net.sf.oriented.util.combinatorics

Class Group

java.lang.Object

net.sf.oriented.util.combinatorics.Group

All Implemented Interfaces:

Iterable<Permutation>

public abstract class Group
extends Object
implements Iterable<Permutation>

This is the mathematically concept of finite group, however we consider every group as a subgroup of a permutation group, and every group element is a Permutation.

Author:

jeremycarroll

Method Summary

Methods

Modifier and Type	Method and Description
Group	filter(Predicate<Permutation> pred) Create a subgroup by accepting some of the elements in the group.
Permutation	identity() The identity element of this group.
static Group	identityGroup(int n) The group consisting of the identity permutation over 0, 1, ....
int	n() The permutations in this group permute the numbers 0, 1, ....
abstract long	order() The number of elements in this group.
static Group	symmetric(int n) The symmetric group of permutations over 0, 1, ....

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface java.lang.Iterable

iterator

Method Detail

identity

public Permutation identity()

The identity element of this group.

order

public abstract long order()

The number of elements in this group.

n

public int n()

The permutations in this group permute the numbers 0, 1, .... n - 1

symmetric

public static Group symmetric(int n)

The symmetric group of permutations over 0, 1, .... n - 1

identityGroup

public static Group identityGroup(int n)

The group consisting of the identity permutation over 0, 1, .... n - 1

filter

public Group filter(Predicate<Permutation> pred)

Create a subgroup by accepting some of the elements in the group.

Parameters:

pred - This predicate must define a subgroup - no checking is provided.