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Maths - Octonion and Clifford Algebra - Code to generate the tables

Here is how I generated the tables for this page.

The tables were generated using this program.

To produce the results the program needs to have an XML input code. Here I have listed this input code next to the output of the program:

 

code program output
<classDef>
<outputTable type="product" format="html" name="octonion (c x c) x c" analyse="on" enableLabels="on">
<mathTypeCompound name="a" type="compound">
<mathTypeCompound name="a" type="compound">
<mathTypeCompound name="a" type="complex"/>
<mathTypeCompound name="a" type="complex"/>
</mathTypeCompound>
<mathTypeCompound name="a" type="complex"/>
</mathTypeCompound>
</outputTable>
<outputTable type="product" format="html" name="octonion c x (c x c)" analyse="on" enableLabels="on">
<mathTypeCompound name="a" type="compound">
<mathTypeCompound name="a" type="complex"/>
<mathTypeCompound name="a" type="compound">
<mathTypeCompound name="a" type="complex"/>
<mathTypeCompound name="a" type="complex"/>
</mathTypeCompound>
</mathTypeCompound>
</outputTable>
</classDef>

Octonion

This is the table often given for octonions:
e e1 e2 e3 e4 e5 e6 e7
e1 -e e4 e7 -e2 e6 -e5 -e3
e2 -e4 -e e5 e1 -e3 e7 -e6
e3 -e7 -e5 -e e6 e2 -e4 e1
e4 e2 -e1 -e6 -e e7 e3 -e5
e5 -e6 e3 -e2 -e7 -e e1 e4
e6 e5 -e7 e4 -e3 -e1 -e e2
e7 e6 e6 -e1 e5 -e3 -e2 -e

analysing commutivity: table does not commute:
for example: e1*e2 != e2*e1

analysing associativity: table does not associate,
for example, (e1* e2)* e3=e4* e3=-e6
is not equal to e1*(e2* e3)=e1*e5=e6
 

 

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see also:

 
Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

cover us uk de jp fr ca Quaternions and Rotation Sequences.

 

Commercial Software Shop

Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them.
cover Dark Basic Professional Edition - It is better to get this professional edition

cover This is a version of basic designed for building games, for example to rotate a cube you might do the following:
make object cube 1,100
for x=1 to 360
rotate object 1,x,x,0
next x

cover Game Programming with Darkbasic - book for above software

 

Can you help?

Please send me any improvements to here. I would appreciate ideas to make the pages more useful including error correction, ideas for new pages, improvements to wording. It helps if you quote the full URL of the page.

 

Terminology and Notation

Specific to this page here:

 

program

I am working on a project which uses these principles, if you would like to help me with this you are welcome to join in, here:

http://sourceforge.net/projects/mjbworld/

This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2008 Martin John Baker - All rights reserved - privacy policy.