/*______________________________________________________________________________
 * 
 * Copyright 2005 Arnaud Bailly - NORSYS/LIFL
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
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 *
 * (1) Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
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 * (2) Redistributions in binary form must reproduce the above copyright
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 *     the documentation and/or other materials provided with the
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 * (3) The name of the author may not be used to endorse or promote
 *     products derived from this software without specific prior
 *     written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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 *
 * Created on 10 mai 2005
 *
 */
package rationals.algebra;

/**
 * An interface implemented by objects that can be coefficients of a 
 * Matrix.
 * <p>
 * A semi-ring is a structure <code>(R,+,*,0,1)</code> such that:
 * <ol>
 * <li><code>(R,+,0)</code> is a commutative monoid </li>
 * <li><code>(R,*,1)</code> is a monoid </li>
 * <li><code>x*(y+z) = x*y + x*z</code> and <code>(y+z)*x = y*x + z*x</code> : multiplication
 * is distributive with respect to addition </li>
 * <li><code>x*0 = 0*x = 0</code>: 0 is an absorbing element for *</li>
 * </ol>
 * 
 * @author nono
 * @version $Id: SemiRing.java 2 2006-08-24 14:41:48Z oqube $
 * @see Matrix
 */
public interface SemiRing {

    /**
     * Addition of a Semi-ring element with another element.
     * 
     * @param s1
     * @param s2
     * @return
     */
    public SemiRing plus(SemiRing s2);
    
    /**
     * Multiplication of semiring element with another element.
     * 
     * @param s1
     * @param s2
     * @return
     */
    public SemiRing mult(SemiRing s2);
    
    /**
     * Neutral element for multiplication.
     * 
     * @return
     */
    public SemiRing one();
    
    /**
     * Neutral element for addition.
     * 
     * @return
     */
    public SemiRing zero();
    
}