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.

Version:

1.4

Author:

Mark Hale

Field Summary

Fields inherited from class JSci.maths.groups.FiniteGroup

order

Constructor Summary

Constructors

Constructor and Description
CyclicGroup(int n) Constructs a cyclic group.

Method Summary

Methods

Modifier and Type	Method and Description
boolean	equals(java.lang.Object o) Returns true if this group is isomorphic to another.
JSci.maths.groups.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.

Overrides:

equals in class java.lang.Object

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

getElement

public JSci.maths.groups.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