Difference between revisions of "File:Sufact.png"

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[[Explicit plot]] of functions [[Factorial]] and [[SuFac]]:
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Importing image file
  
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$y=x! ~$ and $~y=\mathrm{SuFac}(x)$ versus $x$.
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This is adaptation of Figure 8.4 from the Russian book "Superfunctions" ([[Суперфункции]], in Russian)
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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.
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</ref>.
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==[[C++]] generator of curves==
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Files [[ado.cin]], [[fac.cin]], [[sufac.cin]] should be loaded in ordert o 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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#include "ado.cin"
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#include "fac.cin"
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#include "sufac.cin"
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// #include "superfactorial.cin"
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//#include "doya.cin"
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//DB Shoko(DB x) { return log(1.+exp(x)*(M_E-1.)); }
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int main(){ int m,n; double x,y; FILE *o;
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//o=fopen("SuperFacPlot.eps","w"); ado(o,802,1010);
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o=fopen("superfacplo.eps","w"); ado(o,802,1010);
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fprintf(o,"401 1 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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for(m=-4;m<5;m++) {M(m,0)L(m,10)}
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for(m=0;m<11;m++) {M(-4,m)L(4,m)}
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fprintf(o,"2 setlinecap .01 W S\n 1 setlinecap 1 setlinejoin\n");
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for(m=0;m<42;m++){x=-.5+.1*m; y=Re(fac(x)); if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W .7 0 0 RGB S\n");
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for(m=0;m<54;m++){x=-4+.1*m; y=Re(superfac(x));if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W 0 0 .7 RGB S\n");
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fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
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system("epstopdf superfacplo.eps");
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system( "open superfacplo.pdf");
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getchar(); system("killall Preview");//for mac
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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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\paperwidth 808pt
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\paperheight 1056pt
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\textwidth 1800pt
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\textheight 1800pt
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\topmargin -108pt
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\oddsidemargin -72pt
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\parindent 0pt
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\pagestyle{empty}
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\usepackage {graphics}
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\usepackage{rotating}
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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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\newcommand \sx {\scalebox}
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\begin{document}
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\begin{picture}(602,1010)
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%\put(0,0){\includegraphics{SuperFacPlot}}
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\put(0,0){\includegraphics{superfacplo}}
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\put(372,978){\sx{4.5}{$y$}}
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\put(372,890){\sx{4.5}{$9$}}
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\put(372,790){\sx{4.5}{$8$}}
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\put(372,690){\sx{4.5}{$7$}}
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\put(372,590){\sx{4.5}{$6$}}
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\put(372,490){\sx{4.5}{$5$}}
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\put(372,390){\sx{4.5}{$4$}}
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\put(372,290){\sx{4.5}{$3$}}
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\put(372,190){\sx{4.5}{$2$}}
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\put(372,90){\sx{4.5}{$1$}}
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\put( 066,-42){\sx{4.5}{$-\!3$}}
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\put(166,-42){\sx{4.5}{$-\!2$}}
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\put(266,-42){\sx{4.5}{$-\!1$}}
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\put(391,-42){\sx{4.5}{$0$}}
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\put(491,-42){\sx{4.5}{$1$}}
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\put(591,-42){\sx{4.5}{$2$}}
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\put(691,-42){\sx{4.5}{$3$}}
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\put(777,-42){\sx{4.5}{$x$}}
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%\put(532,440){\sx{5}{\rot{83}$y\!=\!\mathrm{SuperFactorial}(x)$\ero}}
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\put(532,440){\sx{5}{\rot{83}$y\!=\!\mathrm{SuFac}(x)$\ero}}
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%\put(660,450){\sx{4}{\rot{83}$y\!=\!\mathrm{Factorial}(x)$\ero}} %
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\put(740,500){\sx{5}{\rot{83}$y\!=\!\mathrm{Factorial}(x)$\ero}}
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\end{picture}
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\end{document}
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</nowiki></nomathjax></poem>
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==References==
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<references/>
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[[Category:Factorial]]
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[[Category:SuFac]]
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[[Category:Superfunction]]
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[[Category:Explicit plot]]
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[[Category:Book]]
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[[Category:BookPlot]]
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[[Category:C++]]
  +
[[Category:Latex]]

Latest revision as of 08:53, 1 December 2018

Explicit plot of functions Factorial and SuFac:

$y=x! ~$ and $~y=\mathrm{SuFac}(x)$ versus $x$.

This is adaptation of Figure 8.4 from the Russian book "Superfunctions" (Суперфункции, in Russian) [1].

C++ generator of curves

Files ado.cin, fac.cin, sufac.cin should be loaded in ordert o 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"
#include "fac.cin"
#include "sufac.cin"
// #include "superfactorial.cin"
 //#include "doya.cin"
 //DB Shoko(DB x) { return log(1.+exp(x)*(M_E-1.)); }

int main(){ int m,n; double x,y; FILE *o;
//o=fopen("SuperFacPlot.eps","w"); ado(o,802,1010);
o=fopen("superfacplo.eps","w"); ado(o,802,1010);
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,10)}
for(m=0;m<11;m++) {M(-4,m)L(4,m)}
fprintf(o,"2 setlinecap .01 W S\n 1 setlinecap 1 setlinejoin\n");
for(m=0;m<42;m++){x=-.5+.1*m; y=Re(fac(x)); if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W .7 0 0 RGB S\n");
for(m=0;m<54;m++){x=-4+.1*m; y=Re(superfac(x));if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W 0 0 .7 RGB S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
    system("epstopdf superfacplo.eps");
    system( "open superfacplo.pdf");
    getchar(); system("killall Preview");//for mac
}

Latex generator of labels


\documentclass[12pt]{article}
\paperwidth 808pt
\paperheight 1056pt
\textwidth 1800pt
\textheight 1800pt
\topmargin -108pt
\oddsidemargin -72pt
\parindent 0pt
\pagestyle{empty}
\usepackage {graphics}
\usepackage{rotating}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\begin{document}
\begin{picture}(602,1010)
%\put(0,0){\includegraphics{SuperFacPlot}}
\put(0,0){\includegraphics{superfacplo}}
\put(372,978){\sx{4.5}{$y$}}
\put(372,890){\sx{4.5}{$9$}}
\put(372,790){\sx{4.5}{$8$}}
\put(372,690){\sx{4.5}{$7$}}
\put(372,590){\sx{4.5}{$6$}}
\put(372,490){\sx{4.5}{$5$}}
\put(372,390){\sx{4.5}{$4$}}
\put(372,290){\sx{4.5}{$3$}}
\put(372,190){\sx{4.5}{$2$}}
\put(372,90){\sx{4.5}{$1$}}
\put( 066,-42){\sx{4.5}{$-\!3$}}
\put(166,-42){\sx{4.5}{$-\!2$}}
\put(266,-42){\sx{4.5}{$-\!1$}}
\put(391,-42){\sx{4.5}{$0$}}
\put(491,-42){\sx{4.5}{$1$}}
\put(591,-42){\sx{4.5}{$2$}}
\put(691,-42){\sx{4.5}{$3$}}
\put(777,-42){\sx{4.5}{$x$}}
%\put(532,440){\sx{5}{\rot{83}$y\!=\!\mathrm{SuperFactorial}(x)$\ero}}
\put(532,440){\sx{5}{\rot{83}$y\!=\!\mathrm{SuFac}(x)$\ero}}
%\put(660,450){\sx{4}{\rot{83}$y\!=\!\mathrm{Factorial}(x)$\ero}} %
\put(740,500){\sx{5}{\rot{83}$y\!=\!\mathrm{Factorial}(x)$\ero}}
\end{picture}
\end{document}

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.

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