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.

 

Terminology and Notation

Specific to this page here:

 

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