10 May *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
self.simplify()
#Print Fraction as a String
def __str__(self):
if self.den==1:
return str(self.num)
else:
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
else:
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.
- Add:
- Subtract:
- Multiply:
- Divide:
- 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:
- Two:
- Zero:
- 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.
Scoring
- 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):
10
H(10)=7381/2520
H(10)~=2.92896825
T(10)=2047/1024
T(10)~=1.99902344
Z(10)=1/1024
Z(10)~=0.00097656
R(10,2)=1968329/1270080
R(10,2)~=1.54976773
R(10,3)=19164113947/16003008000
R(10,3)~=1.19753199
R(10,4)=43635917056897/40327580160000
R(10,4)~=1.08203658
R(10,5)=105376229094957931/101625502003200000
R(10,5)~=1.03690734
R(10,6)=52107472322919827957/51219253009612800000
R(10,6)~=1.01734151
R(10,7)=650750820166709327386387/645362587921121280000000
R(10,7)~=1.00834915
R(10,8)=1632944765723715465050248417/1626313721561225625600000000
R(10,8)~=1.00407735Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
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