Good day everyone,
I am Ishan Pandhare, 3rd year student of mathematics
and computing at IIT(BHU) Varanasi. I have been using 
Sympy for some time and have made some contributions as well.
After a brief discussion with some of the potential mentors, I could
draw a clear idea about some of the projects, even though 
I still want to discuss some projects with mentors willing to 
guide in the following:

Polynomial GCD 
<https://github.com/sympy/sympy/wiki/GSoC-Ideas#polynomial-gcd> : As I 
understand there is more than one
algorithm that could be implemented to improve the polynomial
GCD. I have looked at these and would like to discuss the
idea with a mentor. As it stands, improvement in this part could
simultaneously improve a lot of parts of Sympy. Also, I do have
knowledge of abstract algebra and number theory, which could be
useful for this project.

ODE ideas <https://github.com/sympy/sympy/wiki/GSoC-Ideas#other-ode-ideas> : 
Both of the topics related to this idea intrigued me.
The basic idea for "Solving Differential Equations in Terms of Bessel
Functions" has already been implemented and I would like to know the
scope of improvement in that area. Also, I would like to discuss other ideas
mentioned in the wiki, such as "Integrating factor for second order ODEs".
I do have the prerequisite knowledge, having studied DEs for the past
4 years.

Floating point expressions 
<https://github.com/sympy/sympy/wiki/GSoC-Ideas#optimize-floating-point-expressions>
 : 
The central idea of the project is to
improve the speed and accuracy of special functions. As I understand,
the scope of the project deals with either accuracy or speed (for a user-
defined accuracy). I would like to discuss the scope of this project 
with a mentor for further clarity.

Benchmarks and Performance 
<https://github.com/sympy/sympy/wiki/GSoC-Ideas#benchmarks-and-performance> : 
Having contributed to Sympy myself,
I can agree that a new system could be placed for benchmarks that 
could potentially warn about a certain change slowing down Sympy. This 
would encourage the implementation of better algorithms and could make
reviewing a PR much easier. I am very much interested in this idea and
would like to know where it stands as of today.

I would like to request the mentors concerning these projects to let me 
know about their involvement (as I am unaware of who the mentors 
for these projects are). There are other ideas that I would like to 
explore, but as of now, I would like to get a complete picture
of these project ideas. 
Thank you.
Ishan

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