/*
 * $Id$
 */

package edu.jas.gb;


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

import edu.jas.poly.GenSolvablePolynomial;
import edu.jas.structure.RingElem;


/**
 * Solvable Groebner Bases interface. Defines methods for left, right and
 * twosided Groebner bases and left, right and twosided GB tests.
 * @param  coefficient type
 * @author Heinz Kredel.
 */

public interface SolvableGroebnerBase> extends Serializable {


    /**
     * Left Groebner base test.
     * @param F solvable polynomial list.
     * @return true, if F is a left Groebner base, else false.
     */
    public boolean isLeftGB(List> F);


    /**
     * Left Groebner base test.
     * @param modv number of module variables.
     * @param F solvable polynomial list.
     * @return true, if F is a left Groebner base, else false.
     */
    public boolean isLeftGB(int modv, List> F);


    /**
     * Twosided Groebner base test.
     * @param Fp solvable polynomial list.
     * @return true, if Fp is a two-sided Groebner base, else false.
     */
    public boolean isTwosidedGB(List> Fp);


    /**
     * Twosided Groebner base test.
     * @param modv number of module variables.
     * @param Fp solvable polynomial list.
     * @return true, if Fp is a two-sided Groebner base, else false.
     */
    public boolean isTwosidedGB(int modv, List> Fp);


    /**
     * Right Groebner base test.
     * @param F solvable polynomial list.
     * @return true, if F is a right Groebner base, else false.
     */
    public boolean isRightGB(List> F);


    /**
     * Right Groebner base test.
     * @param modv number of module variables.
     * @param F solvable polynomial list.
     * @return true, if F is a right Groebner base, else false.
     */
    public boolean isRightGB(int modv, List> F);


    /**
     * Left Groebner base using pairlist class.
     * @param F solvable polynomial list.
     * @return leftGB(F) a left Groebner base of F.
     */
    public List> leftGB(List> F);


    /**
     * Left Groebner base using pairlist class.
     * @param modv number of module variables.
     * @param F solvable polynomial list.
     * @return leftGB(F) a left Groebner base of F.
     */
    public List> leftGB(int modv, List> F);


    /**
     * Solvable Extended Groebner base using critical pair class.
     * @param F solvable polynomial list.
     * @return a container for an extended left Groebner base of F.
     */
    public SolvableExtendedGB extLeftGB(List> F);


    /**
     * Solvable Extended Groebner base using critical pair class.
     * @param modv module variable number.
     * @param F solvable polynomial list.
     * @return a container for an extended left Groebner base of F.
     */
    public SolvableExtendedGB extLeftGB(int modv, List> F);


    /**
     * Left minimal ordered groebner basis.
     * @param Gp a left Groebner base.
     * @return leftGBmi(F) a minimal left Groebner base of Gp.
     */
    public List> leftMinimalGB(List> Gp);


    /**
     * Twosided Groebner base using pairlist class.
     * @param Fp solvable polynomial list.
     * @return tsGB(Fp) a twosided Groebner base of Fp.
     */
    public List> twosidedGB(List> Fp);


    /**
     * Twosided Groebner base using pairlist class.
     * @param modv number of module variables.
     * @param Fp solvable polynomial list.
     * @return tsGB(Fp) a twosided Groebner base of Fp.
     */
    public List> twosidedGB(int modv, List> Fp);


    /**
     * Right Groebner base using opposite ring left GB.
     * @param F solvable polynomial list.
     * @return rightGB(F) a right Groebner base of F.
     */
    public List> rightGB(List> F);


    /**
     * Right Groebner base using opposite ring left GB.
     * @param modv number of module variables.
     * @param F solvable polynomial list.
     * @return rightGB(F) a right Groebner base of F.
     */
    public List> rightGB(int modv, List> F);


    /**
     * Test if left reduction matrix.
     * @param exgb an SolvableExtendedGB container.
     * @return true, if exgb contains a left reduction matrix, else false.
     */
    public boolean isLeftReductionMatrix(SolvableExtendedGB exgb);


    /**
     * Test if left reduction matrix.
     * @param F a solvable polynomial list.
     * @param G a left Groebner base.
     * @param Mf a possible left reduction matrix.
     * @param Mg a possible left reduction matrix.
     * @return true, if Mg and Mf are left reduction matrices, else false.
     */
    public boolean isLeftReductionMatrix(List> F, List> G,
                    List>> Mf, List>> Mg);

}