File:AuTraPlotT.jpg

Explicit plot of funciton AuTra of real argument.

AuTra is the Abel function for the Trappmann function

$ \mathrm{tra}(z)=z+\exp(z)$

C++ Generator of curves

// Files ado.cin, tania.cin, LambertW.cin, SuZex.cin, AuZex.cin should be loaded to the working directory in order to compile the code below:

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
using namespace std;
#include<complex>
typedef complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "Tania.cin" // need for LambertW
#include "LambertW.cin" // need for AuZex
#include "SuZex.cin"
//#include "AuZex.cin"
z_type tra(z_type z){ return exp(z)+z;}
//z_type F(z_type z){ return log(suzex(z));}
//z_type G(z_type z){ return auzex(exp(z));}
z_type sutra(z_type z){ if( Re(z)<2. || fabs(Im(z))>2. ) return log(suzex(z));
                                                        return tra(sutra(z-1.));}
// z_type autra(z_type z){ return z-Tania(z-1.); }

#include"AuZex.cin"

z_type autra(z_type z){ return auzex(exp(z)); }

#include "ado.cin"
#define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y); 
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;  FILE *o;o=fopen("AuTraPlot.eps","w");  ado(o,812,612);
fprintf(o,"204 304 translate\n 100 100 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");
for(n=-3;n<4;n++) {M(-2,n)L(6,n)}
for(m=-2;m<7;m++) {M(m,-3)L(m,3)}
// 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=-2.01 +.02*m; y=Re(sutra(x));  if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".01 W 0 0 1 RGB S\n");
// DO(m,240){x=-3.02 +.02*m; y=-log(-x);      if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.03) break;} fprintf(o,".01 W .5 0 0 RGB S\n"); 
DO(m,740){x=-1.25 +.02*m; y=Re(autra(x));      if(m==0) M(x,y) else L(x,y)  if(x>6.03||y>6.01) break;} fprintf(o,".03 W .6 0 0 RGB S\n"); 
fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%');  fclose(o);
    system("epstopdf AuTraPlot.eps"); 
    system(    "open AuTraPlot.pdf"); //for macintosh
    getchar(); system("killall Preview"); // For macintosh
}

Latex generator of labels

% % Copyleft 2012 by Dmitrii Kouznetsov%<br> \documentclass[12pt]{article} %<br> \usepackage{geometry} %<br> \usepackage{graphicx} %<br> \usepackage{rotating} %<br> \paperwidth 808pt %<br> \paperheight 608pt %<br> \topmargin -108pt %<br> \oddsidemargin -73pt %<br> \textwidth 940pt %<br> \textheight 940pt %<br> \pagestyle {empty} %<br> \newcommand \sx {\scalebox} %<br> \newcommand \rot {\begin{rotate}} %<br> \newcommand \ero {\end{rotate}} %<br> \newcommand \ing {\includegraphics} %<br> \parindent 0pt \begin{document}%<br> {\begin{picture}(904,608) %<br> %\put(1,9){\ing{arclambertw}} %<br> %\put(1,9){\ing{LambertWplot}} %<br> \put(0,0){\ing{AuTraPlot}} %<br> \put(181,588){\sx{3}{$y$}} %<br> %\put(209,378){\sx{3.1}{$\mathrm e$}} %<br> \put(181,492){\sx{3}{$2$}} %<br> \put(181,394){\sx{3}{$1$}} %<br> \put(181,294){\sx{3}{$0$}} %<br> \put(163,194){\sx{3}{$-\!1$}} %<br> \put(163, 94){\sx{3}{$-\!2$}} %<br> %\put(189,194){\sx{3}{$-\!3$}} %<br> % \put(267,184){\sx{2.9}{$\mathrm e$}} %<br> \put( 82, 276){\sx{3}{$-\!1$}} %<br> \put(197,276){\sx{3}{$0$}} %<br> \put(297,276){\sx{3}{$1$}} %<br> \put(397,276){\sx{3}{$2$}} %<br> \put(497,276){\sx{3}{$3$}} %<br> \put(597,276){\sx{3}{$4$}} %<br> \put(698,276){\sx{3}{$5$}} %<br> %\put(798,276){\sx{2.8}{$6$}} %<br> % \put(898,276){\sx{2.8}{$9$}} %<br> % \put(300,-9){\sx{2.5}{$0$}} %<br> \put(789,280){\sx{3}{$x$}} %<br> \put(382,564){\sx{3.4}{$y\!=\!\mathrm{SuTra}(x)$}} %<br> \put(422,448){\sx{3.4}{\rot{0}$y\!=\!\mathrm{AuTra}(x)$\ero}} %<br> \end{picture} %<br> } %<br> \end{document}