PGABLE: A Matlab Projective Geometric Algebra Tutorial

Last Updated: September 15, 2025
Version 2.2.0
This page contains Matlab software and a tutorial for learning Geometric Algebra. This tutorial is aimed at the sophomore college level, although it may provide a gentle introduction to anyone interested in the topic.

GABLE was a prototype geometric algebra system for OGA (Ordinary Geometric Algebra). The prototype was successful, and in PGABLE, we have added tutorial material on PGA (Plane-based Geometric Algebra, also known as Projective Geometric Algebra). In Version 2.0.0, we added support for CGA (Conformal Geometric Algebra).

The Tutorial

You should download the tutorial:

The Software

You must have Matlab to run PGABLE.

You should install PGABLE as an Add On in Matlab. Alternatively, you can down-load the package as a .zip file.

If you chose to download the zip file, when you unzip the zip file, it will create a folder called 'PGABLE'. You need to add this folder and its subfolders to your Matlab path. To add it to your path, type

>> addpath(genpath('.../PGABLE'))
where "..." is the path to PGABLE. Don't type the ">>", which is the Matlab command prompt.

Note: If you're running an older version of Matlab (ie, pre-2024), you will need to download clip.m and place it in your PGABLE folder. (If clicking on the link opens the file rather than opening a download dialog, then you'll need to right-click and select "Download" from the menu.)

If you encounter any problems or have any comments, please email them to us: smann@uwaterloo.ca.

Related Links

For further information on Geometric Algebra, see the following links:
smann@uwaterloo.ca