More info on the project : Add additional combinatorial (Hopf) algebras and additional bases

[Yashashwi Singhania]

Hi, I was interested in this project for gsoc as I have some interest in abstract algebra and combinatorics. I also do competitive maths. I wanted to have resolution of few doubts I had.

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1. What exactly do we have to do? the project idea states to add more bases but can you please be more specific.
2. What use will they pose?
3. "There are also a number of related non-symmetric but still important polynomials" can you provide some examples?
4. Any resources which could benefit me in exploring this project.
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Regards,
Yashashwi Singhania
IIT (BHU) Varanasi

[tcscrims]

Dear Yashashwi,

   Thank you for your interest. Please be aware that these are ideas for projects and you, the potential contributor, are expected to turn the idea into a full proposal. That being said, here are some additional ideas for you to consider from your questions.

1. As said, you need to provide the bases and related properties, such as multiplication and conversions to/from other bases. There can also be other algebras where you will provide the first such basis/implementation.

2. Use in research computations.

3. Demazure atoms and Grothendieck polynomials to name two, but there are numerous others.

4. There’s a survey paper “Asymmetric function theory” by Pechenik and Searles on various such (quasi/non)symmetric bases. There’s numerous research papers in combinatorics from at least the past 30 years exploring these topics. You can find others by a fairly easy Google search using the relevant keywords.

Best,

Travis

[Yashashwi Singhania]

Hi Travis,

I've setup sage locally, I was wondering if you could help me out in trying some relevant documentation to my project interests. Also what could be a useful first issue for me to solve or raise it myself.

[tcscrims]

Dear Yashashwi,

You can find a list of issues on our issue tracker, many of which can be good for a first PR. One recent one that I found was

https://github.com/sagemath/sage/issues/39710

Best,

Travis

[Yashashwi Singhania]

I had a few other doubts,

1. Which specific bases should be prioritised? is there a dependency order?
2. What specific operations must be implemented for each basis? 

3. Are there existing implementations which should serve as template for the new code? If so, can you please guide me through them.

There are other queries as this is my first time contributing to such a large organisation. Would you suggest me to raise a issue myself and implement one of these bases before the proposal round or add some code to show my experience with the language in the proposal itself. (I regularly surf through the issue trackers but find myself unable to work on a issue. I recently checked #39692 but wasn't able to pull up with something useful.)
Thank you very much for your constant help and support.

Regards,
Yashashwi 

[tcscrims]

Dear Yashashwi,

   Remember, this is your project and proposal to design and write. This is a somewhat open ended project idea, so there are many ways you could design such a project. Many examples can be found in the relevant Sage code in combinat.

You can either raise an issue yourself if you notice something that needs to be fixed (e.g., a typo in the documentation) or you have a feature request. There are also many other issues that are good for first time contributors that can be found on our GH issues list.

Best,

Travis