/*
 * $Id$
 */

package edu.jas.gbmod;

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

import edu.jas.poly.GenPolynomial;
import edu.jas.poly.ModuleList;
import edu.jas.poly.PolynomialList;
import edu.jas.structure.RingElem;

import edu.jas.vector.GenVector;

/**
 * Syzygy interface.
 * Defines Syzygy computations and tests.
 * @param  coefficient type
 * @author Heinz Kredel
 */

public interface Syzygy> extends Serializable {


    /**
     * Syzygy module from Groebner base.
     * F must be a Groebner base.
     * @param F a Groebner base.
     * @return syz(F), a basis for the module of syzygies for F.
     */
    public List>> 
           zeroRelations(List> F);


    /**
     * Syzygy module from Groebner base.
     * F must be a Groebner base.
     * @param modv number of module variables.
     * @param F a Groebner base.
     * @return syz(F), a basis for the module of syzygies for F.
     */
    public List>> 
           zeroRelations(int modv, List> F);


    /**
     * Syzygy module from Groebner base.
     * v must be a Groebner base.
     * @param modv number of module variables.
     * @param v a Groebner base.
     * @return syz(v), a basis for the module of syzygies for v.
     */
    public List>> 
           zeroRelations(int modv, GenVector> v);


    /**
     * Syzygy module from module Groebner base.
     * M must be a module Groebner base.
     * @param M a module Groebner base.
     * @return syz(M), a basis for the module of syzygies for M.
     */
    public ModuleList 
          zeroRelations(ModuleList M);


    /**
     * Test if sysygy.
     * @param Z list of sysygies.
     * @param F a polynomial list.
     * @return true, if Z is a list of syzygies for F, else false.
     */
    public boolean 
           isZeroRelation(List>> Z, 
                          List> F);


    /**
     * Test if sysygy of modules.
     * @param Z list of sysygies.
     * @param F a module list.
     * @return true, if Z is a list of syzygies for F, else false.
     */
    public boolean 
           isZeroRelation(ModuleList Z, ModuleList F);


    /**
     * Resolution of a module.
     * Only with direct GBs.
     * @param M a module list of a Groebner basis.
     * @return a resolution of M.
     */
    public List>
           resolution(ModuleList M);


    /**
     * Resolution of a polynomial list.
     * Only with direct GBs.
     * @param F a polynomial list of a Groebner basis.
     * @return a resolution of F.
     */
    public List // |ResPolPart>
           resolution(PolynomialList F);


    /**
     * Resolution of a polynomial list.
     * @param F a polynomial list of an arbitrary basis.
     * @return a resolution of F.
     */
    public List // |ResPolPart>
           resolutionArbitrary(PolynomialList F);


    /**
     * Resolution of a module.
     * @param M a module list of an arbitrary basis.
     * @return a resolution of M.
     */
    public List>
           resolutionArbitrary(ModuleList M);


    /**
     * Syzygy module from arbitrary base.
     * @param F a polynomial list.
     * @return syz(F), a basis for the module of syzygies for F.
     */
    public List>> 
           zeroRelationsArbitrary(List> F);


    /**
     * Syzygy module from arbitrary base.
     * @param modv number of module variables.
     * @param F a polynomial list.
     * @return syz(F), a basis for the module of syzygies for F.
     */
    public List>> 
           zeroRelationsArbitrary(int modv, List> F);


    /**
     * Syzygy module from arbitrary module base.
     * @param M an arbitrary module base.
     * @return syz(M), a basis for the module of syzygies for M.
     */
    public ModuleList 
           zeroRelationsArbitrary(ModuleList M); 

}