Hi.

On Mar 23, 2011, at 6:43 AM, Tom Bachmann wrote:

> Dear list,
> 
> I would like to express my interest in working no the symbolic
> integration capabilities of sympy as part of a GSOC project.
> 
> My name is Tom Bachmann and I study mathematics (second year) at the
> university of cambridge, england. Here is an overview of my computer
> programming experience: I have previously worked on the Hurd project
> (in C), I did a project that started the port of the kaXen/afterburner
> pre-virtualisation environment to amd64 (in C++), and I have extended
> the wikireader codebase to handle ebooks from project gutenberg
> (mostly python). I can supply more details and/or references if you
> wish. I have also created some "fun projects" on my own, the most
> relevant here being probably what I call "fz" [1], a program to plot
> various special functions in the complex plane and on riemann surfaces
> (in C++). Finally here in cambridge there are so-called "CATAM" [2]
> (computer-aided teaching of all of mathematics) projects on which I
> got excellent results; this may or may not be meaningful to you.
> 
> With this background settled, let me say that I find both of the
> proposed approaches to symbolic integration (resdiue theorem and Mejer
> functions) very interesting. I believe I do understand well the
> mathematics behind both. Depending on what you perceive to be more
> important, I would be happy to work on either, with possibly a slight
> preference for the residue method. What is the state of any existing
> implementation in sympy?
> 
> If there is any specific other information that you want me to supply,
> please don't hesitate to let me know.
> 
> Thanks,
> Tom
> 
> [1] https://bitbucket.org/ness/fz/overview
> [2] http://www.maths.cam.ac.uk/undergrad/catam/
> 

Currently, SymPy is getting pretty strong with indefinite integration, thanks 
to my  project to implement the Risch Algorithm.  However, there is really no 
progress with definite integration.  The integrator basically uses the 
fundamental theorem of calculus (integrate and evaluate at the end points) to 
evaluate definite integrals, and that is it.  So there is definitely much room 
for improvement in this area.

Now, the Meijer G function project would be much more general (i.e., powerful) 
than the residue one, but I think it would also be more difficult.  If you are 
interested in that one, you might look at the paper by Kelly Roach [1].

The residue project would probably be easier, but again, much less powerful.

By the way, the integration algorithms are my particular interest in SymPy, so 
I would like to discuss this more with you. If you want, we can talk on IRC.  
Our channel is #sympy on Freenode.

Finally, I want to remind you that we require all student applicants to submit 
at least one patch to the project that gets reviewed and pushed in.  See 
https://github.com/sympy/sympy/wiki/development-workflow for a guide on how to 
submit a patch.  Some easy to fix issues that can get you started are labeled 
EasyToFix at our issue tracker.  See 
http://code.google.com/p/sympy/issues/list?q=label:EasyToFix.

Aaron Meurer

[1] - K. Roach. Meijer g function representations. In ISSAC ’97: Proceedings of 
the 1997 international symposium on Symbolic and algebraic computation, pages 
205–211, New York, NY, USA, 1997. ACM.

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