GSoC 2017: Implementation of multiple types of coordinate systems for vectors

[Arihant Parsoya]

Hi,

I am Arihant Parsoya, sophomore at IIT Bombay. I am interested in Computer Science and Mathematics.

I have gone through the idea page and I am interested in working on the project named Implementation of multiple types of coordinate systems for vectors.

I have been contributing to sympy for about a year now. I have submitted two PRs related to this idea previously:

[WIP] Multiple Coordinate System

Implemented Spherical Coordinate System

So far, I have used Làme parameters approach to implement multiple coordinates. However, I believe that there is better approach to implement this idea by using metric tensors and obtaining its Christoffel symbols(as suggested by Alan Bromborsky). 

It would be very helpful if anyone can give their ideas or tips regarding this project(APIs, implementation, etc.) 

Thanks,

Arihant Parsoya,

IIT Bombay

[Alan Bromborsky]

I have attached pdf output of examples of coordinate system api in galgebra module.  g is the metric tensor (in this case only the diagonal elements since coordinate systems are orthogonal).

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[Alan Bromborsky]

In my previous email only the first example uses the metric tensor g to define the coordinate system.  In the other examples they defined via the vector manifold function X.  X is the position vector written in terms of the rectangular coordinate components where each component is written in terms of the new coordinates.  Then the partial derivative of X with respect to each new coordinate defines a basis vector in the new coordinate system (not normalized).  From the dot products of these basis vectors the metric tensor g is calculated.