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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.

Constructor Index

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

Method Index

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

Constructors

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

Parameters:
gens - the group generators

Methods

o dimension 
 public final int dimension()
Returns the dimension of the group.

o getElement 
 public ComplexSquareMatrix getElement(DoubleVector v)
Returns an element near the identity.

Parameters:
v - a small element from the Lie algebra
o compose 
 public Object compose(Object a,
                       Object b)
The group composition law.

Parameters:
a - a group element
b - a group element
o identity 
 public Object identity()
Returns the identity element.

o inverse 
 public Object inverse(Object a)
Returns the inverse element.

o isIdentity 
 public final boolean isIdentity(Object a)
Returns true if the element is the identity element of this group.

Parameters:
a - a group element
o 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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