[jordibc]

Well, I got sucked down the same Geometric Algebra rabbit hole, plus another "remarkably concise and intuitive way" one too, which is Clojure.

So I wrote a library that can generate any GA and do all kind of fun operations (which could be used in particular as a basis for a physics engine). Just in case any of this is of your interest too: https://cljdoc.org/d/net.clojars.jordibc/geometric-algebra/