File:Ack4dFragment.jpg

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex>
#define z_type std::complex<double>
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
//#include "tet2f4c.cin"
#include "conto.cin"

#include "filog.cin"

//z_type b=z_type( 1.5259833851700000, 0.0178411853321000);
z_type b=10.;
z_type a=log(b);
z_type Zo=Filog(a);
z_type Zc=conj(Filog(conj(a)));
DB A=32.;

z_type f4ten(z_type z){ //NOT SHIFTED FOR x1 !!!!
#include "GLxw2048.inc"
z_type tenZo=z_type(-0.119193073414549, 0.750583293932439);
z_type tenZc=z_type(-0.119193073414549,-0.750583293932439);

DB Lten= 2.302585092994046;
z_type tenQ=z_type( 0.559580251215472, 1.728281903659204);// =L*Zo+log(L)
z_type tenT=z_type( 3.290552906607012, 1.065409768058325);
// #include "tenzo.inc"
       #include"f2048ten.inc"
       //Aten is defined there
        int j,k,m,n; DB x,y, u, t; z_type c,d, cu,cd;
// z_type E[K],G[K];
       z_type E[2048],G[2048];
       DO(k,K){c=F[k];E[k]=log(c)/Lten;G[k]=exp(c*Lten);}
// the initioalization abouve should run at the compillation
       c=0.;
       DO(k,K){t=Aten*GLx[k]; c+= GLw[k]*( G[k]/(z_type( 1.,t)-z) - E[k]/(z_type(-1.,t)-z) );}
       cu=.5-I/(2.*M_PI)*log( (z_type(1.,-Aten)+z)/(z_type(1., Aten)-z) );
       cd=.5-I/(2.*M_PI)*log( (z_type(1.,-Aten)-z)/(z_type(1., Aten)+z) );
       return c*(Aten/(2.*M_PI)) +tenZo*cu+tenZc*cd;
}
DB x1ten= 0.0377406857309657;
//#include "figx1ten.inc"
DB Lten=log(10.);
z_type F4TEN(z_type z){ DB x=Re(z);
// DB L=log(2.);
                       if(x<-.5) return log(F4TEN(z+1.))/Lten;
                       if(x> .5) return exp(F4TEN(z-1.)*Lten);
                       return f4ten(z+x1ten);
               }
// f4ten end


int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
//z_type Zo=z_type(.31813150520476413, 1.3372357014306895);
//z_type Zc=z_type(.31813150520476413,-1.3372357014306895);
 int M=641,M1=M+1;
 int N=402,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("tet2m2.eps","w");ado(o,1604,804);
// FILE *o;o=fopen("tettenm2.eps","w");ado(o,1604,804);
 FILE *o;o=fopen("amsfig4dFragmen.eps","w");ado(o,1604,804);
 fprintf(o,"802 402 translate\n 100 100 scale 2 setlinecap 1 setlinejoin\n");
 DO(m,M1)X[m]=-8.+.05*(m-.3);
 DO(n,200)Y[n]=-4.+.02*n;
         Y[200]=-.01;
         Y[201]= .01;
 for(n=202;n<N1;n++) Y[n]=-4.+.02*(n-1.);
 for(m=-8;m<9;m++){M(m,-4)L(m,4)}
 for(n=-4;n<5;n++){ M( -8,n)L(8,n)}
 fprintf(o,".008 W 0 0 0 RGB S\n");
 DO(m,M1)DO(n,N1){g[m*N1+n]=990999; f[m*N1+n]=909999;}

 DO(n,N1){y=Y[n];
          for(m=150;m<170;m++)
          {x=X[m]; //printf("%5.2f\n",x);
           z=z_type(x,y);
// c=tetb(z);
           c=F4TEN(z);
           p=Re(c);q=Im(c);
           if(p>-99999. && p<99999. && q>-99999. && q<99999. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
           d=c;
           for(k=1;k<31;k++)
                { m1=m+k*20; if(m1>M) break;
// d=exp(a*d);
                d=exp(d*log(10.));
                p=Re(d);q=Im(d);
                if(p>-99999. && p<99999. && q>-99999. && q<99999. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;}
                }
           d=c;
           for(k=1;k<31;k++)
                { m1=m-k*20; if(m1<0) break;
// d=log(d)/a;
                d=log(d)/log(10.);
                p=Re(d);q=Im(d);
                if(p>-99999. && p<99999. && q>-99999. && q<99999. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;}
                }
        }}

 fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=20;q=1;
 for(m=-4;m<4;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".004 W 0 .6 0 RGB S\n");
 for(m=0;m<4;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".004 W .9 0 0 RGB S\n");
 for(m=0;m<4;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".004 W 0 0 .9 RGB S\n");
 for(m=1;m<5;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<5;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,".03 W .6 0 .6 RGB S\n");
 for(m=-4;m<5;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n");
// y= 0; for(m=0;m<260;m+=6) {x=-2.-.1*m; M(x,y) L(x-.1,y)}
// fprintf(o,".07 W 1 .5 0 RGB S\n");
// y= 0; for(m=3;m<260;m+=6) {x=-2-.1*m; M(x,y) L(x-.1,y)}
// fprintf(o,".07 W 0 .5 1 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
//system( "ggv fig3.eps");
system("epstopdf amsfig4dFragmen.eps");
system( "open amsfig4dFragmen.pdf");
getchar(); system("killall Preview");
}

\documentclass{amsproc}
\usepackage{graphicx}
\usepackage{rotating}
\usepackage{hyperref}
\newcommand \sx {\scalebox}
\newcommand \rme {{\rm e}} %%
%\newcommand \rme {{e}} %%
\newcommand \rmi {{\rm i}} %%imaginary unity \newcommand \ds {\displaystyle}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing \includegraphics
\usepackage{geometry}
\topmargin -94pt
\oddsidemargin -70pt
\paperwidth 1666pt
\paperheight 856pt
\textwidth 1900px
\textheight 900px
\begin{document}
\parindent 0pt

\newcommand \mapax {
\put(18,820){\sx{5}{$y$}}
\put(18,730){\sx{5}{$3$}}
\put(18,630){\sx{5}{$2$}}
\put(18,530){\sx{5}{$1$}}
\put(18,430){\sx{5}{$0$}}
\put(-14,329){\sx{5}{$-1$}}
\put(-14,229){\sx{5}{$-2$}}
\put(-14,129){\sx{5}{$-3$}}
\put(-14, 29){\sx{5}{$-4$}}
\put(14, 0){\sx{5}{$-8$}}
\put(114, 0){\sx{5}{$-7$}}
\put(214, 0){\sx{5}{$-6$}}
\put(314, 0){\sx{5}{$-5$}}
\put(414, 0){\sx{5}{$-4$}}
\put(514, 0){\sx{5}{$-3$}}
\put(614, 0){\sx{5}{$-2$}}
\put(714, 0){\sx{5}{$-1$}}
\put(844, 0){\sx{5}{$0$}}
\put(944, 0){\sx{5}{$1$}}
\put(1044, 0){\sx{5}{$2$}}
\put(1144, 0){\sx{5}{$3$}}
\put(1244, 0){\sx{5}{$4$}}
\put(1344, 0){\sx{5}{$5$}}
\put(1444, 0){\sx{5}{$6$}}
\put(1544, 0){\sx{5}{$7$}}
\put(1634, 0){\sx{5}{$x$}}
}
%\flushright{$b=\mathrm e \approx 2.71$}

{\begin{picture}(1620,850) %%%
\put(50,40){\ing{amsfig4dFragmen}} \mapax
\put(114,660){\sx{8}{$b=10$}}
\put(60,434){\sx{4}{\bf cut}}
\multiput(128,460)(330.2,108){4}{\sx{4}{$v\!=\!0.8$}}
\multiput(120,402)(330.2,-108){4}{\sx{4}{$v\!=\!-0.8$}}
\multiput(374,390)(330.2,-108){4}{\sx{4}{$u\!=\!0$}}

\put(80,796){\sx{4}{$u+\mathrm i v \approx -0.11919307341+ 0.75058329393 \,\mathrm i$}}
\put(80,90){\sx{4}{$u+\mathrm i v \approx -0.11919307341- 0.75058329393 \,\mathrm i$}}
\end{picture}}
\end{document}