Proposal looks good.  Only one comment and one suggestion. -

Comment: You need to be very careful when taking the square root of an expression. Check the degree to which assumptions propagate such as if u and v are declared real does sqrt() know that sqrt(u**2+v**2) is also real.

Suggestion: Consider a vector differential operator class (del operator) and then overloading * and ^ so that if f is a scalar field and V a vector field you can write -

gradient of scalar field = del * f
divergence of vector field = del * V
curl of vector field = del ^ V
Laplacian of scalar field = del * (del * f)

In the future vector differential operators could be more general than del and an algebra of differential operators could be defined. For example if L is a linear transformation (possibly a function of the coordinates) and overload * so that L(V) = L * V then possible differential operator could be -

(del * L) * V

or if M is another linear transformation

(del * L + M) * V

If defined correctly the Laplacian could be del * del.




On 04/01/2017 05:08 PM, szymon.mieszc...@gmail.com wrote:
Hi,
I just put my proposal on wiki page: https://github.com/sympy/sympy/wiki/GSoC-2017-Application-Szymon-Mieszczak:-Implementation-of-multiple-types-of-coordinate-systems-for-vectors

If someone review it, I would be grateful.

Szymon

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