GSoC 2023: Ideas Page

Introduction

Welcome to SageMath's Ideas Page for GSoC 2023! (Last year 2022)

SageMath's GSoC organization homepage -- the hub for submitting applications and where the everything on Google's side is organized. (Timeline)

Please subscribe to the sage-gsoc mailing list and the GAP developer list for discussion on possible GAP GSoC projects. Also, make sure you have gone through the information regarding application procedures, requirements and general advice. The Application Template is also available on that wiki page. Archives of past GSoC project ideas can be found here.

All projects will start with an introduction phase to learn about SageMath’s (or sister projects') internal organization and to get used to their established development process. We also require you to show us that you are able to execute actual development by submitting a relevant patch and/or reviewing a ticket via Trac of the project you are interested in applying to. The developer guide is a great comprehensive resource that can guide you through your first steps in contributing to SageMath.

Apart from the project ideas listed below, there is also a comprehensive list of future feature wishes in our trac issue tracker. They might contain the perfect project idea for you we didn't even think about!

Project Ideas

Here is a list of project proposals with identified mentors. Other well-motivated proposals from students involving SageMath in a substantial way will be gladly considered, as well.

Improve (free) module implementations

SageMath has multiple implementations of free modules:

1. Finite dimensional coordinate representations in the "standard" basis using FreeModule that provides both a dense and sparse implementation. 2. Using CombinatorialFreeModule (CFM) as (possibly infinite dimensional) sparse vectors.

There are various benefits to each implementation. However, they are largely disjoint and would mutually benefit from having a common base classes. In particular, having a dense implementation for CFM elements for applications that require heavier use of (dense) linear algebra. The goal of this project is to refactor these classes to bring them closer together (although they will likely remain separate as they are likely not fully compatible implementations for the parents).

Improve exterior algebra and Gröbner bases code and expand to graded commutative algebras

The exterior (or Grassmann) algebra is a fundamental object in mathematics that recently obtained an implementation of Gröbner bases. However, it is currently quite slow with a goal to improve it (see, e.g., #34437). The second goal of this project would be to implement Gröbner bases for the general graded commutative algebra code within Sage. This includes possibly redoing the underlying implementation to to not rely on the more generic plural for computations (except perhaps those involving ideals). For the ambitious, these computations would be extracted to an independent C++ library for many common rings (implemented using other libraries).

Implement Schubert and Grothendieck polynomials

Schubert calculus can roughly be stated as the study of the intersections of lines, through which certain algebras arise that can be represented using Schubert polynomials and Grothendieck polynomials. The main goal of this project is to finish the implementation started in #6629, as well as implement the symmetric Grothendieck polynomials and their duals in symmetric functions. There are also new methods to compute completions in the ring of symmetric functions, allowing expansions of Grothendieck polynomials in Schur functions.