File:Olga6map.jpg

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
//using namespace std;
#include <complex>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
z_type ArcTania(z_type z) {return z + log(z) - 1. ;}
z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
z_type TaniaTay(z_type z) { int n; z_type s;
s=1.+z*(.5+z*(1./16.+z*(-1./192.+z*(-1./3072.+z*(1.3/6144.+z*(-4.7/147456.
//+z*(7.3/4128768.) //some reserve term
)))))); DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
z_type TaniaNega(z_type z){int n;z_type s=exp(z-exp(z)+1.);
DO(n,4) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
z_type TaniaBig(z_type z){int n;z_type s=z; s=z-log(s)+1.;
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
z_type TaniaS(z_type z){int n; z_type s,t=z+z_type(2.,-M_PI);t*=2./9.; t=I*sqrt(t);
s=-1.+t*(3.+t*(-3.+t*(.75+t*(.3+t*(.9/16.+t*(-.3/7.+t*(-12.51/224. //+t*(-.9/28.)
)))))));
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
z_type Tania(z_type z){ z_type t;
if( fabs(Im(z))< M_PI && Re(z)<-2.51) return TaniaNega(z);
if( abs(z)>7. || Re(z)>3.8 ) return TaniaBig(z);
if( Im(z) > .7 ) return TaniaS(z);
if( Im(z) < -.7) return conj(TaniaS(conj(z)));
return TaniaTay(z);
}

int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
 int M=401,M1=M+1;
 int N=603,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
// FILE *o;o=fopen("taniacontour.eps","w");ado(o,1620,1620);
//FILE *o;o=fopen("13.eps","w");ado(o,1620,1620);
FILE *o;o=fopen("olga6ma.eps","w");ado(o,1220,1220);
fprintf(o,"610 610 translate\n 100 100 scale\n");
DO(m,M1) X[m]=-6.+.03*(m);
DO(n,300)Y[n]=-6.+.02*n;
        Y[300]=-.012;
        Y[301]=-.006;
        Y[302]= .006;
        Y[303]= .012;
for(n=304;n<N1;n++) Y[n]=-6.+.02*(n-3.);
for(m=-6;m<7;m++){if(m==0){M(m,-6.1)L(m,6.1)} else{M(m,-6)L(m,6)}}
for(n=-6;n<7;n++){ M( -6,n)L(6,n)}
fprintf(o,".008 W 0 0 0 RGB 2 setlinecap S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y); // z*=.1;
 c=Tania(log(z)); p=Re(c);q=Im(c);
 if(p>-99. && p<99. && q>-99. && q<99. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
        }}
fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=.6;q=.5;
for(m=-10;m<10;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".009 W 0 .6 0 RGB S\n");
for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".009 W .9 0 0 RGB S\n");
for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".009 W 0 0 .9 RGB S\n");
for(m=1;m<10;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".03 W .9 0 0 RGB S\n");
for(m=1;m<10;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 .9 RGB S\n");
                   conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".01 W .6 0 .6 RGB S\n");
for(m=-9;m<10;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");


// M(-10.*exp(-2.),0)L(-8,0)
M(-exp(-2.),0)L(-8,0)
fprintf(o,"0 setlinecap .01 W 1 1 1 RGB S\n");

y= 0; for(m=1;m<80;m+=4) {x=-.1353352832366127-.1*m; M(x,y) L(x-.08,y)}
fprintf(o,".05 W 1 .5 0 RGB S\n");
y= 0; for(m=3;m<80;m+=4) {x=-.1353352832366127-.1*m; M(x,y) L(x-.08,y)}
fprintf(o,".05 W 0 .5 1 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
       system("epstopdf olga6ma.eps");
       system( "open olga6ma.pdf");
       getchar(); system("killall Preview");
}

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\paperwidth 1268px
\paperheight 1260px
\textwidth 1794px
\textheight 1700px
\topmargin -98px
\oddsidemargin -70px
\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
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%\put(40,20){\ing{suzexD1map}}
%\put(40,20){\ing{ZexD6map}}
\put(50,20){\ing{olga6ma}}
\put(14,1204){\sx{6}{$y$}}
\put(18,1116){\sx{5}{$5$}}
\put(18,1016){\sx{5}{$4$}}
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\put(-22, 516){\sx{5}{$-1$}}
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\put( 18, -20){\sx{5}{$-6$}}
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\put(750, -20){\sx{5}{$1$}}
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\put(950, -20){\sx{5}{$3$}}
\put(1050, -20){\sx{5}{$4$}}
\put(1150, -20){\sx{5}{$5$}}
\put(1234, -20){\sx{6}{$x$}}
\put(170, 616){\sx{6}{\bf cut}}
\put(1060, 614){\sx{6}{$v\!=\!0$}}
\put(710, 1086){\sx{6}{\rot{75}$v\!=\!1$\ero}}
\put(660, 222){\sx{6}{\rot{-77}$v\!=\!-1$\ero}}
\put(86,790){\sx{6}{\rot{-29}$v\!=\!2$\ero}}
\put(100, 438){\sx{6}{\rot{28}$v\!=\!-2$\ero}}
%
\put(78, 1050){\sx{6}{\rot{37}$u\!=\!2$\ero}}
\put(460, 668){\sx{6}{\rot{38}$u\!=\!1$\ero}}

\end{picture}}
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