org.jscience.mathematics.algebraic.algebras
Class sp2_RDim2

java.lang.Object
  extended by org.jscience.mathematics.algebraic.algebras.LieAlgebra
      extended by org.jscience.mathematics.algebraic.algebras.sp2_RDim2

public final class sp2_RDim2
extends LieAlgebra

The sp2_RDim2 class encapsulates sp(2,R) algebras using the 2 dimensional (fundamental) representation. Elements are represented by 3-vectors with a matrix basis.


Method Summary
 AbstractComplexSquareMatrix[] basis()
          Returns the basis used to represent the Lie algebra.
 AbstractComplexSquareMatrix getElement(AbstractDoubleVector v)
          Returns an element as a matrix (vectorbasis).
static sp2_RDim2 getInstance()
          Singleton.
 AbstractDoubleVector multiply(AbstractDoubleVector a, AbstractDoubleVector b)
          Returns the Lie bracket (commutator) of two elements.
 
Methods inherited from class org.jscience.mathematics.algebraic.algebras.LieAlgebra
toString
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Method Detail

getInstance

public static final sp2_RDim2 getInstance()
Singleton.

Returns:
DOCUMENT ME!

getElement

public AbstractComplexSquareMatrix getElement(AbstractDoubleVector v)
Returns an element as a matrix (vectorbasis).

Specified by:
getElement in class LieAlgebra
Parameters:
v - DOCUMENT ME!
Returns:
DOCUMENT ME!

multiply

public AbstractDoubleVector multiply(AbstractDoubleVector a,
                                     AbstractDoubleVector b)
Returns the Lie bracket (commutator) of two elements. Same as the vector cross product.

Specified by:
multiply in class LieAlgebra
Parameters:
a - DOCUMENT ME!
b - DOCUMENT ME!
Returns:
DOCUMENT ME!
Throws:
IllegalDimensionException - DOCUMENT ME!

basis

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

Specified by:
basis in class LieAlgebra
Returns:
DOCUMENT ME!