GSoC 2026 - Interest in “Improve and polish the generation of structures of combinatorial species”

[Akshara Bhardwaj]

Hello Martin Rubey,

My name is Akshara Bhardwaj and I am interested in applying for the “Improve and polish the generation of structures of combinatorial species” project for GSoC 2026.
I have been contributing to SageMath since early 2026, primarily working on issue #28445 (bibliography migration in src/sage/combinat/), where 8 of my branches have been picked up by the release manager.
I have also contributed fixes under issue #32277 (picked up by the release manager) and issue #22680 (all checks passed, awaiting review).
My GitHub is aksharabhardwaj766-commits.
I’ve started looking at src/sage/combinat/species/ to get familiar with the existing implementation and would love to work on the missing operations and their multivariate variants, alongside polishing the existing code.
I have two questions to make sure my proposal is well-scoped:

1. Which of the missing operations would you prioritise for the 175-hour scope?
2. Is there an existing issue or tracking ticket I should reference in the proposal?

I am happy to share a draft proposal for your feedback before the deadline.
Best regards,
Akshara Bhardwaj
GitHub: aksharabhardwaj766-commits

[Martin R]

Hi Akshara!

Just to make sure (I think you are well aware of it), the new framework is in sage/rings/lazy_species.py.

The univariate versions of the Hadamard product, the functorial composition and the arithmetic product have been implemented in https://github.com/sagemath/sage/pull/41655.  This also contains some other improvements, but is not yet merged.  In any case, your work will build on top of that.  The generation of structures has not yet been implemented for any of these three operations.

Therefore, the next things to do are as follows:

a) implement the derivative of a species, and the partial derivative of a multisort species

b) implement the multisort versions of the functorial composition and the Hadamard (or "Cartesian") product

c) check that weights work correctly for all implemented operations

d) implement special implementations for the generation of structures and isomorphism types, in particular the derivative, the functorial composition, the Hadamard product and the arithmetic product.

The most important part of your proposal will be to make it clear that you have a good understanding of combinatorial species, as in Sections 1.0-1.4 and 2.0-2.4 of the book by Bergeron, Labelle and Leroux, see https://www.cambridge.org/core/books/combinatorial-species-and-treelike-structures/D994A1F2877BDE63FF0C9EDE2F9788A8.  I think that everything else is mostly irrelevant, so it would be really good if you include your academic background..  If you are not yet familiar with combinatorial species, but you had some combinatorics classes, and you know how to work with generating functions to count, you will most likely be able to read this in a week or two.  I am very much willing to help, too!

If you want to work on the arithmetic product, this is explained on pages 3-8 of Section 2 of https://arxiv.org/pdf/math/0503436.

There is an old tracking ticket, https://github.com/sagemath/sage/issues/30727, which is now outdated with very few remaining items, and it does not make sense to reference it in your proposal.

Best wishes,

Martin