Hi Sheldon -
inspired by the bugs, rooted in interferences between the procedures in fatou.gp and my std-user-library I was also reviewing the older tetcomplex.gp procedure which you've posted earlier (and which worked in my environment with very little renaming-conventions), and did also some minor edits for numerical improvements (replaced "eval"-procedures by "subst") and deleted all "kill(x)"-calls.
Using the base \( \small B=2 \) I could nicely reproduce the problem in MSE: does exist and then what is \( \small x \gt 2 \) in \( \;^2x = \;^x2 \)
By some other idea I investigated the behave near above the real axis, and specifically I looked at the point \( \small z_0= \text{Re} (L) + \varepsilon I \) and found, that the required height \( h \) to iterate from \( z_0 \) to\( L \) is nearly \( \small 2 \pi I \) , so
\( \small \text{sexp}(2 \pi I+ \text{slog}(z_0 ) )\approx L \qquad \qquad \text{ using }z_0 \text{ with } \varepsilon=1e-6,1e-12,1e-24,... \)
That this is very near suggests, that here equality is intended (and it is also different from the Schröder-method). However, the error is in the near of 0.003 which looks large in comparision to the numerical accuracy for other computations (20 to 30 digits correct by my initialization) .
Could that result be improved by some finetuning? (Or did I speculate wrongly?)
Gottfried
inspired by the bugs, rooted in interferences between the procedures in fatou.gp and my std-user-library I was also reviewing the older tetcomplex.gp procedure which you've posted earlier (and which worked in my environment with very little renaming-conventions), and did also some minor edits for numerical improvements (replaced "eval"-procedures by "subst") and deleted all "kill(x)"-calls.
Using the base \( \small B=2 \) I could nicely reproduce the problem in MSE: does exist and then what is \( \small x \gt 2 \) in \( \;^2x = \;^x2 \)
By some other idea I investigated the behave near above the real axis, and specifically I looked at the point \( \small z_0= \text{Re} (L) + \varepsilon I \) and found, that the required height \( h \) to iterate from \( z_0 \) to\( L \) is nearly \( \small 2 \pi I \) , so
\( \small \text{sexp}(2 \pi I+ \text{slog}(z_0 ) )\approx L \qquad \qquad \text{ using }z_0 \text{ with } \varepsilon=1e-6,1e-12,1e-24,... \)
That this is very near suggests, that here equality is intended (and it is also different from the Schröder-method). However, the error is in the near of 0.003 which looks large in comparision to the numerical accuracy for other computations (20 to 30 digits correct by my initialization) .
Could that result be improved by some finetuning? (Or did I speculate wrongly?)
Gottfried
Gottfried Helms, Kassel
