diff --git a/src/mapper/differentiator.py b/src/mapper/differentiator.py
index b377dce4251e4ab049eb254cd3132f79fc5e4d92..1bf9dc639485c93facd09dfa6d2bc6ca6f8bf5a2 100644
--- a/src/mapper/differentiator.py
+++ b/src/mapper/differentiator.py
@@ -65,9 +65,9 @@ class DifferentiationMapper:
             for i, child in enumerate(expr.Children)
             if not self._isc(child)))
 
-    def map_quotient(self, expr):
-        f = expr.Child1
-        g = expr.Child2
+    def map_rational(self, expr):
+        f = expr.numerator
+        g = expr.denominator
         f_const = self._isc(f)
         g_const = self._isc(g)
 
diff --git a/src/mapper/mapper.py b/src/mapper/mapper.py
index 3175a725a3b6078bb5fda60948e267a56e2b5101..7f17f05cb9193c6f21c91f2f17acb89a0fb4cdb2 100644
--- a/src/mapper/mapper.py
+++ b/src/mapper/mapper.py
@@ -37,14 +37,14 @@ class CombineMapper(ByArityMapper):
                             for child in expr.Children)
 
     def map_polynomial(self, expr):
-        return self.combine((expr.Base.invoke_mapper(self)) 
-                            + (child.invoke_mapper(self)
-                               for child in expr.Children))
+        return self.combine([expr.Base.invoke_mapper(self)] +
+                            [child.invoke_mapper(self)
+                             for child in expr.Children])
 
     def map_call(self, expr):
-        return self.combine((expr.Function.invoke_mapper(self))
-                            + (child.invoke_mapper(self)
-                               for child in expr.Parameters))
+        return self.combine([expr.Function.invoke_mapper(self)] + 
+                            [child.invoke_mapper(self)
+                             for child in expr.Parameters])
 
 
 
diff --git a/src/mapper/stringifier.py b/src/mapper/stringifier.py
index 71c9283ecad572f897c6e1b0e5ae48fb755193a7..d6ad121a2b0522661d174aee94f50c6f15a9f47a 100644
--- a/src/mapper/stringifier.py
+++ b/src/mapper/stringifier.py
@@ -19,9 +19,9 @@ class StringifyMapper:
     def map_product(self, expr):
         return "(%s)" % "*".join(i.invoke_mapper(self) for i in expr.Children)
 
-    def map_quotient(self, expr):
-        return "(%s/%s)" % (expr.Child1.invoke_mapper(self), 
-                            expr.Child2.invoke_mapper(self))
+    def map_rational(self, expr):
+        return "(%s/%s)" % (expr.numerator.invoke_mapper(self), 
+                            expr.denominator.invoke_mapper(self))
 
     def map_power(self, expr):
         return "(%s**%s)" % (expr.Child1.invoke_mapper(self), 
diff --git a/src/primitives.py b/src/primitives.py
index 613f36ca59d6f7f389caacf52ea93b4fad88be97..ff8848b1eaf3671a140384f3f52fae5c97c4949f 100644
--- a/src/primitives.py
+++ b/src/primitives.py
@@ -1,3 +1,4 @@
+import rational as rat
 import mapper.stringifier
 
 
@@ -60,11 +61,11 @@ class Expression(object):
             other = Constant(other)
         if not (other-1):
             return self
-        return RationalExpression(self, other)
+        return make_quotient(self, other)
 
     def __rdiv__(self, other):
         assert not isinstance(other, Expression)
-        return RationalExpression(Constant(other), self)
+        return make_quotient(Constant(other), self)
 
     def __pow__(self, other):
         if not isinstance(other, Expression):
@@ -285,7 +286,7 @@ class Sum(NAryExpression):
             return bool(self.Children[0])
         else:
             # FIXME: Right semantics?
-            return False
+            return True
 
     def invoke_mapper(self, mapper):
         return mapper.map_sum(self)
@@ -318,30 +319,49 @@ class Product(NAryExpression):
     def invoke_mapper(self, mapper):
         return mapper.map_product(self)
 
-class RationalExpression(Expression):
-    def __init__(self, numerator=None, denominator=1, rational=None):
-        if rational:
-            self.Rational = rational
-        else:
-            self.Rational = rat.Rational(numerator, denominator)
+class QuotientExpression(Expression):
+    def __init__(self, numerator, denominator=1):
+        self.Numerator = numerator
+        self.Denominator = denominator
 
     def _num(self):
-        return self.Rational.numerator
+        return self.Numerator
     numerator=property(_num)
 
     def _den(self):
-        return self.Rational.denominator
+        return self.Denominator
     denominator=property(_den)
 
     def __nonzero__(self):
-        return bool(self.Rational)
+        return bool(self.Numerator)
 
     def __hash__(self):
-        return hash(self.Rational)
+        return 0xa0a0aa ^ hash(self.Numerator) ^ hash(self.Denominator)
 
     def invoke_mapper(self, mapper):
         return mapper.map_rational(self)
 
+class RationalExpression(Expression):
+    def __init__(self, numerator, denominator=1):
+        self.Numerator = numerator
+        self.Denominator = denominator
+
+    def _num(self):
+        return self.Numerator
+    numerator=property(_num)
+
+    def _den(self):
+        return self.Denominator
+    denominator=property(_den)
+
+    def __nonzero__(self):
+        return bool(self.Numerator)
+
+    def __hash__(self):
+        return 0xa0a0aa ^ hash(self.Numerator) ^ hash(self.Denominator)
+
+    def invoke_mapper(self, mapper):
+        return mapper.map_rational(self)
 
 class Power(BinaryExpression):
     def invoke_mapper(self, mapper):
@@ -388,3 +408,15 @@ def make_product(components):
 def polynomial_from_expression(expression):
     pass
 
+def make_quotient(numerator, denominator):
+    try:
+        if isinstance(traits.traits(numerator, denominator), EuclideanRingTraits):
+            return RationalExpression(numerator, denominator)
+    except traits.NoCommonTraitsError:
+        pass
+    except traits.NoTraitsError:
+        pass
+
+    return QuotientExpression(numerator, denominator)
+
+# FIXME: add traits types to expressions
diff --git a/src/traits.py b/src/traits.py
index 60d910c464a71ab8ee28a3db888e16fbc0997492..b77c972c9e6e545f0cde2ed1e964b7797bdeff1d 100644
--- a/src/traits.py
+++ b/src/traits.py
@@ -3,13 +3,22 @@ import algorithm
 
 
 
+class NoTraitsError(Exception):
+    pass
+
+class NoCommonTraitsError(Exception):
+    pass
+
+
+
+
 def traits(x):
     try:
         return x.traits()
     except AttributeError:
         if isinstance(x, (complex, float)): return FieldTraits
         if isinstance(x, int): return IntegerTraits
-        raise NotImplementedError
+        raise NoTraitsError
 
 
 
@@ -21,7 +30,8 @@ def common_traits(*args):
         elif isinstance(t_x, t_y.__class__):
             return t_x
         else:
-            raise RuntimeError, "No common traits type between '%s' and '%s'" % \
+            raise NoCommonTraitsError, \
+                  "No common traits type between '%s' and '%s'" % \
                   (t_x.__class__.__name__, t_y.__class__.__name__)
 
     return reduce(common_traits_two, (traits(arg) for arg in args))