jsci.maths.groups

Class DihedralGroup

java.lang.Object

jsci.maths.groups.FiniteGroup

jsci.maths.groups.DihedralGroup

All Implemented Interfaces:

Group, Monoid

public final class DihedralGroup
extends FiniteGroup

The DihedralGroup class represents the nth dihedral group. Elements are represented by rotations and reflections.

Constructor Summary

Constructors

Constructor and Description
DihedralGroup(int n) Constructs a dihedral group.

Method Summary

Modifier and Type	Method and Description
boolean	equals(java.lang.Object o) Returns true if this group is isomorphic to another.
Group.Member[]	getElements() Returns the elements of this group.
int	hashCode()
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

getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

DihedralGroup

public DihedralGroup(int n)

Constructs a dihedral group.

Parameters:

n - the number of rotations/reflections

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

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

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