repthy
Class A_n

Object
  AbstractCollection
      AbstractSet
          ImmutableSet
              Group
                  HashGroup
                      PermGp
                          A_n

All Implemented Interfaces:

Collection, Set

public class A_n

extends PermGp

The group A_n consisting of all even permutations of n elements. The degree is the obvious value n. For aesthetic reasons, we require n to be greater than 1.

Author:

Mark McConnell

Field Summary

Fields inherited from class Group

charTable

Constructor Summary

A_n(int n)
Constructor.

Method Summary

protected void	fillInCharTable() The tables for A1 through A5 are hard-coded; the rest are computed by the super method.
boolean	isSimple() Whether this group is simple.
static void	main(String[] args) For testing.
String	toString()

Methods inherited from class PermGp

getDegree

Methods inherited from class HashGroup

contains, getConjClass, getConjClassIndex, getConjClassNum, iterator, size

Methods inherited from class Group

cyclicSubgpsUpToConj, describeOrder8, elementarySubgps, getCenter, getCentralizer, getCharComparator, getCharTable, getCommutatorSubgroup, getCompositionSeries, getConjClassRep, getEltOrder, getEltOrder, getIdentity, getOrder, getProperNormalSubgroup, getSylow, isAbelian, isCentral, isSubgroupOf, order, power, printTest, tableTest

Methods inherited from class ImmutableSet

add, addAll, clear, remove, removeAll, retainAll

Methods inherited from class AbstractSet

equals, hashCode

Methods inherited from class AbstractCollection

containsAll, isEmpty, toArray, toArray

Methods inherited from class Object

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

Methods inherited from interface Set

containsAll, isEmpty, toArray, toArray

Constructor Detail

A_n

public A_n(int n)

Constructor.

Throws:

IllegalArgumentException - if n is less than 2.

Method Detail

fillInCharTable

protected void fillInCharTable()
                        throws OrthonormalityException,
                               PariNotFoundException

The tables for A₁ through A₅ are hard-coded; the rest are computed by the super method.

Overrides:

fillInCharTable in class Group

Throws:

OrthonormalityException - If the table isn't full at the end, or if anything goes wrong in the middle.

PariNotFoundException

isSimple

public final boolean isSimple()

Description copied from class: Group

Whether this group is simple.

Overrides:

isSimple in class Group

toString

public String toString()

main

public static void main(String[] args)
                 throws OrthonormalityException

For testing. Takes one argument n.

Throws:

OrthonormalityException