Maths - Octonion - Code

Here is how I generated the tables for this page.

The tables were generated using this program.

The output of this program is shown below. To produce the results the program needs to have an XML input code. At the bottom of this page I have listed this input code.

Table for: octonion

a*b b.1 b.i b.j b.k b.l b.li b.lj b.lk
a.1 1 i j k l li lj lk
a.i i -1 k -j li -l -lk lj
a.j j -k -1 i lj lk -l -li
a.k k j -i -1 lk -lj li -l
a.l l -li -lj -lk -1 i j k
a.li li l -lk lj -i -1 -k j
a.lj lj lk l -li -j k -1 -i
a.lk lk -lj li l -k -j i -1

analysing commutivity: table does not commute: for example: i*j != j*i

analysing associativity: table does not associate, for example, (i* j)* l=k* l=lk is not equal to i*(j* l)=i*lj=-lk

XML input code

To produce the results the program needs to have an XML input code listed here:

<classDef>
<outputTable type="product" format="html" name="octonion" analyse="on" enableLabels="on">
<mathTypeHypercomplex name="a" label="octonion" type="complex" elementLabels="1,i,j,k,l,li,lj,lk">
<mathTypeHypercomplex name="b" label="quaternion" type="complex" elementLabels="1,i,j,k">
<mathTypeHypercomplex name="c" label="complex" type="complex" elementLabels="1,i">
</mathTypeHypercomplex>
</mathTypeHypercomplex>
</mathTypeHypercomplex>
</outputTable>
</classDef>

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see also:

If you are interested in this, there is a very good paper by John Baez

Correspondence about this page

Book Shop - Further reading.

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cover us uk de jp fr ca On Quaternions and Octonions

Terminology and Notation

Specific to this page here:

 

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