In all fairness, it should be noted that, for better or worse, GA is not part of the mainstream; modern treatments use differential forms instead. For an accessible account, see, for example, https://www.jpier.org/ac_api/download.php?id=14063009.
Physics is littered with incomplete implementations of GA using a mish-mash of random bits of mathematics because of a perverse insistence on refusing to use the appropriate algebra.
