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*bb.eb.e1b.e2b.e12
a.eee1e2e12
a.e1e1ee12e2
a.e2e2-e12e-e1
a.e12e12-e2e1-e

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

analysing associativity: table associates

g+ 2,0,0

a*bb.eb.e12
a.eee12
a.e12e12-e

analysing commutivity: table commutes

analysing associativity: table associates

g 1,1,0

a*bb.eb.e1b.e2b.e12
a.eee1e2e12
a.e1e1-ee12-e2
a.e2e2-e12e-e1
a.e12e12e2e1e

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

analysing associativity: table associates

g+ 1,1,0

a*bb.eb.e12
a.eee12
a.e12e12e

analysing commutivity: table commutes

analysing associativity: table associates

g 0,2,0

a*bb.eb.e1b.e2b.e12
a.eee1e2e12
a.e1e1-ee12-e2
a.e2e2-e12-ee1
a.e12e12e2-e1-e

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

analysing associativity: table associates

g+ 0,2,0

a*bb.eb.e12
a.eee12
a.e12e12-e

analysing commutivity: table commutes

analysing associativity: table associates

g 1,0,1

a*bb.eb.e1b.e2b.e12
a.eee1e2e12
a.e1e1ee12e2
a.e2e2-e1200
a.e12e12-e200

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

analysing associativity: table associates

g+ 1,0,1

a*bb.eb.e12
a.eee12
a.e12e120

analysing commutivity: table commutes

analysing associativity: table associates

g 0,1,1

a*bb.eb.e1b.e2b.e12
a.eee1e2e12
a.e1e1-ee12-e2
a.e2e2-e1200
a.e12e12e200

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

analysing associativity: table associates

g+ 0,1,1

a*bb.eb.e12
a.eee12
a.e12e120

analysing commutivity: table commutes

analysing associativity: table associates

g 0,0,2

a*bb.eb.e1b.e2b.e12
a.eee1e2e12
a.e1e10e120
a.e2e2-e1200
a.e12e12000

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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