Difference between revisions of "File:AuPow2Plot.jpg"

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Explicit plof of two [[abelpower]] functions:
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Importing image file
  
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$y\!=$[[AuPow]]$_2(x)\!=\! \log_2\!\big(\ln(x)\big)~$, blue curve
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  +
and
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  +
$y\!=$[[AdPow]]$_2(x)\!=\! \log_2\!\big(\ln(1/x)\big)~$, red curve
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  +
==[[C++]] generator of curves==
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File [[ado.cin]] should be loaded in order to compile the code below.
  +
<poem><nomathjax><nowiki>
  +
#include<math.h>
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#include<stdio.h>
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#include<stdlib.h>
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#define DB double
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#define DO(x,y) for(x=0;x<y;x++)
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//#using namespace std;
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//#include <complex>
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//typedef std::complex<double> z_type;
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#define Re(x) x.real()
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#define Im(x) x.imag()
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#define I z_type(0.,1.)
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#include "ado.cin"
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  +
DB B=2.;
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DB F(DB z) { return exp( exp( log(B)*z));}
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DB G(DB z) { return log( log(z) )/log(B);}
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DB H(DB z) { return log( log(1./z))/log(B);}
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DB T(DB z) { return exp(B*log(z));}
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DB U(DB z) { return exp(log(z)/B);}
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  +
int main(){ int m,n; double x,y,t; FILE *o;
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o=fopen("aupow2plo.eps","w"); ado(o,720,740);
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fprintf(o,"10 510 translate 100 100 scale\n");
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#define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
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#define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);
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fprintf(o,"2 setlinecap 1 setlinejoin .03 W 0 0 1 RGB S\n");
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for(m=0;m<8;m++) {M(m,-5)L(m,2)}
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for(n=-5;n<3;n++) {M(0,n)L(7,n)}
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fprintf(o,".01 W 0 0 0 RGB S\n");
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DO(m,98){x=.01+.01*m; y=H(x); if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W 1 0 0 RGB S\n");
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  +
DO(m,601){x=1.03+.01*m; y=G(x); if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W 0 0 1 RGB S\n");
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fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
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system("epstopdf aupow2plo.eps");
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system( "open aupow2plo.pdf");
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getchar(); system("killall Preview");
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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>
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\documentclass[12pt]{article}
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\usepackage{geometry}
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\usepackage{graphicx}
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\usepackage{rotating}
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\paperwidth 760pt
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\paperheight 708pt
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\topmargin -94pt
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\oddsidemargin -81pt
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\textwidth 1100pt
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\textheight 1100pt
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\pagestyle {empty}
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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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\newcommand \ing {\includegraphics}
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\parindent 0pt
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\pagestyle{empty}
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\begin{document}
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\begin{picture}(742,702)
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%\put(51,1){\ing{01plo}}
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\put(51,1){\ing{aupow2plo}}
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\put(24,696){\sx{4}{$y$}}
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\put(24,598){\sx{4}{$1$}}
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\put(24,498){\sx{4}{$0$}}
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\put(-4,398){\sx{4}{$-1$}}
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\put(-4,298){\sx{4}{$-2$}}
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  +
\put(-4,198){\sx{4}{$-3$}}
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\put(-4,098){\sx{4}{$-4$}}
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\put(150,476){\sx{4}{$1$}}
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\put(250,476){\sx{4}{$2$}}
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\put(351,476){\sx{4}{$3$}}
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\put(451,476){\sx{4}{$4$}}
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\put(552,476){\sx{4}{$5$}}
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\put(652,476){\sx{4}{$6$}}
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\put(738,476){\sx{4}{$x$}}
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\put(366,546){\sx{3.7}{\rot{13}$y\!=\!\mathrm{AuPow}_2(x)$\ero}}
  +
%\put(242,66){\sx{3.8}{\rot{82}$y\!=\!\mathrm{AuPow}_2(x)$\ero}}
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\put(80,666){\sx{3.7}{\rot{-77}$y\!=\!\mathrm{AdPow}_2(x)$\ero}}
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\end{picture}
  +
\end{document}
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</nowiki></nomathjax></poem>
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  +
==References==
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<references/>
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  +
[[Category:Abel function]]
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[[Category:AdPow]]
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[[Category:AuPow]]
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[[Category:Book]]
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[[Category:BookPlot]]
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[[Category:Explicit plot]]
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[[Category:Power function]]
  +
[[Category:Superfunction]]
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[[Category:Superfunctions]]

Latest revision as of 08:30, 1 December 2018

Explicit plof of two abelpower functions:

$y\!=$AuPow$_2(x)\!=\! \log_2\!\big(\ln(x)\big)~$, blue curve

and

$y\!=$AdPow$_2(x)\!=\! \log_2\!\big(\ln(1/x)\big)~$, red curve

C++ generator of curves

File ado.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++)
//#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 "ado.cin"

DB B=2.;
DB F(DB z) { return exp( exp( log(B)*z));}
DB G(DB z) { return log( log(z) )/log(B);}
DB H(DB z) { return log( log(1./z))/log(B);}

DB T(DB z) { return exp(B*log(z));}
DB U(DB z) { return exp(log(z)/B);}

int main(){ int m,n; double x,y,t; FILE *o;
o=fopen("aupow2plo.eps","w"); ado(o,720,740);
fprintf(o,"10 510 translate 100 100 scale\n");
#define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);

fprintf(o,"2 setlinecap 1 setlinejoin .03 W 0 0 1 RGB S\n");

for(m=0;m<8;m++) {M(m,-5)L(m,2)}
for(n=-5;n<3;n++) {M(0,n)L(7,n)}
fprintf(o,".01 W 0 0 0 RGB S\n");

DO(m,98){x=.01+.01*m; y=H(x); if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W 1 0 0 RGB S\n");

DO(m,601){x=1.03+.01*m; y=G(x); if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W 0 0 1 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
       system("epstopdf aupow2plo.eps");
       system( "open aupow2plo.pdf");
       getchar(); system("killall Preview");
 }

Latex generator of labels


\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{rotating}
\paperwidth 760pt
\paperheight 708pt
\topmargin -94pt
\oddsidemargin -81pt
\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}
\begin{picture}(742,702)
%\put(51,1){\ing{01plo}}
\put(51,1){\ing{aupow2plo}}
\put(24,696){\sx{4}{$y$}}
\put(24,598){\sx{4}{$1$}}
\put(24,498){\sx{4}{$0$}}
\put(-4,398){\sx{4}{$-1$}}
\put(-4,298){\sx{4}{$-2$}}

\put(-4,198){\sx{4}{$-3$}}
\put(-4,098){\sx{4}{$-4$}}
 \put(150,476){\sx{4}{$1$}}
\put(250,476){\sx{4}{$2$}}
\put(351,476){\sx{4}{$3$}}
\put(451,476){\sx{4}{$4$}}
\put(552,476){\sx{4}{$5$}}
\put(652,476){\sx{4}{$6$}}
\put(738,476){\sx{4}{$x$}}
\put(366,546){\sx{3.7}{\rot{13}$y\!=\!\mathrm{AuPow}_2(x)$\ero}}
%\put(242,66){\sx{3.8}{\rot{82}$y\!=\!\mathrm{AuPow}_2(x)$\ero}}
\put(80,666){\sx{3.7}{\rot{-77}$y\!=\!\mathrm{AdPow}_2(x)$\ero}}
\end{picture}
\end{document}

References

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