[GSoC 2026] Inquiry: Sparse GCD and PolyElement - Hrushii

[Hrushi]

Hi 
I’m Hrushi, a first-year CS student. I’ve been looking at the PolyElement code in rings.py and noticed how it falls back to the dense engine for some cases, which seems to blow up the memory.

Zippel's algorithm appears to be the most efficient method for keeping the relevant portions of the data sparse, and I started to understand it. I even made a small "skeleton" script to test how it would generate random numbers and compute a univariate GCD.

I would like to remark that I saw Luca's thread about this. I do not want to interrupt if someone is way ahead of me, but I am really curious about the math.

So, is there still a chance to work on this? Or maybe a particular section of the sparse engine that could really use some help? If if this is all covered, I can easily step aside. I was just hoping to get some feedback to see if I am on the right track or if there is some other area I should focus on  more.