File:Sutraamap.jpg

Map of agreement for the primary approximation $z\mapsto F_M(z\!+\!x_0)$ of function SuTra

$\displaystyle \mathcal A(z)= - \lg\! \left( \frac { | F_M(z\!+\!x_0)- \mathrm {SuTra}(z) | } { |  F_M(z\!+\!x_0) | + |\mathrm {SuTra}(z) | } \right) $

Levels of $\mathcal A(x\!+\!\mathrm i y)$ are drawm in the $x$, $y$ plane.

This image is used as figure 20.8 of the Book Superfunction (In Russian, 2014; the English version is in preparation, 2015) .

Function SuTra as entire function with logarithmic asymptotic is described also in year 2013 at Hikari .

C++ generator of map
Files ado.cin, conto.cin, sutran.cin should be loaded to the working directory 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;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"

z_type tra(z_type z){ return exp(z)+z;}


 * 1) include"sutran.cin"

// z_type sutrap(z_type z) { int n; z_type c=sutra0(z-36.); DO(n,36) c=tra(c); return c;}

int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; //DB x1=-1.1259817765745026; DO(n,8){ y=Re(suzex(x1)); x=y-1.; x1+=-1.2*x; printf("%18.16f %18.16f\n", x1,y);} getchar; //DB x1=-1.1259817765745026; DO(n,18){ y=Re(sutrap(x1)); x1+=-1.3*y; printf("%18.16f %18.16f\n", x1,y);} getchar;

int M=441,M1=M+1; int N=201,N1=N+1; DB X[M1],Y[N1]; DB *g, *f, *w; // w is working array. g=(DB *)malloc((size_t)((M1*N1)*sizeof(DB))); f=(DB *)malloc((size_t)((M1*N1)*sizeof(DB))); w=(DB *)malloc((size_t)((M1*N1)*sizeof(DB))); char v[M1*N1]; // v is working array //FILE *o;o=fopen("SuTraMap.eps","w"); ado(o,4402,2002); FILE *o;o=fopen("SuTrapag.eps","w"); ado(o,4402,2002); fprintf(o,"2001 1 translate\n 100 100 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); DO(m,M1) X[m]=-20+.1*(m-.5); DO(n,N1) Y[n]=0+.1*(n-.5); //for(n=0;n0 && p<18) g[m*N1+n]=p; // p=Re(c); q=Im(c); if(p>-19 && p<19 && ( x<2. || (fabs(q)>1.e-12 && fabs(p)>1.e-12)) ){ g[m*N1+n]=p;f[m*N1+n]=q;} }} fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.2;q=.4; /* for(m=-8;m<8;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q,q);fprintf(o,".007 W 0 .6 0 RGB S\n"); for(m=0;m<8;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);fprintf(o,".007 W .9 0 0 RGB S\n"); for(m=0;m<8;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".007 W 0 0 .9 RGB S\n"); for(m= 1;m<17;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".02 W .8 0 0 RGB S\n"); for(m= 1;m<17;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".02 W 0 0 .8 RGB S\n"); conto(o,f,w,v,X,Y,M,N, (0. ),-2*p,2*p); fprintf(o,".02 W .5 0 .5 RGB S\n"); for(m=-16;m<17;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".02 W 0 0 0 RGB S\n"); // fprintf(o,"0 setlinejoin 0 setlinecap\n"); // M(-10,0)L(0,0) fprintf(o,"1 1 1 RGB .02 W S\n"); //#include "plofu.cin"

DB angle; M(24,6) for(n=20;n<160;n++){ angle=M_PI/180. * (n-.5); x=5.+17*cos(angle); y=18*sin(angle); L(x,y)} L(-11,6) L(-11,0) fprintf(o,".2 W 1 .5 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (1. ),-2.,2.); fprintf(o,".08 W 1 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (2. ),-2.,2.); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (3. ),-2.,2.); fprintf(o,".08 W 1 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (4. ),-2.,2.); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (5. ),-2.,2.); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (6. ),-2.,2.); fprintf(o,".08 W 1 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (7. ),-2.,2.); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (8. ),-2.,2.); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (9. ),-2.,2.); fprintf(o,".08 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (10. ),-2.,2.); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (11. ),-2.,2.); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (12. ),-2.,2.); fprintf(o,".06 W 0 1 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (13. ),-2.,2.); fprintf(o,".02 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (14. ),-2.,2.); fprintf(o,".03 W 0 .5 1 RGB S\n"); conto(o,g,w,v,X,Y,M,N, (15. ),-2.,2.); fprintf(o,".06 W 0 0 1 RGB S\n"); //conto(o,g,w,v,X,Y,M,N, (15.4 ),-8.,8.); fprintf(o,".04 W 1 0 1 RGB S\n");

fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o); free(f); free(g); free(w); system("epstopdf sutrapag.eps"); system( "open sutrapag.pdf"); //for macintosh getchar; system("killall Preview"); // For macintosh }

Latex generator of labels
\documentclass[12pt]{article} \paperwidth 2190px \paperheight 1044px \textwidth 2394px \textheight 1300px \topmargin -94px \oddsidemargin -72px \usepackage{graphics} \usepackage{rotating} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \newcommand \rmi {\mathrm{i}} \begin{document} \parindent 0pt \sx{.5}{\begin{picture}(4408,1982) \put(0,0){\ing{sutrapag}} \put(44,1955){\sx{8}{$y$}} \put(04,1775){\sx{8}{$18$}} \put(04,1575){\sx{8}{$16$}} \put(04,1375){\sx{8}{$14$}} \put(04,1175){\sx{8}{$12$}} \put(04, 975){\sx{8}{$10$}} \put(040, 775){\sx{8}{$8$}} \put(040, 575){\sx{8}{$6$}} \put(040, 375){\sx{8}{$4$}} \put(040, 175){\sx{8}{$2$}} %\put(020, 80){\sx{8}{$1$}} \put(040, -25){\sx{8}{$0$}} \put(0108,-77){\sx{7}{$-18$}} \put(0308,-77){\sx{7}{$-16$}} \put(0508,-77){\sx{7}{$-14$}} \put(0708,-77){\sx{7}{$-12$}} \put(0908,-77){\sx{7}{$-10$}} \put(1140,-80){\sx{8}{$-8$}} \put(1340,-80){\sx{8}{$-6$}} \put(1540,-80){\sx{8}{$-4$}} \put(1740,-80){\sx{8}{$-2$}} \put(1992,-80){\sx{8}{$0$}} \put(2192,-80){\sx{8}{$2$}} \put(2392,-80){\sx{8}{4}} \put(2592,-80){\sx{8}{6}} \put(2792,-80){\sx{8}{8}} \put(2970,-80){\sx{8}{10}} \put(3170,-80){\sx{8}{12}} \put(3370,-80){\sx{8}{14}} \put(3570,-80){\sx{8}{16}} \put(3770,-80){\sx{8}{18}} \put(3970,-80){\sx{8}{20}} \put(4192,-80){\sx{8}{$x$}} \put(180,1860){\sx{16}{Range used for approximation of SuTra}} \put(400,1200){\sx{19}{$\mathcal A \!>\! 15$}} \put(2020,1520){\sx{18}{$\mathcal A \!=\!15$}} \put(2020,1250){\sx{18}{$\mathcal A \!=\!14$}} \put(2020,1040){\sx{18}{$\mathcal A \!=\!13$}} \put(2020,0840){\sx{18}{$\mathcal A \!=\!12$}} \put(2030,0488){\sx{16}{$\mathcal A \!=\!9$}} \end{picture}} \end{document}