from __future__ import division

try:

from math import gcd

except ImportError:

from fractions import gcd

class Rational(object):

def __init__(self, numer, denom):

# abs used for backward compatibility with fractions.gcd

gcd_num = abs(gcd(numer, denom))

self.numer = numer // gcd_num

self.denom = denom // gcd_num

if self.denom < 0:

self.numer *= -1

self.denom *= -1

def __eq__(self, other):

return self.numer == other.numer and self.denom == other.denom

def __repr__(self):

return '{}/{}'.format(self.numer, self.denom)

def __add__(self, other):

numer = (self.numer * other.denom) + (other.numer * self.denom)

return Rational(numer, other.denom * self.denom)

def __sub__(self, other):

return self + (-other)

def __mul__(self, other):

return Rational(self.numer * other.numer, self.denom * other.denom)

def __truediv__(self, other):

return Rational(self.numer * other.denom, self.denom * other.numer)

def __abs__(self):

return Rational(abs(self.numer), self.denom)

def __pow__(self, power):

return Rational(pow(self.numer, power), pow(self.denom, power))

def __rpow__(self, base):

return base ** (self.numer / self.denom)

def __neg__(self):

return Rational(self.numer * (-1), self.denom)