I plot the image of the halfstrip \( S=\{z\in\mathbb{C}: -1\le\Re(z)\le0, \Im(z)>0\} \) at the mapping with sexp. The \( \mathrm{sexp}(S) \) is marked with colored lines. Let \( s\in S \), and \( z=\mathrm{sexp}(s) \). The red lines indicate \( \Re(s)=-1,-0.8,-0.6,-0.4,-0.2,0 \). The blue lines which indicate \( \Im(z)=0,1,2,3, ... 22 \); these numbers are marked at the graphics. The halff of the yellow sickle indicates the "basic range" G for the slog.
The resolution of my screen happened to be 10 orders of magnitude out of range required to see the details in one figure. Therefore, I plot the sequence of zooms; each next represents the piece corresponding to the smallest sell of the previous one.
The figire confirms that the slog(strip) is winding around the fixed point. In particular, at \( z=-0.5+20i \), we have \( t=\mathrm{sexp}(z)\approx 1.3161315052205+1.338235701329i \), which is again within the "basic range" G for the slog function. G and sexp(S) have many intersecitons. (we need to evaluate the tetration with at least 12 decimal digits in order to see these intersections).
P.S. I have the fast slog and fast sexp. I just finished the tests and I begin the description. Now it is implemented in C++, but I plan to translate it to other languages. If anyone can help with the translation? Has anyone experience with automatic translation from C++ to Mathematica? Is the result of such a translation workable?
The resolution of my screen happened to be 10 orders of magnitude out of range required to see the details in one figure. Therefore, I plot the sequence of zooms; each next represents the piece corresponding to the smallest sell of the previous one.
The figire confirms that the slog(strip) is winding around the fixed point. In particular, at \( z=-0.5+20i \), we have \( t=\mathrm{sexp}(z)\approx 1.3161315052205+1.338235701329i \), which is again within the "basic range" G for the slog function. G and sexp(S) have many intersecitons. (we need to evaluate the tetration with at least 12 decimal digits in order to see these intersections).
P.S. I have the fast slog and fast sexp. I just finished the tests and I begin the description. Now it is implemented in C++, but I plan to translate it to other languages. If anyone can help with the translation? Has anyone experience with automatic translation from C++ to Mathematica? Is the result of such a translation workable?