Enhancing manualintegrate Heuristics and Polynomial Arithmetic Efficiency
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Aadi Jain
Mar 15, 2026, 10:37:52 AM (yesterday) Mar 15
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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 .
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.
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.
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