""" A Rational class, closely followed the example by John W. Shipman of 
New Mexico Tech
http://infohost.nmt.edu/tcc/help/lang/python/examples/rational/rational.pdf

Xiannong Meng
CSCI 204 Fall 2017
"""
class Rational:

    def __init__(self, a = 0, b = 1):
        """ Constructor
        """
        if b == 0:
            raise ZeroDivisionError
        elif isinstance(a, int) == False or isinstance(b, int) == False:
            raise ValueError
        else:
            g = self.gcd ( a, b )
            self.n = a // g
            self.d = b // g

    def __str__(self):
        """ Return a string rep
        """
        return str(self.n) + ' / ' + str(self.d)

    def gcd(self, a, b):
        """ Return the greastest common divisor of a and b
        """
        if b == 0:
            return a
        else:
            return self.gcd(b, a % b)

    def __add__(self, other):
        """ Add two rationals
        """
        return Rational(self.n * other.d + other.n*self.d, \
                        self.d * other.d)

    def __sub__(self, other):
        """ Subtract other from self
        """
        return Rational(self.n * other.d - other.n*self.d, \
                        self.d * other.d)

    def __mul__(self, other):
        """ Multiply self with other
        """
        return Rational(self.n * other.n, self.d * other.d)

    def __floordiv__(self, other):
        """ Divide self by other
        """
        '''
        According to the Stackoverflow post, __floordiv__ is //
        and __truediv__ is /
        https://stackoverflow.com/questions/21859440/error-when-trying-to-overload-an-operator
        '''
        return Rational(self.n * other.d, self.d * other.n)

    def __eq__(self, other):
        """ Compare if two Rationals are equal
        Precondition: 'other' must be a Rational that has been reduced.
        """
        return self.n == other.n and self.d == other.d

    def is_zero(self):
        """ Returns True if this Rational is zero (0/n)
        """
        return self.n == 0
    
    def __gt__(self, other):
        """ Returns True if self > other
        """
        return self.n * other.d > self.d * other.n

    def __ge__(self, other):
        """ Returns True if self >= other
        """
        return self.n * other.d >= self.d * other.n

    def __lt__(self, other):
        """ Returns True if self < other
        """
        return self.n * other.d < self.d * other.n

    def __le__(self, other):
        """ Returns True if self <= other
        """
        return self.n * other.d <= self.d * other.n