Clifford himself called it the geometric algebra, so many prefer to call it that, at least when applied to geometric problems. I think that there is a lot of u

Clifford himself called it the geometric algebra, so many prefer to call it that, at least when applied to geometric problems. I think that there is a lot of useful structure in the geometric algebra that gets thrown out when one moves to talking about its subalgebras (ie. quaternions, dual quaternions, vectors, etc.). Its ultimately up to taste but I often find that I prefer to use the full GA instead of its subalgebras. Often some unexpected beauty or useful result drops out!