'_constant',
         '_symbols',
         '_dimension',
+        '_hash',
     )
 
     def __new__(cls, coefficients=None, constant=0):
         self._constant = constant
         self._symbols = tuple(self._coefficients)
         self._dimension = len(self._symbols)
+        self._hash = hash((tuple(self._coefficients.items()), self._constant))
         return self
 
     def coefficient(self, symbol):
     def dimension(self):
         return self._dimension
 
+    def __hash__(self):
+        return self._hash
+
     def isconstant(self):
         return False
 
         from .polyhedra import Gt
         return Gt(self, other)
 
-    def __hash__(self):
-        return hash((tuple(self.coefficients()), self._constant))
-
     def _toint(self):
         lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
             [value.denominator for value in self.values()])
             raise TypeError('name must be a string or a Symbol instance')
         name = name.strip()
         self = object().__new__(cls)
-        self._coefficients = {name: 1}
+        self._coefficients = OrderedDict([(name, 1)])
         self._constant = 0
         self._symbols = tuple(name)
         self._name = name
         self._dimension = 1
+        self._hash = hash(self._name)
         return self
 
     @property
             self._constant = numerator.constant
         else:
             self._constant = Fraction(numerator, denominator)
-        self._coefficients = {}
+        self._coefficients = OrderedDict()
         self._symbols = ()
         self._dimension = 0
+        self._hash = hash(self._constant)
         return self
 
     def isconstant(self):