Project discussion for GSoC 2020

[Tanav Shah]

Hi

I am Tanav Shah, second year undergraduate student in Computer Science at IIT Roorkee. I am particularly interested in the idea for implementation of Schubert and Grothendieck Polynomials for GSoC 2020. I am well versed with C/C++ and Python programming languages and have good knowledge in the field of combinatorics and algebra. I have gone through the main documentations for contributing to SageMath and am getting familiar with the codebase, especially for the multivariate polynomials. I have already installed the developer version of Sage and have setup the git trac account. I have also looked at some tickets which I could work for on the sage repository.

I am very interested in discrete structures, algorithms and algebra and have taken up courses in these areas. Currently, I am learning more about Newton Polytopes and the symmetric Grothendieck Polynomials, and their implementations and am willing to discuss some ideas with the mentors. I am also reading about the different properties and implementations of the Schubert Polynomials and am quite interested in these fields of mathematics. I am aiming to start contributing in the next few days.

I want to contribute to Sage, especially in the areas concerning polynomials and am looking forward to it.

Regards,

Tanav Shah

[Travis Scrimshaw]

Dear Tanav,

   Thank you for your interest. An understanding of multivariable polynomials is not going to be so useful for this project as these form other "interesting" bases of the ring of polynomials. Instead, I think it would be useful for this project to start familiarize yourself with https://trac.sagemath.org/ticket/6629 and, most importantly, make some (simple) contributions to Sage to get used to the workflow. Most of the work is predicated on doing linear algebra as it is about transitioning between different bases and hopefully utilizing some of the associated combinatorics where possible. It would be great to get a working version of these polynomials in Sage as they are an active area of research.

Best,

Travis