Basic vector code, without a coordinate system class

All calculations essentially occur in the same frame.
i, j, k and x, y, z are imported as base vectors and base scalars by default on importing sympy.vector.
delop is a Del operator instance.

Example:

>>> v = 3*i - j
>>> delop ^ v
0

(delop ^ v represents curl of v)
Exactly. A coordinate system gives a common framework to have a notion of 'coordinates' and 'directions'. Plus, as you said, vectors don't make sense if you don't already know what a coordinate system is. Anyways, if a user has to deal with only _one_ system, then he just writes one line extra, initializing the 'default' frame he would work in,