/*
 * $Id$
 */

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;


/**
 * Factorization algorithms interface.
 * @usage To create objects that implement the Factorization
 *        interface use the FactorFactory. 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 FactorAbstract class which implements
 *        the Factorization interface.
 * 
 * 
 * Factorization<CT> engine;
 * engine = FactorFactory.<CT> getImplementation(cofac);
 * c = engine.factors(a);
 * 
 * 
 * For example, if the coefficient type is BigInteger, the usage looks
 *        like
 * 
 * 
 * BigInteger cofac = new BigInteger();
 * Factorization<BigInteger> engine;
 * engine = FactorFactory.getImplementation(cofac);
 * Sm = engine.factors(poly);
 * 
 * 
 * @see edu.jas.ufd.FactorFactory#getImplementation
 * @author Heinz Kredel
 * @param  coefficient type
 */

public interface Factorization> extends Serializable {


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


    /**
     * GenPolynomial test if a non trivial factorization exsists.
     * @param P GenPolynomial.
     * @return true if P is reducible, else false.
     */
    public boolean isReducible(GenPolynomial P);


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


    /**
     * GenPolynomial factorization of a squarefree polynomial.
     * @param P squarefree and primitive! or monic! GenPolynomial.
     * @return [p_1,...,p_k] with P = prod_{i=1,...,r} p_i.
     */
    public List> factorsSquarefree(GenPolynomial P);


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


    /**
     * GenPolynomial factorization ignoring multiplicities.
     * @param P GenPolynomial.
     * @return [p_1, ..., p_k] with P = prod_{i=1,...,k} p_i**{e_i} for some e_i.
     */
    public List> factorsRadical(GenPolynomial P);


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


    /**
     * 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 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 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);

}