4 ms·

I work with ML. Even a dense vector can be relatively high-dimensional (something like 128-D is common) I'd love to use Geometric / Clifford algebra for rotatio

I work with ML. Even a dense vector can be relatively high-dimensional (something like 128-D is common) I'd love to use Geometric / Clifford algebra for rotations of these vectors; the notation is much more intuitive. However, last time I tried using this library, it insists on generating all the N-vectors, of which there's a combinatoral amount w.r.t. the number of dimensions. For rotations, I really only need bivectors (IIRC) Is there a way to use Geometric Algebra for higher dimensions?

hugohadfield 6y ago
High dimensional GAs are a relatively hot topic of research but something we haven't aimed to target with this library (mostly because its not our main research area). My personal preference for working with high d algebras would be Stéphane Breuils and Vincent Nozick's GARAMON library (https://github.com/vincentnozick/garamon https://github.com/vincentnozick/garamon) (https://link.springer.com/article/10.1007/s00006-019-0987-7 https://link.springer.com/article/10.1007/s00006-019-0987-7), it is efficient and easy to use, and the authors are very friendly and helpful. You could also try out TbGAL (https://github.com/Prograf-UFF/TbGAL https://github.com/Prograf-UFF/TbGAL), I haven't used it myself but the work of the Leandro Fernandes is typically high quality.
DreamScatter 6y ago
My package called Grassmann.jl offers somewhat higher dimensional algebras than the python package here: https://github.com/chakravala/Grassmann.jl https://github.com/chakravala/Grassmann.jl