Re:From scratch: reverse-mode automatic differentiation (in ...
by Someone on Sunday June 14, 2020 @06:07PM
(#23521782)
It’s slightly better. https://en.wikipedia.org/wiki/Risch_algorithm: “The Risch algorithm is used to integrate elementary functions. These are functions obtained by composing exponentials, logarithms, radicals, trigonometric functions, and the four arithmetic operations (+ − × ÷)”
That algorithm isn’t easily programmed, though, and will fail in the many cases where the integral cannot be expressed in elementary functions.
Worse, according to that page, it needs the ability to check whether expressions are zero (https://en.wikipedia.org/wiki/Constant_problem), and that, in general, is undecidable if I understand that page correctly.
That algorithm isn’t easily programmed, though, and will fail in the many cases where the integral cannot be expressed in elementary functions.
Worse, according to that page, it needs the ability to check whether expressions are zero (https://en.wikipedia.org/wiki/Constant_problem), and that, in general, is undecidable if I understand that page correctly.
https://mathworld.wolfram.com/RischAlgorithm.html seems a tiny bit more optimistic about the limitations of this approach, but https://link.springer.com/chapter/10.1007/978-3-319-00894-3_... seems, to me, in line with what Wikipedia says.