I'm not qualified enough to answer your question. What I understand is that PGA is not the only game in town. This framework lets one handle algebra with any number of positive, negative and zero dimensions.

You might find Professor Lasenby's 2020 talk (among others at Bivector Youtube channel) useful: https://www.youtube.com/watch?v=m7v2IUJtC3g

https://www.youtube.com/user/EnkiOrigami/videos