package poly;
/**
 * Represents the polynomial abstraction.  Holds the coefficient.  Has two concrete
 * subclasses, ConstPoly and NonConstPoly, to form the composite pattern.
 <pre>
 * Copyright 2000, by Dung X. Nguyen, All rights reserved.
 </pre>
 * @author Dung X. Nguyen
 * @since 01/26/00
 */
public abstract class APolynomial
{
   /**
   * This APolynomial leading coefficient.
   */
	protected double _coef;

	/**
	 * Returns the leading coefficient of this APolynomial.
	 */
	public double getLeadCoef ()
	{
		return _coef;
	}

	/**
	 * Returns the degree (or order) of this APolynomial.
	 */
	public abstract int getDegree ();

   /**
   * Returns the lower ordered polynomial of this APolynomial, if any.
   * @exception throws NoSuchElementException if this APolynomial is a constant.
   */
	public abstract APolynomial getLowerPoly ();

	/**
   * Computes and returns the sum of this APolynomial with the parameter APolynomial.
   * @param p an APolynomial to be added to this APolynomial.
   * @return an APolynomial representing the sum of this APolynomial and the parameter p.
   */
	public abstract APolynomial add (APolynomial p);


	/**
   * Computes and returns the value of this APolynomial at a "point" x.
   * @param x the "point" at which this APolynomial is to be evaluated.
   * @return the value of this APolynomial evaluated at the parameter x.
   */
	public abstract double eval (double x);

	/**
   * Uses Horner's algorithm to compute and return the value of this APolynomial at a "point" x.
   * @param x the "point" at which this APolynomial is to be evaluated.
   * @return the value of this APolynomial evaluated at the parameter x.
   */
	public abstract double evalHorner (double x);

    /**
     * Computes and returns the quotient of long polynomial division
     * by <code>divisor</code>.
     * @param divisor != zero polynomial.
     * @throw IllegalArgumentException for zero divisor.
     */
    public APolynomial div (APolynomial divisor)
    {
	    return divisor.divmodInto(this)._quotient;
    }

    /**
     * Computes and returns the remainder of long polynomial division
     * by <code>divisor</code>.
     * @param divisor != zero polynomial.
     * @throw IllegalArgumentException for zero divisor.
     */
    public APolynomial mod (APolynomial divisor)
    {
	    return divisor.divmodInto(this)._remainder;
    }

   /**
   * Called by an APolynomial that contains this APolynomial as its lower order polynomial.
   * Relegates to concrete subclass to compute the appropriate String for the lower
   * order polynomial if any.  This is an example of we call a "helper" method for toString().
   */
   protected abstract String toString4LowerPoly ();

	/**
   * Computes and returns the sum of this APolynomial with the double parameter.
   * @param c a constant to be added to this APolynomial.
   * @return an APolynomial representing the sum of this APolynomial and the parameter c.
   */
	protected abstract APolynomial addConst (double c);

	/**
   * Intermediate step in Horner's algorithm to compute and return the value of
   * this APolynomial at a "point" x.
   * @param x the "point" at which this APolynomial is to be evaluated.
   * @param acc the accumulated value of this polynomial so far.
   * @param preDegree the degree of the enclosing higher order APolynomial.
   * @return the value of this APolynomial evaluated at the parameter x.
   */
	protected abstract double evalHornerHelp (double x, double acc, int preDegree);

    /**
     * Divides this APolynomial into a dividend APolynomial.
     * Since div and mod methods do basically the same thing, we combine them
     * into a helper method that does both simultaneously.
     * @param dividend APolynomial to divide into
     * @return the quotient and the remainder in a QRPair.
     * @throw IllegalArgumentException if this APolynomial is the zero polynomial.
     */
   protected abstract QRPair divmodInto(APolynomial dividend);

   /**
   * Multiplies this APolynomial by a monomial.
   * @param coef the leadidng coefficient of a monomial.
   * @param degree the degree of a monomial.
   * @return the result of multiplying this APolynomial by the monomial with coefficient coef and order degree.
   */
   protected abstract APolynomial multMonomial (double coef, int degree);
}