File:Aunemplot.jpg

Explicit plot of function AuNem:

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

for $q\!=\!0$, $q\!=\!1$ and $q\!=\!2$.

C++ generator of curves
Files ado.cin, conto.cin, nembran.cin, arqnem.cin, sunema.txt, aunemco.txt should be loaded in order to compile the 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;x0;n--) { s+=A[m][n]; s*=L; } p[m]=A[m][0]+s; } s=p[M]*t; for(m=M-1; m>1;m--) { s+=p[m]; s*=t;} return t*( 1. + t* (-Q + s) ); }

z_type sune(z_type z){ int m,n; DB x,y; z_type s; DB R=20.+20.*Q*Q; x=Re(z); if(x<-R) return sun(z); y=Im(z); if(fabs(y)>R) return sun(z); n=int(x+R); s=sun(z-(0.+n)); DO(m,n) s=nem(s); return s; }

DB AUNE1=0;

z_type sunem(z_type z){ int m,n; DB x,y; z_type s; DB R=20.+20.*Q*Q; x=Re(z); if(x<-R) return sun(z); y=Im(z); if(fabs(y)>R) return sun(z); n=int(x+R); s=sun(z-(n-AUNE1)); DO(m,n) s=nem(s); return s; }

// z_type sunem(z_type z)( return sine(AUNE1+z));)

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"

DB C[41]; //DB K=Q*Q; int coa{ //C[1]=(0.5 - K)*Q; C[2]=-0.625 + (-0.25 + K/2.)*K; .. return 40; }
 * 1) include "aunemco.txt"

z_type aune0(z_type z){ z_type s; int n; s=C[40]*z; for(n=39;n>0;n--){s+=C[n];s*=z;} return (-.5/z+Q)/z + (1.5+K)*log(z) + (.5*K + (.75+.5*K)*log(2.)) + s ; }

//DB AUNE1=0;

z_type aune1(z_type z){ int n, N=20; DO(n,N) z=arqnem(z); return aune0(z)+(0.+n);}

z_type aunem(z_type z){ int n, N=20; DO(n,N) z=arqnem(z); return aune0(z)+(n-AUNE1);}

z_type aune02(z_type z){ z_type s; int n; s=(C[2]*z+C[1])*z; return (-.5/z+Q)/z + (1.5+K)*log(z) + (.5*K + (.75+.5*K)*log(2.)) + s ; } z_type aune01(z_type z){ z_type s; int n; s=C[1]*z; return (-.5/z+Q)/z + (1.5+K)*log(z) + (.5*K + (.75+.5*K)*log(2.)) +s ; }

int main{ int Max; int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;

FILE *o;o=fopen("aunemplo.eps","w");ado(o,4008,4008); fprintf(o,"4 2004 translate\n 1000 1000 scale 2 setlinecap\n"); for(m=0;m<40;m+=10){ M(.1*m,-2)L(.1*m,2)} for(n=-20;n<21;n+=10){ M(0,.1*n)L(4,.1*n)} fprintf(o,".003 W 0 0 0 RGB 2 setlinecap S\n");

// M(-1,ti)L(1,ti) M(-1,-ti)L(1,-ti) M(tr,-1)L(tr,1) fprintf(o,".002 W 0 0 0 RGB 2 setlinecap S\n"); //M(-1,0) L(0,0) M(tr,ti)L(0,0)L(tr,-ti) //fprintf(o,".006 W 1 1 0 RGB 0 setlinecap S\n");

Q=1.e-6; K=Q*Q; NemZo=nembra(Q); ANemZo=nem(NemZo); tr=Re(ANemZo); ti=Im(ANemZo); co; coa; AUNE1=Re(aune1(1.)); DO(n,401){ y=-2.+.01*n; x=Re(sunem(y)); if(n==0) M(x,y) else L(x,y); if(x> 4) break; } fprintf(o,".03 W 1 0 .3 RGB S\n"); DO(m,400){ x= 4.-.01*m; y=Re(aunem(x)); if(m==0) M(x,y) else L(x,y); if(y<-2) break; } fprintf(o,".01 W 0 0 0 RGB S\n");

Q=1.; K=Q*Q; NemZo=nembra(Q); ANemZo=nem(NemZo); tr=Re(ANemZo); ti=Im(ANemZo); co; coa; AUNE1=Re(aune1(1.)); DO(n,401){ y=-2.+.01*n; x=Re(sunem(y)); if(n==0) M(x,y) else L(x,y); if(x> 4) break; } fprintf(o,".03 W 0 1 0 RGB S\n"); DO(m,400){ x= 4.-.01*m; y=Re(aunem(x)); if(m==0) M(x,y) else L(x,y); if(y<-2) break; } fprintf(o,".01 W 0 0 0 RGB S\n");

Q=2.; K=Q*Q; NemZo=nembra(Q); ANemZo=nem(NemZo); tr=Re(ANemZo); ti=Im(ANemZo); co; coa; AUNE1=Re(aune1(1.)); DO(n,401){ y=-2.+.01*n; x=Re(sunem(y)); if(n==0) M(x,y) else L(x,y); if(x> 4)break; } fprintf(o,".03 W .3 0 1 RGB S\n"); DO(m,400){ x= 4.-.01*m; y=Re(aunem(x)); if(m==0) M(x,y) else L(x,y); if(y<-2)break; } fprintf(o,".01 W 0 0 0 RGB S\n");

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

Latex generator of labels
\documentclass[12pt]{article} \usepackage{graphics} \paperwidth 4010pt \paperheight 4010pt \usepackage{geometry} \usepackage{rotating} \textwidth 4400pt \textheight 4400pt \topmargin -97pt \oddsidemargin -74pt \parindent 0pt \pagestyle{empty} \newcommand \ing {\includegraphics} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \begin{document} \begin{picture}(4008,4008) \put(20,3840){\sx{20}{$y\!=\!\mathrm{AuNem}_q(x)$}} \put(100,2944){\sx{20}{$1$}} \put(100,1940){\sx{20}{$0$}} \put(10, 936){\sx{20}{$-1$}} \put( 946,2040){\sx{20}{$1$}} \put(1950,2040){\sx{20}{$2$}} \put(2954,2040){\sx{20}{$3$}} \put(3870,2040){\sx{20}{$x$}} % \put(0,0){\ing{aunemplo}} % \put(3300,3500){\sx{18}{\rot{7} $q\!=\!0$\ero}} \put(3300,3120){\sx{18}{\rot{7} $q\!=\!1$\ero}} \put(3300,2770){\sx{18}{\rot{6} $q\!=\!2$\ero}} \end{picture} \end{document}