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311 lines
8.6 KiB
Python
Executable File
311 lines
8.6 KiB
Python
Executable File
'''\
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This module implements rational numbers.
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The entry point of this module is the function
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rat(numerator, denominator)
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If either numerator or denominator is of an integral or rational type,
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the result is a rational number, else, the result is the simplest of
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the types float and complex which can hold numerator/denominator.
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If denominator is omitted, it defaults to 1.
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Rational numbers can be used in calculations with any other numeric
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type. The result of the calculation will be rational if possible.
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There is also a test function with calling sequence
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test()
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The documentation string of the test function contains the expected
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output.
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'''
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# Contributed by Sjoerd Mullender
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from types import *
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def gcd(a, b):
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'''Calculate the Greatest Common Divisor.'''
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while b:
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a, b = b, a%b
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return a
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def rat(num, den = 1):
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# must check complex before float
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if isinstance(num, complex) or isinstance(den, complex):
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# numerator or denominator is complex: return a complex
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return complex(num) / complex(den)
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if isinstance(num, float) or isinstance(den, float):
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# numerator or denominator is float: return a float
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return float(num) / float(den)
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# otherwise return a rational
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return Rat(num, den)
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class Rat:
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'''This class implements rational numbers.'''
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def __init__(self, num, den = 1):
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if den == 0:
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raise ZeroDivisionError, 'rat(x, 0)'
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# normalize
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# must check complex before float
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if (isinstance(num, complex) or
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isinstance(den, complex)):
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# numerator or denominator is complex:
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# normalized form has denominator == 1+0j
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self.__num = complex(num) / complex(den)
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self.__den = complex(1)
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return
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if isinstance(num, float) or isinstance(den, float):
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# numerator or denominator is float:
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# normalized form has denominator == 1.0
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self.__num = float(num) / float(den)
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self.__den = 1.0
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return
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if (isinstance(num, self.__class__) or
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isinstance(den, self.__class__)):
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# numerator or denominator is rational
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new = num / den
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if not isinstance(new, self.__class__):
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self.__num = new
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if isinstance(new, complex):
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self.__den = complex(1)
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else:
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self.__den = 1.0
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else:
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self.__num = new.__num
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self.__den = new.__den
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else:
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# make sure numerator and denominator don't
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# have common factors
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# this also makes sure that denominator > 0
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g = gcd(num, den)
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self.__num = num / g
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self.__den = den / g
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# try making numerator and denominator of IntType if they fit
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try:
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numi = int(self.__num)
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deni = int(self.__den)
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except (OverflowError, TypeError):
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pass
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else:
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if self.__num == numi and self.__den == deni:
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self.__num = numi
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self.__den = deni
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def __repr__(self):
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return 'Rat(%s,%s)' % (self.__num, self.__den)
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def __str__(self):
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if self.__den == 1:
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return str(self.__num)
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else:
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return '(%s/%s)' % (str(self.__num), str(self.__den))
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# a + b
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def __add__(a, b):
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try:
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return rat(a.__num * b.__den + b.__num * a.__den,
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a.__den * b.__den)
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except OverflowError:
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return rat(long(a.__num) * long(b.__den) +
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long(b.__num) * long(a.__den),
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long(a.__den) * long(b.__den))
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def __radd__(b, a):
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return Rat(a) + b
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# a - b
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def __sub__(a, b):
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try:
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return rat(a.__num * b.__den - b.__num * a.__den,
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a.__den * b.__den)
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except OverflowError:
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return rat(long(a.__num) * long(b.__den) -
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long(b.__num) * long(a.__den),
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long(a.__den) * long(b.__den))
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def __rsub__(b, a):
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return Rat(a) - b
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# a * b
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def __mul__(a, b):
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try:
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return rat(a.__num * b.__num, a.__den * b.__den)
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except OverflowError:
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return rat(long(a.__num) * long(b.__num),
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long(a.__den) * long(b.__den))
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def __rmul__(b, a):
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return Rat(a) * b
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# a / b
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def __div__(a, b):
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try:
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return rat(a.__num * b.__den, a.__den * b.__num)
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except OverflowError:
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return rat(long(a.__num) * long(b.__den),
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long(a.__den) * long(b.__num))
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def __rdiv__(b, a):
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return Rat(a) / b
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# a % b
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def __mod__(a, b):
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div = a / b
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try:
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div = int(div)
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except OverflowError:
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div = long(div)
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return a - b * div
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def __rmod__(b, a):
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return Rat(a) % b
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# a ** b
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def __pow__(a, b):
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if b.__den != 1:
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if isinstance(a.__num, complex):
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a = complex(a)
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else:
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a = float(a)
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if isinstance(b.__num, complex):
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b = complex(b)
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else:
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b = float(b)
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return a ** b
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try:
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return rat(a.__num ** b.__num, a.__den ** b.__num)
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except OverflowError:
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return rat(long(a.__num) ** b.__num,
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long(a.__den) ** b.__num)
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def __rpow__(b, a):
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return Rat(a) ** b
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# -a
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def __neg__(a):
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try:
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return rat(-a.__num, a.__den)
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except OverflowError:
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# a.__num == sys.maxint
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return rat(-long(a.__num), a.__den)
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# abs(a)
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def __abs__(a):
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return rat(abs(a.__num), a.__den)
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# int(a)
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def __int__(a):
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return int(a.__num / a.__den)
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# long(a)
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def __long__(a):
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return long(a.__num) / long(a.__den)
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# float(a)
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def __float__(a):
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return float(a.__num) / float(a.__den)
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# complex(a)
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def __complex__(a):
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return complex(a.__num) / complex(a.__den)
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# cmp(a,b)
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def __cmp__(a, b):
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diff = Rat(a - b)
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if diff.__num < 0:
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return -1
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elif diff.__num > 0:
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return 1
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else:
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return 0
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def __rcmp__(b, a):
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return cmp(Rat(a), b)
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# a != 0
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def __nonzero__(a):
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return a.__num != 0
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# coercion
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def __coerce__(a, b):
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return a, Rat(b)
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def test():
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'''\
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Test function for rat module.
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The expected output is (module some differences in floating
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precission):
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-1
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-1
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0 0L 0.1 (0.1+0j)
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[Rat(1,2), Rat(-3,10), Rat(1,25), Rat(1,4)]
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[Rat(-3,10), Rat(1,25), Rat(1,4), Rat(1,2)]
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0
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(11/10)
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(11/10)
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1.1
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OK
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2 1.5 (3/2) (1.5+1.5j) (15707963/5000000)
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2 2 2.0 (2+0j)
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4 0 4 1 4 0
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3.5 0.5 3.0 1.33333333333 2.82842712475 1
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(7/2) (1/2) 3 (4/3) 2.82842712475 1
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(3.5+1.5j) (0.5-1.5j) (3+3j) (0.666666666667-0.666666666667j) (1.43248815986+2.43884761145j) 1
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1.5 1 1.5 (1.5+0j)
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3.5 -0.5 3.0 0.75 2.25 -1
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3.0 0.0 2.25 1.0 1.83711730709 0
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3.0 0.0 2.25 1.0 1.83711730709 1
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(3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1
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(3/2) 1 1.5 (1.5+0j)
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(7/2) (-1/2) 3 (3/4) (9/4) -1
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3.0 0.0 2.25 1.0 1.83711730709 -1
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3 0 (9/4) 1 1.83711730709 0
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(3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1
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(1.5+1.5j) (1.5+1.5j)
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(3.5+1.5j) (-0.5+1.5j) (3+3j) (0.75+0.75j) 4.5j -1
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(3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1
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(3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1
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(3+3j) 0j 4.5j (1+0j) (-0.638110484918+0.705394566962j) 0
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'''
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print rat(-1L, 1)
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print rat(1, -1)
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a = rat(1, 10)
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print int(a), long(a), float(a), complex(a)
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b = rat(2, 5)
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l = [a+b, a-b, a*b, a/b]
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print l
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l.sort()
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print l
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print rat(0, 1)
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print a+1
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print a+1L
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print a+1.0
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try:
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print rat(1, 0)
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raise SystemError, 'should have been ZeroDivisionError'
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except ZeroDivisionError:
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print 'OK'
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print rat(2), rat(1.5), rat(3, 2), rat(1.5+1.5j), rat(31415926,10000000)
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list = [2, 1.5, rat(3,2), 1.5+1.5j]
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for i in list:
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print i,
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if not isinstance(i, complex):
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print int(i), float(i),
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print complex(i)
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print
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for j in list:
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print i + j, i - j, i * j, i / j, i ** j,
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if not (isinstance(i, complex) or
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isinstance(j, complex)):
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print cmp(i, j)
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print
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if __name__ == '__main__':
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test()
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