Difference between revisions of "File:AbelFactorialMap.png"

Latest revision as of 08:28, 1 December 2018

Function $f=\mathrm{AbelFactorial}(x+\mathrm i y)$ is shown with lines

$\Re(f)\!=$const anf lines $\Im(f)\!=$ const

C++ Generator of curves

The original generator is misplaced, but the code below does very similar figure

Files fac.cin, facp.cin, afacc.cin, superfactorial.cin, abelfac.cin, conto.cin should be loaded to the working directory un order to compile the C++ code below.

#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
}

Latex Generator of labels

The original generator is misplaced, but the code below does very similar figure

\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}

References

File history

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	17:50, 20 June 2013		675 × 673 (120 KB)	Maintenance script (talk \| contribs)	Importing image file

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