Difference between revisions of "File:Sunot.jpg"

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Solution $x_0=x_0(q)$ of equation
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Importing image file
  
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  +
$\mathrm{SuNe}_q(x_0)=1$
  +
  +
versus $q$.
  +
  +
Here, [[SuNe]] is native [[superfunction]] of the [[Nemtsov function]] costructed with [[exotic iteration]] at its fixed point zero.
  +
  +
Function $x_0$ is used to define function [[SuNem]] with
  +
  +
$\mathrm{SuNem})q(z)=\mathrm{SuNe}_q(x_0(q)+z)$
  +
  +
==References==
  +
<references/>
  +
  +
==[[C++]] generator of curve==
  +
  +
<poem><nomathjax><nowiki>
  +
#include <math.h>
  +
#include <stdio.h>
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#include <stdlib.h>
  +
#define DB double
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#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"
  +
  +
#include "ado.cin"
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#define M(x,y) fprintf(o,"%8.4lf %8.4lf M\n",0.+x,0.+y);
  +
#define L(x,y) fprintf(o,"%8.4lf %8.4lf L\n",0.+x,0.+y);
  +
  +
DB Q;
  +
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 Q=2.;
  +
// 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!
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  +
#include "sune.cin"
  +
  +
DB SUNo=0;
  +
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z_type sunem(z_type z){ return sune(z + SUNo);}
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  +
int main(){ int Max; int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
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// DB rr,ti;
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FILE *o;o=fopen("suno.eps","w");ado(o,620,1220);
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fprintf(o,"110 1010 translate\n 100 100 scale 2 setlinecap\n");
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for(m=0;m<6;m+=1){ M(m,-10)L(m,2)}
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for(n=-10;n<3;n+=1){ M(0,n)L(5,n)}
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fprintf(o,".008 W 0 0 0 RGB 2 setlinecap S\n");
  +
  +
  +
Q=-1; K=Q*Q; x=0; co(); printf("Q=%9.4lf\n",Q);
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DO(n,300) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
  +
  +
M(Q,SUNo)
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  +
DO(m,640){ Q=-.99+.01*m; K=Q*Q; co(); printf("Q=%9.4lf\n",Q);
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DO(n,60) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);}
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L(Q,SUNo)
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if(SUNo<-10.) break;}
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  +
fprintf(o,".03 W .6 0 0 RGB 1 setlinejoin S\n");
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  +
  +
/*
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DO(n,402){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
  +
fprintf(o,".02 W 0 0 0 RGB 1 setlinejoin S\n");
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  +
Q=.5; K=Q*Q; x=0; co(); printf("Q=%9.4lf\n",Q);
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DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
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DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
  +
fprintf(o,".01 W .7 0 .6 RGB 1 setlinejoin S\n");
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  +
  +
Q=1; K=Q*Q; x=0; co(); printf("Q=%9.4lf\n",Q);
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DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
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DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
  +
fprintf(o,".02 W .8 .2 0 RGB 1 setlinejoin S\n");
  +
  +
Q=2; K=Q*Q; x=0; co(); printf("Q=%9.4lf\n",Q);
  +
DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
  +
DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
  +
fprintf(o,".02 W 0 .6 0 RGB 1 setlinejoin S\n");
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  +
Q=8; K=Q*Q; SUNo=-100.; co(); printf("Q=%9.4lf\n",Q);
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DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
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//DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
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//fprintf(o,".015 W 0 0 .8 RGB 1 setlinejoin S\n");
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  +
DO(m,81){Q=8.-.1*m; K=Q*Q;K=Q*Q; co(); printf("Q=%9.4lf\n",Q);
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DO(n,30) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
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}
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  +
Q=10; K=Q*Q; SUNo=-150.; co(); printf("Q=%9.4lf\n",Q);
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DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
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DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
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fprintf(o,".015 W 0 0 .8 RGB 1 setlinejoin S\n");
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*/
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fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
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system("epstopdf suno.eps");
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system( "open suno.pdf"); //mac
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  +
return 0;
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}
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  +
  +
</nowiki></nomathjax></poem>
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  +
  +
==[[Latex]] generator of labels==
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  +
<poem><nomathjax><nowiki>
  +
\documentclass{mcom-l}
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% \documentclass[12pt]{article}
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\usepackage{graphics}
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\paperwidth 608pt
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\paperheight 1208pt
  +
\usepackage{geometry}
  +
\usepackage{rotating}
  +
\textwidth 2560pt
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\textheight 2260pt
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\topmargin -98pt
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\oddsidemargin -84pt
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\parindent 0pt
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\pagestyle{empty}
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\newcommand \ing {\includegraphics}
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\newcommand \sx {\scalebox}
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\newcommand \rot {\begin{rotate}}
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\newcommand \ero {\end{rotate}}
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\begin{document}
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\begin{picture}(720,1220)
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%\put(4,0){\ing{sunemplo4}}
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\put(4,0){\ing{suno}}
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\put(64,1190){\sx{5}{$x_0$}}
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\put(80,1096){\sx{5}{$1$}}
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\put(80,996){\sx{5}{$0$}}
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\put(48,896){\sx{5}{$-1$}}
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\put(48,796){\sx{5}{$-2$}}
  +
\put(48,695){\sx{5}{$-3$}}
  +
\put(48,595){\sx{5}{$-4$}}
  +
\put(48,495){\sx{5}{$-5$}}
  +
\put(48,395){\sx{5}{$-6$}}
  +
\put(48,294){\sx{5}{$-7$}}
  +
\put(48,194){\sx{5}{$-8$}}
  +
\put(48,94){\sx{5}{$-9$}}
  +
%
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\put(202,976){\sx{5}{$1$}}
  +
\put(302,976){\sx{5}{$2$}}
  +
\put(402,976){\sx{5}{$3$}}
  +
\put(502,976){\sx{5}{$4$}}
  +
\put(590,980){\sx{5.2}{$q$}}
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%\put(706,980){\sx{4}{$6$}}
  +
%\put(322,932){\sx{3.4}{\rot{88}$q\!=\!8$\ero}}%
  +
%\put(348,834){\sx{3.4}{\rot{87}$q\!=\!2$\ero}}%
  +
%\put(361,734){\sx{3.4}{\rot{86}$q\!=\!1$\ero}}%
  +
%\put(372,614){\sx{3.4}{\rot{85}$q\!=\!0.5$\ero}}%
  +
%\put(392,518){\sx{3.4}{\rot{83}$q\!=\!0$\ero}}%
  +
\end{picture}
  +
\end{document}
  +
  +
</nowiki></nomathjax></poem>
  +
  +
[[Category:Book]]
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[[Category:BookPlot]]
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[[Category:C++]]
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[[Category:Explicit plot]]
  +
[[Category:Latex]]
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[[Category:Nemtsov function]]
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[[Category:Superfunction]]
  +
[[Category:Superfunctions]]

Latest revision as of 08:53, 1 December 2018

Solution $x_0=x_0(q)$ of equation

$\mathrm{SuNe}_q(x_0)=1$

versus $q$.

Here, SuNe is native superfunction of the Nemtsov function costructed with exotic iteration at its fixed point zero.

Function $x_0$ is used to define function SuNem with

$\mathrm{SuNem})q(z)=\mathrm{SuNe}_q(x_0(q)+z)$

References


C++ generator of curve


#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"

#include "ado.cin"
#define M(x,y) fprintf(o,"%8.4lf %8.4lf M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%8.4lf %8.4lf L\n",0.+x,0.+y);

DB Q;
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 Q=2.;
// 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!

#include "sune.cin"

DB SUNo=0;

z_type sunem(z_type z){ return sune(z + SUNo);}

int main(){ int Max; int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
// DB rr,ti;
FILE *o;o=fopen("suno.eps","w");ado(o,620,1220);
fprintf(o,"110 1010 translate\n 100 100 scale 2 setlinecap\n");
for(m=0;m<6;m+=1){ M(m,-10)L(m,2)}
for(n=-10;n<3;n+=1){ M(0,n)L(5,n)}
fprintf(o,".008 W 0 0 0 RGB 2 setlinecap S\n");


Q=-1; K=Q*Q; x=0; co(); printf("Q=%9.4lf\n",Q);
DO(n,300) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();

M(Q,SUNo)

DO(m,640){ Q=-.99+.01*m; K=Q*Q; co(); printf("Q=%9.4lf\n",Q);
        DO(n,60) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);}
        L(Q,SUNo)
        if(SUNo<-10.) break;}

fprintf(o,".03 W .6 0 0 RGB 1 setlinejoin S\n");


/*
DO(n,402){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
fprintf(o,".02 W 0 0 0 RGB 1 setlinejoin S\n");

Q=.5; K=Q*Q; x=0; co(); printf("Q=%9.4lf\n",Q);
DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
fprintf(o,".01 W .7 0 .6 RGB 1 setlinejoin S\n");


Q=1; K=Q*Q; x=0; co(); printf("Q=%9.4lf\n",Q);
DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
fprintf(o,".02 W .8 .2 0 RGB 1 setlinejoin S\n");

Q=2; K=Q*Q; x=0; co(); printf("Q=%9.4lf\n",Q);
DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
fprintf(o,".02 W 0 .6 0 RGB 1 setlinejoin S\n");

Q=8; K=Q*Q; SUNo=-100.; co(); printf("Q=%9.4lf\n",Q);
DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
//DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
//fprintf(o,".015 W 0 0 .8 RGB 1 setlinejoin S\n");

DO(m,81){Q=8.-.1*m; K=Q*Q;K=Q*Q; co(); printf("Q=%9.4lf\n",Q);
DO(n,30) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
}

Q=10; K=Q*Q; SUNo=-150.; co(); printf("Q=%9.4lf\n",Q);
DO(n,50) { y=Re(sunem(0)); SUNo-= y-1.; printf("%19.16lf %19.16lf\n", SUNo,y);} // getchar();
DO(n,400){ x=-2.01+.01*n; y=Re(sunem(x)); if(n==0) M(x,y) else L(x,y); printf("%6.1lf %18.15lf\n", x,y); if(y>10) break;}
fprintf(o,".015 W 0 0 .8 RGB 1 setlinejoin S\n");
*/

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);

        system("epstopdf suno.eps");
        system( "open suno.pdf"); //mac

return 0;
}


Latex generator of labels


\documentclass{mcom-l}
% \documentclass[12pt]{article}
 \usepackage{graphics}
 \paperwidth 608pt
 \paperheight 1208pt
 \usepackage{geometry}
 \usepackage{rotating}
 \textwidth 2560pt
 \textheight 2260pt
 \topmargin -98pt
 \oddsidemargin -84pt
 \parindent 0pt
 \pagestyle{empty}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\begin{document}

\begin{picture}(720,1220)
%\put(4,0){\ing{sunemplo4}}
\put(4,0){\ing{suno}}
\put(64,1190){\sx{5}{$x_0$}}
\put(80,1096){\sx{5}{$1$}}
\put(80,996){\sx{5}{$0$}}
\put(48,896){\sx{5}{$-1$}}
\put(48,796){\sx{5}{$-2$}}
\put(48,695){\sx{5}{$-3$}}
\put(48,595){\sx{5}{$-4$}}
\put(48,495){\sx{5}{$-5$}}
\put(48,395){\sx{5}{$-6$}}
\put(48,294){\sx{5}{$-7$}}
\put(48,194){\sx{5}{$-8$}}
\put(48,94){\sx{5}{$-9$}}
%
\put(202,976){\sx{5}{$1$}}
\put(302,976){\sx{5}{$2$}}
\put(402,976){\sx{5}{$3$}}
\put(502,976){\sx{5}{$4$}}
\put(590,980){\sx{5.2}{$q$}}
%\put(706,980){\sx{4}{$6$}}
%\put(322,932){\sx{3.4}{\rot{88}$q\!=\!8$\ero}}%
%\put(348,834){\sx{3.4}{\rot{87}$q\!=\!2$\ero}}%
%\put(361,734){\sx{3.4}{\rot{86}$q\!=\!1$\ero}}%
%\put(372,614){\sx{3.4}{\rot{85}$q\!=\!0.5$\ero}}%
%\put(392,518){\sx{3.4}{\rot{83}$q\!=\!0$\ero}}%
\end{picture}
\end{document}

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