Index: Demo/classes/Rat.py
===================================================================
--- Demo/classes/Rat.py	(revision 59590)
+++ Demo/classes/Rat.py	(working copy)
@@ -1,306 +0,0 @@
-'''\
-This module implements rational numbers.
-
-The entry point of this module is the function
-        rat(numerator, denominator)
-If either numerator or denominator is of an integral or rational type,
-the result is a rational number, else, the result is the simplest of
-the types float and complex which can hold numerator/denominator.
-If denominator is omitted, it defaults to 1.
-Rational numbers can be used in calculations with any other numeric
-type.  The result of the calculation will be rational if possible.
-
-There is also a test function with calling sequence
-        test()
-The documentation string of the test function contains the expected
-output.
-'''
-
-# Contributed by Sjoerd Mullender
-
-from types import *
-
-def gcd(a, b):
-    '''Calculate the Greatest Common Divisor.'''
-    while b:
-        a, b = b, a%b
-    return a
-
-def rat(num, den = 1):
-    # must check complex before float
-    if isinstance(num, complex) or isinstance(den, complex):
-        # numerator or denominator is complex: return a complex
-        return complex(num) / complex(den)
-    if isinstance(num, float) or isinstance(den, float):
-        # numerator or denominator is float: return a float
-        return float(num) / float(den)
-    # otherwise return a rational
-    return Rat(num, den)
-
-class Rat:
-    '''This class implements rational numbers.'''
-
-    def __init__(self, num, den = 1):
-        if den == 0:
-            raise ZeroDivisionError('rat(x, 0)')
-
-        # normalize
-
-        # must check complex before float
-        if (isinstance(num, complex) or
-            isinstance(den, complex)):
-            # numerator or denominator is complex:
-            # normalized form has denominator == 1+0j
-            self.__num = complex(num) / complex(den)
-            self.__den = complex(1)
-            return
-        if isinstance(num, float) or isinstance(den, float):
-            # numerator or denominator is float:
-            # normalized form has denominator == 1.0
-            self.__num = float(num) / float(den)
-            self.__den = 1.0
-            return
-        if (isinstance(num, self.__class__) or
-            isinstance(den, self.__class__)):
-            # numerator or denominator is rational
-            new = num / den
-            if not isinstance(new, self.__class__):
-                self.__num = new
-                if isinstance(new, complex):
-                    self.__den = complex(1)
-                else:
-                    self.__den = 1.0
-            else:
-                self.__num = new.__num
-                self.__den = new.__den
-        else:
-            # make sure numerator and denominator don't
-            # have common factors
-            # this also makes sure that denominator > 0
-            g = gcd(num, den)
-            self.__num = num / g
-            self.__den = den / g
-        # try making numerator and denominator of IntType if they fit
-        try:
-            numi = int(self.__num)
-            deni = int(self.__den)
-        except (OverflowError, TypeError):
-            pass
-        else:
-            if self.__num == numi and self.__den == deni:
-                self.__num = numi
-                self.__den = deni
-
-    def __repr__(self):
-        return 'Rat(%s,%s)' % (self.__num, self.__den)
-
-    def __str__(self):
-        if self.__den == 1:
-            return str(self.__num)
-        else:
-            return '(%s/%s)' % (str(self.__num), str(self.__den))
-
-    # a + b
-    def __add__(a, b):
-        try:
-            return rat(a.__num * b.__den + b.__num * a.__den,
-                       a.__den * b.__den)
-        except OverflowError:
-            return rat(int(a.__num) * int(b.__den) +
-                       int(b.__num) * int(a.__den),
-                       int(a.__den) * int(b.__den))
-
-    def __radd__(b, a):
-        return Rat(a) + b
-
-    # a - b
-    def __sub__(a, b):
-        try:
-            return rat(a.__num * b.__den - b.__num * a.__den,
-                       a.__den * b.__den)
-        except OverflowError:
-            return rat(int(a.__num) * int(b.__den) -
-                       int(b.__num) * int(a.__den),
-                       int(a.__den) * int(b.__den))
-
-    def __rsub__(b, a):
-        return Rat(a) - b
-
-    # a * b
-    def __mul__(a, b):
-        try:
-            return rat(a.__num * b.__num, a.__den * b.__den)
-        except OverflowError:
-            return rat(int(a.__num) * int(b.__num),
-                       int(a.__den) * int(b.__den))
-
-    def __rmul__(b, a):
-        return Rat(a) * b
-
-    # a / b
-    def __div__(a, b):
-        try:
-            return rat(a.__num * b.__den, a.__den * b.__num)
-        except OverflowError:
-            return rat(int(a.__num) * int(b.__den),
-                       int(a.__den) * int(b.__num))
-
-    def __rdiv__(b, a):
-        return Rat(a) / b
-
-    # a % b
-    def __mod__(a, b):
-        div = a / b
-        try:
-            div = int(div)
-        except OverflowError:
-            div = int(div)
-        return a - b * div
-
-    def __rmod__(b, a):
-        return Rat(a) % b
-
-    # a ** b
-    def __pow__(a, b):
-        if b.__den != 1:
-            if isinstance(a.__num, complex):
-                a = complex(a)
-            else:
-                a = float(a)
-            if isinstance(b.__num, complex):
-                b = complex(b)
-            else:
-                b = float(b)
-            return a ** b
-        try:
-            return rat(a.__num ** b.__num, a.__den ** b.__num)
-        except OverflowError:
-            return rat(int(a.__num) ** b.__num,
-                       int(a.__den) ** b.__num)
-
-    def __rpow__(b, a):
-        return Rat(a) ** b
-
-    # -a
-    def __neg__(a):
-        try:
-            return rat(-a.__num, a.__den)
-        except OverflowError:
-            # a.__num == sys.maxint
-            return rat(-int(a.__num), a.__den)
-
-    # abs(a)
-    def __abs__(a):
-        return rat(abs(a.__num), a.__den)
-
-    # int(a)
-    def __int__(a):
-        return int(a.__num / a.__den)
-
-    # long(a)
-    def __long__(a):
-        return int(a.__num) / int(a.__den)
-
-    # float(a)
-    def __float__(a):
-        return float(a.__num) / float(a.__den)
-
-    # complex(a)
-    def __complex__(a):
-        return complex(a.__num) / complex(a.__den)
-
-    # cmp(a,b)
-    def __cmp__(a, b):
-        diff = Rat(a - b)
-        if diff.__num < 0:
-            return -1
-        elif diff.__num > 0:
-            return 1
-        else:
-            return 0
-
-    def __rcmp__(b, a):
-        return cmp(Rat(a), b)
-
-    # a != 0
-    def __bool__(a):
-        return a.__num != 0
-
-def test():
-    '''\
-    Test function for rat module.
-
-    The expected output is (module some differences in floating
-    precission):
-    -1
-    -1
-    0 0L 0.1 (0.1+0j)
-    [Rat(1,2), Rat(-3,10), Rat(1,25), Rat(1,4)]
-    [Rat(-3,10), Rat(1,25), Rat(1,4), Rat(1,2)]
-    0
-    (11/10)
-    (11/10)
-    1.1
-    OK
-    2 1.5 (3/2) (1.5+1.5j) (15707963/5000000)
-    2 2 2.0 (2+0j)
-
-    4 0 4 1 4 0
-    3.5 0.5 3.0 1.33333333333 2.82842712475 1
-    (7/2) (1/2) 3 (4/3) 2.82842712475 1
-    (3.5+1.5j) (0.5-1.5j) (3+3j) (0.666666666667-0.666666666667j) (1.43248815986+2.43884761145j) 1
-    1.5 1 1.5 (1.5+0j)
-
-    3.5 -0.5 3.0 0.75 2.25 -1
-    3.0 0.0 2.25 1.0 1.83711730709 0
-    3.0 0.0 2.25 1.0 1.83711730709 1
-    (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1
-    (3/2) 1 1.5 (1.5+0j)
-
-    (7/2) (-1/2) 3 (3/4) (9/4) -1
-    3.0 0.0 2.25 1.0 1.83711730709 -1
-    3 0 (9/4) 1 1.83711730709 0
-    (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1
-    (1.5+1.5j) (1.5+1.5j)
-
-    (3.5+1.5j) (-0.5+1.5j) (3+3j) (0.75+0.75j) 4.5j -1
-    (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1
-    (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1
-    (3+3j) 0j 4.5j (1+0j) (-0.638110484918+0.705394566962j) 0
-    '''
-    print(rat(-1, 1))
-    print(rat(1, -1))
-    a = rat(1, 10)
-    print(int(a), int(a), float(a), complex(a))
-    b = rat(2, 5)
-    l = [a+b, a-b, a*b, a/b]
-    print(l)
-    l.sort()
-    print(l)
-    print(rat(0, 1))
-    print(a+1)
-    print(a+1)
-    print(a+1.0)
-    try:
-        print(rat(1, 0))
-        raise SystemError('should have been ZeroDivisionError')
-    except ZeroDivisionError:
-        print('OK')
-    print(rat(2), rat(1.5), rat(3, 2), rat(1.5+1.5j), rat(31415926,10000000))
-    list = [2, 1.5, rat(3,2), 1.5+1.5j]
-    for i in list:
-        print(i, end=' ')
-        if not isinstance(i, complex):
-            print(int(i), float(i), end=' ')
-        print(complex(i))
-        print()
-        for j in list:
-            print(i + j, i - j, i * j, i / j, i ** j, end=' ')
-            if not (isinstance(i, complex) or
-                    isinstance(j, complex)):
-                print(cmp(i, j))
-            print()
-
-
-if __name__ == '__main__':
-    test()
Index: Lib/rational.py
===================================================================
--- Lib/rational.py	(revision 59566)
+++ Lib/rational.py	(working copy)
@@ -1,306 +1,271 @@
-'''\
-This module implements rational numbers.
+# Contributed by Sjoerd Mullender
 
-The entry point of this module is the function
-        rat(numerator, denominator)
-If either numerator or denominator is of an integral or rational type,
-the result is a rational number, else, the result is the simplest of
-the types float and complex which can hold numerator/denominator.
-If denominator is omitted, it defaults to 1.
-Rational numbers can be used in calculations with any other numeric
-type.  The result of the calculation will be rational if possible.
+"""Rational, infinite-precision, real numbers."""
 
-There is also a test function with calling sequence
-        test()
-The documentation string of the test function contains the expected
-output.
-'''
+import math
+import numbers
+import operator
 
-# Contributed by Sjoerd Mullender
+__all__ = ["Rational"]
 
-from types import *
+RationalAbc = numbers.Rational
 
-def gcd(a, b):
-    '''Calculate the Greatest Common Divisor.'''
+def _gcd(a:numbers.Integral, b:numbers.Integral):
+    """Calculate the Greatest Common Divisor."""
     while b:
         a, b = b, a%b
     return a
 
-def rat(num, den = 1):
-    # must check complex before float
-    if isinstance(num, complex) or isinstance(den, complex):
-        # numerator or denominator is complex: return a complex
-        return complex(num) / complex(den)
-    if isinstance(num, float) or isinstance(den, float):
-        # numerator or denominator is float: return a float
-        return float(num) / float(den)
-    # otherwise return a rational
-    return Rat(num, den)
+class Rational(RationalAbc):
+    """This class implements rational numbers.
 
-class Rat:
-    '''This class implements rational numbers.'''
+    Rational(8, 6) will produce a rational number equivalent to
+    4/3. Both arguments must be convertible to ints. The denominator
+    defaults to 1 so that Rational(3) == 3.
 
-    def __init__(self, num, den = 1):
-        if den == 0:
-            raise ZeroDivisionError('rat(x, 0)')
+    """
 
-        # normalize
+    __slots__ = ('_numerator', '_denominator')
 
-        # must check complex before float
-        if (isinstance(num, complex) or
-            isinstance(den, complex)):
-            # numerator or denominator is complex:
-            # normalized form has denominator == 1+0j
-            self.__num = complex(num) / complex(den)
-            self.__den = complex(1)
-            return
-        if isinstance(num, float) or isinstance(den, float):
-            # numerator or denominator is float:
-            # normalized form has denominator == 1.0
-            self.__num = float(num) / float(den)
-            self.__den = 1.0
-            return
-        if (isinstance(num, self.__class__) or
-            isinstance(den, self.__class__)):
-            # numerator or denominator is rational
-            new = num / den
-            if not isinstance(new, self.__class__):
-                self.__num = new
-                if isinstance(new, complex):
-                    self.__den = complex(1)
-                else:
-                    self.__den = 1.0
-            else:
-                self.__num = new.__num
-                self.__den = new.__den
-        else:
-            # make sure numerator and denominator don't
-            # have common factors
-            # this also makes sure that denominator > 0
-            g = gcd(num, den)
-            self.__num = num / g
-            self.__den = den / g
-        # try making numerator and denominator of IntType if they fit
-        try:
-            numi = int(self.__num)
-            deni = int(self.__den)
-        except (OverflowError, TypeError):
-            pass
-        else:
-            if self.__num == numi and self.__den == deni:
-                self.__num = numi
-                self.__den = deni
+    def __init__(self,
+                 numerator:numbers.Integral, 
+                 denominator:numbers.Integral=1):
+        if (not isinstance(numerator, numbers.Integral) or
+            not isinstance(denominator, numbers.Integral)):
+            raise TypeError("Rational(%(numerator)s, %(denominator)s):"
+                            " Both arguments must be integral." % locals())
 
+        if denominator == 0:
+            raise ZeroDivisionError('Rational(%s, 0)' % numerator)
+
+        g = _gcd(numerator, denominator)
+        self._numerator = int(numerator / g)
+        self._denominator = int(denominator / g)
+
+    @property
+    def numerator(a):
+        return a._numerator
+
+    @property
+    def denominator(a):
+        return a._denominator
+
     def __repr__(self):
-        return 'Rat(%s,%s)' % (self.__num, self.__den)
+        """repr(self)"""
+        return ('rational.Rational(%r,%r)' %
+                (self.numerator, self.denominator))
 
     def __str__(self):
-        if self.__den == 1:
-            return str(self.__num)
+        """str(self)"""
+        if self.denominator == 1:
+            return str(self.numerator)
         else:
-            return '(%s/%s)' % (str(self.__num), str(self.__den))
+            return '(%s/%s)' % (self.numerator, self.denominator)
 
-    # a + b
-    def __add__(a, b):
-        try:
-            return rat(a.__num * b.__den + b.__num * a.__den,
-                       a.__den * b.__den)
-        except OverflowError:
-            return rat(int(a.__num) * int(b.__den) +
-                       int(b.__num) * int(a.__den),
-                       int(a.__den) * int(b.__den))
+    def _operator_fallbacks(monomorphic_operator, fallback_operator):
+        """Generates forward and reverse operators given a purely-rational
+        operator and a function from the operator module.
 
-    def __radd__(b, a):
-        return Rat(a) + b
+        Use this like:
+        __op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
 
-    # a - b
-    def __sub__(a, b):
-        try:
-            return rat(a.__num * b.__den - b.__num * a.__den,
-                       a.__den * b.__den)
-        except OverflowError:
-            return rat(int(a.__num) * int(b.__den) -
-                       int(b.__num) * int(a.__den),
-                       int(a.__den) * int(b.__den))
+        """
+        def forward(a, b):
+            if isinstance(b, RationalAbc):
+                return monomorphic_operator(a, b)
+            elif isinstance(b, float):
+                return fallback_operator(float(a), b)
+            elif isinstance(b, complex):
+                return fallback_operator(complex(a), b)
+            else:
+                return NotImplemented
+        forward.__name__ = '__' + fallback_operator.__name__ + '__'
+        forward.__doc__ = monomorphic_operator.__doc__
 
-    def __rsub__(b, a):
-        return Rat(a) - b
+        def reverse(b, a):
+            if isinstance(a, RationalAbc):
+                return monomorphic_operator(a, b)
+            elif isinstance(a, numbers.Real):
+                return fallback_operator(float(a), float(b))
+            elif isinstance(a, numbers.Complex):
+                return fallback_operator(complex(a), complex(b))
+            else:
+                return NotImplemented
+        reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
+        reverse.__doc__ = monomorphic_operator.__doc__
 
-    # a * b
-    def __mul__(a, b):
-        try:
-            return rat(a.__num * b.__num, a.__den * b.__den)
-        except OverflowError:
-            return rat(int(a.__num) * int(b.__num),
-                       int(a.__den) * int(b.__den))
+        return forward, reverse
 
-    def __rmul__(b, a):
-        return Rat(a) * b
+    def _add(a:RationalAbc, b:RationalAbc):
+        """a + b"""
+        return Rational(a.numerator * b.denominator + 
+                        b.numerator * a.denominator,
+                        a.denominator * b.denominator)
 
-    # a / b
-    def __div__(a, b):
-        try:
-            return rat(a.__num * b.__den, a.__den * b.__num)
-        except OverflowError:
-            return rat(int(a.__num) * int(b.__den),
-                       int(a.__den) * int(b.__num))
+    __add__, __radd__ = _operator_fallbacks(_add, operator.add)
 
-    def __rdiv__(b, a):
-        return Rat(a) / b
+    def _sub(a, b):
+        """a - b"""
+        return Rational(a.numerator * b.denominator - 
+                        b.numerator * a.denominator,
+                        a.denominator * b.denominator)
 
-    # a % b
-    def __mod__(a, b):
-        div = a / b
-        try:
-            div = int(div)
-        except OverflowError:
-            div = int(div)
+    __sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub)
+
+    def _mul(a, b):
+        """a * b"""
+        return Rational(a.numerator * b.numerator, a.denominator * b.denominator)
+
+    __mul__, __rmul__ = _operator_fallbacks(_mul, operator.mul)
+
+    def _div(a:RationalAbc, b:RationalAbc):
+        """a / b"""
+        return Rational(a.numerator * b.denominator, 
+                        a.denominator * b.numerator)
+
+    __truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv)
+
+    def __floordiv__(a, b):
+        """a // b"""
+        return math.floor(a / b)
+
+    def __rfloordiv__(b, a):
+        """a // b"""
+        return math.floor(a / b)
+
+    @classmethod
+    def _mod(cls, a, b):
+        div = a // b
         return a - b * div
+        
+    def __mod__(a, b):
+        """a % b"""
+        return a._mod(a, b)
 
     def __rmod__(b, a):
-        return Rat(a) % b
+        """a % b"""
+        return b._mod(a, b)
 
-    # a ** b
     def __pow__(a, b):
-        if b.__den != 1:
-            if isinstance(a.__num, complex):
-                a = complex(a)
+        """a ** b
+
+        If b is not an integer, the result will be a float since roots
+        are generally irrational. If b is an integer, the result will
+        be rational.
+
+        """
+        if isinstance(b, RationalAbc):
+            if b.denominator == 1:
+                power = b.numerator
+                if power >= 0:
+                    return Rational(a.numerator ** power, 
+                                    a.denominator ** power)
+                else:
+                    return Rational(a.denominator ** -power,
+                                    a.numerator ** -power)
             else:
-                a = float(a)
-            if isinstance(b.__num, complex):
-                b = complex(b)
-            else:
-                b = float(b)
-            return a ** b
-        try:
-            return rat(a.__num ** b.__num, a.__den ** b.__num)
-        except OverflowError:
-            return rat(int(a.__num) ** b.__num,
-                       int(a.__den) ** b.__num)
+                # A fractional power will generally produce an
+                # irrational number.
+                return float(a) ** float(b)
+        else:
+            return float(a) ** b
 
     def __rpow__(b, a):
-        return Rat(a) ** b
+        """a ** b"""
+        if b.denominator == 1 and b.numerator >= 0:
+            # If a is an int, keep it that way if possible.
+            return a ** b.numerator
 
-    # -a
-    def __neg__(a):
-        try:
-            return rat(-a.__num, a.__den)
-        except OverflowError:
-            # a.__num == sys.maxint
-            return rat(-int(a.__num), a.__den)
+        if isinstance(a, RationalAbc):
+            return Rational(a.numerator, a.denominator) ** b
 
-    # abs(a)
-    def __abs__(a):
-        return rat(abs(a.__num), a.__den)
+        if b.denominator == 1:
+            return a ** b.numerator
 
-    # int(a)
-    def __int__(a):
-        return int(a.__num / a.__den)
+        return a ** float(b)
 
-    # long(a)
-    def __long__(a):
-        return int(a.__num) / int(a.__den)
+    def __neg__(a):
+        """-a"""
+        return Rational(-a.numerator, a.denominator)
 
-    # float(a)
-    def __float__(a):
-        return float(a.__num) / float(a.__den)
+    def __abs__(a):
+        """abs(a)"""
+        return Rational(abs(a.numerator), a.denominator)
 
-    # complex(a)
-    def __complex__(a):
-        return complex(a.__num) / complex(a.__den)
-
-    # cmp(a,b)
-    def __cmp__(a, b):
-        diff = Rat(a - b)
-        if diff.__num < 0:
-            return -1
-        elif diff.__num > 0:
-            return 1
+    def __trunc__(a):
+        """trunc(a)"""
+        if a.numerator < 0:
+            return -(abs(a.numerator) // a.denominator)
         else:
-            return 0
+            return a.numerator // a.denominator
 
-    def __rcmp__(b, a):
-        return cmp(Rat(a), b)
+    def __floor__(a):
+        """math.floor(a)"""
+        return a.numerator // a.denominator
 
-    # a != 0
-    def __bool__(a):
-        return a.__num != 0
+    def __ceil__(a):
+        """math.ceil(a)"""
+        floor, remainder = divmod(a.numerator, a.denominator)
+        if remainder == 0:
+            return floor
+        else:
+            return floor + 1
 
-def test():
-    '''\
-    Test function for rat module.
+    def __round__(self, ndigits=None):
+        """round(self, ndigits)"""
+        if ndigits is None:
+            floor, remainder = divmod(self.numerator, self.denominator)
+            if remainder * 2 < self.denominator:
+                return floor
+            elif remainder * 2 > self.denominator:
+                return floor + 1
+            # Deal with the half case:
+            elif floor % 2 == 0:
+                return floor
+            else:
+                return floor + 1
+        shift = 10**abs(ndigits)
+        if ndigits > 0:
+            return Rational(round(shift * self), shift)
+        else:
+            return Rational((self // shift) * shift)
 
-    The expected output is (module some differences in floating
-    precission):
-    -1
-    -1
-    0 0L 0.1 (0.1+0j)
-    [Rat(1,2), Rat(-3,10), Rat(1,25), Rat(1,4)]
-    [Rat(-3,10), Rat(1,25), Rat(1,4), Rat(1,2)]
-    0
-    (11/10)
-    (11/10)
-    1.1
-    OK
-    2 1.5 (3/2) (1.5+1.5j) (15707963/5000000)
-    2 2 2.0 (2+0j)
+    def __eq__(a, b):
+        """a == b"""
+        if isinstance(b, RationalAbc):
+            return (a.numerator == b.numerator and
+                    a.denominator == b.denominator)
+        else:
+            return float(a) == b
+    
+    @classmethod
+    def _makeComparableWithZero(cls, diff):
+        """Helper function for comparison operators.
 
-    4 0 4 1 4 0
-    3.5 0.5 3.0 1.33333333333 2.82842712475 1
-    (7/2) (1/2) 3 (4/3) 2.82842712475 1
-    (3.5+1.5j) (0.5-1.5j) (3+3j) (0.666666666667-0.666666666667j) (1.43248815986+2.43884761145j) 1
-    1.5 1 1.5 (1.5+0j)
+        Returns a value such that comparing with 0 won't recurse.
 
-    3.5 -0.5 3.0 0.75 2.25 -1
-    3.0 0.0 2.25 1.0 1.83711730709 0
-    3.0 0.0 2.25 1.0 1.83711730709 1
-    (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1
-    (3/2) 1 1.5 (1.5+0j)
+        """
+        if isinstance(diff, RationalAbc):
+            return diff.numerator
+        else:
+            return diff
+        
+    def __lt__(a, b):
+        """a < b"""
+        return a._makeComparableWithZero(a - b) < 0
 
-    (7/2) (-1/2) 3 (3/4) (9/4) -1
-    3.0 0.0 2.25 1.0 1.83711730709 -1
-    3 0 (9/4) 1 1.83711730709 0
-    (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1
-    (1.5+1.5j) (1.5+1.5j)
+    def __gt__(a, b):
+        """a > b"""
+        return a._makeComparableWithZero(a - b) > 0
 
-    (3.5+1.5j) (-0.5+1.5j) (3+3j) (0.75+0.75j) 4.5j -1
-    (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1
-    (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1
-    (3+3j) 0j 4.5j (1+0j) (-0.638110484918+0.705394566962j) 0
-    '''
-    print(rat(-1, 1))
-    print(rat(1, -1))
-    a = rat(1, 10)
-    print(int(a), int(a), float(a), complex(a))
-    b = rat(2, 5)
-    l = [a+b, a-b, a*b, a/b]
-    print(l)
-    l.sort()
-    print(l)
-    print(rat(0, 1))
-    print(a+1)
-    print(a+1)
-    print(a+1.0)
-    try:
-        print(rat(1, 0))
-        raise SystemError('should have been ZeroDivisionError')
-    except ZeroDivisionError:
-        print('OK')
-    print(rat(2), rat(1.5), rat(3, 2), rat(1.5+1.5j), rat(31415926,10000000))
-    list = [2, 1.5, rat(3,2), 1.5+1.5j]
-    for i in list:
-        print(i, end=' ')
-        if not isinstance(i, complex):
-            print(int(i), float(i), end=' ')
-        print(complex(i))
-        print()
-        for j in list:
-            print(i + j, i - j, i * j, i / j, i ** j, end=' ')
-            if not (isinstance(i, complex) or
-                    isinstance(j, complex)):
-                print(cmp(i, j))
-            print()
+    def __le__(a, b):
+        """a <= b"""
+        return a._makeComparableWithZero(a - b) <= 0
 
+    def __ge__(a, b):
+        """a >= b"""
+        return a._makeComparableWithZero(a - b) >= 0
 
-if __name__ == '__main__':
-    test()
+    def __bool__(a):
+        """a != 0"""
+        return a.numerator != 0
Index: Lib/numbers.py
===================================================================
--- Lib/numbers.py	(revision 59590)
+++ Lib/numbers.py	(working copy)
@@ -119,12 +119,12 @@
         raise NotImplementedError
 
     @abstractmethod
-    def __div__(self, other):
+    def __truediv__(self, other):
         """self / other; should promote to float or complex when necessary."""
         raise NotImplementedError
 
     @abstractmethod
-    def __rdiv__(self, other):
+    def __rtruediv__(self, other):
         """other / self"""
         raise NotImplementedError
 
Index: Lib/test/test_rational.py
===================================================================
--- Lib/test/test_rational.py	(revision 0)
+++ Lib/test/test_rational.py	(revision 0)
@@ -0,0 +1,156 @@
+"""Tests for Lib/rational.py."""
+
+from test.test_support import run_unittest, verbose
+import math
+import rational
+import unittest
+R = rational.Rational
+
+class RationalTest(unittest.TestCase):
+
+    def assertExactlyEquals(self, expected, actual):
+        """Asserts that both the types and values are the same."""
+        self.assertEquals(type(expected), type(actual))
+        self.assertEquals(expected, actual)
+
+    def testInit(self):
+        def components(r):
+            return (r.numerator, r.denominator)
+        self.assertEquals((-1, 1), components(R(-1, 1)))
+        self.assertEquals((-1, 1), components(R(1, -1)))
+        self.assertEquals((1, 2), components(R(5, 10)))
+        self.assertEquals((7, 15), components(R(7, 15)))
+
+        try:
+            R(12, 0)
+            self.fail("R(12, 0) failed to raise ZeroDivisionError")
+        except ZeroDivisionError as e:
+            self.assertEquals("Rational(12, 0)", str(e))
+
+        self.assertRaises(TypeError, R, 1.5)
+        self.assertRaises(TypeError, R, 1.5 + 3j)
+
+    def testConversions(self):
+        self.assertExactlyEquals(-1, trunc(R(-11, 10)))
+        self.assertExactlyEquals(-2, math.floor(R(-11, 10)))
+        self.assertExactlyEquals(-1, math.ceil(R(-11, 10)))
+        self.assertExactlyEquals(-1, math.ceil(R(-10, 10)))
+
+        self.assertExactlyEquals(0, round(R(-1, 10)))
+        self.assertExactlyEquals(0, round(R(-5, 10)))
+        self.assertExactlyEquals(-2, round(R(-15, 10)))
+        self.assertExactlyEquals(-1, round(R(-7, 10)))
+        
+        self.assertExactlyEquals(0.1, float(R(1, 10)))
+        self.assertExactlyEquals(0.1+0j, complex(R(1,10)))
+
+
+    def testArithmetic(self):
+        self.assertEquals(R(1, 2), R(1, 10) + R(2, 5))
+        self.assertEquals(R(-3, 10), R(1, 10) - R(2, 5))
+        self.assertEquals(R(1, 25), R(1, 10) * R(2, 5))
+        self.assertEquals(R(1, 4), R(1, 10) / R(2, 5))
+
+    def testMixedArithmetic(self):
+        self.assertExactlyEquals(R(11, 10), R(1, 10) + 1)
+        self.assertExactlyEquals(1.1, R(1, 10) + 1.0)
+        self.assertExactlyEquals(1.1 + 0j, R(1, 10) + (1.0 + 0j))
+        self.assertExactlyEquals(R(11, 10), 1 + R(1, 10))
+        self.assertExactlyEquals(1.1, 1.0 + R(1, 10))
+        self.assertExactlyEquals(1.1 + 0j, (1.0 + 0j) + R(1, 10))
+
+        self.assertExactlyEquals(R(-9, 10), R(1, 10) - 1)
+        self.assertExactlyEquals(-0.9, R(1, 10) - 1.0)
+        self.assertExactlyEquals(-0.9 + 0j, R(1, 10) - (1.0 + 0j))
+        self.assertExactlyEquals(R(9, 10), 1 - R(1, 10))
+        self.assertExactlyEquals(0.9, 1.0 - R(1, 10))
+        self.assertExactlyEquals(0.9 + 0j, (1.0 + 0j) - R(1, 10))
+
+        self.assertExactlyEquals(R(1, 10), R(1, 10) * 1)
+        self.assertExactlyEquals(0.1, R(1, 10) * 1.0)
+        self.assertExactlyEquals(0.1 + 0j, R(1, 10) * (1.0 + 0j))
+        self.assertExactlyEquals(R(1, 10), 1 * R(1, 10))
+        self.assertExactlyEquals(0.1, 1.0 * R(1, 10))
+        self.assertExactlyEquals(0.1 + 0j, (1.0 + 0j) * R(1, 10))
+
+        self.assertExactlyEquals(R(1, 10), R(1, 10) / 1)
+        self.assertExactlyEquals(0.1, R(1, 10) / 1.0)
+        self.assertExactlyEquals(0.1 + 0j, R(1, 10) / (1.0 + 0j))
+        self.assertExactlyEquals(R(10, 1), 1 / R(1, 10))
+        self.assertExactlyEquals(10.0, 1.0 / R(1, 10))
+        self.assertExactlyEquals(10.0 + 0j, (1.0 + 0j) / R(1, 10))
+
+        self.assertExactlyEquals(0, R(1, 10) // 1)
+        self.assertExactlyEquals(0.0, R(1, 10) // 1.0)
+        self.assertExactlyEquals(10, 1 // R(1, 10))
+        self.assertExactlyEquals(10.0, 1.0 // R(1, 10))
+
+        self.assertExactlyEquals(R(1, 10), R(1, 10) % 1)
+        self.assertExactlyEquals(0.1, R(1, 10) % 1.0)
+        self.assertExactlyEquals(R(0, 1), 1 % R(1, 10))
+        self.assertExactlyEquals(0.0, 1.0 % R(1, 10))
+
+        # No need for divmod since we don't override it.
+
+        # ** has more interesting conversion rules.
+        self.assertExactlyEquals(R(100, 1), R(1, 10) ** -2)
+        self.assertExactlyEquals(R(100, 1), R(10, 1) ** 2)
+        self.assertExactlyEquals(0.1, R(1, 10) ** 1.0)
+        self.assertExactlyEquals(0.1 + 0j, R(1, 10) ** (1.0 + 0j))
+        self.assertExactlyEquals(4 , 2 ** R(2, 1))
+        self.assertAlmostEquals(1j, (-1) ** R(1, 2))
+        self.assertExactlyEquals(R(1, 4) , 2 ** R(-2, 1))
+        self.assertExactlyEquals(2.0 , 4 ** R(1, 2))
+        self.assertExactlyEquals(0.25, 2.0 ** R(-2, 1))
+        self.assertExactlyEquals(1.0 + 0j, (1.0 + 0j) ** R(1, 10))
+
+    def testComparisons(self):
+        self.assertTrue(R(1, 2) < R(2, 3))
+        self.assertFalse(R(1, 2) < R(1, 2))
+        self.assertTrue(R(1, 2) <= R(2, 3))
+        self.assertTrue(R(1, 2) <= R(1, 2))
+        self.assertFalse(R(2, 3) <= R(1, 2))
+        self.assertTrue(R(1, 2) == R(1, 2))
+        self.assertFalse(R(1, 2) == R(1, 3))
+
+    def testMixedLess(self):
+        self.assertTrue(2 < R(5, 2))
+        self.assertFalse(2 < R(4, 2))
+        self.assertTrue(R(5, 2) < 3)
+        self.assertFalse(R(4, 2) < 2)
+
+        self.assertTrue(R(1, 2) < 0.6)
+        self.assertFalse(R(1, 2) < 0.4)
+        self.assertTrue(0.4 < R(1, 2))
+        self.assertFalse(0.5 < R(1, 2))
+
+    def testMixedLessEqual(self):
+        self.assertTrue(0.5 <= R(1, 2))
+        self.assertFalse(0.6 <= R(1, 2))
+        self.assertTrue(R(1, 2) <= 0.5)
+        self.assertFalse(R(1, 2) <= 0.4)
+        self.assertTrue(2 <= R(4, 2))
+        self.assertFalse(2 <= R(3, 2))
+        self.assertTrue(R(4, 2) <= 2)
+        self.assertFalse(R(5, 2) <= 2)
+
+    def testMixedEqual(self):
+        self.assertTrue(0.5 == R(1, 2))
+        self.assertFalse(0.6 == R(1, 2))
+        self.assertTrue(R(1, 2) == 0.5)
+        self.assertFalse(R(1, 2) == 0.4)
+        self.assertTrue(2 == R(4, 2))
+        self.assertFalse(2 == R(3, 2))
+        self.assertTrue(R(4, 2) == 2)
+        self.assertFalse(R(5, 2) == 2)
+
+    def testStringification(self):
+        self.assertEquals("rational.Rational(7,3)", repr(R(7, 3)))
+        self.assertEquals("(7/3)", str(R(7, 3)))
+        self.assertEquals("7", str(R(7, 1)))
+
+def test_main():
+    run_unittest(RationalTest)
+
+if __name__ == '__main__':
+    test_main()