> I have finalized (almost) how to implement coordinate systems, and yes,
> we are going to have cylindrical as well as spherical coordinates.

Great! But do not hard code the choice of available systems. There are
many many more useful coordinates:

 http://mathworld.wolfram.com/OrthogonalCoordinateSystem.html

>From the second-last paragraph:

"Three-dimensional orthogonal curvilinear coordinate systems of degree two or 
less include
 bipolar cylindrical coordinates, bispherical coordinates, three-dimensional 
Cartesian coordinates,
 confocal ellipsoidal coordinates, confocal paraboloidal coordinates, conical 
coordinates,
 cyclidic coordinates, cylindrical coordinates, elliptic cylindrical 
coordinates,
 oblate spheroidal coordinates, parabolic coordinates, parabolic cylindrical 
coordinates,
 paraboloidal coordinates, prolate spheroidal coordinates, spherical 
coordinates,
 and toroidal coordinates."

At least some of the most important elliptic and parabolic systems
for physics should be added too. (Maybe not as part of your GSOC but
later.) Its not that clear where to put to border towards diff geom now.

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