[BUG] CAS looping forever
03-08-2014, 06:13 PM (This post was last modified: 03-08-2014 06:21 PM by Tugdual.)
Post: #1
 Tugdual Senior Member Posts: 756 Joined: Dec 2013
[BUG] CAS looping forever
Trying to integrate using radians:
$$\int_{3}^{5}\tan (\sin \left ( x \right )+\ln \left ( \left | x \right | \right ))dx$$

Home returns 2.067...
CAS loops forever on emulator and freezes the physical device.

Edit: Epsilon was super small, like 1e-12 which is the default value. I tried to change Epsilon to 0.01 and got a message "Restoring epsilon to 1e-6 from 0.01". Loops again...
03-08-2014, 07:07 PM (This post was last modified: 03-08-2014 07:25 PM by Mark Hardman.)
Post: #2 Mark Hardman Senior Member Posts: 525 Joined: Dec 2013
RE: [BUG] CAS looping forever
(03-08-2014 06:13 PM)Tugdual Wrote:  Trying to integrate using radians:
$$\int_{3}^{5}\tan (\sin \left ( x \right )+\ln \left ( \left | x \right | \right ))dx$$
Home returns 2.067...
CAS loops forever on emulator and freezes the physical device.

Just taking the indefinite integral of $$\int \tan \left ( \sin \left ( x \right ) \right ) dx$$ produces a result that is 122,286 characters long!

integrate((-5*sin(x)+6*e^(cos(x)*((cos(x))²-(sin(x))²-1)/((cos(x))²+(sin(x))²)+sin(x)*2*cos(x)*sin(x)/((cos(x))²+(sin(x))²))*sin(
...<SNIP>...
+(sin(x))²)))²-216*(cos(x))²*(sin(x))²+132*cos(x)^4+132*sin(x)^4+24*(cos(x))²-24*(sin(x))²+2),x)

Impressive if the result is correct.

Mark Hardman

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03-08-2014, 07:33 PM
Post: #3
 parisse Senior Member Posts: 1,224 Joined: Dec 2013
RE: [BUG] CAS looping forever
It does not have an antiderivative that can be expressed with elementary function therefore you must do numeric integration using approx boundaries. I probably should add a check in the autosimplification function, if you set it to none you get the unevaluated "exact" answers without problems.
03-08-2014, 08:21 PM
Post: #4
 Tugdual Senior Member Posts: 756 Joined: Dec 2013
RE: [BUG] CAS looping forever
(03-08-2014 07:33 PM)parisse Wrote:  you must do numeric integration using approx boundaries.
Hi Parisse, it was indeed my intention to look for an approximation. How do you do "an integration using approx boudaries"? Do you mean Home version?
03-08-2014, 08:46 PM (This post was last modified: 03-08-2014 08:46 PM by Mark Hardman.)
Post: #5 Mark Hardman Senior Member Posts: 525 Joined: Dec 2013
RE: [BUG] CAS looping forever
(03-08-2014 08:21 PM)Tugdual Wrote:  How do you do "an integration using approx boudaries"?

He means that you should specify real values for the limits of integration:

$$\int_{3.0}^{5.0}\tan (\sin \left ( x \right )+\ln \left ( \left | x \right | \right ))dx$$

This gives the same approximation you get in Home mode (2.06725680644).

Mark Hardman

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03-08-2014, 11:09 PM
Post: #6 jebem Senior Member Posts: 1,343 Joined: Feb 2014
RE: [BUG] CAS looping forever
I get the same results here, when using approximate (real) boundaries.
However the time to compute the same result is quite different between Home and CAS environments:
Home takes about 2 seconds, and CAS answer is instantaneous !
So the Prime gives the same apparent result, but it is using different algorithms, where one takes significant more time than the other?

Jose Mesquita