JSci.maths.groups
Class U1

java.lang.Object
  JSci.maths.groups.LieGroup
      JSci.maths.groups.U1

public final class U1

extends LieGroup

The U1 class provides an encapsulation for U(1) groups. Unlike the parent LieGroup class, elements are not limited to being near the identity. The methods in this class assume a complex number representation for convenience. The LieGroup methods still provide a matrix representation.

Method Summary

Complex	getElement(double param) Returns an element from within the group.
static U1	getInstance() Constructs a U(1) group.
boolean	isIdentity(Complex a) Returns true if the element is the identity element of this group.
boolean	isInverse(Complex a, Complex b) Returns true if one element is the inverse of the other.
java.lang.String	toString() Returns a string representing this group.

Methods inherited from class JSci.maths.groups.LieGroup

dimension, getElement, identity, isIdentity, isInverse

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Method Detail

getInstance

public static final U1 getInstance()

Constructs a U(1) group. Singleton.

toString

public java.lang.String toString()

Returns a string representing this group.

getElement

public Complex getElement(double param)

Returns an element from within the group.

Parameters:

param - parameter to specify the group element

isIdentity

public boolean isIdentity(Complex a)

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

Parameters:

a - a group element

isInverse

public boolean isInverse(Complex a,
                         Complex b)

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

Parameters:

a - a group element

b - a group element