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Java > Open Source Codes > org > jscience > mathematics > structures > GroupMultiplicative


1 /*
2  * JScience - Java(TM) Tools and Libraries for the Advancement of Sciences.
3  * Copyright (C) 2006 - JScience (http://jscience.org/)
4  * All rights reserved.
5  *
6  * Permission to use, copy, modify, and distribute this software is
7  * freely granted, provided that this notice is preserved.
8  */
9 package org.jscience.mathematics.structures;
10
11 /**
12  * This interface represents a structure with a binary multiplicative
13  * operation (·), satisfying the group axioms (associativity, neutral element,
14  * inverse element and closure).
15  *
16  * @author <a HREF="mailto:jean-marie@dautelle.com">Jean-Marie Dautelle</a>
17  * @version 3.0, February 13, 2006
18  * @see <a HREF="http://en.wikipedia.org/wiki/Mathematical_Group">
19  * Wikipedia: Mathematical Group</a>
20  */
21 public interface GroupMultiplicative<G> extends Structure<G> {
22
23     /**
24      * Returns the product of this object with the one specified.
25      *
26      * @param that the object multiplier.
27      * @return <code>this · that</code>.
28      */
29     G times(G that);
30
31     /**
32      * Returns the multiplicative inverse of this object. It it the object
33      * such as <code>this.times(this.reciprocal()) == ONE </code>,
34      * with <code>ONE</code> being the multiplicative identity.
35      *
36      * @return <code>ONE / this</code>.
37      */
38     G inverse();
39
40 }
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