# Maths - choosing bases - 2D

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.

### g 2,0,0

 a*b b.e b.e1 b.e2 b.e12 a.e e e1 e2 e12 a.e1 e1 e e12 e2 a.e2 e2 -e12 e -e1 a.e12 e12 -e2 e1 -e

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

analysing associativity: table associates

### g+ 2,0,0

 a*b b.e b.e12 a.e e e12 a.e12 e12 -e

analysing commutivity: table commutes

analysing associativity: table associates

### g 1,1,0

 a*b b.e b.e1 b.e2 b.e12 a.e e e1 e2 e12 a.e1 e1 -e e12 -e2 a.e2 e2 -e12 e -e1 a.e12 e12 e2 e1 e

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

analysing associativity: table associates

### g+ 1,1,0

 a*b b.e b.e12 a.e e e12 a.e12 e12 e

analysing commutivity: table commutes

analysing associativity: table associates

### g 0,2,0

 a*b b.e b.e1 b.e2 b.e12 a.e e e1 e2 e12 a.e1 e1 -e e12 -e2 a.e2 e2 -e12 -e e1 a.e12 e12 e2 -e1 -e

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

analysing associativity: table associates

### g+ 0,2,0

 a*b b.e b.e12 a.e e e12 a.e12 e12 -e

analysing commutivity: table commutes

analysing associativity: table associates

### g 1,0,1

 a*b b.e b.e1 b.e2 b.e12 a.e e e1 e2 e12 a.e1 e1 e e12 e2 a.e2 e2 -e12 0 0 a.e12 e12 -e2 0 0

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

analysing associativity: table associates

### g+ 1,0,1

 a*b b.e b.e12 a.e e e12 a.e12 e12 0

analysing commutivity: table commutes

analysing associativity: table associates

### g 0,1,1

 a*b b.e b.e1 b.e2 b.e12 a.e e e1 e2 e12 a.e1 e1 -e e12 -e2 a.e2 e2 -e12 0 0 a.e12 e12 e2 0 0

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

analysing associativity: table associates

### g+ 0,1,1

 a*b b.e b.e12 a.e e e12 a.e12 e12 0

analysing commutivity: table commutes

analysing associativity: table associates

### g 0,0,2

 a*b b.e b.e1 b.e2 b.e12 a.e e e1 e2 e12 a.e1 e1 0 e12 0 a.e2 e2 -e12 0 0 a.e12 e12 0 0 0

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

analysing associativity: table associates

## 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="g 2,0,0" analyse="on" enableLabels="on">
<mathTypeMulti name="a" type="2" sign="0" zero="0" subAlgebra="all"/>
</outputTable>
<outputTable type="product" format="html" name="g+ 2,0,0" analyse="on" enableLabels="on">
<mathTypeMulti name="a" type="2" sign="0" zero="0" subAlgebra="even"/>
</outputTable>
<outputTable type="product" format="html" name="g 1,1,0" analyse="on" enableLabels="on">
<mathTypeMulti name="b" type="2" sign="1" zero="0" subAlgebra="all"/>
</outputTable>
<outputTable type="product" format="html" name="g+ 1,1,0" analyse="on" enableLabels="on">
<mathTypeMulti name="b" type="2" sign="1" zero="0" subAlgebra="even"/>
</outputTable>
<outputTable type="product" format="html" name="g 0,2,0" analyse="on" enableLabels="on">
<mathTypeMulti name="b" type="2" sign="3" zero="0" subAlgebra="all"/>
</outputTable>
<outputTable type="product" format="html" name="g+ 0,2,0" analyse="on" enableLabels="on">
<mathTypeMulti name="b" type="2" sign="3" zero="0" subAlgebra="even"/>
</outputTable>
<outputTable type="product" format="html" name="g 1,0,1" analyse="on" enableLabels="on">
<mathTypeMulti name="b" type="2" sign="0" zero="2" subAlgebra="all"/>
</outputTable>
<outputTable type="product" format="html" name="g+ 1,0,1" analyse="on" enableLabels="on">
<mathTypeMulti name="b" type="2" sign="0" zero="2" subAlgebra="even"/>
</outputTable>
<outputTable type="product" format="html" name="g 0,1,1" analyse="on" enableLabels="on">
<mathTypeMulti name="b" type="2" sign="1" zero="2" subAlgebra="all"/>
</outputTable>
<outputTable type="product" format="html" name="g+ 0,1,1" analyse="on" enableLabels="on">
<mathTypeMulti name="b" type="2" sign="1" zero="2" subAlgebra="even"/>
</outputTable>
<outputTable type="product" format="html" name="g 0,0,2" analyse="on" enableLabels="on">
<mathTypeMulti name="b" type="2" sign="0" zero="3" subAlgebra="all"/>
</outputTable>
</classDef>

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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.

 Geometric Algebra for Physicists - This is intended for physicists so it soon gets onto relativity, spacetime, electrodynamcs, quantum theory, etc. However the introduction to Geometric Algebra and classical mechanics is useful.