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Java > Open Source Codes > JSci > maths > groups > AbelianGroup


1 package JSci.maths.groups;
2
3 /**
4 * This interface defines an abelian group.
5 * @version 1.0
6 * @author Mark Hale
7 */
8 public interface AbelianGroup {
9         /**
10         * Returns the identity element.
11         */
12         Member zero();
13         /**
14         * Returns true if the member is the identity element of this group.
15         * @param g a group member
16         */
17         boolean isZero(Member g);
18         /**
19         * Returns true if one member is the negative of the other.
20         * @param a a group member
21         * @param b a group member
22         */
23         boolean isNegative(Member a, Member b);
24
25         /**
26         * This interface defines a member of an abelian group.
27         */
28         interface Member extends JSci.maths.Member {
29                 /**
30                 * The group composition law.
31                 * @param g a group member
32                 */
33                 Member add(Member g);
34                 /**
35                 * Returns the inverse member.
36                 */
37                 Member negate();
38                 /**
39                 * The group composition law with inverse.
40                 * @param g a group member
41                 */
42                 Member subtract(Member g);
43         }
44 }
45
46
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