The following warnings occurred:
Warning [2] Undefined array key 217875 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217885 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217886 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217887 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217893 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217903 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217908 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217914 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217913 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217986 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $thread - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $fid - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217887 - Line: 331 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 331 errorHandler->error_callback
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 304 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217893 - Line: 331 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 331 errorHandler->error_callback
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 304 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217913 - Line: 331 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 331 errorHandler->error_callback
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 304 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217914 - Line: 331 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 331 errorHandler->error_callback
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 304 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 217986 - Line: 331 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 331 errorHandler->error_callback
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 304 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $theme - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $theme - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $lang - Line: 5 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 5 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Attempt to read property "messages_in_thread" on null - Line: 5 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 5 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks





Hard or wanted CAS stuff



#11

I'm testing my CAS and am looking for some "hard" problems.

Have you run into CAS use cases that were just a little too much for your 50g (or your TI CAS whatever calc--for those of us who crossed into enemy territory, lately ;-))?

Something like symbolically integrating

'sin(ln(x))+cos(ln(x))' 
which will not yield a result on the 50g.

Apart from those, what are the top three things you always wished the 50g had (in the CAS department)?

Thank you!


#12

Hello Oliver,

I think this example isn't a very good choice, because with a simple substitution the integral can be performed. It's a lack, that the CAS (of the HP 50g) that doesn't recognizes this. But if you are working in the STEP BY STEP mode you get the information "Invalid unary operator" which indicates a necessary substitution, this and the following integration can easily performed with this handy CAS.

Sincerely
peacecalc


#13

Hi peacecalc,

Thanks for your note. I had not noticed that this integral can be done in step-by-step mode, nor the simple substitution. This may well be not a good example. It was just meant to show a function on which the CAS chokes. I'm looking for cases like that (and even more so cases that don't work at all), to see how my other CAS performs.

My biggest curiosity is about what's felt to be missing in the 50g CAS (so I can look into patching those holes).

Cheers.

Edited: 15 Apr 2012, 8:43 a.m.


#14

Hello Oliver,

my problem with your question is, that I'm not as good in algebra like the HP 50g ;-P. That means, when the calc isn't able to perform for instance an symbolic integral you have more possibilities:

a) there doesn't exist a closed form of the integral
b) it is a problem which can be solved with a little changement (substituion or partial fraction and so on)
c) there exists a solution, but in form of a sum with an infinite number of terms (like the solution of the mathematic pendicular without the approximation for small angles).
d) there exists a closed solution but the CAS doesn't find it.
and so on...

My solution for this is: IF the CAS failed THEN I keyed in the wrong input. Because there exist a) (see above), it is not always the right decision, but as a working hypothesis it leads you correctly (I'm hoping) through the mathematical fog.

Sincerely
peacecalc

#15

I tried on my early version TI-92 which does not find a solution for the integral. Derive 6 on the PC has no problems returning a solution. I doubt that Derive is really the ancestor of the TI-92 CAS because there are way to many differences.

The Nspire CAS PC software (1.3) does compute the integral symbolically. Time to test my more recent TI-92plus or Voyage 200.

Edit: My TI-89 with OS 2.09 can handle the integral. As a general note: AFAIK TI-CAS cannot solve step by step so you cannot see what's going wrong if it cannot find a solution.


Edited: 15 Apr 2012, 11:05 a.m.

#16

What about symbolically integrating Kahan's integral?
I don't know whether TI CAS can do it. W|A can:

integrate (sqrt(x)/(x - 1) - 1/ln(x)) from x = 0 to x = 1


Edited: 15 Apr 2012, 1:38 p.m.


#17

Hi Gerson,

Quote:
I don't know whether TI CAS can do it.



My TI 92 Plus can.

     /1
|
I = | (sqrt(x)/(x-1) - 1/ln(x))dx = .036489973974, time= 31 sec
/0

George

#18

Hi George,

Quote:
My TI 92 Plus can.

It cannot find a closed form solution however. By the way, the last significant digits in the TI-92 Plus answer are wrong (39 instead of 85).

TI-92 Plus: .0364899739739
HP-15C LE: .03648997377
Actual: .03648997397857652.. (2 - ln(4) - EulerGamma)

Cheers,

Gerson.

#19

That's a good one, Gerson. It works, and leaves me with li() in the result expression, which I know I have to implement now. Thank you for that!

#20

I did not try it yet with CAS' help, but even with a pencil and a pile of paper you should know the way how to solve it: the cumulative distribution function (integrating the Gaussian distribution) in terms of elementary functions. According to this wiki it is not possible, but IIRC there is simple trick.

At least, CAS could help to go the 'long' way: integrate the Taylor's expansion of the Gaussian distribution. I did it once w/o CAS to make an HP41 program for the cumulative distribution function (like Q on the HP32E).

Ciao.....Mike


Possibly Related Threads…
Thread Author Replies Views Last Post
  How to copy files from 9114B to hard drive via PIL-box? Joe Horn 23 10,026 12-14-2013, 11:57 PM
Last Post: Geoff Quickfall
  HP Prime: CAS taylor Alberto Candel 5 3,877 12-13-2013, 09:45 PM
Last Post: Alberto Candel
  HP Prime CAS curiosity bluesun08 11 4,716 12-10-2013, 01:03 PM
Last Post: Han
  [HP-Prime CAS] "Warning, ^ (Command) Is ambiguous on non square matrices"?? CompSystems 1 2,141 12-07-2013, 07:15 PM
Last Post: CompSystems
  HP Prime: complex numbers in CAS. Alberto Candel 1 1,856 12-06-2013, 02:36 PM
Last Post: parisse
  [HP Prime] plotfunc() bug in CAS Chris Pem10 2 2,364 12-04-2013, 02:46 PM
Last Post: Chris Pem10
  HP Prime: Home/CAS? Alasdair McAndrew 11 3,783 11-26-2013, 02:48 PM
Last Post: Alberto Candel
  HP Prime numerical precision in CAS and HOME Javier Goizueta 5 2,355 11-16-2013, 03:51 AM
Last Post: Paul Dale
  Need CAS help Michael de Estrada 6 2,588 11-13-2013, 01:29 AM
Last Post: cyrille de Brébisson
  HP Prime - CAS functions in Spreadsheet App CR Haeger 6 2,398 11-11-2013, 12:37 AM
Last Post: Michael de Estrada

Forum Jump: