File:Sunemplot.jpg

Explicit plot of function SuNem for three different values of parameter.

$y=\mathrm{SuNem}_q(x)~ ~ $ versus $x$ for

$q\!=\!0$, (red)

$q\!=\!1$, (green)

$q\!=\!2$, (blue)

C++ generator of curves
Files ado.cin, conto.cin, sune.cin, sunema.txt should be loaded in order to compile the C++ code below. //using namespace std; typedef std::complex z_type;
 * 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 "conto.cin"

DB Q; z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); } z_type nem1(z_type z){ return 1.+z*z*(3.+z*(4.*Q)); }  // WARNING: Q is global!

/* z_type NemZo=nembra(Q); z_type ANemZo=nem(NemZo); DB tr=Re(ANemZo); DB ti=Im(ANemZo);
 * 1) include "sune.cin"
 * 1) include"nembran.cin"


 * 1) include "arqnem.cin"

DB SUNo=0;

z_type sunem(z_type z){ return sune(z + SUNo);}

int main{ int Max; int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; // DB rr,ti; FILE *o;o=fopen("sunemplo.eps","w");ado(o,620,1020); fprintf(o,"410 10 translate\n 100 100 scale 2 setlinecap\n"); for(m=-4;m<3;m+=1){ M(m,0)L(m,10)} for(n=0;n<11;n+=1){ M(-4,n)L(2,n)} fprintf(o,".008 W 0 0 0 RGB 2 setlinecap S\n");

Q=0; co; printf("Q=%9.4lf\n",Q); DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar; //for(m=-4;m<4;m++) {x=m; y=Re(sunem(x)); printf("%6.1lf %18.15lf\n", x,y); } DO(n,124){ x=-4.1+.05*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y);  printf("%6.1lf %18.15lf\n", x,y);  if(y>10) break;} fprintf(o,".03 W .7 0 0 RGB 1 setlinejoin S\n");

Q=1; co; printf("Q=%9.4lf\n",Q); DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar; //for(m=-4;m<4;m++) {x=m; y=Re(sunem(x)); printf("%6.1lf %18.15lf\n", x,y); } DO(n,124){ x=-4.1+.05*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y);  printf("%6.1lf %18.15lf\n", x,y);  if(y>10) break;} fprintf(o,".03 W 0 .5 0 RGB 1 setlinejoin S\n");

Q=2; co; printf("Q=%9.4lf\n",Q); DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar; //for(m=-4;m<4;m++) {x=m; y=Re(sunem(x)); printf("%6.1lf %18.15lf\n", x,y); } DO(n,124){ x=-4.1+.05*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y);  printf("%6.1lf %18.15lf\n", x,y);  if(y>10) break;} fprintf(o,".03 W 0 0 .7 RGB 1 setlinejoin S\n");

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o); system("epstopdf sunemplo.eps"); system(   "open sunemplo.pdf"); //mac

return 0; }

Latex generator of curves
\documentclass[12pt]{article} \usepackage{graphics} \paperwidth 618pt \paperheight 1012pt \usepackage{geometry} \usepackage{rotating} \textwidth 1260pt \textheight 1260pt \topmargin -100pt \oddsidemargin -72pt \parindent 0pt \pagestyle{empty} \newcommand \ing {\includegraphics} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \begin{document} \begin{picture}(620,1012) \put(0,0){\ing{sunemplo}} \put(420,988){\sx{3.3}{$y$}} \put(420,898){\sx{3.3}{$9$}} \put(420,798){\sx{3.3}{$8$}} \put(420,698){\sx{3.3}{$7$}} \put(420,598){\sx{3.3}{$6$}} \put(420,498){\sx{3.3}{$5$}} \put(420,398){\sx{3.3}{$4$}} \put(420,298){\sx{3.3}{$3$}} \put(420,198){\sx{3.3}{$2$}} \put(420, 98){\sx{3.3}{$1$}} %\put(420, -7){\sx{3.3}{$0$}} \put( 80,14){\sx{3.3}{$-3$}} \put(180,14){\sx{3.3}{$-2$}} \put(280,14){\sx{3.3}{$-1$}} \put(402,14){\sx{3.3}{$0$}} \put(502,14){\sx{3.3}{$1$}} \put(592,14){\sx{3.3}{$x$}} \put(516,616){\sx{4}{\rot{86}$q\!=\!2$\ero}}% \put(572,616){\sx{4}{\rot{85}$q\!=\!1$\ero}}% \put(600,410){\sx{4}{\rot{82}$q\!=\!0$\ero}}% \end{picture} \end{document}