GSoC 2020: Developing the Group Theory Functionality of SymPy

[Tanmay Sinha]

Hello everyone! I am Tanmay Kumar Sinha, a 3rd year undergraduate student of Computer Science at IIIT Hyderabad, India. I have a 2 year experience with Python, and am comfortable with the language.

I am interested in computational mathematics, and mathematics in general. I am well versed with linear algebra, calculus, and probability.I have taken a very basic introductory group theory course, and an advanced course on mathematical structures, and have read the first few chapters of Dummit and Foote.

I had played around with SymPy during my summer break, and it was the first time I had an encounter with a symbolic mathematical system. I am familiar with the basic way in which the library is used, and would like to learn some more.

For this years GSoC, I would like to extend the functionality of the group theory system in SymPy. I propose to do the following:-

1.) Implementation of Quotient Groups:- For the 2018 project of GSoC, an attempt was made to implement the computation of quotient groups of finitely presented groups, but this was not completed. I propose to finish this work.

2.) Implementing Hall Subgroups:- Check whether the given group is solvable, and if so, returns a Hall subgroup or list of Hall subgroups.

3.) Implementation of group automorphisms:- Computation of the automorphism group of a given group G.

The above list is non exhaustive - any more suggestions and ideas would be appreciated. Also, some readings for the project would also be helpful - I am already reading a Handbook of Computational Group Theory. I would like to know if there is anything beyond that that is needed.

Also, any ideas for where to get started would also be helpful.