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It seems yes there is a reason if you need integrals. From TFA: "You can also try having Wolfram Alpha compute it, and it will time out. We will need to be more
by muench 5y ago
It seems yes there is a reason if you need integrals. From TFA: "You can also try having Wolfram Alpha compute it, and it will time out. We will need to be more creative."
- whatshisface 5y agoMathematica/Maple/Sagemath don't have a freemium timeout mechanic and can solve a lot more. Truth be told I think that integration techniques are much less broadly crucial for everyone to learn than they used to be, although you need to have some clue of what's going on because you need to be able to guide yourself towards posing problems in such a way that the integrals that can be solved.
- dragonwriter 5y ago> Mathematica/Maple/Sagemath don't have a freemium timeout mechanic and can solve a lot more. Mathematica/Maple don't have freemium timeouts because they are not free; Sagemath, OTOH, is a good point.
- deleted 5y ago[deleted]
- kaba0 5y agoBut there are integrals that you can easily solve by hand but both WolframAlpha and sage will (effectively) timeout on them. And I’m not even talking about something made deliberately hard for computers to symbolically analyze.
- whatshisface 5y agoReally? I've never seen one, could you give some examples?
- bzbarsky 5y agoFor Wolfram Alpha, I just tried the integral from https://en.wikipedia.org/wiki/Contour_integration#Example_2_%E2%80%93_Cauchy_distribution https://en.wikipedia.org/wiki/Contour_integration#Example_2_... and it times out. The by-hand solution is pretty straightforward, if you know contour integration.
- dasudasu 5y agoThis is when 99.99% of the population would just whip out a numerical solver.
- hyperbovine 5y agoIt's going to take you a while to numerically solve that integral for the uncountably many values of \alpha that you are being asked to...
- benlivengood 5y agoIt's probably best to return a function that takes alpha as a parameter and numerically integrates for whichever finite set of alphas are required by the caller.
- fooker 5y agoThe usual method is to computer a reasonable number of solutions and do curve fitting.
- Kranar 5y agoIt's the algorithm in and of itself that serves as the solution to the integral.
- mr_mitm 5y agoSometimes you are looking for deeper insights in some equations that can only be achieved by finding symbolic solutions. You would never figure out that black holes are a solution to the Einstein field equations of you just threw a numerical solver at it, for example. (Bad example because that's arguably the easiest solution to them but I hope you get my point.)
- jjgreen 5y ago0.01% would whip out a numerical solver; 99.98% would go "huh?"