GSOC 16 : implementation-of-vector-integration

[Ashwani Gautam]

Hi There,
I will be applying for GSOC this year. I do all of my numerical work done in python thus i consider myself fair in Python. While going through the Ideas page i found the following topics pretty interesting to me.

1.) implementation of vector integration.
2.) classical mechanics efficient equation of motion generation with python.

I request Jason Moore and also other mentors to please provide  starting point of either of these.Thank You.

[Alan Bromborsky]

The question is do you only want to implement vector integration in 3 dimensions (Green's and Stoke's theorems) or in n dimensions (generalized Stoke's theorem in differential geometry) and in flat space or for a general manifold?  -

https://en.wikipedia.org/wiki/Stokes'_theorem

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[Jason Moore]

FYI, The vector module currently only supports three dimensional vector analysis.

Jason
moorepants.info
+01 530-601-9791

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[Ashwani Gautam]

Hi, since jason pointed put that the vector module currently only supports three dimensional vector analysis, its now only 3 dimensional problem of vector integration.
Yes i do know about both the theorem(Green and Stokes) from my first year undergraduate classes.
Though i still fail to catch "flat space or a general manifold", can you please give some links about, where to read them.
I am still looking at you to tell me from where to start .

[Aaron Meurer]

SymPy also has a diffgeom submodule which may be appropriate more
general integration.

Aaron Meurer

> https://groups.google.com/d/msgid/sympy/10dc670c-dffd-48ee-a44c-b9dea3d1fdd7%40googlegroups.com.

[Alan Bromborsky]

Since you are just starting you probably want to limit yourself to 3-dimensions.  In doing a quick look a the physics vector module (please someone correct me if I am wrong) it looks as if the only coordinate system implemented is rectangular (as opposed to cylindrical, spherical, etc.)  For separable coordinates in 3D see -

https://en.wikipedia.org/wiki/Orthogonal_coordinates#Table_of_orthogonal_coordinates

One of the great advantages of vector integration comes when you can do it in different coordinate systems since picking the right coordinate system can greatly simplify the problem.  If the thing you are integrating has cylindrical or spherical symmetry you want to do the integration in a cylindrical or spherical coordinate system.  If the physics vector module doesn't have these coordinate systems available you may want to implement them first before doing Green's and Stoke's theorems.

For others reading this please note that there are more general integration theorems than the generalized Stoke's theorem from differential geometry.  See the following link -

 https://en.wikipedia.org/wiki/Geometric_calculus#Fundamental_theorem_of_geometric_calculus

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[Ashwani Gautam]

Yes i agree, smart choice of coordinate system can greatly simplify the math involved, also it would take less time.
So, should i start adding code for Rectangular, cylindrical and spherical coordinates in physics vector module.

Aaron/Jason you want to add something here ?

[Jason Moore]

This work has been started:

https://github.com/sympy/sympy/pull/9937

I'd recommend helping finish that PR.

Jason
moorepants.info
+01 530-601-9791

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[Ashwani Gautam]

I am looking into it.

[parthpar...@gmail.com]

can you direct so that i can help
i want to contribute