**Dear SymPy Community**,

I'm a first-year dual-degree student in **Mathematics & AI** at Shanghai
Jiao Tong University. I’m excited to contribute to SymPy’s codegen
capabilities, specifically targeting the **"Efficient Jacobian/Hessian
Evaluation for Optimization and ODE Integration"** project for GSoC 2025.

**Why This Project?**
During my coursework on numerical optimization and ODE modeling, I
encountered bottlenecks in generating efficient derivative functions for
large-scale problems. SymPy’s symbolic differentiation paired with codegen
could bridge this gap, and I aim to integrate recent advancements (e.g.,
#26773’s Jacobian optimizations) into a unified API.

**Technical Vision**:
1. **CSE Optimization**: Eliminate redundant calculations via common
subexpression elimination.
2. **Sparsity Detection**: Automatically identify zero elements in Jacobian
matrices for ODE problems, enabling sparse storage formats.
3. **High-Performance Codegen**: Leverage `lambdify` and LLVM to generate
C/Fortran code with near-handwritten performance.

**Request for Guidance**:
1. Are there ongoing discussions or roadblocks around derivative codegen I
should prioritize?
2. Would a prototype integrating Riccardo’s Jacobian method with `lambdify`
be valuable as a starting point?
3. Is there interest in sparse Jacobian support for ODE problems, and are
there preferred sparse formats (e.g., COO/CSC)?

I’m eager to refine my proposal with community feedback. Thank you for your
time!

**GitHub**: voyager-jhk

Best regards,
Peiqi Li

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