Timeline for How to code around known MMa special-case failures?
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Dec 11, 2014 at 4:42 | vote | accept | Jerry Guern | ||
| Dec 2, 2014 at 1:21 | comment | added | Szabolcs | @RolfMertig I didn't manage to run either on my machine (OS X). Here's maxima instead (gives 0) and sympy (best result so far, but very slow). | |
| Dec 2, 2014 at 1:01 | history | edited | Jerry Guern | CC BY-SA 3.0 |
fixed sign typo
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| Dec 2, 2014 at 0:47 | comment | added | Nasser |
fyi, this is what Maple gives for Integrate[Cos[m*x]*Cos[n*x], {x, 0, 2 Pi}, Assumptions -> Element[{m, n}, Integers]] !Mathematica graphics but one has to use the AllSolutions to get this.
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| Dec 2, 2014 at 0:30 | comment | added | Rolf Mertig | @Scabolcy Did you try FriCAS or Open-Axiom? Axiom ( aka ScratchPad) had a clean type design (theoretically; in practice it is quite hard to get anything non-purely mathematical done). | |
| Dec 2, 2014 at 0:07 | comment | added | Szabolcs | @Daniel They're still not doing well enough to satisfy the complaint here. MuPad figures out the $\cos mx \; \cos nx$ case but not the $e^{ix}\cos mx$ one. Maple simplifies straight to 0, ignoring the possibility of $m=n$ or $m=1$. | |
| Dec 1, 2014 at 23:56 | comment | added | Daniel Lichtblau |
@Szabolcs Thats certainly an interesting route taken by Maple and MuPad. That said, I do not foresee Mathematica also going that way unless and until we do one of two things. (1) Make some changes at a fairly deep level to Refine and related functions that use Assumptions. (2) Make some fairly deep changes in Integrate to bypass much of the assumptions handling in the presence of explicit assumptions of integrality.
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| Dec 1, 2014 at 23:55 | comment | added | Szabolcs | And some more | |
| Dec 1, 2014 at 23:45 | comment | added | Szabolcs | Not trying to make any sort of point here, I was just curious how other systems would handle the basic $\int_0^{2\pi} \cos nx \; \cos mx \; dx$, $n,m \in \mathbb{Z}$ example. Here's Maple and MuPad. | |
| Dec 1, 2014 at 21:52 | comment | added | Jerry Guern | @SjoerdC.deVries True about the "infinitely large", can't handle them all. But it's bizarre and inexplicable to me that Wolfram wouldn't have designed MMa to handle THESE to cases correctly, given that they are the entire basis of Fourier Analysis and hence cornerstones of EE and SigProc. | |
| Dec 1, 2014 at 21:52 | answer | added | Daniel Lichtblau | timeline score: 20 | |
| Dec 1, 2014 at 21:48 | comment | added | Sjoerd C. de Vries | I have a hunch that the set of special cases is infinitely large, so there's probably no general method to handle them all. It may be possible to anticipate a restricted set of known cases though. | |
| Dec 1, 2014 at 21:39 | comment | added | Jerry Guern | @Szabolcs I get wrong results in each of the case I listed. And I know Limit will fix the problem if I happened to know that f[x] was a Cos[], but I usually won't know what f[x] is beforehand, so I need a general method that anticipates and handles these problems. | |
| Dec 1, 2014 at 21:38 | review | Close votes | |||
| Dec 2, 2014 at 2:23 | |||||
| Dec 1, 2014 at 21:36 | history | edited | Jerry Guern | CC BY-SA 3.0 |
added 66 characters in body
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| Dec 1, 2014 at 21:35 | comment | added | Jerry Guern | @rm-rf I clarified the question. | |
| Dec 1, 2014 at 21:33 | comment | added | Szabolcs |
Could you amend your question and point out the specific wrong results you get? The $n=m$ case can be handled with Limit.
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| Dec 1, 2014 at 21:32 | comment | added | Jerry Guern | @Hector, I reworded that part. The error happens for Cos[nx]*Cos[mx] because MMa ignores the special case m == n. | |
| Dec 1, 2014 at 21:30 | history | edited | Jerry Guern | CC BY-SA 3.0 |
added 50 characters in body
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| Dec 1, 2014 at 21:16 | comment | added | Hector |
I did Integrate[Cos[m*x]*Cos[m*x], {x, 0, 2 Pi}, Assumptions -> {Element[m, Integers]}] and I got a sensible answer. It seems you had a typo in Assumptions.
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| Dec 1, 2014 at 21:12 | history | edited | Sjoerd C. de Vries | CC BY-SA 3.0 |
corrected incorrect function definitions
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| Dec 1, 2014 at 20:57 | history | asked | Jerry Guern | CC BY-SA 3.0 |
