jhypercomplex.multiplication_tables

Class MultiplicationTableTripling

java.lang.Object

jhypercomplex.multiplication_tables.MultiplicationTableTripling

public class MultiplicationTableTripling
extends java.lang.Object

Copyright © 2005-2015 by Markus Maute. All rights reserved.

Author:

Markus Maute (http:///www.jalgebra.com)

Constructor Summary

Constructors

Constructor and Description
MultiplicationTableTripling()

Method Summary

Methods

Modifier and Type	Method and Description
static java.lang.String[][]	getTripledMultiplicationTable(BinaryProductStructure orig_algebra, java.lang.String[] new_base_elements, int sign1, int sign2) Given three sets of basis elements a, b, c of the original algebra, the (Cayley-Dickson) tripling formula used (due to "Alternative twisted tensor products and Cayley algebras" by H.

Methods inherited from class java.lang.Object

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

Constructor Detail

MultiplicationTableTripling

public MultiplicationTableTripling()

Method Detail

getTripledMultiplicationTable

public static java.lang.String[][] getTripledMultiplicationTable(BinaryProductStructure orig_algebra,
                                                 java.lang.String[] new_base_elements,
                                                 int sign1,
                                                 int sign2)
                                                          throws java.lang.Exception

Given three sets of basis elements a, b, c of the original algebra, the (Cayley-Dickson) tripling formula used (due to "Alternative twisted tensor products and Cayley algebras" by H. Albuquerque, F. Panaite) is given by e = (a,b,c)(d,e,f) = (ac-ld*b, da+bc*, ) 'e' defining the set of basis elements of the new algebra. '*' being the conjugation. The product is the one of the original algebra.

Parameters:

ori_algebra - Original algebra

ori_mult_table - Names of the additional base elements (number equals the one of the original algebra).

sign1 - -1,0 or 1.

sign2 - -1,0 or 1.

Returns:

Multiplication table of the resulting algebra, having 4 times as many elements.

Throws:

java.lang.Exception