On Sun, Mar 22, 2009 at 5:13 PM, asmeurer <asmeu...@gmail.com> wrote:
>> * Implement the (generalized) hypergeometric differential equation and
>> add hypergeometric functions like Bessel and Airy functions to SymPy
>> (these functions are needed to solve many important ODEs from physics
>> and elsewhere)
> We haven't learned about these yet (remember that I am presently only
> half way through the semester in my ODE's class), but from what I can
> tell, they involve series solutions.  I only have three months to do
> this.  If I have time to do series, then I will go ahead and to it,
> but for my applications, I think it might hurt it if I make my project
> impossible.

I think this is fairly straightforward work; the solutions have
standardized forms
and don't require implementing any series. If you're not sure if
you'll have time,
it can be good to include it in the application anyway, but state clearly
that you'll do it only if you have time. Assuming you are interested in the
task, that is.

> One of the nice things about implementing ODEs is that I
> can shoot for a realistic goal and if I achieve it faster than I
> thought I would, then I could easily logically continue the project
> from there by implementing more advanced types of solutions, i.e.,
> series, numerical, systems of ODEs, etc.

Of course.

>> * Implement automatic transformation of high-order ODEs to systems of
>> first-order ODEs. Write wrappers for numerical ODE solvers in mpmath
>> and/or SciPy  so that numerical solutions can be obtained conveniently
>> in SymPy.
> Writing wrappers might no be as difficult.  Is there already a
> standard for wrappers in sympy?

There are existing wrappers to look at, but not exactly any standard.

>> Though I will not be mentoring, I will be happy to provide guidance
>> about any of the above if necessary.
> I see from your blog that you participated in gsoc last year.  Do you
> perhaps have any advice for me, especially with regards to the
> application process?

The best advice is probably to discuss your application with the
developers, as you're already doing. Include a schedule plan
in your application.

Fredrik

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