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325 lines
10 KiB
Python
325 lines
10 KiB
Python
"""Tests for binary operators on subtypes of built-in types."""
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import unittest
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from test import test_support
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def gcd(a, b):
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"""Greatest common divisor using Euclid's algorithm."""
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while a:
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a, b = b%a, a
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return b
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def isint(x):
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"""Test whether an object is an instance of int or long."""
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return isinstance(x, int) or isinstance(x, int)
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def isnum(x):
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"""Test whether an object is an instance of a built-in numeric type."""
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for T in int, int, float, complex:
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if isinstance(x, T):
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return 1
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return 0
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def isRat(x):
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"""Test wheter an object is an instance of the Rat class."""
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return isinstance(x, Rat)
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class Rat(object):
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"""Rational number implemented as a normalized pair of longs."""
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__slots__ = ['_Rat__num', '_Rat__den']
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def __init__(self, num=0, den=1):
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"""Constructor: Rat([num[, den]]).
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The arguments must be ints or longs, and default to (0, 1)."""
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if not isint(num):
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raise TypeError("Rat numerator must be int or long (%r)" % num)
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if not isint(den):
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raise TypeError("Rat denominator must be int or long (%r)" % den)
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# But the zero is always on
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if den == 0:
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raise ZeroDivisionError("zero denominator")
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g = gcd(den, num)
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self.__num = int(num//g)
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self.__den = int(den//g)
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def _get_num(self):
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"""Accessor function for read-only 'num' attribute of Rat."""
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return self.__num
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num = property(_get_num, None)
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def _get_den(self):
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"""Accessor function for read-only 'den' attribute of Rat."""
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return self.__den
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den = property(_get_den, None)
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def __repr__(self):
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"""Convert a Rat to an string resembling a Rat constructor call."""
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return "Rat(%d, %d)" % (self.__num, self.__den)
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def __str__(self):
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"""Convert a Rat to a string resembling a decimal numeric value."""
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return str(float(self))
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def __float__(self):
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"""Convert a Rat to a float."""
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return self.__num*1.0/self.__den
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def __int__(self):
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"""Convert a Rat to an int; self.den must be 1."""
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if self.__den == 1:
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try:
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return int(self.__num)
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except OverflowError:
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raise OverflowError("%s too large to convert to int" %
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repr(self))
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raise ValueError("can't convert %s to int" % repr(self))
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def __long__(self):
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"""Convert a Rat to an long; self.den must be 1."""
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if self.__den == 1:
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return int(self.__num)
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raise ValueError("can't convert %s to long" % repr(self))
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def __add__(self, other):
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"""Add two Rats, or a Rat and a number."""
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if isint(other):
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other = Rat(other)
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if isRat(other):
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return Rat(self.__num*other.__den + other.__num*self.__den,
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self.__den*other.__den)
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if isnum(other):
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return float(self) + other
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return NotImplemented
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__radd__ = __add__
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def __sub__(self, other):
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"""Subtract two Rats, or a Rat and a number."""
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if isint(other):
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other = Rat(other)
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if isRat(other):
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return Rat(self.__num*other.__den - other.__num*self.__den,
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self.__den*other.__den)
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if isnum(other):
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return float(self) - other
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return NotImplemented
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def __rsub__(self, other):
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"""Subtract two Rats, or a Rat and a number (reversed args)."""
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if isint(other):
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other = Rat(other)
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if isRat(other):
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return Rat(other.__num*self.__den - self.__num*other.__den,
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self.__den*other.__den)
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if isnum(other):
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return other - float(self)
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return NotImplemented
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def __mul__(self, other):
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"""Multiply two Rats, or a Rat and a number."""
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if isRat(other):
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return Rat(self.__num*other.__num, self.__den*other.__den)
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if isint(other):
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return Rat(self.__num*other, self.__den)
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if isnum(other):
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return float(self)*other
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return NotImplemented
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__rmul__ = __mul__
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def __truediv__(self, other):
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"""Divide two Rats, or a Rat and a number."""
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if isRat(other):
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return Rat(self.__num*other.__den, self.__den*other.__num)
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if isint(other):
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return Rat(self.__num, self.__den*other)
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if isnum(other):
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return float(self) / other
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return NotImplemented
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def __rtruediv__(self, other):
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"""Divide two Rats, or a Rat and a number (reversed args)."""
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if isRat(other):
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return Rat(other.__num*self.__den, other.__den*self.__num)
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if isint(other):
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return Rat(other*self.__den, self.__num)
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if isnum(other):
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return other / float(self)
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return NotImplemented
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def __floordiv__(self, other):
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"""Divide two Rats, returning the floored result."""
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if isint(other):
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other = Rat(other)
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elif not isRat(other):
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return NotImplemented
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x = self/other
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return x.__num // x.__den
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def __rfloordiv__(self, other):
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"""Divide two Rats, returning the floored result (reversed args)."""
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x = other/self
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return x.__num // x.__den
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def __divmod__(self, other):
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"""Divide two Rats, returning quotient and remainder."""
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if isint(other):
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other = Rat(other)
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elif not isRat(other):
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return NotImplemented
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x = self//other
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return (x, self - other * x)
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def __rdivmod__(self, other):
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"""Divide two Rats, returning quotient and remainder (reversed args)."""
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if isint(other):
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other = Rat(other)
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elif not isRat(other):
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return NotImplemented
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return divmod(other, self)
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def __mod__(self, other):
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"""Take one Rat modulo another."""
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return divmod(self, other)[1]
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def __rmod__(self, other):
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"""Take one Rat modulo another (reversed args)."""
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return divmod(other, self)[1]
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def __eq__(self, other):
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"""Compare two Rats for equality."""
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if isint(other):
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return self.__den == 1 and self.__num == other
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if isRat(other):
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return self.__num == other.__num and self.__den == other.__den
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if isnum(other):
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return float(self) == other
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return NotImplemented
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def __ne__(self, other):
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"""Compare two Rats for inequality."""
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return not self == other
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class RatTestCase(unittest.TestCase):
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"""Unit tests for Rat class and its support utilities."""
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def test_gcd(self):
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self.assertEqual(gcd(10, 12), 2)
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self.assertEqual(gcd(10, 15), 5)
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self.assertEqual(gcd(10, 11), 1)
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self.assertEqual(gcd(100, 15), 5)
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self.assertEqual(gcd(-10, 2), -2)
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self.assertEqual(gcd(10, -2), 2)
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self.assertEqual(gcd(-10, -2), -2)
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for i in range(1, 20):
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for j in range(1, 20):
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self.assert_(gcd(i, j) > 0)
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self.assert_(gcd(-i, j) < 0)
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self.assert_(gcd(i, -j) > 0)
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self.assert_(gcd(-i, -j) < 0)
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def test_constructor(self):
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a = Rat(10, 15)
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self.assertEqual(a.num, 2)
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self.assertEqual(a.den, 3)
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a = Rat(10, 15)
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self.assertEqual(a.num, 2)
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self.assertEqual(a.den, 3)
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a = Rat(10, -15)
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self.assertEqual(a.num, -2)
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self.assertEqual(a.den, 3)
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a = Rat(-10, 15)
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self.assertEqual(a.num, -2)
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self.assertEqual(a.den, 3)
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a = Rat(-10, -15)
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self.assertEqual(a.num, 2)
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self.assertEqual(a.den, 3)
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a = Rat(7)
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self.assertEqual(a.num, 7)
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self.assertEqual(a.den, 1)
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try:
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a = Rat(1, 0)
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except ZeroDivisionError:
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pass
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else:
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self.fail("Rat(1, 0) didn't raise ZeroDivisionError")
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for bad in "0", 0.0, 0j, (), [], {}, None, Rat, unittest:
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try:
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a = Rat(bad)
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except TypeError:
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pass
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else:
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self.fail("Rat(%r) didn't raise TypeError" % bad)
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try:
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a = Rat(1, bad)
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except TypeError:
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pass
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else:
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self.fail("Rat(1, %r) didn't raise TypeError" % bad)
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def test_add(self):
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self.assertEqual(Rat(2, 3) + Rat(1, 3), 1)
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self.assertEqual(Rat(2, 3) + 1, Rat(5, 3))
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self.assertEqual(1 + Rat(2, 3), Rat(5, 3))
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self.assertEqual(1.0 + Rat(1, 2), 1.5)
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self.assertEqual(Rat(1, 2) + 1.0, 1.5)
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def test_sub(self):
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self.assertEqual(Rat(7, 2) - Rat(7, 5), Rat(21, 10))
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self.assertEqual(Rat(7, 5) - 1, Rat(2, 5))
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self.assertEqual(1 - Rat(3, 5), Rat(2, 5))
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self.assertEqual(Rat(3, 2) - 1.0, 0.5)
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self.assertEqual(1.0 - Rat(1, 2), 0.5)
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def test_mul(self):
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self.assertEqual(Rat(2, 3) * Rat(5, 7), Rat(10, 21))
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self.assertEqual(Rat(10, 3) * 3, 10)
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self.assertEqual(3 * Rat(10, 3), 10)
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self.assertEqual(Rat(10, 5) * 0.5, 1.0)
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self.assertEqual(0.5 * Rat(10, 5), 1.0)
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def test_div(self):
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self.assertEqual(Rat(10, 3) / Rat(5, 7), Rat(14, 3))
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self.assertEqual(Rat(10, 3) / 3, Rat(10, 9))
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self.assertEqual(2 / Rat(5), Rat(2, 5))
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self.assertEqual(3.0 * Rat(1, 2), 1.5)
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self.assertEqual(Rat(1, 2) * 3.0, 1.5)
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def test_floordiv(self):
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self.assertEqual(Rat(10) // Rat(4), 2)
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self.assertEqual(Rat(10, 3) // Rat(4, 3), 2)
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self.assertEqual(Rat(10) // 4, 2)
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self.assertEqual(10 // Rat(4), 2)
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def test_eq(self):
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self.assertEqual(Rat(10), Rat(20, 2))
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self.assertEqual(Rat(10), 10)
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self.assertEqual(10, Rat(10))
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self.assertEqual(Rat(10), 10.0)
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self.assertEqual(10.0, Rat(10))
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def test_future_div(self):
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exec(future_test)
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# XXX Ran out of steam; TO DO: divmod, div, future division
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future_test = """
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from __future__ import division
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self.assertEqual(Rat(10, 3) / Rat(5, 7), Rat(14, 3))
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self.assertEqual(Rat(10, 3) / 3, Rat(10, 9))
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self.assertEqual(2 / Rat(5), Rat(2, 5))
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self.assertEqual(3.0 * Rat(1, 2), 1.5)
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self.assertEqual(Rat(1, 2) * 3.0, 1.5)
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self.assertEqual(eval('1/2'), 0.5)
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"""
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def test_main():
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test_support.run_unittest(RatTestCase)
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if __name__ == "__main__":
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test_main()
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