public abstract class Polynomial {
    /**
     * Returns the degree of the polynomial.
     * 
     * @return the largest exponent with a non-zero coefficient.  If all terms have
     * zero exponents, it returns 0.
     */
    public abstract int getDegree();
    
    /**
     * Returns the coefficient corresponding to the given exponent.  Returns 0 if there
     * is no term with that exponent in the polynomial.
     *
     * @param d the exponent whose coefficent is returned.
     * @return the coefficient of the term of whose exponent is d.
     */
    public abstract double getCoeff (int d);
    
    /**
     * @return true if the polynomial represents the zero constant
     */
    public abstract boolean isZero();

    /**
     * Returns a polynomial by adding the parameter to this.  Neither this nor the parameter are 
     * modified.
     * 
     * @param q the polynomial to add to this.  q should not be null.
     * @return this + q
     * @exception NullPointerException if q is null
     */
    public abstract Polynomial add (Polynomial q);
    
    /**
     * Returns a polynomial by multiplying the parameter with this.  Neither this nor the parameter are 
     * modified.  q should not be null.
     * 
     * @param q the polynomial to multiply with this
     * @return this * q
     * @exception NullPointerException if q is null
     */
    public abstract Polynomial multiply (Polynomial q);
    
    /**
     * Returns a  polynomial by subtracting the parameter from this.  Neither this nor the parameter are 
     * modified.
     * 
     * @param q the polynomial to subtract from this.  q should not be null.
     * @return this - q
     * @exception NullPointerException if q is null
     */
    public abstract Polynomial subtract (Polynomial q);
    
    /**
     * Returns a polynomial by negating this.  this is not modified.
     * @return -this
     */
    public abstract Polynomial minus ();
}