Difference between revisions of "File:AuPow2Plot.jpg"

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

% File aupow2plo.eps should be generated with the code above in order to Latex the document below.

\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

Keywords

«Abel function», «[[]]», «Abelpower», «AdPow», «AuPow», «Superpower», «Superfunctions», «Table of superfunctions»,