Transforming an ADT into java interface

Problem:

Implement the ADT below:
ADT: Polynomial
degree(): int
derivative(): Polynomial
equals(Point): Boolean
sum(Polynomial): Polynomial
toString(): String
valueAt(Real): Real

Output:

Not applicable.

Solution:

public class MyPolynomial implements Polynomial {
 private double[] c; // coefficients
 public MyPolynomial(double[] a) { // a[i] = coeffficient of x^i
 int n = c.length;
 c = new double[n];
 System.arraycopy(a, 0, c, 0, n);
 }
 public int degree() {
 return c.length - 1;
 }
 public Polynomial derivative() {
 double da[] = new double[c.length-1];
 for (int i=0; i<da.length; i++) {
 da[i] = (i+1)*c[i+1];
 }
 return new MyPolynomial(da);
 }
 public boolean equals(Object object) {
 if (object==this) {
 return true;
 } else if (!(object instanceof MyPolynomial)) {
 return false;
 }
 MyPolynomial that = (MyPolynomial)object;
 return java.util.Arrays.equals(that.c, this.c);
 }
 public Polynomial sum(Polynomial p) {
 if (!(p instanceof MyPolynomial)) {
 throw new IllegalArgumentException("use a MyPolynomial object");
 }
 MyPolynomial that = (MyPolynomial)p;
 double[] pc = that.c;
 int n = Math.max(c.length, pc.length);
 MyPolynomial q = new MyPolynomial(new double[n]);
 for (int i=0; i<n; i++) {
 q.c[i] = c[i] + pc[i];
 }
 return q;
 }
 public String toString() {
 StringBuilder buf = new StringBuilder();
 int n = c.length;
 if (n > 0 && c[0] != 0.0) {
 buf.append(c[0]);
 }
 if (n > 1 && c[1] != 0.0) {
 buf.append(String.format(" + %.2f", c[1]));
 }
for (int i=2; i<n; i++) {
 if (c[i] != 0.0) {
 buf.append(String.format(" + %.2f^%d", c[i], i));
 }
 }
 return buf.toString();
 }
 public double valueAt(double x) {
 double y = 0.0;
 for (int i=0; i<c.length; i++) {
 y += c[i]*Math.pow(x, i);
 }
 return y;
 }
}