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)
If you want to just transform coordinate tuples to tuples in new coordinate systems, it works just fine, you are simply required to specify a manifold and a patch on the manifold (coordinate systems lie on patches).

In any case, transformations of differential operators are better to be reimplemented as special cases. Differentiation in diffgeom is much more different than in the usual 3D space.

Maybe that you could reuse part of the code from diffgeom, or just copy some parts.