Get[FileNameJoin[{NotebookDirectory[],"Packages","RigidAlgebra2D.wl"}]]

p:=px e[1]+py e[2]+pz e[3]

g:=gx e[2,3]+gy e[3,1]+gz e[1,2]

Reflection

Simplify[-g\[Antigeometric]p\[Antigeometric]Antirev[g],{gx^2+gy^2==1}]//BasisForm

-OperatorMatrix[g,{gx^2+gy^2==1}]//MatrixForm

Translation

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

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

OperatorMatrix[translation]//MatrixForm

License

MIT License

Copyright (c) 2025 Eric Lengyel

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the “Software”), to deal
in the Software without restriction, including without limitation the rights
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copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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SOFTWARE.