = bool(poly.constant_coefficient())
+
+    for monom in poly:
+        vars_in_term = [str(v) for v in monom.variables()]
+
+        if not vars_in_term:
             continue
 
-        if sum(exp) == 0:
-            has_const = True
-            continue
-
-        term = monomial_to_str(exp, names)
-        vars_in_term = [names[i] for i, e in enumerate(exp) if e != 0]
+        term = "*".join(vars_in_term)
         families = {v[0] for v in vars_in_term}
 
         if families == {"R"}:
diff --git a/src/tea3/tea3model.py b/src/tea3/tea3model.py
index a1992e6..caca556 100644
--- a/src/tea3/tea3model.py
+++ b/src/tea3/tea3model.py
@@ -1,4 +1,4 @@
-from sage.all import GF, PolynomialRing
+from sage.all import GF, BooleanPolynomialRing
 
 from tea3.constants import TEA3_SBOX, T_F1, T_F2
 from tea3.pretty_print import pretty_print, pretty_print_vec
@@ -14,7 +14,8 @@ class Tea3Model:
             [f"R{i}{j}" for i in range(8) for j in range(8)]
         )
 
-        self.S = PolynomialRing(self.F, names)
+        name_string = ",".join(names)
+        self.S = BooleanPolynomialRing(len(names), name_string)
         self.v = self.S.gens()
 
         self.x_bits = [list(self.v[i*8:(i+1)*8]) for i in range(5)]
@@ -99,7 +100,7 @@ def G32(X, Y):
 
 
 t = Tea3Model()
-for i in range(3):
+for i in range(4):
     print("step "+str(i))
     t.step()
-    print(pretty_print_vec(t.R_bits[0]))
+    print(pretty_print(t.R_bits[0][0]))