Difference between revisions of "File:Adpow2map.jpg"

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[[Complex map]] of function [[AdPow]]$_2$:
−
Importing image file
  
  +
  +
$u\!+\!\mathrm i v=\mathrm{AdPow}_2(x\!+\!\mathrm i y)$
  +
  +
where $~\mathrm{AdPow}_2(z)=\ln(\ln(1./z))/\ln(a)$
  +
  +
==[[C++]] generator of map==
  +
File [[conto.cin]] should be loaded in order to compile the code below.
  +
<poem><nomathjax><nowiki>
  +
#include <math.h>
  +
#include <stdio.h>
  +
#include <stdlib.h>
  +
#define DB double
  +
#define DO(x,y) for(x=0;x<y;x++)
  +
#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"
  +
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  +
int M=502,M1=M+1;
  +
int N=502,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("adpower2ma.eps","w");ado(o,1020,1020);
  +
fprintf(o,"510 510 translate\n 100 100 scale\n");
  +
DO(m,M1) X[m]=-5.+.02*(m-.5);
  +
for(n=0;n<250;n++) Y[n]=-5.+.02*(n);
  +
Y[250]=-.006;
  +
Y[251]= .006;
  +
for(n=252;n<N1;n++)Y[n]=-5.+.02*(n-1);
  +
//DO(m,M1) X[m]=Y[m];
  +
  +
for(m=-5;m<6;m++){if(m==0){M(m,-5.1)L(m,5.1)} else{M(m,-5)L(m,5)}}
  +
for(n=-5;n<6;n++){ M( -5,n)L(5,n)}
  +
fprintf(o,".01 W 0 0 0 RGB S\n");
  +
DO(m,M1)DO(n,N1){g[m*N1+n]=999999; f[m*N1+n]=999999;}
  +
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
  +
DO(n,N1){y=Y[n]; z=z_type(x,y);
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// c=exp(pow(2.,z));
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c=log(log(1./z))/log(2.);
  +
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 1 setlinecap\n"); p=1;q=.5;
  +
for(m=-11;m<11;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".013 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,".012 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,".012 W 0 0 .9 RGB S\n");
  +
for(m=1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".028 W .9 0 0 RGB S\n");
  +
for(m=1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".028 W 0 0 .9 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".028 W .6 0 .6 RGB S\n");
  +
for(m=-10;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".024 W 0 0 0 RGB S\n");
  +
m=0; conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".024 W 0 0 0 RGB S\n");
  +
for(m=1;m<11;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".024 W 0 0 0 RGB S\n");
  +
  +
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  +
system("epstopdf adpower2ma.eps");
  +
system( "open adpower2ma.pdf");
  +
getchar(); system("killall Preview");//for mac
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of labels==
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt]{article}
  +
\usepackage{graphicx}
  +
\usepackage{geometry}
  +
\usepackage{rotating}
  +
\paperwidth 1044px
  +
\paperheight 1036px
  +
\topmargin -98px
  +
\oddsidemargin -90px
  +
\textwidth 2000px
  +
\textheight 2000px
  +
\newcommand \ing {\includegraphics}
  +
\newcommand \sx {\scalebox}
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\begin{document}
  +
\begin{picture}(1030,1026) \normalsize
  +
\put(30,20){\ing{"adpower2ma"}}
  +
\put(16,1016){\sx{3}{$y$}}
  +
\put(16,918){\sx{3}{$4$}}
  +
\put(16,818){\sx{3}{$3$}}
  +
\put(16,718){\sx{3}{$2$}}
  +
\put(16,618){\sx{3}{$1$}}
  +
\put(16,518){\sx{3}{$0$}}
  +
\put(-10,418){\sx{3}{$-1$}}
  +
\put(-10,318){\sx{3}{$-2$}}
  +
\put(-10,218){\sx{3}{$-3$}}
  +
\put(-10,118){\sx{3}{$-4$}}
  +
\put(-10,18){\sx{3}{$-5$}}
  +
\put(10,-1){\sx{3}{$-5$}}
  +
\put(110,-1){\sx{3}{$-4$}}
  +
\put(210,-1){\sx{3}{$-3$}}
  +
\put(310,-1){\sx{3}{$-2$}}
  +
\put(410,-1){\sx{3}{$-1$}}
  +
\put(534,-1){\sx{3}{$0$}}
  +
\put(634,-1){\sx{3}{$1$}}
  +
\put(734,-1){\sx{3}{$2$}}
  +
\put(834,-1){\sx{3}{$3$}}
  +
\put(934,-1){\sx{3}{$4$}}
  +
\put(1028,-1){\sx{3.1}{$x$}}
  +
\put(150,522){\rot{0}{ \sx{3}{\bf cut}} \ero}
  +
%\put(150,68){\rot{0.}{ \sx{3}{$v\!=\!0$}} \ero}
  +
%\put(790,522){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}
  +
\put(246,422){\rot{34}{ \sx{3}{$u\!=\!1.6$}} \ero}
  +
\put(332,344){\rot{54}{ \sx{3}{$u\!=\!1.4$}} \ero}%%
  +
\put(295,900){\rot{84}{ \sx{3}{$u\!=\!1.4$}} \ero}%
  +
\put(430,882){\rot{63}{ \sx{3}{$u\!=\!1.2$}} \ero}
  +
\put(526,845){\rot{50}{ \sx{3}{$u\!=\!1$}} \ero}
  +
\put(490,662){\rot{-5}{ \sx{3}{$v\!=\!2$}} \ero}%%
  +
\put(750,742){\rot{89}{ \sx{3}{$v\!=\!-3.6$}} \ero}
  +
\put(816,740){\rot{74}{ \sx{3}{$v\!=\!-3.8$}} \ero}
  +
\put(866,698){\rot{53}{ \sx{3}{$v\!=\!-4$}} \ero}
  +
\put(900,636){\rot{32}{ \sx{3}{$v\!=\!-4.2$}} \ero}
  +
\put(914,570){\rot{13}{ \sx{3}{$v\!=\!-4.4$}} \ero}%
  +
\put(916,478){\rot{-14}{ \sx{3}{$v\!=\!4.4$}} \ero}%
  +
\put(550,523){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}
  +
\put(950,523){\rot{0}{ \sx{3}{\bf cut}} \ero}
  +
\put(540,500){\rot{-1}{ \sx{3}{$v\!=\!1$}} \ero}
  +
\put(510,450){\rot{-1}{ \sx{3}{$v\!=\!2$}} \ero}
  +
\put(170,740){\rot{23}{ \sx{3}{$v\!=\!-3$}} \ero}%
  +
\put(520,270){\rot{30}{ \sx{3}{$v\!=\!3$}} \ero}
  +
%\put(136,100){\rot{-2}{ \sx{3}{$v\!=\!3.2$}} \ero}%
  +
\put(298,100){\rot{9}{ \sx{3}{$v\!=\!3.2$}} \ero}%
  +
\put(970,196){\rot{-62}{ \sx{3}{$v\!=\!4$}} \ero}
  +
%
  +
\put(746,432){\rot{65}{ \sx{3}{$u\!=\!-0.2$}} \ero}
  +
\put(778,420){\rot{57}{ \sx{3}{$u\!=\!0$}} \ero}
  +
\put(800,390){\rot{51}{ \sx{3}{$u\!=\!0.2$}} \ero}
  +
\put(846,358){\rot{50}{ \sx{3}{$u\!=\!0.4$}} \ero}
  +
\put(902,308){\rot{47}{ \sx{3}{$u\!=\!0.6$}} \ero}
  +
\put(965,227){\rot{41}{ \sx{3}{$u\!=\!0.8$}} \ero}
  +
%
  +
\put(948,62){\rot{19}{ \sx{3}{$u\!=\!1$}} \ero}
  +
\end{picture}
  +
\end{document}
  +
</nowiki></nomathjax></poem>
  +
  +
==References==
  +
<references/>
  +
  +
[[Category:AdPow]]
  +
[[Category:Abel function]]
  +
[[Category:Abelpower]]
  +
[[Category:AdPow]]
  +
[[Category:Book]]
  +
[[Category:BookMap]]
  +
[[Category:Complex map]]
  +
[[Category:Superfunctions]]

Latest revision as of 08:29, 1 December 2018

Complex map of function AdPow$_2$:

$u\!+\!\mathrm i v=\mathrm{AdPow}_2(x\!+\!\mathrm i y)$

where $~\mathrm{AdPow}_2(z)=\ln(\ln(1./z))/\ln(a)$

C++ generator of map

File conto.cin should be loaded in order to compile the code below.


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#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"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=502,M1=M+1;
int N=502,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("adpower2ma.eps","w");ado(o,1020,1020);
fprintf(o,"510 510 translate\n 100 100 scale\n");
DO(m,M1) X[m]=-5.+.02*(m-.5);
for(n=0;n<250;n++) Y[n]=-5.+.02*(n);
Y[250]=-.006;
Y[251]= .006;
for(n=252;n<N1;n++)Y[n]=-5.+.02*(n-1);
//DO(m,M1) X[m]=Y[m];

for(m=-5;m<6;m++){if(m==0){M(m,-5.1)L(m,5.1)} else{M(m,-5)L(m,5)}}
for(n=-5;n<6;n++){ M( -5,n)L(5,n)}
fprintf(o,".01 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=999999; f[m*N1+n]=999999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
// c=exp(pow(2.,z));
       c=log(log(1./z))/log(2.);
      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 1 setlinecap\n"); p=1;q=.5;
for(m=-11;m<11;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".013 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,".012 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,".012 W 0 0 .9 RGB S\n");
for(m=1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".028 W .9 0 0 RGB S\n");
for(m=1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".028 W 0 0 .9 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".028 W .6 0 .6 RGB S\n");
for(m=-10;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".024 W 0 0 0 RGB S\n");
             m=0; conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".024 W 0 0 0 RGB S\n");
for(m=1;m<11;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".024 W 0 0 0 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf adpower2ma.eps");
      system( "open adpower2ma.pdf");
      getchar(); system("killall Preview");//for mac
}

Latex generator of labels


\documentclass[12pt]{article}
\usepackage{graphicx}
\usepackage{geometry}
\usepackage{rotating}
\paperwidth 1044px
\paperheight 1036px
\topmargin -98px
\oddsidemargin -90px
\textwidth 2000px
\textheight 2000px
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\begin{document}
\begin{picture}(1030,1026) \normalsize
\put(30,20){\ing{"adpower2ma"}}
\put(16,1016){\sx{3}{$y$}}
\put(16,918){\sx{3}{$4$}}
\put(16,818){\sx{3}{$3$}}
\put(16,718){\sx{3}{$2$}}
\put(16,618){\sx{3}{$1$}}
\put(16,518){\sx{3}{$0$}}
\put(-10,418){\sx{3}{$-1$}}
\put(-10,318){\sx{3}{$-2$}}
\put(-10,218){\sx{3}{$-3$}}
\put(-10,118){\sx{3}{$-4$}}
\put(-10,18){\sx{3}{$-5$}}
\put(10,-1){\sx{3}{$-5$}}
\put(110,-1){\sx{3}{$-4$}}
\put(210,-1){\sx{3}{$-3$}}
\put(310,-1){\sx{3}{$-2$}}
\put(410,-1){\sx{3}{$-1$}}
\put(534,-1){\sx{3}{$0$}}
\put(634,-1){\sx{3}{$1$}}
\put(734,-1){\sx{3}{$2$}}
\put(834,-1){\sx{3}{$3$}}
\put(934,-1){\sx{3}{$4$}}
\put(1028,-1){\sx{3.1}{$x$}}
\put(150,522){\rot{0}{ \sx{3}{\bf cut}} \ero}
%\put(150,68){\rot{0.}{ \sx{3}{$v\!=\!0$}} \ero}
%\put(790,522){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}
\put(246,422){\rot{34}{ \sx{3}{$u\!=\!1.6$}} \ero}
\put(332,344){\rot{54}{ \sx{3}{$u\!=\!1.4$}} \ero}%%
\put(295,900){\rot{84}{ \sx{3}{$u\!=\!1.4$}} \ero}%
\put(430,882){\rot{63}{ \sx{3}{$u\!=\!1.2$}} \ero}
\put(526,845){\rot{50}{ \sx{3}{$u\!=\!1$}} \ero}
\put(490,662){\rot{-5}{ \sx{3}{$v\!=\!2$}} \ero}%%
\put(750,742){\rot{89}{ \sx{3}{$v\!=\!-3.6$}} \ero}
\put(816,740){\rot{74}{ \sx{3}{$v\!=\!-3.8$}} \ero}
\put(866,698){\rot{53}{ \sx{3}{$v\!=\!-4$}} \ero}
\put(900,636){\rot{32}{ \sx{3}{$v\!=\!-4.2$}} \ero}
\put(914,570){\rot{13}{ \sx{3}{$v\!=\!-4.4$}} \ero}%
\put(916,478){\rot{-14}{ \sx{3}{$v\!=\!4.4$}} \ero}%
\put(550,523){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}
\put(950,523){\rot{0}{ \sx{3}{\bf cut}} \ero}
\put(540,500){\rot{-1}{ \sx{3}{$v\!=\!1$}} \ero}
\put(510,450){\rot{-1}{ \sx{3}{$v\!=\!2$}} \ero}
\put(170,740){\rot{23}{ \sx{3}{$v\!=\!-3$}} \ero}%
\put(520,270){\rot{30}{ \sx{3}{$v\!=\!3$}} \ero}
%\put(136,100){\rot{-2}{ \sx{3}{$v\!=\!3.2$}} \ero}%
\put(298,100){\rot{9}{ \sx{3}{$v\!=\!3.2$}} \ero}%
\put(970,196){\rot{-62}{ \sx{3}{$v\!=\!4$}} \ero}
%
\put(746,432){\rot{65}{ \sx{3}{$u\!=\!-0.2$}} \ero}
\put(778,420){\rot{57}{ \sx{3}{$u\!=\!0$}} \ero}
\put(800,390){\rot{51}{ \sx{3}{$u\!=\!0.2$}} \ero}
\put(846,358){\rot{50}{ \sx{3}{$u\!=\!0.4$}} \ero}
\put(902,308){\rot{47}{ \sx{3}{$u\!=\!0.6$}} \ero}
\put(965,227){\rot{41}{ \sx{3}{$u\!=\!0.8$}} \ero}
%
\put(948,62){\rot{19}{ \sx{3}{$u\!=\!1$}} \ero}
\end{picture}
\end{document}

References

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