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GSoC 2026

Improve and Polish the Generation of Structures of Combinatorial Species

SageMath's LazyCombinatorialSpecies framework (sage/rings/lazy_species.py) represents combinatorial species as lazy sequences of symmetric-group actions and supports molecular decompositions, generating series, and structure enumeration. Recent work in PR #41655 adds the Hadamard product, functorial composition, and arithmetic product at the level of molecular data, but these operations lack structure generation. The derivative operation is also missing entirely. This project will: (a) implement the derivative and multisort partial derivatives, with cycle index, generating series, and pointing methods (b) extend the Hadamard product and functorial composition to multisort species (c) systematically verify that weights propagate correctly across all operations (d) implement structures() and isotypes() methods for the derivative, Hadamard product, functorial composition, and (time permitting) the arithmetic product. Every new method will be verified against the existing _test_structures consistency checks. The project concludes with full documentation and a pull request.

Project details

Contributor

Parth Chavan

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