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:

using namespace std; typedef complex z_type; //#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.); }
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)
 * 4) include "Tania.cin" // need for LambertW
 * 5) include "LambertW.cin" // need for AuZex
 * 6) include "SuZex.cin"


 * 1) include"AuZex.cin"

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

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