File:ShokotaniaT.png

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

C++ generator of curves

// files doya.cin and ado.cin should be loaded in the working directory 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. % <br> \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