Hello SymPy Community,

My name is *Sai Kumar*, and I am excited to propose improvements to SymPy's 
solvers as part of my project idea for *Google Summer of Code (GSoC) 2025*. 
SymPy is a powerful symbolic mathematics library, but its solvers have 
certain limitations that, if addressed, could enhance their *robustness, 
efficiency, and usability*.

To extend SymPy’s problem-solving capabilities, I propose implementing new 
solver functionalities, including:

   1. *Matrix equation solvers* (e.g., solving equations of the form AX+XB=C
   ).
   2. *Integral equation solvers* (e.g., Fredholm and Volterra integral 
   equations).
   3. *Optimization and Diophantine equation solvers* to support a broader 
   range of mathematical problems.

These enhancements would make SymPy more versatile for both *symbolic and 
numerical computations*. I would love to discuss this further and receive 
feedback from the community on how best to approach these improvements.

Looking forward to your insights!

Best regards,
*Sai Kumar*

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