GSoC - Further Contributions to SageMath

[Shriya M]

Hello Dr. Scrimshaw,

I hope you are doing well! You may not remember me, but we met during Sage Days 114 at The Institute of Mathematical Sciences, Chennai.

I am currently doing my second Masters in Mathematics at King's College London.

I did my undergrad thesis under Dr. Amritanshu Prasad- The Institute of Mathematical Sciences, Chennai. My work with vector partitions focused on extending the theoretical understanding of enumerating them with given constraints. This project enhanced the functionality of the Vector Partitions module in SageMath. (ticket #34827)

One of the GSoC '24 projects caught my attention as a potential project for me to get involved with: "Direct Implementation of Chow rings of Matroids". I had the following questions regarding the same:

1. The project description states that using an explicit Gröbner basis for computing the Chow ring of a Matroid gives more features than the current model. Can you explain how this happens?

2. I'd like to know some future prospects and applications of this project that you may have in mind.

3. I'm currently residing in the UK as an international student and my visa permits me to work every week for a maximum of 20 hours. I want to know if I'm eligible to work as a GSoc contributor.

Thanks and I look forward to your reply!
Shriya.

[tcscrims]

Hi Shriya,

   Thank you for your message.

1. Have a GB (Gröbner basis) means we can write any element in the quotient to a unique standard form. In particular, we can tell if two elements are equal in the quotient ring if and only if they reduce to the same element. For the generic implementation currently, the GB needs to be computed, which is very expensive. In addition, we know some extra properties about the resulting basis (of the quotient) that the generic implementation would not know about. So with the appropriate category, we get all of the other generic implementations from that category. It also allows us to add additional features that might be useful (such as the Poincaré duality) only for the Chow rings of matroids.

2. I won’t be using this in my research; the implementation was a way for me to understand the construction. However, this was used for the log-concavity of characteristics functions of matroids. So this functionality will likely be useful to people who are doing research in that field.

3. You can find the criteria here: https://developers.google.com/open-source/gsoc/faq#what_are_the_eligibility_requirements_for_participation. From what is listed and you are saying, I believe you are eligible. If you’re accepted, we will likely have to adjust the timeline to not violate your visa conditions. I believe there is an email address somewhere that you can use to directly ask Google as well.

Feel free to also directly email me too with your proposal. We can also discuss the possibility of a different project that is closer to your masters work.

Let me know if you have any further questions.

Best,

Travis