[update] Ah, got it working with Pari/GP v. 2.7 in a winxp-32bit virtual machine. Great, so I can recompute my example in MSE. I'll look for the incompatibility reasons and shall tell them later.[/update]

Here is the comparision of the regular/Schröder-solution and the (extended/generalized) Kneser-mechanism (see bottom of posting).

(This is the link to the discussion in MSE : http://math.stackexchange.com/questions/...ing-us-all )

-------------------------------------------------------

Hi Sheldon -

this is what I've done and what I've got with the just-downloaded fatou.gp: (this is the old Pari/GP 2.2.11-version)

Here is the comparision of the regular/Schröder-solution and the (extended/generalized) Kneser-mechanism (see bottom of posting).

(This is the link to the discussion in MSE : http://math.stackexchange.com/questions/...ing-us-all )

-------------------------------------------------------

Hi Sheldon -

this is what I've done and what I've got with the just-downloaded fatou.gp: (this is the old Pari/GP 2.2.11-version)

Code:

`\r f:\download\fatou.gp`

seriesprecision = 21 significant terms

format = g0.15

help(); help2(); andrewjay(); for other functions

\p 38 /* precis=38; 32-35 digits. default \p 28 ~=24 decimal digits; */

/* generates Abel function for iterating z <= exp(z)-1+k; f(z) */

loop(k,nlim,nskip,looplim); sexpinit(b); /* b=exp(exp(k-1)); */

loop(1); sexpinit(exp(1)); /* two examples for tetration for base e */

slog(z); sexp(z); abel(z); invabel(z,est);

sexptaylor(center,radius,samples); slogtaylor(c,r,s);

invabeltaylor(c,r,s); abeltaylor(c,r,s);

fmode=0:abel 1:invabel 2:slog 3:sexp

MakeGraph(width,height,x0,y0,x1,y1,filename, n); /* f(z); fmode */

debugprint=0; quietmode=0; x2mode=0; /* x2mode=1; iterate z^2+z+k */

prtpoly(wtaylor,t,name);

setmaxconvergence(); /* base i is hard to compute */

thlogk=1;

ctr=19/20;

ir=57/64;

ctfactor=85/100;

disabautoctfactor=1;

staylorstop=40;

sexpinit(I);

seriesprecision = 21 significant terms

format = g0.15

1 0.474349095548301 0.0458093729068993 23 4 20

2 0.236926728615837 0.409974883179566 41 6 40

3 3.91014217666629 E144 4.33918410729562 E143 61 7 60

*** vector: negative number of components in vector.

sexp(0.5)

*** if: incorrect type in comparison.

Gottfried Helms, Kassel