jsci.maths.algebras

Class sp2_RDim2

java.lang.Object

jsci.maths.algebras.LieAlgebra

jsci.maths.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

Modifier and Type	Method and Description
AbstractComplexSquareMatrix[]	basis() Returns the basis used to represent the Lie algebra.
AbstractComplexSquareMatrix	getElement(AbstractDoubleVector v) Returns an element as a matrix (vector*basis).
static sp2_RDim2	getInstance() Singleton.
AbstractDoubleVector	multiply(AbstractDoubleVector a, AbstractDoubleVector b) Returns the Lie bracket (commutator) of two elements.

Methods inherited from class jsci.maths.algebras.LieAlgebra

toString

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Method Detail

getInstance

public static final sp2_RDim2 getInstance()

Singleton.

getElement

public AbstractComplexSquareMatrix getElement(AbstractDoubleVector v)

Returns an element as a matrix (vector*basis).

Specified by:

getElement in class LieAlgebra

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

basis

public AbstractComplexSquareMatrix[] basis()

Returns the basis used to represent the Lie algebra.

Specified by:

basis in class LieAlgebra