// YOUR NAMES HERE!!!!

public class Polynomial {
  double[] a;  // array of coefficients
  
  
  // default Constructor creates the zero polynomial
  public Polynomial(){
    a = new double[1];
    a[0] = 0.0D;
  }
  
  
  // Constructor based on an array of coefficents
  public Polynomial(double[] A){
    a = new double[1]; // REPLACE
    a[0] = 0.0D;       // REPLACE
  }
  
  
  // Copy Constructor
  public Polynomial(Polynomial p){
    a = new double[1]; // REPLACE
    a[0] = 0.0D;       // REPLACE
  }
  
  
  // return ith coefficient (0 returns constant term)
  public double coeff(int i){
    return 0.0;  // REPLACE
  }
  
  
  // returns the degree of this polynomial based on array length
  public int degree() {
    return 0;  // REPLACE
  }
  
  
  // toString method - works as is!
  public String toString(){
    String s="";
    for(int i=a.length-1; i>=0; i--){
      s+=a[i];
      if (i!=0) s+="x^"+i+" + ";
    }
    return s;
  }
  
  
  // Evaluate polynomial at x
  // consider using Horner's method: 
  //   f(x) = a[0] + x(a[1] + x(a[2] + x(... + x(a[n-1]+ xa[n])...)))
  public double f(double x){
    return 0.0;  // REPLACE
  }
  
  
  // add the constant b to each term of p
  public static Polynomial add(Polynomial p, double b){
    return new Polynomial();  // REPLACE
  }
  
  
  // multiply each term of p by the constant b
  public static Polynomial multiply(Polynomial p, double b){
    return new Polynomial();  // REPLACE
  }
  
  
  // add two polynomials
  public static Polynomial add(Polynomial p1, Polynomial p2){
    return new Polynomial();  // REPLACE
  }
  
  
  // multiply two polynomials
  public static Polynomial multiply(Polynomial p1, Polynomial p2){
    return new Polynomial();  // REPLACE
  }
  
  
  // Use the power rule to differentiate p(x)
  // be careful when degree is zero
  public Polynomial derivative(){
    return new Polynomial();  // REPLACE
  }
  
  
  // Use the power rule to integrate p(x), assume constant C is zero
  public Polynomial integrate(){
    return new Polynomial();  // REPLACE
  }
  
  
  // Integrate this polynomial from x0 to x1
  public double integral(double x0, double x1) {
    Polynomial p = integrate();  // REPLACE
    return 0.0;  // REPLACE
  }
  
  
  public static void main(String args[]){
    Polynomial p[] = new Polynomial[10];
    int n = 0;
    p[n++] = new Polynomial();                                   // p(x) = 0;
    p[n++] = new Polynomial(new double[] {1.0});                 // p(x) = 1;
    p[n++] = new Polynomial(new double[] {2.0, -1.0});           // p(x) = -x + 2;
    p[n++] = new Polynomial(new double[] {6.0, 5.0, 1.0});       // p(x) = x^2 + 5x + 6;
    p[n++] = new Polynomial(new double[] {1.0, 5.0, 7.0, 3.0});  // p(x) = 3x^3 + 7x^2 + 5x + 1
    
    for (int i = 0;  i < n;  i++) {
      System.out.println("p(x) = " + p[i]);
      System.out.println("degree: " + p[i].degree());
      Polynomial r = new Polynomial(p[i]);
      System.out.println("r(x) = " + r);
      System.out.println("degree: " + r.degree());
      
      System.out.printf("p(%f) = %f = %f\n", 0.0, p[i].f(0.0), p[i].coeff(0));
      System.out.printf("p(%f) = %f\n", 1.0, p[i].f(1.0));
      System.out.printf("p(%f) = %f\n", -1.0, p[i].f(-1.0));
      
      Polynomial q = p[i].derivative();
      System.out.println("p'(x) = " + q);
      System.out.println("p' degree: " + q.degree());
      
      q = p[i].integrate();
      System.out.println("P(x) = " + q);
      System.out.println("P degree: " + q.degree());
      
      double v = p[i].integral(1.0, 2.0);
      System.out.println("integral from 1.0 to 2.0 = " + v);
      
      r = Polynomial.add(p[i],1.0);
      System.out.println("p(x) + 1 = " + r);
      System.out.println("degree: " + r.degree());
      
      r = Polynomial.multiply(p[i],2.0);
      System.out.println("p(x) * 2 = " + r);
      System.out.println("degree: " + r.degree());
      
      r = Polynomial.multiply(p[i],p[(i-1+n)%n]);
      System.out.println("(" + p[i] + ") * (" + p[(i-1+n)%n] + ") = " + r);
      System.out.println("degree: " + r.degree());
      
      r = Polynomial.add(p[i],p[(i-1+n)%n]);
      System.out.println("(" + p[i] + ") + (" + p[(i-1+n)%n] + ") = " + r);
      System.out.println("degree: " + r.degree());
      System.out.println("--------------------------------------------------------");
    }
  }
}