Quick way to get the repelling fixed point from the attracting fixed point?

[JmsNxn]

I want that in PARI-GP, and everything I've read says that pari doesn't support complex Lambert W, and additionally only has the principal branch.

Thank you though, I want \(W_{-1}\) not \(W_1\), I knew I was screwing something up.

You answered my question, but I'm still confused how to run this in Pari-GP. That's still confusing me.

How do I write

Code:

LambertW(sqrt(2) + O(y),-1) = 4 + O(y)\\

Hi James -

two ways: either use Mike3's implementation (I'd attached the Pari/GP-code to my earlier answer) or download the latest Pari/GP version 2.14 (which firms as "development version" at the "bleeding edge" ;-) )from the Pari-group's website.    With Mike3's implementation he didn't call it "LambertW()" but simply "lambw()" or so; I renamed it in the downloaded Pari/GP-source simply for my own convenience.

Gottfried

GREAT! I'll get the pari development version! Didn't know that was a thing, lol.