JSci.maths.algebras.LieAlgebra Maven / Gradle / Ivy
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JSci is a set of open source Java packages. The aim is to encapsulate scientific methods/principles in the most natural way possible. As such they should greatly aid the development of scientific based software.
It offers: abstract math interfaces, linear algebra (support for various matrix and vector types), statistics (including probability distributions), wavelets, newtonian mechanics, chart/graph components (AWT and Swing), MathML DOM implementation, ...
Note: some packages, like javax.comm, for the astro and instruments package aren't listed as dependencies (not available).
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package JSci.maths.algebras;
import JSci.maths.*;
import JSci.maths.matrices.AbstractComplexSquareMatrix;
import JSci.maths.vectors.AbstractDoubleVector;
import JSci.maths.fields.ComplexField;
/**
* The LieAlgebra class provides an abstract encapsulation for Lie algebras.
* Elements are represented by vectors with a matrix basis.
* @jsci.planetmath LieAlgebra
* @version 1.2
* @author Mark Hale
*/
public abstract class LieAlgebra extends Object {
private String label;
/**
* Constructs a Lie algebra.
* @param aLabel a label that identifies this algebra
*/
public LieAlgebra(String aLabel) {
label=aLabel;
}
/**
* Returns a string representing this algebra.
*/
public final String toString() {
return label;
}
/**
* Returns an element as a matrix (vector*basis).
*/
public abstract AbstractComplexSquareMatrix getElement(AbstractDoubleVector v);
/**
* Returns the Lie bracket (commutator) of two elements.
*/
public abstract AbstractDoubleVector multiply(AbstractDoubleVector a, AbstractDoubleVector b);
/**
* Returns the basis used to represent the Lie algebra.
*/
public abstract AbstractComplexSquareMatrix[] basis();
}