Inquiry for GSoC 2026 Proposal: Factorization and Multivariate Polynomials

[Sri Ram]

Dear SymPy Development Team,

I am Sriram Lohith, an undergraduate in Computer Science and Engineering, eager to participate in the "Multivariate polynomials and factorization" project for GSoC 2026.

Examined portions of the source: dmpzzwang (EEZ implementation) + dmpzzmignotebound (dense-heavy).

Sparse absence ->suggest heap calculations (Monagan/Pearce) + Hypothesis perturbation.

The existing Kronecker's approach in factortools.py minimize effective multivariate factorization, even with the dmpzzwang EEZ implementation. This limits SymPy's integration, simplification, and partial fraction capabilities.

Heap-based arithmetic (Monagon & Pearce, 2001) and Zippel SPMOD provide confirmed sparse enhancements compared to recursive dense representations.

my abilities:

- Competitive programming: DSA enhancement -> heap/geobucket polynomial arithmetic

- Python/ML: Hypothesis evaluation for algebraic fuzzing

-Git/Version control: have experience in working on version control enviranment

- factortools.py examined: dmpzzmignottebound dense-only ->sparse objective

- sympy/sympy has been forked, and sparse dummies have been recognized

well, I’m considering making a proposal

1.Heap-based sparse_mul/add ->2x acceleration dmpzzmignottebound compared to dense

2. Zippel SPMOD primitive GCD ->integrate dmpzzwang EEZ
3. Square-free factorization -> GF(p) extension (queryUSECYCLOTOMICFACTOR)
4. Validation: Hypothesis property tests + sympy_benchmarks

i have some questions,pls solve
1. Current Wang EEZ-GCD status in factortools.py—priority gaps?
2. Arithmetic preference: geobuckets vs heaps for multivariate?
3. @Oscar Benjamin: Available for polys mentorship?

GitHub:github.com/sriram11200504/gsoc-prep

Eager for feedback to refine this proposal.

Best regards,  
Sriram Lohith  
github.com/sriram11200504