Timeline for Does there exist a complete implementation of the Risch algorithm?
Current License: CC BY-SA 4.0
16 events
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| Feb 27 at 20:52 | history | edited | Timothy Chow | CC BY-SA 4.0 |
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| Nov 11, 2021 at 15:38 | history | edited | Timothy Chow | CC BY-SA 4.0 |
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| Oct 19, 2020 at 13:37 | comment | added | Timothy Chow | @MichaelBächtold : I could be missing some subtlety but I think that's right. Just now I took a quick look at Risch's original paper and it seems to me that the base case of the induction requires only zero-recognition of constants. | |
| Oct 19, 2020 at 9:02 | comment | added | Michael Bächtold | @TimothyChow does Risch only require zero-recognition of constants? I thought it also requires zero-recogniton of elementary functions. | |
| Oct 17, 2020 at 18:24 | comment | added | Ben McKay | Landau required students who wanted to study with him to be able to compute every indefinite integral that can be computed in elementary functions. Perhaps his students had the Risch code built into their synapses. | |
| Oct 16, 2020 at 14:29 | history | edited | Timothy Chow | CC BY-SA 4.0 |
Added note about Barry Trager
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| Oct 15, 2020 at 13:11 | answer | added | Dima Pasechnik | timeline score: 27 | |
| Oct 15, 2020 at 12:29 | vote | accept | Timothy Chow | ||
| Oct 15, 2020 at 12:17 | comment | added | Timothy Chow | Bottom line is, zero-recognition of constants isn't the sticking point in practice. I'd be happy to see an implementation whose only "gap" is zero-recognition of constants (and of course the constraints imposed by finite time and memory). | |
| Oct 15, 2020 at 12:13 | comment | added | Timothy Chow | @AndrejBauer : It does assume that zero-recognition can be performed in the underlying field of constants. But if your initial expression involves only algebraic numbers (satisfying known polynomial equations with integer coefficients) then there is an algorithm for zero-recognition, that is conjectural only in the sense that the guarantee that it terminates depends on Schanuel's conjecture. When the algorithm terminates, it gives the right answer, and since Schanuel's conjecture is surely true, the algorithm will always terminate. See Richardson's paper on the elementary constant problem. | |
| Oct 15, 2020 at 8:04 | history | became hot network question | |||
| Oct 15, 2020 at 6:51 | comment | added | Andrej Bauer | I thought Risch's algorithm was contigent on having the ability to perform zero-testing that isn't quite algorithmically justified? | |
| Oct 15, 2020 at 6:05 | review | Suggested edits | |||
| Oct 15, 2020 at 8:20 | |||||
| Oct 15, 2020 at 1:43 | answer | added | Sam Blake | timeline score: 47 | |
| Oct 15, 2020 at 0:10 | history | edited | Timothy Chow | CC BY-SA 4.0 |
added 55 characters in body
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| Oct 15, 2020 at 0:04 | history | asked | Timothy Chow | CC BY-SA 4.0 |