I would love to go forward, together with Antoine to make this a viable 
project idea (the symbolic ideas mentioned by Antoine before like 
implementing spatial discretization to deal with infinite dimensional 
systems) and work on it (but not too domain specific, as Aaron pointed 
out), if he has no issues with it.

Aaron, would you (or any other mentor) be willing to guide us through this 
(making this into a well defined GSoC project idea and planning a line of 
action)?

Antoine, I would love to hear from you too, on how you want this idea to go 
ahead, and/or if you have any issues with us working on this together.

Regards --
Avi Shrivastava

On Wednesday, January 16, 2019 at 12:57:51 AM UTC+5:30, Aaron Meurer wrote:
>
> Purely numerical algorithms are out of scope for SymPy. See 
> https://github.com/sympy/sympy/wiki/GSoC-2019-Ideas#non-ideas. 
>
> However, the symbolic ideas mentioned by Antoine are interesting and 
> could be in scope for SymPy so long as they are not too domain 
> specific. 
>
> Aarn Meurer 
>
> On Wed, Jan 9, 2019 at 9:10 PM <[email protected] <javascript:>> 
> wrote: 
> > 
> > Dear Aaron, 
> > 
> > An extension of the quadrature module could include :- 
> > 
> > 1. for implementing the computation of multi - dimensional integrals :- 
> > 
> >     a. Monte Carlo methods 
> >     b. Sparse Grids 
> >     c. Bayesian Quadrature 
> > 
> > 2. for implementing the computation of one - dimensional integrals :- 
> > 
> >     a. Clenshaw Curtis Quadrature 
> >     b. Gauss Kronrod Quadrature 
> >     c. Tanh-Sinh Quadrature 
> >     d. Romberg's method 
> > 
> > These are a few of the methods that can be in included in the quadrature 
> module (for computation of one - dimensional and multi - dimensional 
> integrals) thereby making it a lot better. 
> > 
> > Would love your (or any mentor's) insights in this, so that this can be 
> taken progressively ahead. 
> > Please do let me know about what you think of implementing these 
> methods. 
> > 
> > Regards -- 
> > Avi Shrivastava 
> > 
> > On Wednesday, January 9, 2019 at 5:08:48 AM UTC+5:30, Aaron Meurer 
> wrote: 
> >> 
> >> Can you give an example of the sort of thing the code from this would 
> look like? 
> >> 
> >> Aaron Meurer 
> >> 
> >> On Sun, Jan 6, 2019 at 5:11 AM <[email protected]> wrote: 
> >> > 
> >> > Antoine, 
> >> > Yes I would love to work on this project with you. But we need to 
> first see how much work can be done in this area (the mentioned project) 
> and then we could divide the work too. Also, we could extend this to a 
> bigger project and then start working on it. 
> >> > 
> >> > A mentor would be highly appreciated to guide us through this. 
> >> > 
> >> > On Friday, January 4, 2019 at 12:44:32 AM UTC+5:30, Antoine Falaize 
> wrote: 
> >> >> 
> >> >> +1 
> >> >> 
> >> >> I currently develop the PyPHS package, that makes an intensive use 
> of sympy to derive symbolically numerical methods for the simulation of a 
> class of finite dimensional dynamical systems (namely, the port-Hamiltonian 
> systems). Then, the actual simulation code is generated for a variety of 
> langage (python, C++ and FAUST). 
> >> >> 
> >> >> And I plan to go a step further by implementing spatial 
> discretization to deal with infinite dimensional systems as well. 
> >> >> 
> >> >> I would love to participate in any way to this project! 
> >> >> 
> >> >> Best regards; 
> >> >> 
> >> >> Antoine Falaize (afalaize) 
> >> > 
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