JSci.maths.groups
Class CyclicGroup

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

All Implemented Interfaces:

AbelianGroup, Group, Monoid

public final class CyclicGroup

extends FiniteGroup

implements AbelianGroup

The CyclicGroup class represents the nth cyclic group. Elements are represented by the integers mod n.

PlanetMath references:

CyclicGroup

Nested Class Summary

(package private) class

CyclicGroup.Member

Field Summary

Fields inherited from class JSci.maths.groups.FiniteGroup

order

Constructor Summary

CyclicGroup(int n)
Constructs a cyclic group.

Method Summary

boolean	equals(java.lang.Object o) Returns true if this group is isomorphic to another.
CyclicGroup.Member	getElement(int i) Returns an element from the group.
Group.Member[]	getElements() Returns the elements of this group.
Monoid.Member	identity() Returns the identity element.
boolean	isIdentity(Monoid.Member g) Returns true if the member is the identity element of this group.
boolean	isInverse(Group.Member a, Group.Member b) Returns true if one member is the inverse of the other.
boolean	isNegative(AbelianGroup.Member a, AbelianGroup.Member b) Returns true if one member is the negative (inverse) of the other.
boolean	isZero(AbelianGroup.Member g) Returns true if the member is the identity element of this group.
java.lang.String	toString()
AbelianGroup.Member	zero() Returns the identity element.

Methods inherited from class JSci.maths.groups.FiniteGroup

order

Methods inherited from class java.lang.Object

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

Constructor Detail

CyclicGroup

public CyclicGroup(int n)

Constructs a cyclic group.

Parameters:

n - the order of the group

Method Detail

equals

public boolean equals(java.lang.Object o)

Returns true if this group is isomorphic to another.

toString

public java.lang.String toString()

getElement

public CyclicGroup.Member getElement(int i)

Returns an element from the group.

Parameters:

i - the integer representing the element

getElements

public Group.Member[] getElements()

Returns the elements of this group.

Specified by:

getElements in class FiniteGroup

zero

public AbelianGroup.Member zero()

Returns the identity element.

Specified by:

zero in interface AbelianGroup

isZero

public boolean isZero(AbelianGroup.Member g)

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

Specified by:

isZero in interface AbelianGroup

Parameters:

g - a group member

isNegative

public boolean isNegative(AbelianGroup.Member a,
                          AbelianGroup.Member b)

Returns true if one member is the negative (inverse) of the other.

Specified by:

isNegative in interface AbelianGroup

Parameters:

a - a group member

b - a group member

identity

public Monoid.Member identity()

Returns the identity element.

Specified by:

identity in interface Monoid

isIdentity

public boolean isIdentity(Monoid.Member g)

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

Specified by:

isIdentity in interface Monoid

Parameters:

g - a group member

isInverse

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

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

Specified by:

isInverse in interface Group

Parameters:

a - a group member

b - a group member