[JAVA]Your assignment is to write a class called Polynomial. A polynomial is a f

Question

[JAVA]Your assignment is to write a class called Polynomial. A polynomial is a function of the following form:

f(n) = ck nk + ck-1 nk-1 + … + c1 n + c0

c0, c1, c2, …, ck are called coefficients. We call k the degree of the polynomial. For our purposes, we will assume that the coefficients are all integers (positive, negative, or 0). The coefficient ck should be nonzero.

I have placed a file named hw1.jar in the D2L Homework assignment 1 dropbox folder. It contains 2 source files called Polynomial.java and TestHW1.java. You may use the code in Polynomial.java as a starting point for your program, or if you prefer you can write your own code from scratch. The TestHW1 class tests the methods of the Polynomial class on a few cases. Please upload the Polynomial.java file once you have completed it.

I recommend that you store the coefficients of a Polynomial object in an instance variable which is an array of integers.

You should write the following methods for the Polynomial class:

a. (1/2 point) A constructor. It is passed 1 parameter: an array of integers which represents the coefficients of the polynomial.

b. (1 point) A method called simplify. It is a void method which is passed 0 parameters. It ensures that the polynomial’s kth coefficient is not 0. If a polynomial is created which has no non-zero coefficients, then it should be represented as an array of length 0. The simplify method should be called within the constructor.

c. (2 points) A toString method. As is usually the case in Java, toString is passed 0 parameters and returns a String representation of an object. Examples of the kind of string that toString should return for polynomials can be found below.

d. (1/2 point) A degree method. It returns an integer, which is the degree of the polynomial.

e. (1 point) An evaluate method. It is passed 1 parameter x, which is an integer. It should return an integer, which represents f(x), the value of the polynomial f(n) when n is equal to x.

As I said, I have written some test code in the file TestHW1.java. You may use this to your own code; however, you may wish to write your own main method which tests your Polynomial class more thoroughly. I may use different examples than the ones in TestHW1 when I grade your assignment. Here are the contents of TestHW1.java:

package hw1;

public class TestHW1 { public static void main(String[] args) {   int coeffs1[] = {1, -1, 2};   // f(n) = n^2 - n + 2   int coeffs2[] = {2, 0, 1, 0}; // f(n) = 2n^3 + n   int coeffs3[] = {0, 0, 1, 0}; // f(n) = n (after simpliciation)   int coeffs4[] = { };          // f(n) = 0   Polynomial p1 = new Polynomial(coeffs1);   Polynomial p2 = new Polynomial(coeffs2);   Polynomial p3 = new Polynomial(coeffs3);   Polynomial p4 = new Polynomial(coeffs4);     System.out.println("Polynomial 1: " + p1);   System.out.println("Polynomial 2: " + p2);   System.out.println("Polynomial 3: " + p3);   System.out.println("Polynomial 4: " + p4);

System.out.println(" Values for f(n) = " + p1);   for (int i=-6; i<=6; i+=3)    System.out.println("f(" + i + ") = " + p1.evaluate(i));   System.out.println(" Values for f(n) = " + p2);   for (int i=-6; i<=6; i+=3)     System.out.println("f(" + i + ") = " + p2.evaluate(i));   System.out.println(" Values for f(n) = " + p3);   for (int i=-6; i<=6; i+=3)    System.out.println("f(" + i + ") = " + p3.evaluate(i));   System.out.println(" Values for f(n) = " + p4);   for (int i=1; i<100; i+=50)    System.out.println("f(" + i + ") = " + p4.evaluate(i)); } }


Note that in Java, an array can be declared and initialized in one statement, by placing { } around the array’s initial contents. For example::
int x[] = {1, 2, 3, 4};
is the same as:
int x[] = new int[4]; for (int i=0; i<4; i++)    x[i] = i+1;

Also note the effects of the simplify method: the coefficients {0, 0, 1, 0} should be changed by the simplify method to {1, 0}.

Here is sample output which my own solution produces when I run the above main method.

Polynomial 1: n^2 - n + 2 Polynomial 2: 2n^3 + n Polynomial 3: n Polynomial 4: 0

Values for f(n) = n^2 - n + 2 f(-6) = 44 f(-3) = 14 f(0) = 2 f(3) = 8 f(6) = 32

Values for f(n) = 2n^3 + n f(-6) = -438 f(-3) = -57 f(0) = 0 f(3) = 57 f(6) = 438

Values for f(n) = n f(-6) = -6 f(-3) = -3 f(0) = 0 f(3) = 3 f(6) = 6

Values for f(n) = 0 f(1) = 0 f(51) = 0

Explanation / Answer

public class Polynomial { private int[] coef; // coefficients private int deg; // degree of polynomial (0 for the zero polynomial) // a * x^b public Polynomial(int a, int b) { coef = new int[b+1]; coef[b] = a; deg = degree(); } // return the degree of this polynomial (0 for the zero polynomial) public int degree() { int d = 0; for (int i = 0; i

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