This code is a collection of some SageMath functions I have written while doing research on various algebraically and combinatorially significant polynomials. It is provided “as-is” for others to use how they would like. The code is not optimized in any way beyond what was necessary for me to do what I needed to do. For now, code should be considered under active development and you should not write code against this library assuming the interfaces will remain unchanged. Certain functions may also be implemented in SageMath, but I have chosen to rewrite them, either out of ignorance or because SageMath’s implementation did not meet my own needs.
- Double Schubert polynomials
- Grothendieck polynomials
- Quantum Schubert polynomials
- Quantum Grothendieck polynomials
- Key polynomials / Type A Demazure characters
- Demazure atom polynomials
- Nonsymmetric Hall-Littlewood polynomials (via action of Demazure-Lusztig operators)
In the spirit of collaboration, if you find a bug, mistake, or improvement, please feel free to make a GitHub issue or, even better, a pull request. Ideally, open source code leads to improvements and time-savings for everyone involved. I will try to address things as they come up, but this project is not my highest priority as I must engage in other professional responsibilities that take higher priority. If you would like to add any of this code to SageMath, please feel free; the code is licensed under GPL-3.0 to make it compatible with SageMath’s licensing. I would appreciate attribution for any part that is my contribution.
Combinatorial Polynomials © 2024 by George H. Seelinger is licensed under the GPL-3.0 License.