CSCI 2421 homework 3

Program objectives

The objectives of this assignment are as follows.

An ability to analyze a problem, and identify and define the computing requirements appropriate to its solution (ABET b).

Point value

This program is worth 15 points. The distribution of points will be as follows.

Background

A polynomial is a function of the following form:

d p(n) =∑a_inⁱ , where d is an integer and the a_i are the coefficients with a_d ≠ 0.

i=0 p(n) is said to be a polynomial in n of degree d.

Problem

Create a class named polynomial that uses a dynamic array to perform the following arithmetic for polynomials, p₁ and p₂.

1. p₁ + p₂
2. p₁ * p₂
3. p₁ (n), n ∈ Z

Input

1. A text file consisting of two rows of space-delimited integers. Each row represents the coefficients, a_i for a polynomial p. The first number on each row represents a₀ and the last number a_d. Notice that any a_i (except a_d) may be 0. No coefficient will be missing, even if it is 0. The name of the text file will be available in positional parameter, argv[1].
2. A number, n ∈ Z input on the command line in positional parameter argv[2] that is used to evaluate polynomial p₁. For example, if p₁ = (1, 0, 3, 0, 0) and n=2, then p₁(2) = 28. Notice that argv[2] is type char*, so it must be converted to type int by your program (a global function).

Class requirements

1. Use a dynamic array to implement your polynomial.
2. Define a constant member to evaluate a polynomial at a value n.
3. Define a “setter” to set any coefficient requested.
4. Define a “getter” to return any coefficient requested.
5. Overload operators + and * for the polynomial class.
6. Overload operator << for polynomial class.
7. Operator << should display the polynomial as an n-tuple in the order highest term to lowest term. For example,

(3, -2, 0, 0, 7) ≡ 3x⁴ – 2x³ + 7

Driver

1. Greet the user.
2. Instantiate p₁ and p₂.
3. Read the text file and set the coefficients of p₁ and p₂.
4. Perform the polynomial arithmetic per the problem specification and display the annotated results.
5. Convert argv[2] to an int, evaluate p₁ at this value, and display the annotated result.

Notes

1. Use an appropriate annotation with all output.
2. Make sure that main is short. It should basically be making top-level function calls.
3. Use good program style that includes, but is not limited to, header comments, pre and post conditions, macro guards, whitespace and indentation, self-documenting names, symbolic constants where appropriate (use all caps for the name of each symbolics), separation of interface and implementation, correctly submitted program file (tar archive), and a greeting to start the program.
4. You are not restricted to the polynomial members listed above; that is, you may define other members that you feel necessary.
5. Be sure to use error checking where appropriate.