Maths - Dual Quaternions - Generating Multipication Table

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: Dual Quaternion

a*b b.1 b.i b.j b.k b.ε b.εi b.εj b.εk
a.1 1 i j k ε εi εj εk
a.i i -1 k -j εi -εk εj
a.j j -k -1 i εj εk -εi
a.k k j -i -1 εk -εj εi
a.e ε -εi -εj -εk 0 0 0 0
a.ei εi ε -εk εj 0 0 0 0
a.ej εj εk ε -εi 0 0 0 0
a.ek εk -εj εi e 0 0 0 0

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

analysing associativity: table does not associate, for example,
(i* j)* ε=k* ε=εk is not equal to i*(j* ε)=i*εj=-εk

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="dualquaternion" type="dual" elementLabels="1,i,j,k,e,ei,ej,ek">
<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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metadata block
see also:

 

Correspondence about this page Amy de Buitléir has written this document and kindly allowed me to publish it here.

Book Shop - Further reading.

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

 

Terminology and Notation

Specific to this page here:

 

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