File:AbelFactorialMap.png

 #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 complex<double> z_type;
 #define Re(x) x.real()
 #define Im(x) x.imag()
 #define I z_type(0.,1.)
 #include "fac.cin"
 //#include "sinc.cin"
 #include "facp.cin"
 #include "afacc.cin"
 #include "superfactorial.cin"
 #include "abelfac.cin"
 #include "conto.cin"

int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
   int M=403,M1=M+1;
   int N=401,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("AbelFacMap.eps","w");ado(o,402,402);
 fprintf(o,"201 201 translate\n 20 20 scale\n");
 DO(m,M1)X[m]=-8.04+.04*(m+.5);
// DO(m,M1){t=-1.+.022*m; X[m]=.2+t-1.11*exp(-1.9*t);}
 DO(n,N1)Y[n]=-8.04+.04*(n+.5);
// DO(n,N1){t=-8.04+.04*(n+.5); t*=.97; Y[n]=t-.25*sin(0.6127874523307*t);}

 for(m=-8;m<9;m++){if(m==0){M(m,-8.5)L(m,8.5)} else{M(m,-8)L(m,8)}}
 for(n=-8;n<9;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]=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);
 // c=afacc(z);
 // c=fac(z);
 // c=superfac(z);
        c=abelfac(z);
 // p=abs(c-d)/(abs(c)+abs(d)); p=-log(p)/log(10.)-1.;
        p=Re(c);q=Im(c);
        if(p>-20 && p<20 &&
 // (fabs(y)>.034 ||x>-.9 ||fabs(x-int(x))>1.e-3) &&
           q>-20 && q<20 && fabs(q)> 1.e-16
        )
        {g[m*N1+n]=p;f[m*N1+n]=q;}
                        }}
 //fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=1.8;q=.7;

 fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.4;q=.8;
 for(m=-5;m<5;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".01 W 0 .5 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,".01 W .8 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,".01 W 0 0 .8 RGB S\n");
 for(m=1;m<15;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".04 W .8 0 0 RGB S\n");
 for(m=1;m<15;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 .8 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (0. ),-9,9); fprintf(o,".04 W .5 0 .5 RGB S\n");
 for(m=-14;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 0 RGB S\n");
           m=0; conto(o,g,w,v,X,Y,M,N, (0.+m),-9,9); fprintf(o,".04 W 0 0 0 RGB S\n");
 for(m=1;m<17;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 0 RGB S\n");
 //#include"plofu.cin"
 // x=0.8856031944;
 // conto(o,g,w,v,X,Y,M,N,0.8856031944,-p,p); fprintf(o,".004 W .2 .2 0 RGB S\n");

 M(2,0)L(-8.1,0) fprintf(o,"0 setlinejoin 0 setlinecap .05 W 1 1 1 RGB S\n");
 DO(m,25){ M(2-.4*(m+.2),0)L(2-.4*(m+.4),0);} fprintf(o,".09 W 1 .4 0 RGB S\n");
 DO(m,25){ M(2-.4*(m+.7),0)L(2-.4*(m+.9),0);} fprintf(o,".09 W 0 .4 1 RGB S\n");
 //M(x,0)L(-8.1,0) fprintf(o,"[.19 .21]0 setdash .05 W 0 0 0 RGB S\n");
 // May it be, that, some printers do not interpret well the dashing ?

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

 \documentclass[12pt]{article}
 \usepackage{geometry}
 \usepackage{graphicx}
 \usepackage{rotating}
% \paperwidth 340pt
% \paperheight 336pt
 \paperwidth 680pt
 \paperheight 672pt
 %\topmargin -96pt
 %\oddsidemargin -98pt
 \topmargin -104pt
 \oddsidemargin -128pt
 \textwidth 1100pt
 \textheight 1100pt
 \pagestyle {empty}
 \newcommand \sx {\scalebox}
 \newcommand \rot {\begin{rotate}}
 \newcommand \ero {\end{rotate}}
 \newcommand \ing {\includegraphics}
 \parindent 0pt
 \pagestyle{empty}
 \begin{document}
 \sx{2}{ \begin{picture}(362,362)
 \put(0,0){\ing{AbelFacMap}}
 \put(30,357){\sx{1.3}{$y$}}
 \put(30,317){\sx{1.3}{$6$}}
 \put(30,277){\sx{1.3}{$4$}}
 \put(30,237){\sx{1.3}{$2$}}
 \put(29,196){\sx{1.3}{$0$}}
 \put(20,156){\sx{1.3}{$-2$}}
 \put(20,116){\sx{1.3}{$-4$}}
 \put(20,76){\sx{1.3}{$-6$}}
 \put(20,36){\sx{1.3}{$-8$}}
 \put(70,30){\sx{1.3}{$-6$}}
 \put(110,30){\sx{1.3}{$-4$}}
 \put(150,30){\sx{1.3}{$-2$}}
 \put(198,30){\sx{1.3}{$0$}}
 \put(238,30){\sx{1.3}{$2$}}
 \put(278,30){\sx{1.3}{$4$}}
 \put(318,30){\sx{1.3}{$6$}}
 \put(354,30){\sx{1.3}{$x$}}
\put(50,306){\sx{1.3}{$u\!=\!1.8$}}
\put(50,255){\sx{1.3}{$v\!=\!0.6$}}
\put(90,198){\sx{1.3}{\bf cut}} %central
\put(50,150){\sx{1.3}{$v\!=\!-0.6$}}
\put(48,90){\sx{1.3}{$u\!=\!1.8$}}
% column
\put(170,344){\sx{1.3}{$u\!=\!1.6$}}
%\put(250,314){\sx{1.3}{$u\!=\!1.2$}}
\put(119,230){\sx{1.3}{$v\!=\!0.8$}}
\put(109,170){\sx{1.3}{$v\!=\!-\!0.8$}}
\put(144,090){\sx{1.3}{$u\!=\!1.6$}}
\put(252,084){\sx{1.3}{$u\!=\!1.4$}}
% column<br>
\put(319,344){\sx{1.3}{$u\!=\!1.4$}}
\put(304,306){\sx{1.3}{$v\!=\!0.4$}}
\put(313,278){\sx{1.3}{$u\!=\!1.2$}}
\put(309,236){\sx{1.3}{$v\!=\!0.2$}}
%\put(266,247){\sx{1.}{$u\!=\!0.8856031944$}}
\put(306,209){\sx{1.3}{$u\!=\!1$}}
\put(331,198){\sx{1.3}{$v\!=\!0$}} %central
\put(312,118){\sx{1.3}{$u\!=\!1.2$}}
\put(304,90){\sx{1.3}{$v\!=\!-0.4$}}
\put(320, 50){\sx{1.3}{$u\!=\!1.4$}}
 \end{picture}
 }
 \end{document}