complex base tetration program

[Gottfried]

[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 )


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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.