Please use Java to complete the following: - Write a method that wil input a seq
ID: 3828696 • Letter: P
Question
Please use Java to complete the following:
- Write a method that wil input a sequence of coefficients and exponents and form them into a linked polynomial.
- Write a method that will subtract two polynomials.
- Write a method that will compute the first, second, and third derivative of a polynomial.
- Write a method that will multiply a polynomial by a scalar.
- Write a method that, given a polynomial and an integer, evaluates the polynomial at that number.
- Write a method that will print a polynomial as a sequence of coefficients and exponents, arranged attractively.
Be sure to include an appropriate driver for your code.
Explanation / Answer
/* Code for Polynomial equation */
public class Java_polynomial {
private int[] coef;
private int deg;
public Java_polynomial(int a, int b) {
coef = new int[b+1];
coef[b] = a;
deg = degree();
}
// return c = a + b
public Java_polynomial plus(Java_polynomial b) {
Java_polynomial a = this;
Java_polynomial c = new Java_polynomial(0, Math.max(a.deg, b.deg));
for (int i = 0; i <= a.deg; i++) c.coef[i] += a.coef[i];
for (int i = 0; i <= b.deg; i++) c.coef[i] += b.coef[i];
c.deg = c.degree();
return c;
}
// return (a - b)
public Java_polynomial minus(Java_polynomial b) {
Java_polynomial a = this;
Java_polynomial c = new Java_polynomial(0, Math.max(a.deg, b.deg));
for (int i = 0; i <= a.deg; i++) c.coef[i] += a.coef[i];
for (int i = 0; i <= b.deg; i++) c.coef[i] -= b.coef[i];
c.deg = c.degree();
return c;
}
// return (a * b)
public Java_polynomial mul(Java_polynomial b) {
Java_polynomial a = this;
Java_polynomial c = new Java_polynomial(0, a.deg + b.deg);
for (int i = 0; i <= a.deg; i++)
for (int j = 0; j <= b.deg; j++)
c.coef[i+j] += (a.coef[i] * b.coef[j]);
c.deg = c.degree();
return c;
}
public boolean eq(Java_polynomial b) {
Java_polynomial a = this;
if (a.deg != b.deg) return false;
for (int i = a.deg; i >= 0; i--)
if (a.coef[i] != b.coef[i]) return false;
return true;
}
public int degree() {
int d = 0;
for (int i = 0; i < coef.length; i++)
if (coef[i] != 0) d = i;
return d;
}
// use Horner's method to compute and return the polynomial evaluated at x
public int evaluate(int x) {
int p = 0;
for (int i = deg; i >= 0; i--)
p = coef[i] + (x * p);
return p;
}
// differentiate this Java_polynomial and return it
public Java_polynomial differentiate() {
if (deg == 0) return new Java_polynomial(0, 0);
Java_polynomial deriv = new Java_polynomial(0, deg - 1);
deriv.deg = deg - 1;
for (int i = 0; i < deg; i++)
deriv.coef[i] = (i + 1) * coef[i + 1];
return deriv;
}
// convert to string representation
public String toString() {
if (deg == 0) return "" + coef[0];
if (deg == 1) return coef[1] + "x + " + coef[0];
String s = coef[deg] + "x^" + deg;
for (int i = deg-1; i >= 0; i--) {
if (coef[i] == 0) continue;
else if (coef[i] > 0) s = s + " + " + ( coef[i]);
else if (coef[i] < 0) s = s + " - " + (-coef[i]);
if (i == 1) s = s + "x";
else if (i > 1) s = s + "x^" + i;
}
return s;
}
// test client
public static void main(String[] args) {
Java_polynomial zero = new Java_polynomial(0, 0);
Java_polynomial p1 = new Java_polynomial(5, 3);
Java_polynomial p2 = new Java_polynomial(3, 2);
Java_polynomial p3 = new Java_polynomial(6, 4);
Java_polynomial p4 = new Java_polynomial(7, 1);
Java_polynomial p = p1.plus(p2).plus(p3).plus(p4);
Java_polynomial q1 = new Java_polynomial(7, 2);
Java_polynomial q2 = new Java_polynomial(2, 0);
Java_polynomial q = q1.plus(q2);
/* To Add Both Polynomial */
Java_polynomial r = p.plus(q);
/* Multiply Both Polynomial */
Java_polynomial s = p.mul(q);
System.out.println("p(x) = " + p);
System.out.println("q(x) = " + q);
System.out.println("p(x) + q(x) = " + r);
System.out.println("q(x) - p(x) = " + q.minus(p));
System.out.println("p(x) * q(x) = " + s);
System.out.println("p(3) = " + p.evaluate(3));
System.out.println("p'(x) = " + p.differentiate());
System.out.println("p''(x) = " + p.differentiate().differentiate());
System.out.println("p'''(x) = " + p.differentiate().differentiate().differentiate());
}
}