/*
 * JScience - Java(TM) Tools and Libraries for the Advancement of Sciences.
 * Copyright (C) 2006 - JScience (http://jscience.org/)
 * All rights reserved.
 * 
 * Permission to use, copy, modify, and distribute this software is
 * freely granted, provided that this notice is preserved.
 */
package org.jscience.mathematics.structure;

/**
 * This interface represents a structure with a binary multiplicative 
 * operation (·), satisfying the group axioms (associativity, neutral element,
 * inverse element and closure).
 * 
 * @author Jean-Marie Dautelle
 * @version 3.0, February 13, 2006
 * @see 
 *      Wikipedia: Mathematical Group
 */
public interface GroupMultiplicative extends Structure {

    /**
     * Returns the product of this object with the one specified.
     *
     * @param  that the object multiplier.
     * @return this · that.
     */
    G times(G that);

    /**
     * Returns the multiplicative inverse of this object. It it the object
     * such as this.times(this.inverse()) == ONE ,
     * with ONE being the multiplicative identity.
     *
     * @return ONE / this.
     */
    G inverse();

}