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# Class JSci.maths.groups.LieGroup

    java.lang.Object
       |
       +----JSci.maths.groups.LieGroup

public class LieGroup
extends Object
implements Group

The LieGroup class provides an encapsulation for Lie groups. Elements are represented by complex matrices, and are limited to being near the identity.

##

LieGroup(ComplexSquareMatrix[])
  Constructs a Lie group from a Lie algebra.

##

compose(Object, Object)
  The group composition law.
dimension()
  Returns the dimension of the group.
getElement(DoubleVector)
  Returns an element near the identity.
identity()
  Returns the identity element.
inverse(Object)
  Returns the inverse element.
isIdentity(Object)
  Returns true if the element is the identity element of this group.
isInverse(Object, Object)
  Returns true if one element is the inverse of the other.

##

LieGroup

     public LieGroup(ComplexSquareMatrix gens[])

  Constructs a Lie group from a Lie algebra.

  Parameters:
    gens - the group generators

##

dimension

     public final int dimension()

  Returns the dimension of the group.

getElement

     public ComplexSquareMatrix getElement(DoubleVector v)

  Returns an element near the identity.

  Parameters:
    v - a small element from the Lie algebra

compose

     public Object compose(Object a,
                           Object b)

  The group composition law.

  Parameters:
    a - a group element
    b - a group element

identity

     public Object identity()

  Returns the identity element.

inverse

     public Object inverse(Object a)

  Returns the inverse element.

isIdentity

     public final boolean isIdentity(Object a)

  Returns true if the element is the identity element of this group.

  Parameters:
    a - a group element

isInverse

     public final boolean isInverse(Object a,
                                    Object b)

  Returns true if one element is the inverse of the other.

  Parameters:
    a - a group element
    b - a group element

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