>> The answer to your question is essentially "yes" ...
Thank you for your detailed response and links. I had in fact found
some of them when searching, but clearly hadn't read them carefully
enough. In particular, I had missed the use of vector_frame in the
documentation of Affine Connections,
The answer to your question is essentially "yes", since Sage can deal with
any kind of vector frame, not necessarily coordinate frames, see
http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/vectorframe.html
In particular, a connection can be defined by its coefficie
