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  

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