Integrator loops endlessly for lambert_w(1/x)

Just to be clear about it, I wasn't suggesting that we use a workaround
instead of addressing the problem in the simplifier, it just reminded me of
this issue with the derivative of Lambert's W, which in the present form is
rather cumbersome to simplify.


Viktor
 

-----Original Message-----
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Dieter Kaiser
Sent: Friday, December 26, 2008 2:32 PM
To: willisb at unk.edu
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] Integrator loops endlessly for lambert_w(1/x)

Hello Barton,

Yes, the bug we have found for the integration of lambert_w(1/x) is not
related
to the code of the lambert_w function and of the integrator. It is a bug of
the
simplifier.

Changing the derivative would help for the lambert_w function, but other
functions or expressions may produced again the problem. 

I have not found another example until yet. But a depper understandig of
what is
going on in the simplifier may help to produce more failures of the
integrator.

I think the best would be not to try to find a workaround for the lambert_w
function, but to cure the bug in the simplifier.

Dieter Kaiser

-----Urspr?ngliche Nachricht-----
Von: willisb at unk.edu [mailto:willisb at unk.edu] 
Gesendet: Freitag, 26. Dezember 2008 18:00
An: Viktor T. Toth
Cc: 'Dieter Kaiser'; maxima at math.utexas.edu
Betreff: Re: [Maxima] Integrator loops endlessly for lambert_w(1/x)

-----maxima-bounces at math.utexas.edu wrote: -----

>A?while?back,?I?proposed?using?a?different?expression?for?the?derivative
>of Lambert's?W,?as?it?leads?to?better?simplification:

Dieter found a bug that is unrelated to lambert_w, I think:

 (%i7) %e^(-f(1/x))/(x*(1+f(1/x)));
 (%o7) %e^(-f(1/x))/(x*(f(1/x)+1))

 (%i8) ?resimplify(%);
 (%o8) %e^(-f(1/x))/((f(1/x)+1)*x)

 (%i9) ?resimplify(%);
 (%o9) %e^(-f(1/x))/((f(1/x)+1)*x)

 (%i10) ?resimplify(%);
 (%o10) %e^(-f(1/x))/(x*(f(1/x)+1))

I don't understand the dosimp flag, but surely (%o9) and (%o10)
should be identical.


Barton





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