Maths - Double Quaternions Code generation

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: Double Quaternion

a*b b.1 b.i b.j b.k b.D b.Di b.Dj b.Dk
a.1 1 i j k D Di Dj Dk
a.i i -1 k -j Di -D -Dk Dj
a.j j -k -1 i Dj Dk -D -Di
a.k k j -i -1 Dk -Dj Di -D
a.D D -Di -Dj -Dk 1 -i -j -k
a.Di Di D -Dk Dj i 1 k -j
a.Dj Dj Dk D -Di j -k 1 i
a.Dk Dk -Dj Di D 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)* D=k* D=Dk is not equal to i*(j* D)=i*Dj=-Dk

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="doublequaternion" type="doubl" elementLabels="1,i,j,k,D,Di,Dj,Dk">
<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:

 

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

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