Timeline for Computer algebra errors
Current License: CC BY-SA 4.0
25 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 2, 2023 at 7:33 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Nov 5, 2022 at 4:02 | history | edited | KConrad | CC BY-SA 4.0 |
added 181 characters in body
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| Nov 4, 2022 at 21:10 | comment | added | Akiva Weinberger | For anyone coming across this thread in the future, they may enjoy this 3Blue1Brown video on the topic: youtube.com/watch?v=851U557j6HE | |
| Dec 3, 2021 at 16:45 | comment | added | username | I'll wait until the Riemann Hypothesis is disproved by a counter example to be truly surprised. | |
| Oct 26, 2019 at 3:05 | comment | added | The_Sympathizer | Note that that last fraction is suuuuuuper close to $\frac{1}{2}$ (best seen by punching it, with care, into a high-precision calculation package.). So while it looks dramatically significant when written as a fraction, it is actually a dramatically subtle deviation when you consider what the represented number really is. | |
| May 6, 2018 at 15:55 | comment | added | Neapolitan | @AlexShpilkin, yes I see---sorry for the noise. Reading back through the comments, this confusion has been answered before. Perhaps you could put your note beside the link in the answer? Thnx | |
| May 4, 2018 at 20:48 | comment | added | Alex Shpilkin | @Neapolitan The linked page integrates $\sin x / x$ times $\sin(x/3) / x$ times ... as opposed to $\operatorname{sinc} x\equiv\sin x / x$ times $\operatorname{sinc}(x/3)\equiv 3\sin(x/3) / x$ times ..., which changes the constant factor by $n!!\,$. | |
| Apr 16, 2018 at 1:02 | comment | added | Neapolitan | Linked page gives the sequence $\pi$ times 1/2, 1/6, 1/30, 1/210, 1/1890, 1/20790, 1/270270 for the first seven terms, not 1/2, 1/2, ... | |
| Aug 18, 2016 at 18:18 | comment | added | Jacques Carette | @Voyska No, it was not reported as a bug, just as an 'oddity' (or something like that). Jon was not mean, but playful in a devious way. He will be missed. | |
| Aug 17, 2016 at 17:16 | comment | added | Red Banana | @JacquesCarette How did he trick you? It's not clear. Did he say it was a bug but he knew it wasn't? | |
| Nov 29, 2013 at 1:50 | comment | added | Jacques Carette | @polkovnikov.ph Indeed. | |
| Nov 27, 2013 at 14:54 | comment | added | polkovnikov.ph | @JacquesCarette That vendor was Maple, right? | |
| May 11, 2013 at 4:23 | comment | added | Will Sawin | @Joel: That gets canceled by the difference between $\operatorname{sinc}$ and $\sin$, except for a constant factor, which I think accounts for the difference. | |
| Feb 13, 2013 at 15:03 | history | edited | Ryan Reich | CC BY-SA 3.0 |
prettify latex
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| Apr 27, 2011 at 2:31 | comment | added | JRN | @Harald, the integral in the link has the term $x^{-(n+1)/2}$, while the integral in the answer does not. Perhaps this is the reason for the differences in values? | |
| Apr 27, 2011 at 0:37 | history | edited | Dan Piponi | CC BY-SA 3.0 |
deleted 2 characters in body
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| Aug 9, 2010 at 22:21 | comment | added | user6096 | @sigfpe In the integral that follows the words "in an algebra package:" you integrate sinc(x) divided by x, not sin(x) divided by x. I believe that this is the point of confusion. | |
| May 28, 2010 at 5:54 | comment | added | Dan Piponi | @Harald The whole point is that it is miraculous! I checked all the integrals above in Mathematica again and they appear to be correct. | |
| May 25, 2010 at 1:58 | comment | added | Harald Hanche-Olsen | Um, the values given in the answer don't seem to match the values given in the link. I tend to believe the link more, since merely having the numerator 1 in the first several integrals (and then not) seems rather less miraculous than the first several integrals having identical values (and then not). Is it a case of cut-and-paste disease, or have I misunderstood? Also, the first integral as written diverges at 0. I guess the extra division by $x$ does not belong. | |
| May 24, 2010 at 23:40 | history | edited | Dan Piponi | CC BY-SA 2.5 |
Added new link for "Borwein integrals".
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| Feb 17, 2010 at 4:19 | comment | added | Dan Piponi | @Jacques It's wonderful to hear from the 'poor vendor'. Thanks for replying. | |
| Feb 17, 2010 at 4:03 | comment | added | Jacques Carette | The actual person at that "poor vendor" was me. I must have spent 3 days on this problem before I figured out that Jon had tricked me. And, indeed, I am an expert in computer algebra, but do not know much Fourier analysis. But Jon's proof for why this is 'correct' is quite geometrical. | |
| Feb 16, 2010 at 19:29 | comment | added | Dan Piponi | @fedja I disagree. It merely shows the reasonable state of affairs that someone expert in one field, having to borrow theorems from another field, may get a surprise. | |
| Jan 29, 2010 at 18:47 | comment | added | fedja | Which means that nobody knows Fourier analysis nowdays. Very sad and discouraging story... | |
| Jan 13, 2010 at 2:14 | history | answered | Dan Piponi | CC BY-SA 2.5 |