Add rational.Rational as an implementation of numbers.Rational with infinite

precision. This has been discussed at http://bugs.python.org/issue1682. It's
useful primarily for teaching, but it also demonstrates how to implement a
member of the numeric tower, including fallbacks for mixed-mode arithmetic.

I expect to write a couple more patches in this area:
 * Rational.from_decimal()
 * Rational.trim/approximate() (maybe with different names)
 * Maybe remove the parentheses from Rational.__str__()
 * Maybe rename one of the Rational classes
 * Maybe make Rational('3/2') work.

1 files changed, 0 insertions, 310 deletions

diff --git a/Demo/classes/Rat.py b/Demo/classes/Rat.py
deleted file mode 100755
index 55543b6..0000000
--- a/Demo/classes/Rat.py
+++ /dev/null
@@ -1,310 +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(long(a.__num) * long(b.__den) +
-                       long(b.__num) * long(a.__den),
-                       long(a.__den) * long(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(long(a.__num) * long(b.__den) -
-                       long(b.__num) * long(a.__den),
-                       long(a.__den) * long(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(long(a.__num) * long(b.__num),
-                       long(a.__den) * long(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(long(a.__num) * long(b.__den),
-                       long(a.__den) * long(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 = long(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(long(a.__num) ** b.__num,
-                       long(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(-long(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 long(a.__num) / long(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 __nonzero__(a):
-        return a.__num != 0
-
-    # coercion
-    def __coerce__(a, b):
-        return a, Rat(b)
-
-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(-1L, 1)
-    print rat(1, -1)
-    a = rat(1, 10)
-    print int(a), long(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+1L
-    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,
-        if not isinstance(i, complex):
-            print int(i), float(i),
-        print complex(i)
-        print
-        for j in list:
-            print i + j, i - j, i * j, i / j, i ** j,
-            if not (isinstance(i, complex) or
-                    isinstance(j, complex)):
-                print cmp(i, j)
-            print
-
-
-if __name__ == '__main__':
-    test()