File:SuTraPlo3T.jpg

Plot of funciton SuTra, id est, Superfunction of the Trappmann function $\mathrm{Tra}(z)\!=z\!+\!\exp(z)$.

The thick blue curve shows $y\!=\!\mathrm{SuTra}(x)$

The thin dark brown curve shows the asymptotics, $y\!=\! - \ln(-x)$

The additional horizontal gridline shows $1\!+\!\mathrm e=\mathrm{SuTra}(2)$

C++ generator of curves
// Files ado.cin, SuZex.cin, LambertW.cin and Tania.cin sould be loaded to the working directory in order to compile the C++ code below.

using namespace std; typedef complex z_type; //#include "AuZex.cin"
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x2. ) return log(suzex(z)); return tra(sutra(z-1.));}

main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("SuTraPlo3.eps","w");  ado(o,604,812); fprintf(o,"302 202 translate\n 100 100 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); for(n=-2;n<7;n++) {M(-3,n)L(3,n)} for(m=-3;m<4;m++) {M(m,-2)L(m,6)} // M(M_E,0)L(M_E,1) M(0,M_E)L(1,M_E) M(0,1.+M_E) L(2,1.+M_E) fprintf(o,".004 W S\n"); // DO(m,700){x=.01 +.02*m; y=Re(LambertW(LambertW(x)));if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;} fprintf(o,".033 W 1 0 0 RGB S\n"); // DO(m,700){x=.01 +.02*m; y=Re(LambertW(x));if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;} fprintf(o,".04 W 1 .5 0 RGB S\n"); // M(0,0) L(12.03,12.03) fprintf(o,".04 W 0 1 0 RGB S\n"); DO(m,700){x=-5.02 +.02*m; y=Re(sutra(x)); if(m==0) M(x,y) else L(x,y) if(x>3.03||y>6.1) break;} fprintf(o,".03 W 0 0 1 RGB S\n"); DO(m,240){x=-5.02 +.02*m; y=-log(-x);     if(m==0) M(x,y) else L(x,y) if(x>3.03||y>6.03) break;} fprintf(o,".01 W .5 0 0 RGB S\n"); fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o); system("epstopdf SuTraPlo3.eps"); system(   "open SuTraPlo3.pdf"); //for macintosh getchar; system("killall Preview"); // For macintosh }
 * 1) include "ado.cin"
 * 2) define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
 * 3) define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);

Latex generator of labels
% file SuTraPlo3.pdf should be generated with the code above in order to compile the Latex document below. % Copyleft 2012 by Dmitrii Kouznetsov \documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphicx} \usepackage{rotating} \paperwidth 608pt \paperheight 816pt \topmargin -98pt \oddsidemargin -71pt \textwidth 900pt \textheight 900pt \pagestyle {empty} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \parindent 0pt \pagestyle{empty} \begin{document} \begin{picture}(602,805) \put(310,794){\sx{4}{$y$}} \put(220,566){\sx{3.8}{$1\!+\!\mathrm e$}} \put(310,690){\sx{4}{$5$}} \put(310,590){\sx{4}{$4$}} \put(310,490){\sx{4}{$3$}} \put(310,390){\sx{4}{$2$}} \put(310,289){\sx{4}{$1$}} \put(312,187){\sx{4}{$0$}} \put(290, 87){\sx{4}{$-\!1$}} %\put(325,098){\sx{4}{$0$}}

\put(068,206){\sx{4}{$-\!2$}} \put(168,206){\sx{4}{$-\!1$}} \put(291,206){\sx{4}{$0$}} \put(392,206){\sx{4}{$1$}} \put(492,206){\sx{4}{$2$}} \put(578,206){\sx{4}{$x$}} \put(462,308){\sx{4.2}{\rot{70}$y\!=\!\mathrm{SuTra}(x)$\ero}} \put(44,314){\sx{3.8}{\rot{0}$y\!=\!-\!\ln(-\!x)$\ero}} %\put(10,10){\ing{ExpQ2plot}} %\put(10,10){\ing{SuZexPlot511}} \put(0,0){\ing{SuTraplo3}} %\put(0,0){\ing{SuTraplo3}} \end{picture} \end{document}