JSci.maths.groups
Class QuaternionGroup

java.lang.Object
  JSci.maths.groups.FiniteGroup
      JSci.maths.groups.QuaternionGroup

All Implemented Interfaces:

Group, Monoid

public final class QuaternionGroup
extends FiniteGroup

The QuaternionGroup class represents the quaternion group.

PlanetMath references:

QuaternionGroup

Nested Class Summary

(package private) class

QuaternionGroup.Member

Field Summary

Fields inherited from class JSci.maths.groups.FiniteGroup

order

Method Summary

Group.Member[]	getElements() Returns the elements of this group.
static QuaternionGroup	getInstance() Constructs the quaternion group.
Monoid.Member	identity() Returns the identity element.
boolean	isIdentity(Monoid.Member a) Returns true if the element is the identity element of this group.
boolean	isInverse(Group.Member a, Group.Member b) Returns true if one element is the inverse of the other.
java.lang.String	toString()

Methods inherited from class JSci.maths.groups.FiniteGroup

order

Methods inherited from class java.lang.Object

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

Method Detail

getInstance

public static final QuaternionGroup getInstance()

Constructs the quaternion group. Singleton.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

getElements

public Group.Member[] getElements()

Returns the elements of this group.

Specified by:

getElements in class FiniteGroup

identity

public Monoid.Member identity()

Returns the identity element.

isIdentity

public boolean isIdentity(Monoid.Member a)

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

Parameters:

a - a group element

isInverse

public boolean isInverse(Group.Member a,
                         Group.Member b)

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

Parameters:

a - a group element

b - a group element