can the prime really not solve this integral?

02282014, 05:47 AM
(This post was last modified: 02282014 05:48 AM by DeucesAx.)
Post: #21




RE: can the prime really not solve this integral?
(02272014 07:08 PM)parisse Wrote: We almost never test the CAS in degree mode, therefore more bugs are expected there. The reason here is that for numeric integration with an infinite boundary you must make a change of variable, here we set tan(y)=x for y in 0..pi/2, dx=(1+tan(y)^2)*dy ... except that in degree mode you must add a pi/180 factor. No pressure, I'm sure once I'm done with college the prime will be a formidable calculator. And heck, I just need to eat rahmen noodles instead of regular pasta for the next 6 month to pay for the prime, no biggie. (02272014 09:11 PM)Manolo Sobrino Wrote: That integral appears when you integrate the Planck distribution to all frequencies in order to recover the StefanBoltzmann law, also in the Debye theory of specific heat. The functions defined by these integrals are called Debye functions. See AbramowitzStegun §27.1Well at least I now know that I did the simplification by hand to get there correctly. Thank the spaghetti monster almighty. 

02282014, 07:59 AM
Post: #22




RE: can the prime really not solve this integral?
(02272014 09:11 PM)Manolo Sobrino Wrote:That's exactly what I meant by a trick to find the exact answer for the definite integral.(02272014 12:21 PM)parisse Wrote: You get a numeric answer with: Quote:(Now that I'm thinking about it, it shouldn't be too difficult to implement a large class of definite integrals by the Residue theorem. That would be come in handy.)There is already a class of definite integrals that are handled by the residue theorem. But this one requires a trick before one can apply it, I can not implement that. Expanding 1/(exp(x)1) is a better trick, but I don't know if that can lead to something sufficiently general (I don't like tables). And it's not that important anyway, since the numeric answer is reliable. 

02282014, 08:15 AM
Post: #23




RE: can the prime really not solve this integral?
(02282014 04:52 AM)rkf Wrote:(02272014 07:08 PM)parisse Wrote: We almost never test the CAS in degree mode, therefore more bugs are expected there. The reason here is that for numeric integration with an infinite boundary you must make a change of variable, here we set tan(y)=x for y in 0..pi/2, dx=(1+tan(y)^2)*dy ... except that in degree mode you must add a pi/180 factor. Yes, to use a HPPrime properly, I would recommend to have a HP50G by hand, just in case. I tried to solve it on my 4 years old HP50G, and voilá, the numeric answer was easy to get (pls see attachments). Jose Mesquita RadioMuseum.org member 

02282014, 08:50 AM
Post: #24




RE: can the prime really not solve this integral?
(02282014 05:47 AM)DeucesAx Wrote:From your first post in this thread, it seems you already own a ti89 and a ti nspire CAS, therefore I don't believe you will really need 6 months of restrictions to pay your Prime.(02272014 07:08 PM)parisse Wrote: We almost never test the CAS in degree mode, therefore more bugs are expected there. The reason here is that for numeric integration with an infinite boundary you must make a change of variable, here we set tan(y)=x for y in 0..pi/2, dx=(1+tan(y)^2)*dy ... except that in degree mode you must add a pi/180 factor. FYI, I have already fixed the bug and sent the patch to HP. I make my best to fix bugs as soon as I know them and publish corrected version of Xcas, but I'm obviously not responsible for HP firmware releases. In the meantime, put your calculator in radian, that's the normal unit of angle when using a CAS. 

02282014, 11:30 AM
Post: #25




RE: can the prime really not solve this integral?  
02282014, 11:42 AM
(This post was last modified: 02282014 11:47 AM by CR Haeger.)
Post: #26




RE: can the prime really not solve this integral?
(02282014 01:51 AM)jte Wrote: Are you performing a signed area computation for X^3/(e^X1), from 0 to 100, in the Function app Plot view? I just tried this on the emulator and on the device. Neither hanged for me — both quickly brought up a numerical approximation. Yes  both hang at "calculating" for me 0> any positive number. On Symb to reset. Dont know if related to CAS settings pg 2: 10, 1, 100, 1E12, 1E15 and 40 in order or something else. Also noted that in CAS, integrating 0 to say >1500 starts giving "adaptive method failure, will try with Romberg..." error. Integrating 0> <1500 gives 6.49 approximation. 

02282014, 11:19 PM
Post: #27




RE: can the prime really not solve this integral?
(02282014 11:42 AM)CR Haeger Wrote:(02282014 01:51 AM)jte Wrote: Are you performing a signed area computation for X^3/(e^X1), from 0 to 100, in the Function app Plot view? I just tried this on the emulator and on the device. Neither hanged for me — both quickly brought up a numerical approximation. I've just tried it here on a device with the CAS settings above (with 1E15 for the "Probability" setting), but a numerical approximation simply came up quickly. What firmware are you using? Does it occur with default factory settings on your device? To be sure we're looking at the same function, would it be convenient / possible for you to post a photo of the SYMB view? 

03012014, 12:03 AM
Post: #28




RE: can the prime really not solve this integral?
Thanks jte.
Using latest 11/25 ROM on both hhc. I'll try to send along a SYMB screenshot. 

03012014, 05:52 AM
Post: #29




RE: can the prime really not solve this integral?
I've just tried rev. 5447 (the Nov 25, 2013 release) on my device here and it didn't hang in the signed area computation in the Function plot view.
I did manage to recreate the "adaptive method failure, will try with Romberg…" in the CAS view. 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)