Timeline for Quantifying difficulty of integrals versus inverses
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 21, 2023 at 1:03 | comment | added | LSpice |
At least for me, I read ahead before processing, so that, by the time I registered the urging to try the problem before reading the answer, I had already read the answer. I hope you don't mind that I added the >! spoiler syntax to give others the fun of trying for themselves if they wanted.
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| Mar 21, 2023 at 1:02 | history | edited | LSpice | CC BY-SA 4.0 |
Spoiler'd answer
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| Mar 21, 2023 at 0:37 | history | edited | user44143 | CC BY-SA 4.0 |
corrected statement about inverting $x^2\pm\sqrt{x}$
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| Mar 20, 2023 at 18:01 | vote | accept | Benjamin Dickman | ||
| Mar 15, 2023 at 19:18 | history | edited | user44143 | CC BY-SA 4.0 |
stated a best case for lcosure of invertible functions
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| Mar 15, 2023 at 16:18 | comment | added | user44143 | @Gro-Tsen, that's a good point, and I revised the answer to reflect it. | |
| Mar 15, 2023 at 16:15 | history | edited | user44143 | CC BY-SA 4.0 |
revised to distinguish global and elementary comparisons
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| Mar 15, 2023 at 14:00 | comment | added | user44143 | @BenjaminDickman, I can check integrability easily enough; there are general algorithms for that. But I don't have a nice check for invertibility; it would be messy to check on which expressions Mathematica gives up, and (since no one has found an algorithm to determine when elementary expressions are zero) I doubt that a general algorithm has been found. | |
| Mar 15, 2023 at 13:58 | comment | added | Gro-Tsen | Maybe you should clarify what you mean by “invertible” each time, because it can be taken to mean ①that an inverse exists — globally — as a function (i.e., we are dealing with a bijection), or ②that an inverse exists — on a certain domain — in a certain form, e.g., as an elementary function; and the two questions are pretty much orthogonal (an elementary bijection may have a non-elementary inverse, but conversely, a non-bijection may have an elementary inverse on each part of its domain). I assumed OP was more concerned about ② but I may be wrong. | |
| Mar 15, 2023 at 13:31 | comment | added | Benjamin Dickman | this is great; if a depth $n$ for $n > 2$ search isn't too time consuming (for you and/or for Mathematica) then I'd be quite interested to see what the data look like as one goes deeper | |
| Mar 15, 2023 at 10:01 | history | edited | user44143 | CC BY-SA 4.0 |
added 94 characters in body
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| Mar 15, 2023 at 9:43 | history | edited | user44143 | CC BY-SA 4.0 |
added some empirical data following Gro-Tsen's idea
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| Mar 14, 2023 at 20:53 | history | edited | user44143 | CC BY-SA 4.0 |
added example with probability distributions
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| Mar 14, 2023 at 20:04 | history | answered | user44143 | CC BY-SA 4.0 |