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Java > Open Source Codes > JSci > maths > algebras > LieAlgebra


1 package JSci.maths.algebras;
2
3 import JSci.maths.*;
4 import JSci.maths.matrices.AbstractComplexSquareMatrix;
5 import JSci.maths.vectors.AbstractDoubleVector;
6 import JSci.maths.fields.ComplexField;
7
8 /**
9 * The LieAlgebra class provides an abstract encapsulation for Lie algebras.
10 * Elements are represented by vectors with a matrix basis.
11 * @jsci.planetmath LieAlgebra
12 * @version 1.2
13 * @author Mark Hale
14 */

15 public abstract class LieAlgebra extends Object JavaDoc {
16         private String JavaDoc label;
17         /**
18         * Constructs a Lie algebra.
19         * @param aLabel a label that identifies this algebra
20         */

21         public LieAlgebra(String JavaDoc aLabel) {
22                 label=aLabel;
23         }
24         /**
25         * Returns a string representing this algebra.
26         */

27         public final String JavaDoc toString() {
28                 return label;
29         }
30         /**
31         * Returns an element as a matrix (vector*basis).
32         */

33         public abstract AbstractComplexSquareMatrix getElement(AbstractDoubleVector v);
34         /**
35         * Returns the Lie bracket (commutator) of two elements.
36         */

37         public abstract AbstractDoubleVector multiply(AbstractDoubleVector a, AbstractDoubleVector b);
38         /**
39         * Returns the basis used to represent the Lie algebra.
40         */

41         public abstract AbstractComplexSquareMatrix[] basis();
42 }
43
44
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