Hard or wanted CAS stuff



#2

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!


#3

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


#4

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.


#5

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

#6

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.

#7

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.


#8

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

#9

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.

#10

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!

#11

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


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