File:ShokotaniaT.png

Explicit plots of the Shoko function (thick curve) and the Tania function (thin curve).

This picture reproduces Fig.5.1 from page 46 of book «Superfunctions» ^[1], 2020.

The same picture appears also in the Russian version «Суперфункции» ^[2], 2014; Fig.5.1, 47.

C++ generator of curves

// files doya.cin and ado.cin should be loaded in order to compile the C++ 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 complex<double> z_type;
 #define Re(x) x.real()
 #define Im(x) x.imag()
 #define I z_type(0.,1.)
 #include "ado.cin"
 #include "doya.cin"

 DB Shoko(DB x) { return log(1.+exp(x)*(M_E-1.)); }

 main(){ int m,n; double x,y; FILE *o;
 o=fopen("ShokoTania.eps","w"); ado(o,802,460);
 fprintf(o,"401 1 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);
 for(m=-4;m<5;m++) {M(m,0)L(m,4)}
 for(m=0;m<5;m++) {M(-4,m)L(4,m)}
 fprintf(o,"2 setlinecap .01 W S\n");
 for(m=0;m<81;m++) {x=-4.+.1*m; y=Shoko(x); if(m==0) M(x,y) else L(x,y);}
 fprintf(o,"1 setlinecap 1 setlinejoin .04 W 0 0.6 0 RGB S\n");
 for(m=0;m<81;m++) {x=-4.+.1*m; y=Re(Tania(x)); if(m==0) M(x,y) else L(x,y);}
 fprintf(o,"1 setlinecap 1 setlinejoin .014 W 0.4 0 .4 RGB S\n");
 fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
     system("epstopdf ShokoTania.eps");
     system(    "open ShokoTania.pdf");            
     getchar(); system("killall Preview");//for mac
 }

Latex generator of labels

% file ShokoTania.pdf should be generated with the code above in order to compile the Latex document below. % <poem><nomathjax><nowiki>

\documentclass[12pt]{article} %<br>
\usepackage{geometry} %<br>
\usepackage{graphics} %<br>
\usepackage{rotating} %<br>
\paperwidth 804pt %<br>
\paperheight 460pt %<br>
\topmargin -111pt %<br>
\oddsidemargin -73pt %<br>
\parindent 0pt %<br>
\pagestyle{empty} %<br>
\newcommand \sx {\scalebox} %<br>
\newcommand \rot {\begin{rotate}} %<br>
\newcommand \ero {\end{rotate}} %<br>
\begin{document} %<br>
\begin{picture}(802,462) %<br>
\put(0,0){\includegraphics{ShokoTania}} %<br>
\put(380,440){\sx{3.2}{$y$}} %<br>
\put(380,392){\sx{3.2}{$4$}} %<br>
\put(380,292){\sx{3.2}{$3$}} %<br>
\put(380,192){\sx{3.2}{$2$}} %<br>
\put(380, 92){\sx{3.2}{$1$}} %<br>
\put( 75, 4){\sx{3.2}{$-\!3$}} %<br>
\put(175, 4){\sx{3.2}{$-\!2$}} %<br>
\put(275, 4){\sx{3.2}{$-\!1$}} %<br>
\put(394, 4){\sx{3.2}{$0$}} %<br>
\put(494, 4){\sx{3.2}{$1$}} %<br>
\put(594, 4){\sx{3.2}{$2$}} %<br>
\put(694, 4){\sx{3.2}{$3$}} %<br>
\put(784, 4){\sx{3.2}{$x$}} %<br>
\put(442,140){\sx{3.2}{\rot{41} $y\!=\!\mathrm{Shoko}(x)$\ero}} %<br>
\put(468,102){\sx{3.2}{\rot{32} $y\!=\!\mathrm{Tania}(x)$\ero}} %<br>
\end{picture} %<br>
\end{document} %<br>

% Copyleft 2012 by Dmitrii Kouznetsov

References

Keywords

«[[]]», «Shoko function», «Tania function», «Трехстишия»,