> don't handle high dimensional (even 32D, fairly primitive by ML standards) spaces.

You're confusing two different notions of dimensionality here. The Geometric Algebra of 32D is actually a 2^16 (i.e. 65536) dimensional vector space. So it's like talking about vectors in 65536 dimensions, or the space of 256x256 matrices.

I had a problem where I wanted to rotate a high dimensional vector. This was ages ago, so I don't remember the exact terminology. What I ended up doing is writing out the geometric algebra equations by hand (with only the first order bivectors IIRC) and coding that up.

Having an option in the library to not have all the higher order bivectors if I don't need higher order operations would be nice.

Yeah what you want then is a 'sparse' bivector.

> The Geometric Algebra of 32D is actually a 2^16 (i.e. 65536) dimensional vector space.

Rather a 2^32-dimensional vector space. :-)

Time to give Julia a shot! It has this amazing package [1] for geometric algebras in up to a very high number of dimensions.

[1]: https://github.com/chakravala/Grassmann.jl