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by epistasis
847 days ago
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I doubt there's any sort of fundamental flaw in sympy. Getting more and more solutions is mostly about putting in lots of work to tweak the bag of tricks. There is no universal algorithm for solving integrals. As an open source project depending on volunteers (or is it just the one major author?) I am impressed that sympy does as much as it does. |
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Not that I want to dispute this, but depending on what you meant, there is in fact such an algorithm: https://en.wikipedia.org/wiki/Risch_algorithm
Though often it is not implemented because it is quite complex (its details covering two thick books) and many of the special cases it covers rarely crop up in the real world, so the effort isn't worth it.
The caveat of Risch's algorithm is that it only "works" if the function you are trying to integrate has an elementary antiderivative. Many of the problems that Mathematica can solve (but SymPy fails at) involved special (i.e. non-elementary) functions.