In lectures we have just defined integrals, and said that if we take a derivative of some set of functions, it is much harder to go back to the original set of functions, if we only know the set of derivatives. However, I recently started reading about one way functions(Wikipedia, nothing serious for now) and I wonder, if thus the derivative is a one way function ?
2026-04-04 15:03:54.1775315034
Is derivative a one way function?
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I'd say not really, because of the Risch algorithm. It can, at least in principle, compute the anti-derivative of any elementary function if that function has an elementary anti-derivative. The complete description of the algorithm takes more than 100 pages though, so it is definitely much harder than systematically computing the derivative. Maybe Wikipedia is a good starting point if you want to learn more on the subject: https://en.wikipedia.org/wiki/Risch_algorithm