Hello SymPy Developers,

I am interested in applying to GSoC 2020 so here's my introduction.

I'm a grad student at the University of Rhode Island, currently in my 
second semester pursuing a Master's Degree in Computer Science. I have 
strong interests in mathematics in general and specifically the 
intersection of mathematics and computer science. I have been programming 
in python on and off since about 2015, when I worked on my undergraduate AI 
project (a basic chat bot). More recently I used python for a computer 
vision project in my previous job. The project involved extracting 
structured information from images of identity cards.

Maple is the CAS I'm most familiar with as I'm using it for course I'm 
taking. I had heard of Sage before but didn't know that SymPy was its 
backend for symbolic computation. For GSoC 2020, I want to work on 
summation algorithms. With SymPy only implementing Gosper's algorithm now, 
there are a lot of expression classes whose summations cannot be computed. 
Before the summer, I will be implementing an algorithm that uses generating 
functions (link to paper <https://dl.acm.org/doi/10.1145/74540.74568>) to 
sum hybrid functions as a project for the course. This algorithm can find 
sums containing special functions like the harmonic numbers and fibonacci 
numbers, which SymPy is mostly unable to do now. (For example, 
summation(k*harmonic(k), 
(k,1,n)) does not produce a closed form). My implementation for the course 
will be in the Maple programming language, and my first task would be 
porting that to SymPy. Once that is done, I want to move on to implementing 
Karr's algorithm, first for the indefinite case and then the definite case. 
I think implementing an algorithm I'm already familiar with first might be 
better than to dive headfirst into the more complex Karr's algorithm. What 
are your thoughts on this?

Another relevant piece of information: my major professor (Dr. Ed Lamagna) 
is a computer algebra researcher and has contributed to the implementation 
of some algorithms in Maple. I will be able to ask him for advice in case 
I'm stuck on something.

Thanks,
Neeraj

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