File:Vladi07.jpg
Vladi07.jpg (741 × 383 pixels, file size: 100 KB, MIME type: image/jpeg)
Maps of agreement of approximations of natural tetration with elementary functions fima and maclo, used in the implementation fsexp.cin.
Left: $D=D_6(x\!+\!\mathrm i y)$;
$\displaystyle D_6(z)= - \ln \left( \frac
Refereces
- ↑
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. - ↑ http://mizugadro.mydns.jp/PAPERS/2010vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45. Figure 7.
C++ generator of the first picture
Fsexp.cin, ado.cin, conto.cin, plodi.cin should be loaded 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++)
#include <complex>
typedef std::complex<double> z_type;
//#include <complex.h>
//#define z_type complex<double>
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "fsexp.cin"
#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
int M=100,M1=M+1;
int N=101,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
FILE *o;o=fopen("vladi07a.eps","w");ado(o,82,82);
fprintf(o,"41 11 translate\n 10 10 scale\n");
DO(m,M1) X[m]=-4.+.08*(m-.5);
DO(n,N1)Y[n]= -1 +.08*(n-.5);
for(m=-3;m<4;m++) { if(m==0){M(m,-0.1)L(m,6.1)} else {M(m,0)L(m,6)} }
for(n=0;n<7;n++) { M( -3,n)L(3,n)}
fprintf(o,".006 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; printf("run at x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
c=tai3(z);
// d=fima1(z);
d=fima(z);
p=abs(c-d)/(abs(c)+abs(d));
p=-log(p)/log(10.);
// p=Re(c); q=Im(c);
if(p>-999 && p<999 && fabs(p)> 1.e-8 && fabs(p-1.)>1.e-8) g[m*N1+n]=p;
// if(q>-999 && q<999 && fabs(q)> 1.e-8) f[m*N1+n]=q;
}}
#include"plodi.cin"
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
system("epstopdf vladi07a.eps");
system( "open vladi07a.pdf");//macintosh
// getchar(); system("killall Preview"); //macintosh
}
C++ generator of the second picture
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex>
typedef std::complex<double> z_type;
//#include <complex.h>
//#define z_type complex<double>
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "fsexp.cin"
#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
int M=100,M1=M+1;
int N=101,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
FILE *o;o=fopen("vladi07b.eps","w");ado(o,82,82);
fprintf(o,"41 11 translate\n 10 10 scale\n");
DO(m,M1) X[m]=-4.+.08*(m-.5);
DO(n,N1)Y[n]= -1 +.08*(n-.5);
for(m=-3;m<4;m++) { if(m==0){M(m,-0.1)L(m,6.1)} else {M(m,0)L(m,6)} }
for(n=0;n<7;n++) { M( -3,n)L(3,n)}
fprintf(o,".006 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; printf("run at x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
c=tai3(z);
d=maclo(z);
// d=fima1(z);
p=abs(c-d)/(abs(c)+abs(d));
p=-log(p)/log(10.);
// p=Re(c); q=Im(c);
if(p>-999 && p<999 && fabs(p)> 1.e-8 && fabs(p-1.)>1.e-8) g[m*N1+n]=p;
// if(q>-999 && q<999 && fabs(q)> 1.e-8) f[m*N1+n]=q;
}}
#include"plodi.cin"
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
system("epstopdf vladi07b.eps");
system( "open vladi07b.pdf");//macintosh
// getchar(); system("killall Preview");//macintosh
}
Latex combiner
\documentclass[12pt]{article}
\usepackage{graphicx}
\usepackage{rotating}
\usepackage{geometry}
\paperwidth 356px
%\paperheight 134px
\paperheight 184px
\topmargin -98pt
\oddsidemargin -94pt
\pagestyle{empty}
\begin{document}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \tafiax {
\put(7,68){\sx{.5}{$y$}}
%\put(5,74){\sx{.5}{$\Im(z)$}}
%\put(7,69){\sx{.5}{$6$}}
\put(7,59){\sx{.5}{$5$}}
\put(7,49){\sx{.5}{$4$}}
\put(7,39){\sx{.5}{$3$}}
\put(7,29){\sx{.5}{$2$}}
\put(7,19){\sx{.5}{$1$}}
\put(7, 9){\sx{.5}{$0$}}
\put( 7 ,6){\sx{.5}{$-\!3$}}
\put(17 ,6){\sx{.5}{$-\!2$}}
\put(27 ,6){\sx{.5}{$-\!1$}}
\put(40 , 6){\sx{.5}{$0$}}
\put(50 , 6){\sx{.5}{$1$}}
\put(60 , 6){\sx{.5}{$2$}}
%\put(70 , 6){\sx{.5}{$3$}}
%\put(78 , 6){\sx{.5}{$\Re(z)$}}
\put(70 , 6){\sx{.5}{$x$}}
}
%\sx{2.33}{\begin{picture}(96,75)
\sx{2.33}{\begin{picture}(80,75)
%\put(0,0){\includegraphics{figtaifima}}
\put(0,0){\includegraphics{vladi07a}}
\tafiax
\put(31,54){\sx{.45}{$D\!>\!14$}}
\end{picture}}
\sx{2.33}{\begin{picture}(84,70)
%\put(0,0){\includegraphics{figtaimaclo}}
\put(0,0){\includegraphics{vladi07b}}
\tafiax
\put(33,55){\sx{.52}{$D\!<\!1$}}
\put(33,24){\sx{.45}{$D\!>\!14$}}
\end{picture}}
\end{document}
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 06:14, 1 December 2018 | | 741 × 383 (100 KB) | Maintenance script (talk | contribs) | Importing image file |
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