Difference between revisions of "File:Aunemplot.jpg"

From TORI
Jump to: navigation, search
(Importing image file)
 
 
Line 1: Line 1:
  +
Explicit plot of function [[AuNem]]:
−
Importing image file
  
  +
  +
$y=\mathrm{AuNem}_q(x)$
  +
  +
for
  +
$q\!=\!0$,
  +
$q\!=\!1$ and
  +
$q\!=\!2$.
  +
  +
==References==
  +
<references/>
  +
  +
==[[C++]] generator of curves==
  +
  +
Files
  +
[[ado.cin]],
  +
[[conto.cin]],
  +
[[nembran.cin]],
  +
[[arqnem.cin]],
  +
[[sunema.txt]],
  +
[[aunemco.txt]]
  +
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++)
  +
//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"
  +
  +
DB Q=1.e-6;
  +
z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); }
  +
z_type nem1(z_type z){ return 1.+z*z*(3.+z*(4.*Q)); } // WARNING: Q is global!
  +
  +
DB K=Q*Q;
  +
DB A[37][19];
  +
int co(){
  +
#include "sunema.txt"
  +
return 0;}
  +
  +
z_type sun(z_type z){ z_type p[37],s; int m,M,n,N;
  +
z_type L=log(-z);
  +
z_type t=1./sqrt(-2.*z);
  +
M=36;
  +
for(m=2;m<M+1;m++){ N=m/2; s=A[m][N]*L; for(n=N-1;n>0;n--) { s+=A[m][n]; s*=L; }
  +
p[m]=A[m][0]+s;
  +
}
  +
s=p[M]*t; for(m=M-1; m>1;m--) { s+=p[m]; s*=t;}
  +
return t*( 1. + t* (-Q + s) );
  +
}
  +
  +
z_type sune(z_type z){ int m,n; DB x,y; z_type s;
  +
DB R=20.+20.*Q*Q;
  +
x=Re(z); if(x<-R) return sun(z);
  +
y=Im(z); if(fabs(y)>R) return sun(z);
  +
n=int(x+R);
  +
s=sun(z-(0.+n));
  +
DO(m,n) s=nem(s);
  +
return s;
  +
}
  +
  +
DB AUNE1=0;
  +
  +
z_type sunem(z_type z){ int m,n; DB x,y; z_type s;
  +
DB R=20.+20.*Q*Q;
  +
x=Re(z); if(x<-R) return sun(z);
  +
y=Im(z); if(fabs(y)>R) return sun(z);
  +
n=int(x+R);
  +
s=sun(z-(n-AUNE1));
  +
DO(m,n) s=nem(s);
  +
return s;
  +
}
  +
  +
// z_type sunem(z_type z)( return sine(AUNE1+z));)
  +
  +
#include"nembran.cin"
  +
z_type NemZo=nembra(Q);
  +
z_type ANemZo=nem(NemZo);
  +
DB tr=Re(ANemZo);
  +
DB ti=Im(ANemZo);
  +
  +
#include "arqnem.cin"
  +
  +
DB C[41];
  +
//DB K=Q*Q;
  +
int coa(){ //C[1]=(0.5 - K)*Q; C[2]=-0.625 + (-0.25 + K/2.)*K; ..
  +
#include "aunemco.txt"
  +
return 40;
  +
}
  +
  +
z_type aune0(z_type z){ z_type s; int n;
  +
s=C[40]*z; for(n=39;n>0;n--){s+=C[n];s*=z;}
  +
return (-.5/z+Q)/z + (1.5+K)*log(z) + (.5*K + (.75+.5*K)*log(2.)) + s ;
  +
}
  +
  +
//DB AUNE1=0;
  +
  +
z_type aune1(z_type z){ int n, N=20; DO(n,N) z=arqnem(z);
  +
return aune0(z)+(0.+n);}
  +
  +
z_type aunem(z_type z){ int n, N=20; DO(n,N) z=arqnem(z);
  +
return aune0(z)+(n-AUNE1);}
  +
  +
  +
z_type aune02(z_type z){ z_type s; int n; s=(C[2]*z+C[1])*z;
  +
return (-.5/z+Q)/z + (1.5+K)*log(z) + (.5*K + (.75+.5*K)*log(2.)) + s ; }
  +
z_type aune01(z_type z){ z_type s; int n; s=C[1]*z;
  +
return (-.5/z+Q)/z + (1.5+K)*log(z) + (.5*K + (.75+.5*K)*log(2.)) +s ; }
  +
  +
int main(){ int Max; int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  +
  +
FILE *o;o=fopen("aunemplo.eps","w");ado(o,4008,4008);
  +
fprintf(o,"4 2004 translate\n 1000 1000 scale 2 setlinecap\n");
  +
for(m=0;m<40;m+=10){ M(.1*m,-2)L(.1*m,2)}
  +
for(n=-20;n<21;n+=10){ M(0,.1*n)L(4,.1*n)}
  +
fprintf(o,".003 W 0 0 0 RGB 2 setlinecap S\n");
  +
  +
// M(-1,ti)L(1,ti) M(-1,-ti)L(1,-ti) M(tr,-1)L(tr,1) fprintf(o,".002 W 0 0 0 RGB 2 setlinecap S\n");
  +
//M(-1,0) L(0,0) M(tr,ti)L(0,0)L(tr,-ti)
  +
//fprintf(o,".006 W 1 1 0 RGB 0 setlinecap S\n");
  +
  +
  +
Q=1.e-6; K=Q*Q; NemZo=nembra(Q); ANemZo=nem(NemZo); tr=Re(ANemZo); ti=Im(ANemZo); co(); coa(); AUNE1=Re(aune1(1.));
  +
DO(n,401){ y=-2.+.01*n; x=Re(sunem(y)); if(n==0) M(x,y) else L(x,y); if(x> 4) break; } fprintf(o,".03 W 1 0 .3 RGB S\n");
  +
DO(m,400){ x= 4.-.01*m; y=Re(aunem(x)); if(m==0) M(x,y) else L(x,y); if(y<-2) break; } fprintf(o,".01 W 0 0 0 RGB S\n");
  +
  +
  +
Q=1.; K=Q*Q; NemZo=nembra(Q); ANemZo=nem(NemZo); tr=Re(ANemZo); ti=Im(ANemZo); co(); coa(); AUNE1=Re(aune1(1.));
  +
DO(n,401){ y=-2.+.01*n; x=Re(sunem(y)); if(n==0) M(x,y) else L(x,y); if(x> 4) break; } fprintf(o,".03 W 0 1 0 RGB S\n");
  +
DO(m,400){ x= 4.-.01*m; y=Re(aunem(x)); if(m==0) M(x,y) else L(x,y); if(y<-2) break; } fprintf(o,".01 W 0 0 0 RGB S\n");
  +
  +
Q=2.; K=Q*Q; NemZo=nembra(Q); ANemZo=nem(NemZo); tr=Re(ANemZo); ti=Im(ANemZo); co(); coa(); AUNE1=Re(aune1(1.));
  +
DO(n,401){ y=-2.+.01*n; x=Re(sunem(y)); if(n==0) M(x,y) else L(x,y); if(x> 4)break; } fprintf(o,".03 W .3 0 1 RGB S\n");
  +
DO(m,400){ x= 4.-.01*m; y=Re(aunem(x)); if(m==0) M(x,y) else L(x,y); if(y<-2)break; } fprintf(o,".01 W 0 0 0 RGB S\n");
  +
  +
fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
  +
system("epstopdf aunemplo.eps");
  +
system( "open aunemplo.pdf"); //mac
  +
return 0;}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of labels==
  +
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt]{article}
  +
\usepackage{graphics}
  +
\paperwidth 4010pt
  +
\paperheight 4010pt
  +
\usepackage{geometry}
  +
\usepackage{rotating}
  +
\textwidth 4400pt
  +
\textheight 4400pt
  +
\topmargin -97pt
  +
\oddsidemargin -74pt
  +
\parindent 0pt
  +
\pagestyle{empty}
  +
\newcommand \ing {\includegraphics}
  +
\newcommand \sx {\scalebox}
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\begin{document}
  +
\begin{picture}(4008,4008)
  +
\put(20,3840){\sx{20}{$y\!=\!\mathrm{AuNem}_q(x)$}}
  +
\put(100,2944){\sx{20}{$1$}}
  +
\put(100,1940){\sx{20}{$0$}}
  +
\put(10, 936){\sx{20}{$-1$}}
  +
\put( 946,2040){\sx{20}{$1$}}
  +
\put(1950,2040){\sx{20}{$2$}}
  +
\put(2954,2040){\sx{20}{$3$}}
  +
\put(3870,2040){\sx{20}{$x$}}
  +
%
  +
\put(0,0){\ing{aunemplo}}
  +
%
  +
\put(3300,3500){\sx{18}{\rot{7} $q\!=\!0$\ero}}
  +
\put(3300,3120){\sx{18}{\rot{7} $q\!=\!1$\ero}}
  +
\put(3300,2770){\sx{18}{\rot{6} $q\!=\!2$\ero}}
  +
\end{picture}
  +
\end{document}
  +
</nowiki></nomathjax></poem>
  +
  +
  +
  +
[[Category:Abel function]]
  +
[[Category:AuNem]]
  +
[[Category:Book]]
  +
[[Category:BookPlot]]
  +
[[Category:C++]]
  +
[[Category:Explicit plot]]
  +
[[Category:Latex]]
  +
[[Category:Nemtsov function]]
  +
[[Category:Superfunctions]]

Latest revision as of 08:30, 1 December 2018

Explicit plot of function AuNem:

$y=\mathrm{AuNem}_q(x)$

for $q\!=\!0$, $q\!=\!1$ and $q\!=\!2$.

References


C++ generator of curves

Files ado.cin, conto.cin, nembran.cin, arqnem.cin, sunema.txt, aunemco.txt 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++)
//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"

DB Q=1.e-6;
z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); }
z_type nem1(z_type z){ return 1.+z*z*(3.+z*(4.*Q)); } // WARNING: Q is global!

DB K=Q*Q;
DB A[37][19];
int co(){
#include "sunema.txt"
return 0;}

z_type sun(z_type z){ z_type p[37],s; int m,M,n,N;
z_type L=log(-z);
z_type t=1./sqrt(-2.*z);
M=36;
for(m=2;m<M+1;m++){ N=m/2; s=A[m][N]*L; for(n=N-1;n>0;n--) { s+=A[m][n]; s*=L; }
                p[m]=A[m][0]+s;
                }
s=p[M]*t; for(m=M-1; m>1;m--) { s+=p[m]; s*=t;}
        return t*( 1. + t* (-Q + s) );
}

z_type sune(z_type z){ int m,n; DB x,y; z_type s;
DB R=20.+20.*Q*Q;
x=Re(z); if(x<-R) return sun(z);
y=Im(z); if(fabs(y)>R) return sun(z);
n=int(x+R);
s=sun(z-(0.+n));
DO(m,n) s=nem(s);
return s;
}

DB AUNE1=0;

z_type sunem(z_type z){ int m,n; DB x,y; z_type s;
DB R=20.+20.*Q*Q;
x=Re(z); if(x<-R) return sun(z);
y=Im(z); if(fabs(y)>R) return sun(z);
n=int(x+R);
s=sun(z-(n-AUNE1));
DO(m,n) s=nem(s);
return s;
}

// z_type sunem(z_type z)( return sine(AUNE1+z));)

#include"nembran.cin"
z_type NemZo=nembra(Q);
z_type ANemZo=nem(NemZo);
DB tr=Re(ANemZo);
DB ti=Im(ANemZo);

#include "arqnem.cin"

DB C[41];
//DB K=Q*Q;
int coa(){ //C[1]=(0.5 - K)*Q; C[2]=-0.625 + (-0.25 + K/2.)*K; ..
#include "aunemco.txt"
return 40;
}

z_type aune0(z_type z){ z_type s; int n;
s=C[40]*z; for(n=39;n>0;n--){s+=C[n];s*=z;}
return (-.5/z+Q)/z + (1.5+K)*log(z) + (.5*K + (.75+.5*K)*log(2.)) + s ;
}

//DB AUNE1=0;

z_type aune1(z_type z){ int n, N=20; DO(n,N) z=arqnem(z);
return aune0(z)+(0.+n);}

z_type aunem(z_type z){ int n, N=20; DO(n,N) z=arqnem(z);
return aune0(z)+(n-AUNE1);}


z_type aune02(z_type z){ z_type s; int n; s=(C[2]*z+C[1])*z;
                return (-.5/z+Q)/z + (1.5+K)*log(z) + (.5*K + (.75+.5*K)*log(2.)) + s ; }
z_type aune01(z_type z){ z_type s; int n; s=C[1]*z;
                return (-.5/z+Q)/z + (1.5+K)*log(z) + (.5*K + (.75+.5*K)*log(2.)) +s ; }

int main(){ int Max; int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;

FILE *o;o=fopen("aunemplo.eps","w");ado(o,4008,4008);
fprintf(o,"4 2004 translate\n 1000 1000 scale 2 setlinecap\n");
for(m=0;m<40;m+=10){ M(.1*m,-2)L(.1*m,2)}
for(n=-20;n<21;n+=10){ M(0,.1*n)L(4,.1*n)}
fprintf(o,".003 W 0 0 0 RGB 2 setlinecap S\n");

// M(-1,ti)L(1,ti) M(-1,-ti)L(1,-ti) M(tr,-1)L(tr,1) fprintf(o,".002 W 0 0 0 RGB 2 setlinecap S\n");
//M(-1,0) L(0,0) M(tr,ti)L(0,0)L(tr,-ti)
//fprintf(o,".006 W 1 1 0 RGB 0 setlinecap S\n");


Q=1.e-6; K=Q*Q; NemZo=nembra(Q); ANemZo=nem(NemZo); tr=Re(ANemZo); ti=Im(ANemZo); co(); coa(); AUNE1=Re(aune1(1.));
DO(n,401){ y=-2.+.01*n; x=Re(sunem(y)); if(n==0) M(x,y) else L(x,y); if(x> 4) break; } fprintf(o,".03 W 1 0 .3 RGB S\n");
DO(m,400){ x= 4.-.01*m; y=Re(aunem(x)); if(m==0) M(x,y) else L(x,y); if(y<-2) break; } fprintf(o,".01 W 0 0 0 RGB S\n");


Q=1.; K=Q*Q; NemZo=nembra(Q); ANemZo=nem(NemZo); tr=Re(ANemZo); ti=Im(ANemZo); co(); coa(); AUNE1=Re(aune1(1.));
DO(n,401){ y=-2.+.01*n; x=Re(sunem(y)); if(n==0) M(x,y) else L(x,y); if(x> 4) break; } fprintf(o,".03 W 0 1 0 RGB S\n");
DO(m,400){ x= 4.-.01*m; y=Re(aunem(x)); if(m==0) M(x,y) else L(x,y); if(y<-2) break; } fprintf(o,".01 W 0 0 0 RGB S\n");

Q=2.; K=Q*Q; NemZo=nembra(Q); ANemZo=nem(NemZo); tr=Re(ANemZo); ti=Im(ANemZo); co(); coa(); AUNE1=Re(aune1(1.));
DO(n,401){ y=-2.+.01*n; x=Re(sunem(y)); if(n==0) M(x,y) else L(x,y); if(x> 4)break; } fprintf(o,".03 W .3 0 1 RGB S\n");
DO(m,400){ x= 4.-.01*m; y=Re(aunem(x)); if(m==0) M(x,y) else L(x,y); if(y<-2)break; } fprintf(o,".01 W 0 0 0 RGB S\n");

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
        system("epstopdf aunemplo.eps");
        system( "open aunemplo.pdf"); //mac
return 0;}

Latex generator of labels


 \documentclass[12pt]{article}
 \usepackage{graphics}
 \paperwidth 4010pt
 \paperheight 4010pt
 \usepackage{geometry}
 \usepackage{rotating}
 \textwidth 4400pt
 \textheight 4400pt
 \topmargin -97pt
 \oddsidemargin -74pt
 \parindent 0pt
 \pagestyle{empty}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\begin{document}
\begin{picture}(4008,4008)
\put(20,3840){\sx{20}{$y\!=\!\mathrm{AuNem}_q(x)$}}
\put(100,2944){\sx{20}{$1$}}
\put(100,1940){\sx{20}{$0$}}
\put(10, 936){\sx{20}{$-1$}}
\put( 946,2040){\sx{20}{$1$}}
\put(1950,2040){\sx{20}{$2$}}
\put(2954,2040){\sx{20}{$3$}}
\put(3870,2040){\sx{20}{$x$}}
%
\put(0,0){\ing{aunemplo}}
%
\put(3300,3500){\sx{18}{\rot{7} $q\!=\!0$\ero}}
\put(3300,3120){\sx{18}{\rot{7} $q\!=\!1$\ero}}
\put(3300,2770){\sx{18}{\rot{6} $q\!=\!2$\ero}}
\end{picture}
\end{document}

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current06:10, 1 December 2018Thumbnail for version as of 06:10, 1 December 20188,322 × 8,322 (1.39 MB)Maintenance script (talk | contribs)Importing image file
  • You cannot overwrite this file.

The following 2 pages link to this file:

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. If the file has been modified from its original state, some details may not fully reflect the modified file.
Retrieved from "https://mizugadro.mydns.jp/t/index.php?title=File:Aunemplot.jpg&oldid=18285"