A Numerical Tower For Geometric Algebra

Note: In this post I will avoid my preferred overbar notation, and instead write negatives using a “minus sign” (like − 123) for consistency with Scheme/Racket notation.

Introduction

I’ve recently taken an interest in geometric algebra (“GA”, not to be confused with algebraic geometry!), which goes beyond the usual “number line” in a way that elegantly models geometric ideas such as circles, volumes, rotations, etc. I don’t want to motivate or advocate for GA itself, since there are plenty of much better resources out there. Hence I’m going to focus on explanation and implementation of some basic foundations of GA, since that’s a good way to check my own understanding of the subject!

Here’s the start of the implementation, to get us going:

#lang racket