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#!/usr/bin/env python

VERBOSE=False

class Rational:
    zaehler = 1
    nenner = 1
    ggt = 1

    def __init__(self,z,n):
        if (not type(n) == type(1)) or (not type(z) == type(1)):
            raise TypeError, 'Numerator and Denominator have to be integers!'
        if n == 0:
            raise DivisionByZero, 'Denominator is Zero!'
        if n < 0:
            print 'Warning: Denominator shall be a positive integer'
            print '         You entered: %d' % n
            n *= -1
            z *= -1
        self.zaehler = z
        self.nenner = n
        self.simplify()
        
    def find_ggt(self):
        "Find the greatest common denominator"
        
        for i in range(min(abs(self.zaehler),abs(self.nenner)),1,-1):
            if (not self.zaehler%i and not self.nenner%i):
                if VERBOSE: print "GGT gefunden:", i
                self.ggt = i
                return i
        else:
            if VERBOSE: print "Kein GGT gefunden"
            return None

    def simplify(self):
        "Simplify/reduce the fraction"
        
        if self.ggt == 1:
            self.find_ggt()
        if self.ggt != 1:
            self.zaehler /= self.ggt
            self.nenner /= self.ggt
        return str(self)

    def floatify(self):
        "Return a float"
        
        return self.zaehler/float(self.nenner)

    def __add__(self,other):
        return Rational(
            self.zaehler*other.nenner + other.zaehler*self.nenner,
            self.nenner*other.nenner
        )
        
    def __mul__(self,other):
        return Rational(
            self.zaehler*other.zaehler,
            self.nenner*other.nenner
        )
            
    def __str__(self):
        if self.zaehler == 0:
            return "%d" % 0
        if self.nenner == 1:
            return "%d" % self.zaehler
        return "%d / %d" % (self.zaehler,self.nenner)
    
if __name__ == '__main__':
    r = Rational(-49,7)
    s = Rational(-2,12)
    t,u = r+s,r*s
    print r, r.floatify()
    print u,u.floatify()
    print t,t.floatify()