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