GSoC 2026 Enhancing manualintegrate Heuristics and Polynomial Arithmetic Efficiency

[Aadi Jain]

Dear SymPy Mentors,

My name is Aadi Jain and I am proposing to enhance the manualintegrate module for GSoC 2026. I have been looking at the rules and how they work like human intuition and I want to help to make it better.

I have been checking how the engine handles substitutions and looking at cases where it fails in the test suite. I found some areas where we can improve. For example I am working on rules for Rationalizing Substitutions. This will help turn radical integrands into rational ones, which is something a student would normally do but our Integration Engine does not do it well right now.

I am also looking at how we can simplify algebra and make integration faster. I think using arithmetic algorithms, like the Urdhva Tiryagbhyam method might help reduce the time it takes for integrands that need a lot of efficient coefficient-based multiplication.  I want to know if the SymPy community thinks this is a way to optimize the Integration Engine .

As I work on my project proposal I would like your guidance on a few points :

Is the SymPy community more interested in adding new substitution rules like rationalizing substitutions to the Integration Engine ?

Would it be helpful to explore arithmetic optimizations for the heavy pre-processing steps in the manualintegrate module?

I am trying a lot of things right now and I want to make sure my proposal is what the SymPy community needs in the long run.

Thank you for your time and, for letting me learn from the community.

Best regards,
Aadi Jain
GitHub:  https://github.com/jainaadi098