[hamish_todd]

>"untyped"

It's amazing because that's the diametric opposite of what I'd consider to be true this is what the non-GA approach does, and which we avoid!

The modern approach to GA, eg https://en.wikipedia.org/wiki/Plane-based_geometric_algebra, distinguishes planes-through-the-origin, points, lines-through-the-origin, and lines-at-infinity. These four different types all get called "vectors" in the ordinary mindset. The cross product is said to take in two "vectors" and give you a "vector", but in reality it's generally taking two planes and giving you a line. This is talked about in the fourth paragraph of the wiki article :)

[nextaccountic]

My question was more like, will all those four mathematical objects (alongside other stuff like scalars) be represented as a single data type in a given library that implements geometric algebra, or will they be given distinct data types?

Someone else answered that they might be given a single data type, but it's possible to give more precise types, which seem cool!

(do you have any library to mention, alongside the ones already mentioned?)

[ath92]

I’d never seen this explanation of what a cross product is before. It really clicked for me, even just reading it as text. Thanks!