Re: More info on the project : Add additional combinatorial (Hopf) algebras and additional bases
Chirag V
Sorry everyone, it seems my previous message had some formatting issues, resending here in plane text for better readability:
Hello SageMath team,
I am Chirag, a second-year undergraduate with a strong interest in Mathematics and Programming. I came across the project: "Add additional combinatorial (Hopf) algebras and additional bases" and found it interesting to work on.
Although I don’t have a strong background in different types of algebras, I am very curious and have already been working on building my foundations for the project.
I have set up SageMath locally and have been exploring the codebase to understand how abstract mathematical structures are translated into efficient Python code.
After going through past year’s GSoC discussions on this project idea, I’d like to share my current understanding of the technical path and seek your advice on whether this direction is appropriate:
I have identified several key resources that I plan to use to define the necessary algebraic rules for the project:
- Molev (2009) [https://arxiv.org/abs/0807.2127] as a resource for the algebraic rules of double Schur functions.
- Buch (2002) [https://arxiv.org/abs/math/0111043] for the set-valued tableaux approach to Grothendieck polynomials.
-Pechenik and Searles (2019) [https://arxiv.org/abs/1904.01358] survey, which provides context on the non-symmetric polynomials mentioned in the project description.
Technically, I intend to utilise the WithRealizations pattern found in monomial.py and schur.py.
My goal is to implement the core basis classes, combinatorial formulas, the necessary product/coproduct rules and creating efficient transition maps to ensure these new bases convert seamlessly to and from the standard Schur basis.
I have already begun contributing to familiarise myself with the workflow, and you can see my recent PR here: https://github.com/sagemath/sage/pull/41623.
Since the mentor for this project is currently TBD, I would appreciate your insight on a few points:
1. Is there a specific person I should discuss these implementations with to ensure they align with community priorities?
2. Should I prioritize the "breadth" of many new bases or a "deep" implementation of a few?
3. Are there any other specific resources or papers you would suggest I look into to further strengthen my foundations for this project?
4. Are there any "Good First Issues" or specific documentation gaps that you would recommend I tackle to better understand the implementation?
I look forward to your feedback and hope to contribute to the project.
Best regards,
Chirag
Hello SageMath team,
I am Chirag, a second-year undergraduate with a strong interest in Mathematics and Programming. I came across the project: "Add additional combinatorial (Hopf) algebras and additional bases" and found it interesting to work on.
Although I don’t have a strong background in different types of algebras, I am very curious and have already been working on building my foundations for the project.
I have set up SageMath locally and have been exploring the codebase to understand how abstract mathematical structures are translated into efficient Python code.
After going through past year’s GSoC discussions on this project idea, I’d like to share my current understanding of the technical path and seek your advice on whether this direction is appropriate:
I have identified several key resources that I plan to use to define the necessary algebraic rules for the project:
- Molev (2009) [https://arxiv.org/abs/0807.2127] as a resource for the algebraic rules of double Schur functions.
- Buch (2002) [https://arxiv.org/abs/math/0111043] for the set-valued tableaux approach to Grothendieck polynomials.
-Pechenik and Searles (2019) [https://arxiv.org/abs/1904.01358] survey, which provides context on the non-symmetric polynomials mentioned in the project description.
Technically, I intend to utilise the WithRealizations pattern found in monomial.py and schur.py.
My goal is to implement the core basis classes, combinatorial formulas, the necessary product/coproduct rules and creating efficient transition maps to ensure these new bases convert seamlessly to and from the standard Schur basis.
I have already begun contributing to familiarise myself with the workflow, and you can see my recent PR here: https://github.com/sagemath/sage/pull/41623.
Since the mentor for this project is currently TBD, I would appreciate your insight on a few points:
1. Is there a specific person I should discuss these implementations with to ensure they align with community priorities?
2. Should I prioritize the "breadth" of many new bases or a "deep" implementation of a few?
3. Are there any other specific resources or papers you would suggest I look into to further strengthen my foundations for this project?
4. Are there any "Good First Issues" or specific documentation gaps that you would recommend I tackle to better understand the implementation?
I look forward to your feedback and hope to contribute to the project.
Best regards,
Chirag
