repthy
Class C_n

Object
  AbstractCollection
      AbstractSet
          ImmutableSet
              Group
                  C_n

All Implemented Interfaces:

Collection, Set

public class C_n

extends Group

The cyclic group C_n of order n with generator g. The character table is filled in automatically. The columns of the character table are in order by the powers of g; the rows are in order as the character's value on g goes around the unit circle, counter-clockwise from 1.

The user can either provide a generator g or use the default, the permutation (0 1 2 ... n-1). The method getGenerator() returns g.

Author:

Mark McConnell

Field Summary

Fields inherited from class Group

charTable

Constructor Summary

C_n(GroupElt g)
Constructor.

C_n(int n)
Constructor.

Method Summary

boolean	contains(Object o)
protected void	fillInCharTable() Handles the cyclic case directly.
protected Comparator	getCharComparator() This class orders the rows of the character table by hand.
Set	getConjClass(int i) Returns (a copy of) the i-th conjugacy class.
int	getConjClassIndex(GroupElt x) Returns i such that x is in the i-th conjugacy class.
int	getConjClassNum() Returns the number of conjugacy classes.
GroupElt	getGenerator()
Subgroup	getSylow(int p) Returns one of the Sylow p-subgroups of this group, as a Subgroup in which the underlying subgroup is a PGroup.
boolean	isSimple() Whether this group is simple.
Iterator	iterator()
static void	main(String[] args) For testing.
int	size()
String	toString()

Methods inherited from class Group

cyclicSubgpsUpToConj, describeOrder8, elementarySubgps, getCenter, getCentralizer, getCharTable, getCommutatorSubgroup, getCompositionSeries, getConjClassRep, getEltOrder, getEltOrder, getIdentity, getOrder, getProperNormalSubgroup, 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

C_n

public C_n(GroupElt g)

Constructor.

C_n

public C_n(int n)

Constructor.

Throws:

IllegalArgumentException - If n is less than 1.

Method Detail

contains

public boolean contains(Object o)

iterator

public Iterator iterator()

size

public final int size()

getConjClassNum

public final int getConjClassNum()

Description copied from class: Group

Returns the number of conjugacy classes.

Specified by:

getConjClassNum in class Group

getConjClass

public final Set getConjClass(int i)

Description copied from class: Group

Returns (a copy of) the i-th conjugacy class. The inverse operation is Group.getConjClassIndex(repthy.GroupElt).

Implementations may choose to return a SortedSet. If they do, code that needs to pick one element out of the conjugacy class will always pick the first. See Group.getConjClassRep(int).

It's recommended that the Set returned be unmodifiable.

Specified by:

getConjClass in class Group

getConjClassIndex

public int getConjClassIndex(GroupElt x)

Returns i such that x is in the i-th conjugacy class. The inverse operation is getConjClass(int).

Specified by:

getConjClassIndex in class Group

Throws:

NullPointerException - if x is not in the group.

getSylow

public Subgroup getSylow(int p)

Description copied from class: Group

Returns one of the Sylow p-subgroups of this group, as a Subgroup in which the underlying subgroup is a PGroup.

Overrides:

getSylow in class Group

fillInCharTable

protected void fillInCharTable()
                        throws OrthonormalityException

Handles the cyclic case directly.

Overrides:

fillInCharTable in class Group

Throws:

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

getGenerator

public final GroupElt getGenerator()

isSimple

public boolean isSimple()

Description copied from class: Group

Whether this group is simple.

Overrides:

isSimple in class Group

toString

public String toString()

getCharComparator

protected Comparator getCharComparator()

This class orders the rows of the character table by hand.

Overrides:

getCharComparator in class Group

main

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

For testing. Takes one argument n.

Throws:

OrthonormalityException