:00000,?>: as result of interval

[Beginner]

Hello,

I tried to calculate the interval

e^x^3

in the limits between 0 and 6 with my new HP Prime (version C) as recommended by a benchmark test I found online on youtube.

I recieve the result :ooooo,?>: while the HP Prime (Version A) on youtube showed the correct result in less than a second.

Is there a new "bug" or did I choose false settings?

[Tim Wessman]

Hello,

This is a "non-normalized" number and is a result of a newer firmware. However, you should be doing this operation in the CAS where it will work fine. Press the CAS button, try again, and you will see the expected result.

[Beginner]

Hello,

thanks for your advice! In the CAS mode all went well.

What is a "non normalized" number? In what other situations could such a result appear on the screen?

Perhaps it would be helpful to give an explanation in the "help" menue if this output is typical for a certain set of mathematical tasks?

Or will this problem probably disappear again in a further update of the firmware?

Again: Thank you for your help!

[Tim Wessman]

It will disappear.

Non-normalized means that when the result was processed, it returned a special type of number that should never appear to the user. The display code doesn't make a "nice" format for these since they are only for internal use.

In the earlier firmware, the calculator could only approximate that integral. Now, it can solve it symbolically as well. You'll see this when you do the operation in the CAS.

However, in HOME since it is "numeric" only, the result returns a vector of two results (a symbolic one, and a numeric approximation). The symbolic value is being converted into this "non-normalized" number instead of using the second, approximate evaluation. That is the mistake that is happening on our end.

[Beginner]

Hello,

I begin to realise how complex it must be to creat such a marvelous tool as a calculator and how much time it must take until it is "ready"... And the HP Prime is worth investing all the energy - it has really great features. I hope that it will be able to replace the TI Nspire in the long run which is used now by so many schools. In the end the HP Prime will be far easier to use - and I really like it. :-)) Thanks for all the efforts!

And now back to the minutiae...

If I do not tic "exact" in the CAS settings, I get numeric solutions of the intervall in the CAS mode and in the home mode as well. That solves the problem for now.

If I tick "exact" in the CAS settings, I get the "non normalised" number in the home mode. In the CAS mode I get the following solution:

1/3*(Gamma (1/3, -216)-Gamma (1/3))-1/3*(Gamma ( 1/3,0)-Gamma(1/3)) 5,96393809188E91

Now I tried to alter the limits of the intervall (after deleting the tick at the "exact"-box in the CAS settings)). I found out, that it is possible to increase the upper end until 8.5 (solution: 2,3747181486 E264).

Beyond that limit the calculator shows an hourglass and after several seconds it displays "Error: Invalid input" - allthough the calculator can calculate numbers of 9,9999999E499.

So it should be possible to increase the limit even further and get a valid result.

[cyrille de brébisson]

Hello,

I did some digging there...

The answer:
1/3*(Gamma (1/3, -216)-Gamma (1/3))-1/3*(Gamma ( 1/3,0)-Gamma(1/3)) 5,96393809188E91

Means that the CAS tried to solve the input (int(e^x^3, x, 0, 6)) in 2 different ways.
One is symbolic (returned the expression) and the second is numerical (returned the number).

It then tried to verify that they matched...

However, the calculation of Gamma (1/3, -216) returned as undefined (the reason is that the numbers are so large (10^91) that the numerical algo used to calculate them do not converge. SO, instead of returning a bad approximate value (which the 5,9e91 number is), it returned an error.

If you look at the function (e^x^3) between 0 and 6, you will see that its value vary enormously. As a result, all the first part of the integration (if you think of it as a summation of area) is completely lost in the final result.
Yes, Prime (and most other calculators) will give you a number as a result, but these number are in lots of way meaningless... This is what the CAS is trying to tell you (in a roundabout way).


Now, the fact that in home you get that wiered :00000,.>: is caused by the fact that the home version of integral was not designed to handle such special cases.

Cyrille

[parisse]

This is now fixed in giac
In CAS, the incomplete lower gamma function would be required to properly evaluate this integral (exact value that can be evaluated numerically).
The approx value returned in CAS with int(exp(x^3),x,0,6.0) is correct.

[Beginner]

Thank you all for your efforts!

In the meantime a purchased a HP 50g as a "companion" to my HP Prime. (For me it is still difficult to get into the handling... the HP Prime is much easier. But I want to explore, why this "old" calculator is still so admired by engineers and technicians.)

So I successfully tried to calculate the intervall from 0 up to 9 of the function e^x^3 and got (after several minutes; I probably did not choose the correct flags) the result 1.64236213185 E314. (But it seems not to be possible to go further and increase the upper value to 10.)

Why is it not possible to do this with the HP Prime? It should be possible, as both HP calculators have a range up to E499.

With the TI NSpire (which to my mind is far less attractive than the HP Prime) it is possible to calculate the interval between 0 and 13 of the function e^x^3 in a few seconds. The TI Nspire can operate numbers up to E999.

I wanted to demonstrate the advantages of the HP Prime to my colleagues - and they compared the calculation power of my HP Prime to their TI Nspires. It was not as convincing as I had anticipated. But I really LIKE the HP Prime and would be glad if it could outscore the TI in the long run. And the step from the HP 50g to the HP Prime makes the handling for a new user much easier. So I really appreciate this development.