cayleytable
Class groupCreator

java.lang.Object
  cayleytable.groupCreator

public class groupCreator
extends java.lang.Object

Class used to create and store a group in groupMatrix object.

Author:

Jeffrey Barr

Field Summary

private groupMatrix

group groupMatrix object that is created and stored by this class.

Constructor Summary

groupCreator()
Constructor that creates a new instance of groupCreator with an empty group groupMatrix object.

groupCreator(int size)
Constructor that creates a new instance of groupCreator with a group groupMatrix object of specific order.

Method Summary

boolean	createCyclicGroup(int size) Method to update group groupMatrix object with a new cyclic group of given order.
boolean	createDefineRelationGroup(java.util.ArrayList<java.lang.String> generatorList, java.util.ArrayList<groupRelation> relationships) Method to update group groupMatrix object with a new defined relationship group that is defined by relationships and generators that are passed to the method.
boolean	createEmptyGroup(int size) Method to update group groupMatrix object with a new empty group of given order.
private java.util.ArrayList	createFinalElementList(java.util.ArrayList<java.lang.String> generatorList) Method to determine all the elements of a group given the orders of a list of generators of the group being created in createDefineRelationGroup
groupMatrix	createInnerAutFromElement(int element) Method to calculate the inner automorphism of a single element of the group groupMatrix object.
groupMatrix	createInnerAutFromTwoElements(int elmtA, int elmtB) Method to calculate the inner automorphism of for two elements of the group groupMatrix object.
boolean	createInnerAutGroup() Method to calculate and store the inner automorphism of the group groupMatrix object.
boolean	createXProdGroup(groupMatrix g1, groupMatrix g2) Method to update group groupMatrix object with a new cross product group that is a combination of two groups that are passed to the method.
private java.util.ArrayList<java.lang.String>	fillList(java.util.ArrayList<java.lang.String> finalElements, java.util.ArrayList<java.util.ArrayList<java.lang.String>> elementMatrix, java.util.ArrayList<java.lang.String> generatorList, java.lang.String nextElement, int count) Recursive method used by createFinalElementList to determine the final list of elements that are to be
groupMatrix	getGroup() Returns group groupMatrix object created by groupCreator.
boolean	resetGroup(groupMatrix newGroup) Resets the group groupMatrix object in the class groupCreator with a new groupMatrix object passed to the method.

Methods inherited from class java.lang.Object

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

Field Detail

group

private groupMatrix group

groupMatrix object that is created and stored by this class.

Constructor Detail

groupCreator

public groupCreator()

Constructor that creates a new instance of groupCreator with an empty group groupMatrix object.

groupCreator

public groupCreator(int size)

Constructor that creates a new instance of groupCreator with a group groupMatrix object of specific order.

Parameters:

size - Order of empty groupMatrix object to create

Method Detail

getGroup

public groupMatrix getGroup()

Returns group groupMatrix object created by groupCreator.

Returns:

Current group groupMatrix object created and stored in the class.

resetGroup

public boolean resetGroup(groupMatrix newGroup)

Resets the group groupMatrix object in the class groupCreator with a new groupMatrix object passed to the method.

Parameters:

newGroup - groupMatrix object that is to replace the group groupMatrix object.

Returns:

Boolean value representing success of updating the group groupMatrix object.

createEmptyGroup

public boolean createEmptyGroup(int size)

Method to update group groupMatrix object with a new empty group of given order.

Parameters:

size - Order of empty group groupMatrix object to create and store.

Returns:

Boolean value representing success of updating the group groupMatrix object.

createCyclicGroup

public boolean createCyclicGroup(int size)

Method to update group groupMatrix object with a new cyclic group of given order.

Parameters:

size - Order of cyclic group groupMatrix object to create and store.

Returns:

Boolean value representing success of updating the group groupMatrix object.

createXProdGroup

public boolean createXProdGroup(groupMatrix g1,
                                groupMatrix g2)

Method to update group groupMatrix object with a new cross product group that is a combination of two groups that are passed to the method.

Parameters:

g1 - First groupMatrix object passed to the method for cross product calculation.

g2 - Second groupMatrix object passed to the method for cross product calculation.

Returns:

Boolean value representing success of updating the group groupMatrix object.

createDefineRelationGroup

public boolean createDefineRelationGroup(java.util.ArrayList<java.lang.String> generatorList,
                                         java.util.ArrayList<groupRelation> relationships)

Method to update group groupMatrix object with a new defined relationship group that is defined by relationships and generators that are passed to the method.

Parameters:

generatorList - ArrayList of String objects that are the order of each of the generators of the group.

relationships - ArrayList of groupRelation objects that contain the relationships between the generators.

Returns:

Boolean value representing success of updating the group groupMatrix object.

createFinalElementList

private java.util.ArrayList createFinalElementList(java.util.ArrayList<java.lang.String> generatorList)

Method to determine all the elements of a group given the orders of a list of generators of the group being created in createDefineRelationGroup

Parameters:

generatorList - ArrayList of String objects that are the order of each of the generators of the group.

Returns:

The final list of elements that comprise the group being created in createDefineRelationGroup

fillList

private java.util.ArrayList<java.lang.String> fillList(java.util.ArrayList<java.lang.String> finalElements,
                                                       java.util.ArrayList<java.util.ArrayList<java.lang.String>> elementMatrix,
                                                       java.util.ArrayList<java.lang.String> generatorList,
                                                       java.lang.String nextElement,
                                                       int count)

Recursive method used by createFinalElementList to determine the final list of elements that are to be

Parameters:

finalElements - Current list of all elements that have thus far been derived for the group.

elementMatrix - ArrayList of ArrayList of String objects where each String is one of the possible elements derived from one generator each ArrayList of Strings is the list of all possible elements derived from one generator and each ArrayList of ArrayList of Strings is the list of all possible elements derived from one generator for all the generators

generatorList - ArrayList of String objects that are the order of each of the generators of the group.

nextElement - Current element being built recursively for the final element list

count - Number of recursive steps that has been run of fillList

Returns:

The final list of elements thus far derived for the group that comprise the group being created in createDefineRelationGroup

createInnerAutGroup

public boolean createInnerAutGroup()

Method to calculate and store the inner automorphism of the group groupMatrix object.

Returns:

Boolean value representing success of updating the group groupMatrix object.

createInnerAutFromTwoElements

public groupMatrix createInnerAutFromTwoElements(int elmtA,
                                                 int elmtB)

Method to calculate the inner automorphism of for two elements of the group groupMatrix object. Each cell in the group now equals the value of xygy^-1x^-1 where x and y are the elements and g is current element in the cell of the group for which the inner automorphism is calculated.

Parameters:

elmtA - First integer representing element in group for which the inner automorphism is calculated

elmtB - Second integer representing element in group for which the inner automorphism is calculated

Returns:

groupMatrix object that holds the inner automorphism for the group groupMatrix object.

createInnerAutFromElement

public groupMatrix createInnerAutFromElement(int element)

Method to calculate the inner automorphism of a single element of the group groupMatrix object. Each cell in the group now equals the value of xgx^-1 where x is the single element and g is current element in the cell of the group for which the inner automorphism is calculated.

Parameters:

element - Integer representing element in group for which the inner automorphism is calculated

Returns:

groupMatrix object that holds the inner automorphism group for an element.