Hi everyone,

It vedant Dusane from this side. As i am contributing to sympy from last 
few month on one fix and* important issue* that will help sympy i*mproving 
code safety, developer* *productivity, reduce future bugs*, and many more. 
I have* merged some PRs* on Add type annotation. On that bases i am 
planning to prepare a full GSoC scope. 

I would like to propose the  *project idea *related to the* improvement of 
type annotations* and type safety within the *"sympy.polys"* system, 
especially within* core files* such as *"polytools.py," "polyutils.py,"* 
etc.

Polynomials is an elementary part of the computational algebra library 
delivered by SymPy. Many of the *library’s higher-level functions* are 
built upon the polynomial subsystem. As I was *conditioning* the type 
annotations in *"polytools.py*", I saw that there are *certain functions* 
that require type information that is *not available yet and uses generic 
types.*

My proposed approach would be to:


   1.  Systematically* reviewing *the important *polynomial modules* 
   ("polytools", "polyutils", "polyclasses" and "domains")
   2. *Adding precise* and* correct type annotations* according to actual 
   return values and behavior
   3.  *Improved type clarity* for polynomial representations,* generators*, 
   and *domain interactions*
   4. *Ensuring* complete compatibility with *existing behavior, correct 
   ruff format and passing all test cases and mypy checks*


The aim is to enhance maintainability, static correctness, and developer 
experience without changing runtime functionality.

Any review or guidance will help me a lot

Thank you 
- vedant Dusane

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