Re: lambertw

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Ilya Zakharevich [2023-11-21 04:50]:
>   gp > ?lambertw
>   lambertw(y,{branch=0}): solution of the implicit equation
>   x*exp(x)=y. In the p-adic case, gives a solution of x*exp(x)=y if x
>   has positive valuation, of x+log(x)=log(y) otherwise.
> 
> First, I would rewrite it as log(x)+x = log(y) to make the match more
> clear.

Done.

> Second, I suspect that what is meant is
> 
>    y has positive valuation
> 
> (not “x”).

Indeed. We were further missing the condition "p odd" for this branch.
For 2-adics, the condition was v_2(y) > 1; in fact, the case v_2(y) < 1
was incorrectly implemented (raised an exception).

All fixed in master. Thanks for your report !

Cheers,

    K.B.
-- 
Pr. Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/