Difference between revisions of "File:Autraplot.jpg"

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Explicit plot of function [[AuTra]] and two its asymptotics.
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Importing image file
  
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This image is used as figure 20.9 of the Book
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[[Superfunction]] (In Russian, 2014; the English version is in preparation, 2015)
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<ref>
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https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br>
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http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf <br>
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http://mizugadro.mydns.jp/BOOK/202.pdf
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Д.Кузнецов. Суперфункции. Lambert Academic Publishing, 2014
  +
</ref>.
  +
  +
Function [[SuTra]]
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as entire function with logarithmic asymptotic is described also in year 2013 at Hikari
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<ref>
  +
http://www.m-hikari.com/ams/ams-2013/ams-129-132-2013/kouznetsovAMS129-132-2013.pdf D.Kouznetsov. Entire Function with Logarithmic Asymptotic. Applied Mathematical Sciences, Vol. 7, 2013, no. 131, 6527 - 6541
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</ref>.
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==References==
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<references/>
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  +
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==[[C++]] generator of curves==
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  +
Files [[ado.cin]], [[conto.cin]],
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[[sutran.cin]]
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should be loaded to the working directory in order to compile the code below
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<poem><nomathjax><nowiki>
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#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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z_type tra(z_type z){ return exp(z)+z;}
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#include "ado.cin"
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#include "arctran.cin"
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#include "sutran.cin"
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#include "autran.cin"
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#define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
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#define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
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int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("autraplo.eps","w"); ado(o,412,412);
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fprintf(o,"104 204 translate\n 100 100 scale\n");
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fprintf(o,"1 setlinejoin 2 setlinecap\n");
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for(n=-2;n<3;n++) {M(-1,n)L(3,n)}
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for(m=-1;m<4;m++) {M(m,-2)L(m,2)}
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// M(M_E,0)L(M_E,1) M(0,M_E)L(1,M_E)
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//M(0,1.+M_E) L(2,1.+M_E)
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fprintf(o,".004 W S\n");
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//DO(m,700){x=-2.01 +.02*m; y=Re(sutran(x)); if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".01 W 0 0 1 RGB S\n");
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//DO(m,740){x=-3.1 +.02*m; y=Re(sutran(x)); if(m==0) M(y,x) else L(y,x) if(x>3.03||y>6.01) break;} fprintf(o,".03 W 0 1 1 RGB S\n");
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//DO(m,740){x=-1.25 +.02*m; y=Re(autra(x)); if(m==0) M(x,y) else L(x,y) if(x>6.03||y>6.01) break;} fprintf(o,".03 W 1 .5 0 RGB S\n");
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DO(m,740){x=-1.1 +.02*m; y=Re(autran(x)); if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".03 W 1 0 0 RGB S\n");
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DO(m,740){x=-1.1 +.02*m; y=.5*x-exp(-x)+1.1259817765745026; if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".01 W 0 0 0 RGB S\n");
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DO(m,740){x=-1.1 +.02*m; y=.5*x-exp(-x)+1.1259817765745026-exp(x)/6.; if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".01 W 0 0 0 RGB S\n");
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//DO(m,740){x=-1.25 +.02*m; y=.5*x-exp(-x)+1.1259817765745026-exp(x)/6.+exp(2*x)/16; if(m==0) M(x,y) else L(x,y) if(x>6.03||y>6.01) break;} fprintf(o,".01 W 0 0 0 RGB S\n");
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fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o);
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system("epstopdf autraplo.eps");
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system( "open autraplo.pdf"); //for macintosh
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getchar(); system("killall Preview"); // For macintosh
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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 406pt
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\paperheight 412pt
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\topmargin -98pt
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\oddsidemargin -75.6pt
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\textwidth 900pt
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\textheight 900pt
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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}(402,404)
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\put(112,391){\sx{2.2}{$y$}}
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\put(112,296){\sx{2.2}{$1$}}
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\put(112,196){\sx{2.2}{$0$}}
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\put(102, 96){\sx{2.2}{$-1$}}
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\put(99,180){\sx{2.2}{$0$}}
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\put(199,180){\sx{2.2}{$1$}}
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\put(299,180){\sx{2.2}{$2$}}
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\put(390,180){\sx{2.2}{$x$}}
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\put(0,0){\ing{autraplo}}
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\put(153,303){\sx{2}{\rot{35}$y\!=\!x_0\!+\!x/2\!-\!\mathrm e^{-x}$\ero}}
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\put(267,325){\sx{2.2}{\rot{17}$y\!=\!\mathrm{AuTra}(x)$\ero}}
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%\put(185,128){\sx{2.2}{$y\!=\!x/2\!-\!\mathrm e^x\!+\!1.1259817765745026-exp(x)/6.+exp(2*x)/16)$}}
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\put(166,122){\sx{2}{$y\!=\!x_0\!+\!x/2\!-\!\mathrm e^{-x}\!+\!\mathrm e^x/6$}}
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\end{picture}
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\end{document}
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</nowiki></nomathjax></poem>
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[[Category:Book]]
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[[Category:BookMap]]
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[[Category:Explicit plot]]
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[[Category:C++]]
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[[Category:Special function]]
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[[Category:Latex]]
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[[Category:Superfunction]]
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[[Category:SuTra]]
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[[Category:Trappmann function]]

Latest revision as of 08:30, 1 December 2018

Explicit plot of function AuTra and two its asymptotics.


This image is used as figure 20.9 of the Book Superfunction (In Russian, 2014; the English version is in preparation, 2015) [1].

Function SuTra as entire function with logarithmic asymptotic is described also in year 2013 at Hikari [2].

References

  1. ↑ https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0
    http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf
    http://mizugadro.mydns.jp/BOOK/202.pdf Д.Кузнецов. Суперфункции. Lambert Academic Publishing, 2014
  2. ↑ http://www.m-hikari.com/ams/ams-2013/ams-129-132-2013/kouznetsovAMS129-132-2013.pdf D.Kouznetsov. Entire Function with Logarithmic Asymptotic. Applied Mathematical Sciences, Vol. 7, 2013, no. 131, 6527 - 6541


C++ generator of curves

Files ado.cin, conto.cin, sutran.cin should be loaded to the working directory 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.)
z_type tra(z_type z){ return exp(z)+z;}
#include "ado.cin"
#include "arctran.cin"
#include "sutran.cin"
#include "autran.cin"

#define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("autraplo.eps","w"); ado(o,412,412);
fprintf(o,"104 204 translate\n 100 100 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");
for(n=-2;n<3;n++) {M(-1,n)L(3,n)}
for(m=-1;m<4;m++) {M(m,-2)L(m,2)}
// M(M_E,0)L(M_E,1) M(0,M_E)L(1,M_E)
//M(0,1.+M_E) L(2,1.+M_E)
fprintf(o,".004 W S\n");
//DO(m,700){x=-2.01 +.02*m; y=Re(sutran(x)); if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".01 W 0 0 1 RGB S\n");
//DO(m,740){x=-3.1 +.02*m; y=Re(sutran(x)); if(m==0) M(y,x) else L(y,x) if(x>3.03||y>6.01) break;} fprintf(o,".03 W 0 1 1 RGB S\n");
//DO(m,740){x=-1.25 +.02*m; y=Re(autra(x)); if(m==0) M(x,y) else L(x,y) if(x>6.03||y>6.01) break;} fprintf(o,".03 W 1 .5 0 RGB S\n");
DO(m,740){x=-1.1 +.02*m; y=Re(autran(x)); if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".03 W 1 0 0 RGB S\n");
DO(m,740){x=-1.1 +.02*m; y=.5*x-exp(-x)+1.1259817765745026; if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".01 W 0 0 0 RGB S\n");
DO(m,740){x=-1.1 +.02*m; y=.5*x-exp(-x)+1.1259817765745026-exp(x)/6.; if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.01) break;} fprintf(o,".01 W 0 0 0 RGB S\n");
//DO(m,740){x=-1.25 +.02*m; y=.5*x-exp(-x)+1.1259817765745026-exp(x)/6.+exp(2*x)/16; if(m==0) M(x,y) else L(x,y) if(x>6.03||y>6.01) break;} fprintf(o,".01 W 0 0 0 RGB S\n");
fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o);
    system("epstopdf autraplo.eps");
    system( "open autraplo.pdf"); //for macintosh
    getchar(); system("killall Preview"); // For macintosh
}

Latex generator of labels


\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{rotating}
\paperwidth 406pt
\paperheight 412pt
\topmargin -98pt
\oddsidemargin -75.6pt
\textwidth 900pt
\textheight 900pt
\pagestyle {empty}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\parindent 0pt
\pagestyle{empty}
\begin{document}
\begin{picture}(402,404)
\put(112,391){\sx{2.2}{$y$}}
\put(112,296){\sx{2.2}{$1$}}
\put(112,196){\sx{2.2}{$0$}}
\put(102, 96){\sx{2.2}{$-1$}}
\put(99,180){\sx{2.2}{$0$}}
\put(199,180){\sx{2.2}{$1$}}
\put(299,180){\sx{2.2}{$2$}}
\put(390,180){\sx{2.2}{$x$}}
\put(0,0){\ing{autraplo}}
\put(153,303){\sx{2}{\rot{35}$y\!=\!x_0\!+\!x/2\!-\!\mathrm e^{-x}$\ero}}
\put(267,325){\sx{2.2}{\rot{17}$y\!=\!\mathrm{AuTra}(x)$\ero}}
%\put(185,128){\sx{2.2}{$y\!=\!x/2\!-\!\mathrm e^x\!+\!1.1259817765745026-exp(x)/6.+exp(2*x)/16)$}}
\put(166,122){\sx{2}{$y\!=\!x_0\!+\!x/2\!-\!\mathrm e^{-x}\!+\!\mathrm e^x/6$}}
\end{picture}
\end{document}

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