I read that a couple times. I found it unsatisfying because you are dropping terms that happen to have a coefficient of zero without a clear explanation of how those terms are even well formed in the first place.

I suppose this could be answered if you explicitly stated what set the geometric product acted on. As a guess, and from skimming Wikipedia, it’s the direct sum of scalars, vectors, bivectors, etc, up through n-vectors. So 2 + x∧y + 3x∧y∧z is a valid output. And it’s probably straightforward to show that the geometric product is actually defined on this space.

(Hi Marc!)