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++]] |
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+ | [[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
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