[Soc2015-general] SymPy: Implementing Multiple Coordinate Systems

[Wanlin Xie]

Dear Mentors,

My name is Wanlin. I'm a first year undergraduate student in Columbia
University. I am applying to GSoC and would like to work on the SymPy
project under your supervision. I love the symbolic deductions in
mathematics and think that SymPy is so interesting. The project I am
applying for is implementing multiple coordinate systems in SymPy. I am now
finishing multivariable calculus and completed the introduction of
differential equations in high school so I think that I have a good
background as well as the passion for this project.
    My idea is to first split the Vector class into two classes 2D and 3D.
>From there, 2D branches down to Cartesian and Polar coordinates, while 3D
branches down to Spherical, Cylindrical, and Cartesian coordinates. Then I
will relate the different variables through equations that can convert
equations, shapes, solids, etc. from one coordinate system to another. I
can also implement the use of Jacobians and figure out a way to do
transformations in just any variable system. I was wondering what work has
been done about these multiple coordinate systems, and if this is a good
direction to go in. Any advice will be greatly appreciated.

Thank you so much!

Wanlin Xie
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