GSoC Application Implementation of multiple types of coordinate systems for vectors

[szymon.m...@gmail.com]

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

[Alan Bromborsky]

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.

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[szymon.m...@gmail.com]

Thank you for your comment and suggestion.There are helpful.
Overloading operator is definitely great idea. It would be great to implement this feature.

[Alan Bromborsky]

This may be getting too far afield but consider a scalar differential operator class to build the vector differential operator class.  It is easy to define an algebra for the scalar differential operator class.  See section 2.3.3 in attached document.

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[szymon.m...@gmail.com]

Thank you for this manuscript and concept.

I wish I started working on proposal so late and I couldn't think on your idea carefully before deadline.
Python is great language to overloading operator, but we need do it wisely from structural point of view.
I just add short description in my proposal, and I will think about it in April an May.

BTW:
I've found one typo in your document. On page 20 in the first line you have "A general general multivector linear differential".

Szymon

[Alan Bromborsky]

Thank you I will correct it. 

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