File:Arqnemplot.jpg

Explicit plot of function ArqNem for various values of parameter.

$y=\mathrm{ArqNem}_q(x)$

versus $x$ for $q\!=\!0$, $q\!=\!1$, $q\!=\!2$, $q\!=\!4$ and for $q\!=\!10$

C++ generator of curves
//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=1.e-6; // subject to change in main 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"nembran.cin"
 * 1) include "arqnem.cin"

/* The routine arnemR is sufficient to plot figures, but I test arqnem ! z_type arnemR(z_type z){ DB q=Q; DB q2=q*q; DB q3=q2*q; z_type a=q-z; z_type b=1.+4.*q*z; z_type r=81.*(a*a)+12.*(b*b*b); z_type R=sqrt(r); z_type s=27.*a + 3.*R; z_type S=pow(s,1./3.); z_type B=(0.26456684199469993*S)/q - (1.2599210498948732*b)/(q*S); z_type h=0.25/q2 + B; z_type H=sqrt(h); z_type g=0.5/q2 - B + (.25+2.*q2)/(q3*H); z_type G=sqrt(g); return - 0.25/q - 0.5*H + 0.5*G ;}

int main{ int Max; int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; //FILE *o;o=fopen("03.eps","w");ado(o,2520,1520); FILE *o;o=fopen("arqnemplo.eps","w");ado(o,2520,1520); fprintf(o,"10 10 translate\n 1000 1000 scale 2 setlinecap\n"); for(m=0;m<26;m+=5){ M(.1*m,0)L(.1*m,1.5)} for(n=0;n<16;n+=5){ M(0,.1*n)L(2.5,.1*n)} fprintf(o,".003 W 0 0 0 RGB 2 setlinecap S\n");

//Q=10.;       DO(m,351){x=-.24+.01*m; y=Re(arnemR(x)); if(m==0) M(x,y) else L(x,y); if(x>2.5) break;} Q=10.; DO(m,351){x=1.e-6+.01*m; y=Re(arnemR(x)); if(m==0) M(x,y) else L(x,y); if(x>2.5) break;} fprintf(o,".01 W .9 0 .9 RGB 1 setlinejoin S\n");

//Q=4.; DO(m,351){x=-.38+.01*m; y=Re(arnemR(x)); if(m==0) M(x,y) else L(x,y); if(x>2.5) break;} Q=4.;  DO(m,351){x=1.e-6+.01*m; y=Re(arnemR(x)); if(m==0) M(x,y) else L(x,y); if(x>2.5) break;} fprintf(o,".01 W .1 .1 1 RGB 1 setlinejoin S\n");

//Q=2.; DO(m,351){x=-.57+.01*m; y=Re(arnemR(x)); if(m==0) M(x,y) else L(x,y); if(x>2.5) break;} Q=2.;  DO(m,351){x=1.e-6+.01*m; y=Re(arnemR(x)); if(m==0) M(x,y) else L(x,y); if(x>2.5) break;} fprintf(o,".01 W 0 .8 .8 RGB 1 setlinejoin S\n");

//Q=1.; DO(m,351){x=-1.+.01*(m+.1); y=Re(arnemR(x)); if(m==0) M(x,y) else L(x,y); if(x>2.5) break;} Q=1.;  DO(m,351){x=1.e-6+.01*m; y=Re(arnemR(x)); if(m==0) M(x,y) else L(x,y); if(x>2.5) break;} fprintf(o,".01 W 0 .8 0 RGB 1 setlinejoin S\n");

//Q=1.e-6;DO(m,351){x=-1.+.01*m; y=Re(arnemR(x)); if(m==0) M(x,y) else L(x,y);} Q=1.e-6; DO(m,351){x=1.e-6+.01*m; y=Re(arnemR(x)); if(m==0) M(x,y) else L(x,y); if(x>2.5) break; } fprintf(o,".01 W 1 0 0 RGB 1 setlinejoin S\n");

//Q=1; DO(m,251){x=-1.+.01*m; y=Re(nem(x)); if(m==0) M(y,x) else L(y,x); if(y>2.5) break; } //Q=2; DO(m,251){x=-1.+.01*m; y=Re(nem(x)); if(m==0) M(y,x) else L(y,x); if(y>2.5) break; } //Q=4; DO(m,251){x=-.8+.01*m; y=Re(nem(x)); if(m==0) M(y,x) else L(y,x); if(y>2.5) break; } //Q=10; DO(m,251){x=-.5+.01*m; y=Re(nem(x)); if(m==0) M(y,x) else L(y,x); if(y>2.5) break; }

Q=0; DO(m,251){x=.01*m; y=Re(nem(x)); if(m==0) M(y,x) else L(y,x); if(y>2.5) break; } Q=1; DO(m,251){x=.01*m; y=Re(nem(x)); if(m==0) M(y,x) else L(y,x); if(y>2.5) break; } Q=2; DO(m,251){x=.01*m; y=Re(nem(x)); if(m==0) M(y,x) else L(y,x); if(y>2.5) break; } Q=4; DO(m,251){x=.01*m; y=Re(nem(x)); if(m==0) M(y,x) else L(y,x); if(y>2.5) break; } Q=10;DO(m,251){x=.01*m; y=Re(nem(x)); if(m==0) M(y,x) else L(y,x); if(y>2.5) break; } fprintf(o,".002 W 0 0 0 RGB 1 setlinejoin S\n");

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o); system("epstopdf arqnemplo.eps"); system(   "open arqnemplo.pdf"); //mac return 0;}

Latex generator of labels
\documentclass[12pt]{article} \usepackage{graphics} \paperwidth 2520pt \paperheight 1520pt \usepackage{geometry} \usepackage{rotating} \textwidth 2560pt \textheight 2260pt \topmargin -97pt \oddsidemargin -84pt \parindent 0pt \pagestyle{empty} \newcommand \ing {\includegraphics} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \begin{document} \begin{picture}(2520,1520) \put(10,10){\ing{arqnemplo}} \put(30,1410){\sx{12}{$y\!=\!\mathrm{ArqNem}_q(x)$}} \put(30,980){\sx{12}{$1$}} \put(30,480){\sx{12}{$0.5$}} \put(420,42){\sx{12}{$0.5$}} \put(990,42){\sx{12}{$1$}} \put(1428,42){\sx{12}{$1.5$}} \put(1990,42){\sx{12}{$2$}} \put(2448, 42){\sx{12}{$x$}} \put(2100,1060){\rot{11}\sx{11}{$q\!=\!0$}\ero} \put(2150,890){\rot{9}\sx{11}{$q\!=\!1$}\ero} \put(2180,792){\rot{8}\sx{11}{$q\!=\!2$}\ero} \put(2240,714){\rot{6}\sx{11}{$q\!=\!4$}\ero} \put(2200,590){\rot{5}\sx{11}{$q\!=\!10$}\ero} \end{picture} \end{document}