org.jscience.mathematics.algebraic.algebras
Class LieAlgebra

java.lang.Object
  extended by org.jscience.mathematics.algebraic.algebras.LieAlgebra
Direct Known Subclasses:
so3_1Dim4, sp2_RDim2, sp2_RDim3, su2Dim2, su2Dim3, su3Dim3

public abstract class LieAlgebra
extends java.lang.Object

The LieAlgebra class provides an abstract encapsulation for Lie algebras. Elements are represented by vectors with a matrix basis.


Constructor Summary
LieAlgebra(java.lang.String aLabel)
          Constructs a Lie algebra.
 
Method Summary
abstract  AbstractComplexSquareMatrix[] basis()
          Returns the basis used to represent the Lie algebra.
abstract  AbstractComplexSquareMatrix getElement(AbstractDoubleVector v)
          Returns an element as a matrix (vector*basis).
abstract  AbstractDoubleVector multiply(AbstractDoubleVector a, AbstractDoubleVector b)
          Returns the Lie bracket (commutator) of two elements.
 java.lang.String toString()
          Returns a string representing this algebra.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Constructor Detail

LieAlgebra

public LieAlgebra(java.lang.String aLabel)
Constructs a Lie algebra.

Parameters:
aLabel - a label that identifies this algebra
Method Detail

toString

public final java.lang.String toString()
Returns a string representing this algebra.

Overrides:
toString in class java.lang.Object

getElement

public abstract AbstractComplexSquareMatrix getElement(AbstractDoubleVector v)
Returns an element as a matrix (vector*basis).


multiply

public abstract AbstractDoubleVector multiply(AbstractDoubleVector a,
                                              AbstractDoubleVector b)
Returns the Lie bracket (commutator) of two elements.


basis

public abstract AbstractComplexSquareMatrix[] basis()
Returns the basis used to represent the Lie algebra.