Re: Finding fixed points in gp

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Sat, Oct 29, 2016 at 12:22:25AM -0400, Charles Greathouse wrote:
> Is there a good way to find fixed points in gp?

Do you mean you want to solve f(z)-z = 0 over the complex plane ?
In general, you want to use Newton interation.

> I found some code (simplified version below) which finds them by direct
> iteration, but I have to wonder if there's a more elegant way, either in
> general or in this particular case:
> 
> li(z)=-eint1(-log(z));
> Eps_= 4.0*10.0^(-default(realprecision));
> z=1+I; zlast=0;
> for(k=1, 1e6, z=li(z); if(abs(z-zlast)<Eps_, break); zlast=z)

Well, this is a pathological case since li(0) is not defined.

Cheers,
Bill.