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def gcd( x, y ):
while y:
z = x
x = y
y = z % y
return x
class Rational:
def __init__( self, top = 1, bottom = 1 ):
if bottom == 0:
raise ZeroDivisionError, "Cannot have 0 denominator"
self.numerator = abs( top )
self.denominator = abs( bottom )
self.sign = ( top * bottom ) / ( self.numerator * self.denominator )
self.simplify()
def simplify( self ):
common = gcd( self.numerator, self.denominator )
self.numerator /= common
self.denominator /= common
def __neg__( self ):
return Rational( -self.sign * self.numerator, self.denominator )
def __add__( self, other ):
return Rational(self.sign * self.numerator * other.denominator +
other.sign * other.numerator * self.denominator,
self.denominator * other.denominator )
def __sub__( self, other ):
return self + ( -other )
def __mul__( self, other ):
return Rational( self.numerator * other.numerator,
self.sign * self.denominator *
other.sign * other.denominator )
def __div__( self, other ):
return Rational( self.numerator * other.denominator,
self.sign * self.denominator *
other.sign * other.numerator )
def __truediv__( self, other ):
return self.__div__( other )
def __eq__( self, other ):
return ( self - other ).numerator == 0
def __lt__( self, other ):
return ( self - other ).sign < 0
def __gt__( self, other ):
return ( self - other ).sign > 0
def __le__( self, other ):
return ( self < other ) or ( self == other )
def __ge__( self, other ):
return ( self > other ) or ( self == other )
def __ne__( self, other ):
return not ( self == other )
def __abs__( self ):
return Rational( self.numerator, self.denominator )
def __str__( self ):
if self.sign == -1:
signString = "-"
else:
signString = ""
if self.numerator == 0:
return "0"
elif self.denominator == 1:
return "%s%d" % ( signString, self.numerator )
else:
return "%s%d/%d" % ( signString, self.numerator, self.denominator )
def __int__( self ):
return self.sign * divmod( self.numerator, self.denominator )[ 0 ]
def __float__( self ):
return self.sign * float( self.numerator ) / self.denominator
def __coerce__( self, other ):
if type( other ) == type( 1 ):
return ( self, Rational( other ) )
else:
return None
rational1 = Rational()
rational2 = Rational( 10, 30 )
rational3 = Rational( -7, 14 )
print "rational1:", rational1
print "rational2:", rational2
print "rational3:", rational3
print
print rational1, "/", rational2, "=", rational1 / rational2
print rational3, "-", rational2, "=", rational3 - rational2
print rational2, "*", rational3, "-", rational1, "=", rational2 * rational3 - rational1
rational1 += rational2 * rational3
print "\nrational1 after adding rational2 * rational3:", rational1
print
print rational1, "<=", rational2, ":", rational1 <= rational2
print rational1, ">", rational3, ":", rational1 > rational3
print
print "The absolute value of", rational3, "is:", abs( rational3 )
print
print rational2, "as an integer is:", int( rational2 )
print rational2, "as a float is:", float( rational2 )
print rational2, "+ 1 =", rational2 + 1
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