Vector calculus

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There is a fair amount of functionality, although I don't know if you'll find what specifically what you want. Here are some suggestions:

• Evaluate vector? in a notebook cell or at a sage: prompt to see the introductory documentation for vectors in Sage.

• See the reference manual for Matrices

• Coordinate transformations were included in the Function Plotting section of the manual (although I find it a little confusing). See e.g. Spherical coordinate system.

• The section of the reference manual on Plotting vector fields

There is also a bunch of work going on in differential geometry which may be of interest: http://www.sagemath.org/doc/reference... and http://trac.sagemath.org/sage_trac/ti.... However, if there are things that are not implemented, patches are always welcome!