*Python Creating objects with overloaded operators

Creating objects with overloaded operators allows you to use the object like a built in data type. In this lab, you will create a fraction class. By overloading its operators, you can easily use your class to solve mathematical problems related to fractions.
Part 1: Complete Fraction Class
Complete the implementation of the Fraction class provided below.
class Fraction:
#Constructor. Puts fraction in simplest form
def __init__(self,a,b):
self.num = a
self.den = b
#Print Fraction as a String
def __str__(self):
if self.den==1:
return str(self.num)
return str(self.num)+”/”+str(self.den)
#Get the Numerator
def getNum(self):
return self.num
#Get the Denominator
def getDen(self):
return self.den
#Give Numerical Approximation of Fraction
def approximate(self):
return self.num/self.den
#Simplify fraction
def simplify(self):
x = self.gcd(self.num,self.den)
self.num = self.num // x
self.den = self.den // x
#Find the GCD of a and b
def gcd(self,a,b):
if b==0:
return a
return self.gcd(b,a % b)
#Complete these methods in lab
def __add__(self,other):
return 0
def __sub__(self,other):
return 0
def __mul__(self,other):
return 0
def __truediv__(self,other):
return 0
def __pow__(self,exp):
return 0

Complete Implementation of the following methods. All of these methods will return an instance of the Fraction class.





Power (when k>0 and k is an integer):

Part 2: Fraction Problems
Create a file lab3.py. In this file, use your fraction class to implement functions for each of the following formula. You program should ask the user for the value of n to use in the summations.
Remember that a summation symbol just tells you to add all the values in a range.

Write functions for each of the below expressions.

Harmonic Series:



Partial Riemann Zeta:

Your program will ask for n as input. Compute each of the functions for the given input n. When computing the Riemann Zeta function, print values for b=2,3,4,5,6,7,8.
Verify that the input is a valid number. If it is not, ask repeatedly until a valid number is given.
Once you have been given a valid input, print out the values of each of the functions in the order H, T, Z, R. See below execution trace for exact layout.


Part 1

6pts – Add
6pts – Subtract
6pts – Multiply
6pts – True Divide
6pts – Power

Part 2

10pts – H Function
10pts – T Function
10pts – Z Function
10pts – R Function

Example Execution Trace
Welcome to Fun with Fractions!
Enter Number of iterations (integer>0):
Bad Input
Enter Number of iterations (integer>0):

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