In Python the following are operators:
+ - * ** / // % << >> & | ^ ~ < > <= >= == != <>
Simple examples of a few:
2 + 1 2*1 2.0-1.0 2/3+1/4
Hey wait a minute what was that last one? 2/3+1/4, according to Python, this is 0! That's not what we wanted now was it? We would like to work with rational numbers in python, so we'll begin by creating a new class called "Rational"
class Rational(object): def __init__(self, numerator=0, denomiator=1): self.numer = numerator self.denom = denomiator self.fixSign() #will explain later self.reduce() #will explain later
Here I have defined the class and put in an initializing function, what __init__ does is creates an object with the initial parameters if no parameters are supplied for the object. If parameters are supplied, the object will be created with the supplied parameters.
Next we will want to overload some operators so we can use our new class.
def __add__(self,rhs): #self and rhs are Rational objects n1 = self.numer #numerator of the self object d1 = self.denom #denominator of the self object n2 = rhs.numer #numerator of the rhs object d2 rhs.denom #denominator of the rhs object r = Rational(d2*n1+d1*n2,d1*d2) #creates a new object with d2*n1+d1*n2 as the numerator, and d1*d2 as the denominator return r def __sub__(self,rhs): n1 = self.numer #numerator of the self object d1 = self.denom #denominator of the self object n2 = rhs.numer #numerator of the rhs object d2 = rhs.denom #denominator of the rhs object r = Rational(d2*n1-d1*n2,d1*d2) #creates a new object with d2*n1-d1*n2 as the numerator, and d1*d2 as the denominator return r
__add__ and __sub__ are the Python names used for the + and - operators. Now that we have these operators overloaded, we can use + and - on Rational objects just as we would on integers or floats.
Before we get to using our operators, let's first create a few more functions that make life easier.
def gcd(self,a,b): if b == 0: return a return self.gcd(b,a%b) def fixSigns(self): #takes - sign out of the denominator if self.denom <0: #check if denominator is negative self.numer = -self.numer #switch sign of numerator self.denom = -self.denom #switch sign of denominator def reduce(self): #reduce the fraction d = 1 if self.denom != 0 and self.numer !=0: #make sure the fraction != 0 d = self.gcd(self.numer, self.denom) #finds the greatest common denominator in order to reduce if d > 1: #reduce away! self.numer /= d self.denom /= d def __str__(self): #rules for printing our objects s = "%d /% d" % (self.numer,self.denom) return s
gcd finds the greatest common denominator of the numerator and denominator
fixSigns is used to remove negatives from the denominator
reduce reduces the fraction by using the greatest common denominator function
__str__ gives a rule on how we want our object printed
Complete class:
class Rational(object): def __init__(self, numerator=0, demoniator=1): self.numer = numerator self.denom = demoniator self.fixSign() self.reduce() def __add__(self,rhs): #self and rhs are Rational objects n1 = self.numer #numerator of the self object d1 = self.denom #denominator of the self object n2 = rhs.numer #numerator of the rhs object d2 rhs.denom #denominator of the rhs object r = Rational(d2*n1+d1*n2,d1*d2) #creates a new object with d2*n1+d1*n2 as the numerator, and d1*d2 as the denominator return r def __sub__(self,rhs): n1 = self.numer #numerator of the self object d1 = self.denom #denominator of the self object n2 = rhs.numer #numerator of the rhs object d2 = rhs.denom #denominator of the rhs object r = Rational(d2*n1-d1*n2,d1*d2) #creates a new object with d2*n1-d1*n2 as the numerator, and d1*d2 as the denominator return r def gcd(self,a,b): if b == 0: return a return self.gcd(b,a%b) def fixSigns(self): #takes - sign out of the denominator if self.denom <0: #check if denominator is negative self.numer = -self.numer #switch sign of numerator self.denom = -self.denom #switch sign of denominator def reduce(self): #reduce the fraction d = 1 if self.denom != 0 and self.numer !=0: #make sure the fraction != 0 d = self.gcd(self.numer, self.denom) #finds the greatest common denominator in order to reduce if d > 1: #reduce away! self.numer /= d self.denom /= d def __str__(self): #rules for printing our objects s = "%d /% d" % (self.numer,self.denom) return s
Now that we have all this done, we can start using our class and operators. Let's test!
from rational import * def main(): r1 = Rational(4,9) r2 = Rational(2,7) r3 = Rational(1,3) r4 = Rational(4,6) #use our __str__ function print "r1: ", r1 print "r2: ", r2 print "r3: ", r3 print "r4: ", r4 #use our operators print "r2-r1: ", (r2-r1) print "r1+r3: ", (r1+r3) r5 = r3+r4 print r3, " + ", r2, " = ", r3 a,b,c,d = 1,4,3,6 print "%d/%d + %d/%d = %s" %(a,b,c,d,Rational(a,b) + Rational(c,d)) print "%d/%d - %d/%d = %s" %(a,b,c,d,Rational(a,b) - Rational(c,d)) if __name__ == "__main__": main()
Python output:
r1: 4 / 9 r2: 2 / 7 r3: 1 / 3 r4: 2 / 3 r2-r1: -10 / 63 r1+r3: 7 / 9 1 / 3 + 2 / 7 = 1 / 3 1/4 + 3/6 = 3 / 4 1/4 - 3/6 = -1 / 4
Now that we've overloaded the + and - operators, we can easily continue to overload more as needed. Perhaps you'd like to overload == (__eq__) or != (__ne__), you can do so by the same method.
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