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GSoC 2019: Ideas Page

Introduction

Welcome to Sagemath's Ideas Page for GSoC 2019! (Last year 2018)

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

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

Improve Support of Representation Theory

Representation theory is the study of symmetries and is an important part of modern mathematics with applications to other fields, such as physics and chemistry. GAP supports doing computations using the characters of representations, but it often does not contain constructions nor manipulations of the modules. There is currently some limited support within Sage for representations as a proof-of-concept, but this needs to be expanded and refined. Things that can be added are tensor products (for bialgebras), dual representations (for Hopf algebras), induction and restriction functors, methods to construct representations of groups (e.g., symmetric group), Lie algebra representations, etc.

Implement Lie Superalgebras

Lie superalgebras were introduced by Kac in order to unify bosons and fermions and are currently an active topic of research. Lie algebras have been implemented in Sage and the that framework has been tested and is mostly stable. The next step is to extend this framework to Lie superalgebras and provide implementations of the basic and finite-dimensional Lie superalgebras. This project could also aim to cover some of their representation theory or quantum groups.

Refactor RSK and implement new insertion rules

The Robinson-Schensted-Knuth (RSK) bijection is a core part of modern day combinatorics involving tableaux and symmetric functions. The current implementation includes the classical RSK insertion and two generalizations called Edelman-Greene and Hecke insertion. However, the current design does not scale well as new insertion algorithms are implemented in Sage (e.g., super RSK 24894 and dual/coRSK 25070). The goal of this project is to refactor the code to use the same design patterns as the growth diagrams. This project would also include writing new insertion rules.