GSoC 2026: Interest in "Coordinate graded commutative and exterior algebra implementations"

[Yossef Moftah]

Hello Dr. Scrimshaw,

My name is Yossef Moftah, a 3rd-year Computer Science student from Egypt. I am writing to express my strong interest in the GSoC 2026 project: "Coordinate the graded commutative algebra and exterior algebra implementations and Gröbner bases."

I have already spent time familiarizing myself with the SageMath ecosystem and have successfully:

• Built Sage from source on both Fedora Linux and Windows 10.

• Read the Developer’s Guide, specifically the sections on coding standards and the git workflow.

• Experimented with the internal benchmarking tools to understand performance profiling.

Technical Background:

• Performance & Systems: Developed a C++ chess engine (2000 ELO) and experimented with Cython for optimization.

• Algorithms: Active competitive programmer (1st place in my university’s local contest).

• Python: have experience through NLP , Machine Learnig ,Generative AI , and other personal projects focused on AI.

Current Focus & Questions: I am currently diving into the mathematical theory behind the project. While my CS background is strong, the abstract algebra involved (specifically Graded Commutative Algebra) is more advanced than my university coursework.

1. Gröbner Bases: To what extent should I prioritize the deep theoretical proofs versus the computational implementation for this specific project?

2. Doctests: I am adapting to Sage’s doctest-heavy workflow. Should I begin by looking for "beginner-friendly" issues in sage.algebras to practice writing these according to Sage standards?

I am eager to contribute and would appreciate any guidance on specific modules I should study first to best prepare for this project.

Best regards,

Yossef Moftah [https://github.com/Yossef-moftah-dev]

[tcscrims]

Dear Yossef,

   Thank you for your interest. I apologize for my delayed response.

This project requires both a strong foundation in algebra (specifically linear algebra) and programming optimization. It doesn't make sense to me when you ask about "prioritizing deep theoretical proofs," but you will require both of these aspects to be successful at the full project. One variant would be having the graded commutative algebras be able to communicate with the exterior algebra and external libraries such as Macaulay2.

I also think you might have a fundamental misconception about what SageMath's workflow is. While doctests are a very important part of contributing code, it is not correct to say the workflow is doctest-heavy (this also does not make sense to me either). However, you are required to have submitted at least one PR to be in consideration to be accepted as a contributor to GSoC for SageMath.

Let me know if you have any questions.

Best,
Travis

[Yossef Moftah]

Subject: Re: GSoC Project — Progress Update & Questions

Dear Dr. Scrimshaw,

Thank you for the candid feedback — it helped me refocus.

PR:
I have opened a PR that has received positive review:
https://github.com/sagemath/sage/pull/41778

PROJECT UNDERSTANDING:
Based on your description, my understanding of the project goals:
  (1) Improve the interaction between the exterior algebra and
      graded commutative algebra implementations.
  (2) Improve the Gröbner basis implementation for exterior
      algebras.

Regarding your point about enabling communication with external
libraries such as Macaulay2 — my current thinking is that a
native implementation of graded commutative algebras (rather
than relying on an external library) would be the
stronger approach, since it would allow direct coercion between
ExteriorAlgebra and GradedCommutativeAlgebra within SageMath's
own framework. But I may be wrong about this tradeoff, and I
would value your perspective.

PROGRESS — MATH:
Over the past two weeks I have been working through:
  - Judson's "Abstract Algebra: Theory and Applications"
    (rings, integral domains, polynomial rings, ideals)
  - Cox, Little, and O'Shea's "Ideals, Varieties, and
    Algorithms" (affine varieties, ideals — finished Ch. 1,
    now starting Ch. 2 on Gröbner bases)

PROGRESS — CODE:
Beyond the PR above, I have been reading through
clifford_algebra.py, exterior_algebra_groebner.pyx, and
commutative_dga.py to understand the current architecture.
I notice that ExteriorAlgebra is built on the Clifford algebra
framework (with Q=0) while GradedCommutativeAlgebra uses a
different internal structure, and there is no coercion path
between them — which I understand is part of what this
project aims to resolve.

QUESTION:
Given my current progress in both the math and the codebase,
am I on a reasonable path toward being ready for this project?
Is there a specific area you think I should prioritize or
something I am missing?

I apologize for the long gap in communication — I was
observing Ramadan and wanted to build more foundation before
reaching out, but I understand that regular short updates
are more useful going forward.

Best regards,
Yossef Moftah

[tcscrims]

Dear Yossef,

   I don't think learning about algebraic geometry will help much for this project. Furthermore, many aspects of the classical theory of Groebner bases does not hold in the exterior/Clifford/graded differential algebra setting. Be careful about this. Also, what you're saying about GradedCommutativeAlgebra doesn't make sense. We already have this object implemented in SageMath. Additionally, it is your project to propose, so until you can send me a more complete project draft, I can't say anything about the feasibility of the project.

Best,

Travis