/*
 * $Id$
 */

package edu.jas.ufd;


import java.io.Serializable;
import java.util.List;
import java.util.SortedMap;

import edu.jas.poly.GenPolynomial;
import edu.jas.structure.GcdRingElem;


/**
 * Squarefree decomposition interface.
 * @param  coefficient type
 * @author Heinz Kredel
 * @usage To create objects that implement the Squarefree
 *        interface use the SquarefreeFactory. It will select an
 *        appropriate implementation based on the types of polynomial
 *        coefficients C. To obtain an implementation use
 *        getImplementation(), it returns an object of a class
 *        which extends the SquarefreeAbstract class which
 *        implements the Squarefree interface.
 * 
 * 
 * Squarefree<CT> engine;
 * engine = SquarefreeFactory.<CT> getImplementation(cofac);
 * c = engine.squarefreeFactors(a);
 * 
 * 
 * For example, if the coefficient type is BigInteger, the usage looks like
 * 
 * 
 * BigInteger cofac = new BigInteger();
 * Squarefree<BigInteger> engine;
 * engine = SquarefreeFactory.getImplementation(cofac);
 * Sm = engine.sqaurefreeFactors(poly);
 * 
 * 
 * @see edu.jas.ufd.SquarefreeFactory#getImplementation
 */

public interface Squarefree> extends Serializable {


    /**
     * GenPolynomial greatest squarefree divisor.
     * @param P GenPolynomial.
     * @return squarefree(pp(P)).
     */
    public GenPolynomial squarefreePart(GenPolynomial P);


    /**
     * GenPolynomial test if is squarefree.
     * @param P GenPolynomial.
     * @return true if P is squarefree, else false.
     */
    public boolean isSquarefree(GenPolynomial P);


    /**
     * GenPolynomial list test if squarefree.
     * @param L list of GenPolynomial.
     * @return true if each P in L is squarefree, else false.
     */
    public boolean isSquarefree(List> L);


    /**
     * GenPolynomial squarefree factorization.
     * @param P GenPolynomial.
     * @return [p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i}
     *         and p_i squarefree.
     */
    public SortedMap, Long> squarefreeFactors(GenPolynomial P);


    /**
     * GenPolynomial is (squarefree) factorization.
     * @param P GenPolynomial.
     * @param F = [p_1,...,p_k].
     * @return true if P = prod_{i=1,...,r} p_i, else false.
     */
    public boolean isFactorization(GenPolynomial P, List> F);


    /**
     * GenPolynomial is (squarefree) factorization.
     * @param P GenPolynomial.
     * @param F = [p_1 -> e_1, ..., p_k -> e_k].
     * @return true if P = prod_{i=1,...,k} p_i**e_i, else false.
     */
    public boolean isFactorization(GenPolynomial P, SortedMap, Long> F);


    /**
     * GenPolynomial squarefree and co-prime list.
     * @param A list of GenPolynomials.
     * @return B with gcd(b,c) = 1 for all b != c in B and for all non-constant
     *         a in A there exists b in B with b|a and each b in B is
     *         squarefree. B does not contain zero or constant polynomials.
     */
    public List> coPrimeSquarefree(List> A);


    /**
     * GenPolynomial squarefree and co-prime list.
     * @param a polynomial.
     * @param P squarefree co-prime list of GenPolynomials.
     * @return B with gcd(b,c) = 1 for all b != c in B and for non-constant a
     *         there exists b in P with b|a. B does not contain zero or constant
     *         polynomials.
     */
    public List> coPrimeSquarefree(GenPolynomial a, List> P);


    /**
     * Test if list of GenPolynomials is squarefree and co-prime.
     * @param B list of GenPolynomials.
     * @return true, if for all b != c in B gcd(b,c) = 1 and 
     *          each b in B is squarefree, else false. 
     */
    public boolean isCoPrimeSquarefree(List> B);

}