Hi SymPy Community,

I’m Krishnav Bajoria, a third-year student at IIT BHU,Varanasi in the 
department of Mathematics and Computing(GitHub handle - 
krishnavbajoria02).I am proficient in Python and have had a fairly strong 
mathematical background which was also the reason that led me to start 
contributing in SymPy. In terms of my contributions to SymPy, I have had 
three PRs merged—two related to *assumptions* and one in codegen/
*utilities.lambdify* —and a few more under review.(Link to the PRs: 
https://github.com/sympy/sympy/pull/27511,https://github.com/sympy/sympy/pull/27512,https://github.com/sympy/sympy/pull/27552)

As I was exploring potential GSoC projects, I became particularly 
interested in two from the ideas page:

   1. *Improvements to the Assumptions System*
   2. *The Risch Integration Algorithm*

Since I’ve already worked a bit on *assumptions*, I’ve been delving deeper 
into the discussions and implementation details to understand its current 
state. I wanted to share what I’ve gathered so far and get feedback on 
whether I’m on the right track, or if there are other key areas I should 
focus on.
*Assumptions System: What I’ve Studied So Far*
   
   - *Old vs. New Assumptions System*:
      - The transition from the old rule-based system,which attached 
      inferences directly to the objects as attributes, to the new 
      predicate-based system,which separates inferences from objects and 
      evaluates them dynamically, was meant to enhance flexibility. However, 
      there are still inconsistencies where the new system does not propagate 
      certain facts correctly.
   - *Key Issues and Challenges*:
      - Some assumptions are incorrectly inferred or not inferred at all 
      due to missing rules.
      - Symbolic variables (e.g., x.is_real) sometimes fail to evaluate 
      correctly when additional constraints are introduced.
      - Cases where the assumptions system contradicts itself in different 
      parts of SymPy.
      - Performance concerns—some assumption queries take longer than 
      expected due to inference chains.
   - *Areas I’ve Been Exploring for Improvements*:
      - Understanding *handlers* in the new system and whether they need 
      restructuring.
      - Reviewing past discussions on improving assumptions and identifying 
      still-relevant open issues.
      - Exploring ways to *improve inference accuracy*, especially in edge 
      cases.
      - Considering whether any aspects of the *old system*could be 
      reintroduced to address current limitations.
   
I’d appreciate to hear from the community—does this list cover the main 
areas that need attention? Are there any other fundamental issues I should 
be looking at?
*Considering Risch Integration*

Apart from assumptions, I’ve also started reading about the *Risch 
integration algorithm*. I haven’t explored it as deeply yet, but I find it 
intriguing and would like to get insights on its feasibility as a GSoC 
project.

At this stage, I’m just considering both projects for discussion and plan 
to *finalize my choice* based on the feedback and guidance from the 
community.

Thank you for your time and consideration. I look forward to your response!

Best Regards,
Krishnav Bajoria.

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