*Dear Maintainers,*

I’d like to share my *performance-focused GSoC proposal* for SymPy.

Originally, I planned a SymEngine integration proposal (which was removed 
from the ideas list). I then discussed this idea with *Ondřej Čertík*, who 
indicated that he could mentor such a project. However, I understand that 
other maintainers have reservations about SymEngine. Therefore, I *wanted 
to expand my proposal* to include *broader Python-based optimizations* and 
optional backends (e.g. *Python-Flint*) so that we can tackle performance 
more holistically.

A few days ago, I asked for permission to create a Wiki page, and *Aaron* 
kindly approved it.

You can find my proposal on the SymPy Wiki here: *[Wiki Proposal Link 
<https://github.com/sympy/sympy/wiki/GSoC-2025-Application-Firat-Bezir:-Optimizing-Symbolic-Computation-in-SymPy-for-Speed-and-Efficiency>]*
.
I would *greatly appreciate any feedback* on which areas (e.g., polynomial 
routines, domain usage, matrix ops, etc.) should be prioritized, or how 
best to incorporate optional backends without complicating SymPy’s core. 

I recognize that the *performance improvements* outlined in this proposal 
*touch 
on multiple parts* of SymPy. Although the project is potentially large, I 
plan to break it down into *manageable milestones* for GSoC, focusing on 
the most impactful and realistic goals first. I’d love to have your *input* 
on which sub-tasks are highest priority or most beneficial to the 
community, so I can ensure the final deliverables remain both *achievable* 
and *valuable* within the GSoC timeframe.

Thank you in advance for your time and insights. I look forward to refining 
this project based on your suggestions!

Best regards,
*Fırat Bezir*
*([email protected] <[email protected]>)*

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