univariate polynomial is a mathematical expression involving a sum of powers in one variable multiplied by coefficients.

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COMP2101: Introduction to Computer Science Fall 2019

Problem definition:

A univariate polynomial is a mathematical expression involving a sum of powers in one variable multiplied by coefficients. A univariate polynomial with constant coefficients is given by

an x n + an−1 xn−1 + . . . + a2 x2 + a1 x + a0.

The highest power in a univariate polynomial is called its order, or sometimes its degree. For example, x7 – 4 x5 + 1 is a polynomial of degree 7, as 7 is the highest power of x.

In this assignment you are requested to design and implement a Python program that reads expressions and a set of x values from a text file called expressions.txt, determines whether the expression is a polynomial, finds the degree of the polynomial, and evaluates the expression for different values of x provided in the text file. For each expression, your program should first read the equation and check whether it is a polynomial equation or not. The expression is considered polynomial if it involves only sum of non-negative integer powers of x multiplied by integer coefficients. If the expression is a polynomial then you should store it as lists of coefficients and powers of x. Your program should then find the degree of the polynomial and for each value of x provided in the next line of the file evaluate the value of the polynomial f(x). Your program should also validate the values of x to be real numbers and count the number of invalid values

The exponents in the expressions are defined by the symbol ^ followed by the exponent (i.e. power) value as shown in Figure 1. For example, x5 – x4 + 4 x2 – 5 x – 13 would be written as x^5 – x^4 + 4 x^2 – 5 x – 13 in the text file expressions.txt.

Figure 1: First few lines of expressions.txt

Your program should:

1. Use meaningful variable names, and meaningful comments to describe the solution.

2. Read expressions and values of x from the file txt

3. Use exceptions. At least one exception handling should be used in your program to check for file opening.

4. Check whether the read expression is

5. Validate the values of x to be real numbers

 

1. Evaluate the polynomial for each valid value of x

2. Use appropriate messages and a suitable output format to display the result (see program sample runs shown in Figure 2)

3. Name the file containing your Python source code: HW4_SECxx_xxxxx.py; where xx and xxxxx are your SECTION and Student ID numbers. For example, a student with ID 75600 and section 20 should submit a file called py.

4. Upload your Python program to Moodle by the

Grading Table:

Item	Mark
Part(i): (written as comments at the beginning of your program)
Your name, Id, section, purpose of program, and input/output data	/1
Algorithm	/3
Test plan	/2
Part(ii): Your Python Program
Comments	/1
Using proper variable naming (accordance to Python convention)	/1
File Operations (opening/closing, checking file error)	/2
Reading expressions into two lists: coefficients and powers	/3
Checking whether the expression is polynomial and giving appropriate message	/2
Finding the order of the polynomial	/1
Reading and validating the values of x	/2
Finding and giving appropriate message for any invalid x value	/1
Computing f(x) for each valid value of x	/2
Displaying the results properly	/2
Program runs without errors	/1
Proper Naming & Submission	/1
T O T A L	/25

 

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