Get[FileNameJoin[{NotebookDirectory[],"Packages","ConformalAlgebra1D.wl"}]]

p:=px e[3,1]-py e[2,3]

q:=qx e[3,1]-qy e[2,3]

a:=ax e[1]+ay e[2]+az e[3]

d:=dz e[1,2]+dx e[2,3]+dy e[3,1]

Reflection

Simplify[-q\[Antigeometric]a\[Antigeometric]Antirev[q]]//BasisForm

Simplify[-q\[Antigeometric]p\[Antigeometric]Antirev[q]]//BasisForm

-OperatorMatrix[q]//MatrixForm

Translation

translation:=tx/2 e[3]+e[1,2,3]

translation\[Antigeometric]p\[Antigeometric]Antirev[translation]//BasisForm

OperatorMatrix[translation]//MatrixForm

Dilation

dilation:=(1-σ)/2(e[1]+mx e[3])+(1+σ)/2e[1,2,3]

Simplify[dilation\[Antigeometric]p\[Antigeometric]Antirev[dilation]]//BasisForm

Simplify[OperatorMatrix[dilation]]//MatrixForm

License

MIT License

Copyright (c) 2025 Eric Lengyel

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