Difference between pages "File:Vladi07.jpg" and "File:Vladi08.jpg"
Line 1: | Line 1: | ||
− | + | Agreement of approximations of tetration by elementary functions with the original representation through the Cauchi integral is shown in the left hand side map. |
|
+ | The similar map at the right hand side represents the comparison to the similar representation through the Cauchi integral, but the contour of integration is displaced for 1/2 to the left. |
||
− | Left: $D=D_6(x\!+\!\mathrm i y)$; |
||
+ | |||
+ | Levels $D=\mathrm{const}$ are drawn with step 2, but the exception is dome for level $D=1$, this level is drawn with thick lines. |
||
$\displaystyle |
$\displaystyle |
||
+ | {\rm fse}(z)=\left\{ \begin{array}{ccrcccr} |
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− | D_6(z)= - \ln \left( \frac |
||
− | { |
+ | {\rm fima}(z) &,& 4.5& \!<\! &\Im(z) \\ |
− | { |
+ | {\rm tai}(z) &,& 1.5& \!<\! &\Im(z) &\!\le\!& 4.5 \\ |
+ | {\rm maclo}(z) &,& -1.5& \le &\Im(z) &\!\le\!& 1.5 \\ |
||
− | \right)$ |
||
+ | {\rm tai}(z^{*})^{*} &,& -4.5& \le &\Im(z) &\!<\!&\!\! -1.5 \\ |
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+ | {\rm fima}(z^{*})^{*} &,& & &\Im(z) &\!<\!&\!\! -4.5 |
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+ | \end{array} |
||
+ | \right.$ |
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+ | Mnemonics for the name of the approximation: Fast Super Exponent. |
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− | right: $D=D_7(x\!+\!\mathrm i y)$; |
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+ | |||
+ | The agreement plotted is |
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$\displaystyle |
$\displaystyle |
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− | + | D=D_{8}(z)=-\lg\left( \frac |
|
− | {|\mathrm{ |
+ | {|\mathrm{fse}(z)-F_{4}(z)|} |
− | {|\mathrm{ |
+ | {|\mathrm{fse}(z)|+|F_{4}(z)|} |
− | \right) |
+ | \right) |
+ | $ |
||
+ | where $F_4$ denotes the 4th [[ackermann]], id set, natural [[tetration]] evaluated through the Cauchi integral |
||
− | Levels $D=\mathrm{const}$ are drawn with step 2, but the exception is dome for level $D=1$, this level is drawn with thick lines. |
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+ | <ref> |
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+ | http://www.ams.org/mcom/2009-78-267/S0025-5718-09-02188-7/home.html <br> |
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+ | http://www.ils.uec.ac.jp/~dima/PAPERS/2009analuxpRepri.pdf <br> |
||
+ | http://mizugadro.mudns.jp/PAPERS/2009analuxpRepri.pdf |
||
+ | D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670. |
||
+ | </ref>. |
||
− | Usage: this is figure 14. |
+ | Usage: this is figure 14.11 of the book [[Суперфункции]] (2014, In Russian) <ref> |
https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br> |
https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br> |
||
http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf <br> |
http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf <br> |
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Line 30: | Line 45: | ||
http://mizugadro.mydns.jp/PAPERS/2010vladie.pdf |
http://mizugadro.mydns.jp/PAPERS/2010vladie.pdf |
||
D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45. |
D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45. |
||
− | Figure |
+ | Figure 8. |
</ref>. |
</ref>. |
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Line 44: | Line 59: | ||
<poem><nomathjax><nowiki> |
<poem><nomathjax><nowiki> |
||
+ | |||
#include <math.h> |
#include <math.h> |
||
#include <stdio.h> |
#include <stdio.h> |
||
Line 51: | Line 67: | ||
#include <complex> |
#include <complex> |
||
typedef std::complex<double> z_type; |
typedef std::complex<double> z_type; |
||
− | //#include <complex.h> |
||
− | //#define z_type complex<double> |
||
#define Re(x) x.real() |
#define Re(x) x.real() |
||
#define Im(x) x.imag() |
#define Im(x) x.imag() |
||
#define I z_type(0.,1.) |
#define I z_type(0.,1.) |
||
+ | //#include "superex.cin" |
||
#include "fsexp.cin" |
#include "fsexp.cin" |
||
+ | #include "f4natu.cin" |
||
+ | //z_type FSEXP(z_type z){DB y=Im(z); |
||
+ | z_type fsexp(z_type z){DB y=Im(z); |
||
+ | if(y> 4.5) return fima(z); |
||
+ | if(y> 1.5) return tai3(z); |
||
+ | if(y>-1.5) return maclo(z); |
||
+ | if(y>-4.5) return conj(tai3(conj(z))); |
||
+ | return conj(fima(conj(z))); |
||
+ | } |
||
+ | //#include "superlo.cin" |
||
#include "conto.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 main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; |
||
+ | z_type Zo=z_type(.31813150520476413, 1.3372357014306895); |
||
+ | z_type Zc=z_type(.31813150520476413,-1.3372357014306895); |
||
int M=100,M1=M+1; |
int M=100,M1=M+1; |
||
Line 66: | Line 93: | ||
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array. |
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 |
char v[M1*N1]; // v is working array |
||
− | FILE *o;o=fopen(" |
+ | //FILE *o;o=fopen("figcf4small.eps","w");ado(o,0,0,82,82); |
+ | FILE *o;o=fopen("vladi08a.eps","w");ado(o,82,82); |
||
fprintf(o,"41 11 translate\n 10 10 scale\n"); |
fprintf(o,"41 11 translate\n 10 10 scale\n"); |
||
DO(m,M1) X[m]=-4.+.08*(m-.5); |
DO(m,M1) X[m]=-4.+.08*(m-.5); |
||
− | DO(n,N1)Y[n]= |
+ | 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(m=-3;m<4;m++) { if(m==0){M(m,-0.1)L(m,6.1)} else {M(m,0)L(m,6)} } |
||
Line 79: | Line 107: | ||
DO(m,M1){x=X[m]; printf("run at x=%6.3f\n",x); |
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); |
DO(n,N1){y=Y[n]; z=z_type(x,y); |
||
− | c= |
+ | c=fsexp(z); |
− | + | d=F4natu(z); |
|
− | + | p=abs(c-d);///(abs(c)+abs(d)); |
|
− | p=abs(c-d)/(abs(c)+abs(d)); |
||
p=-log(p)/log(10.); |
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(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; |
// if(q>-999 && q<999 && fabs(q)> 1.e-8) f[m*N1+n]=q; |
||
}} |
}} |
||
− | |||
#include"plodi.cin" |
#include"plodi.cin" |
||
+ | //M(-2,0)L(-3.1,0) fprintf(o,".04 W 0 0 0 RGB [.1 .1] 1 setdash S\n"); |
||
− | |||
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); |
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); |
||
− | + | // system( "gv fig08a.eps"); |
|
− | system( |
+ | system("epstopdf vladi08a.eps"); |
− | + | system( "open vladi08a.pdf"); // for linux |
|
+ | // getchar(); system("killall Preview");// for macintosh |
||
} |
} |
||
+ | |||
</nowiki></nomathjax></poem> |
</nowiki></nomathjax></poem> |
||
==[[C++]] generator of the second picture== |
==[[C++]] generator of the second picture== |
||
+ | |||
+ | [[vladif5c.cin]] also should be loaded |
||
+ | |||
<poem><nomathjax><nowiki> |
<poem><nomathjax><nowiki> |
||
Line 108: | Line 139: | ||
#include <complex> |
#include <complex> |
||
typedef std::complex<double> z_type; |
typedef std::complex<double> z_type; |
||
− | //#include <complex.h> |
||
− | //#define z_type complex<double> |
||
#define Re(x) x.real() |
#define Re(x) x.real() |
||
#define Im(x) x.imag() |
#define Im(x) x.imag() |
||
#define I z_type(0.,1.) |
#define I z_type(0.,1.) |
||
+ | //#include "superex.cin" |
||
#include "fsexp.cin" |
#include "fsexp.cin" |
||
+ | //#include "f4natu.cin" |
||
+ | #include "vladif5c.cin" |
||
+ | //z_type FSEXP(z_type z){DB y=Im(z); |
||
+ | z_type fsexp(z_type z){DB y=Im(z); |
||
+ | if(y> 4.5) return fima(z); |
||
+ | if(y> 1.5) return tai3(z); |
||
+ | if(y>-1.5) return maclo(z); |
||
+ | if(y>-4.5) return conj(tai3(conj(z))); |
||
+ | return conj(fima(conj(z))); |
||
+ | } |
||
+ | //#include "superlo.cin" |
||
#include "conto.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 main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; |
||
+ | z_type Zo=z_type(.31813150520476413, 1.3372357014306895); |
||
+ | z_type Zc=z_type(.31813150520476413,-1.3372357014306895); |
||
int M=100,M1=M+1; |
int M=100,M1=M+1; |
||
Line 123: | Line 166: | ||
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array. |
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 |
char v[M1*N1]; // v is working array |
||
− | FILE *o;o=fopen(" |
+ | //FILE *o;o=fopen("figcf5small.eps","w");ado(o,0,0,82,82); |
+ | FILE *o;o=fopen("vladi08b.eps","w");ado(o,82,82); |
||
fprintf(o,"41 11 translate\n 10 10 scale\n"); |
fprintf(o,"41 11 translate\n 10 10 scale\n"); |
||
− | DO(m,M1) |
+ | DO(m,M1)X[m]=-4.+.08*(m-.5); |
− | DO(n,N1)Y[n]= |
+ | 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(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++) { |
+ | for(n= 0;n<7;n++) { M( -3,n)L(3,n)} |
fprintf(o,".006 W 0 0 0 RGB S\n"); |
fprintf(o,".006 W 0 0 0 RGB S\n"); |
||
Line 136: | Line 180: | ||
DO(m,M1){x=X[m]; printf("run at x=%6.3f\n",x); |
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); |
DO(n,N1){y=Y[n]; z=z_type(x,y); |
||
− | c= |
+ | c=fsexp(z); |
− | d= |
+ | d=F5(z); |
− | + | p=abs(c-d);///(abs(c)+abs(d)); |
|
− | p=abs(c-d)/(abs(c)+abs(d)); |
||
p=-log(p)/log(10.); |
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) |
+ | 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) |
+ | // if(q>-999 && q<999 && fabs(q)> 1.e-8) f[m*N1+n]=q; |
− | }} |
+ | }} |
#include"plodi.cin" |
#include"plodi.cin" |
||
+ | //M(-2,0)L(-3.1,0) fprintf(o,".04 W 0 0 0 RGB [.1 .1] 1 setdash S\n"); |
||
− | |||
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); |
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); |
||
− | system("epstopdf |
+ | system("epstopdf vladi08b.eps"); |
− | system( "open |
+ | system( "open vladi08b.pdf");//linux |
− | // |
+ | //getchar(); system("killall Preview"); |
} |
} |
||
− | |||
</nowiki></nomathjax></poem> |
</nowiki></nomathjax></poem> |
||
Line 162: | Line 204: | ||
\usepackage{rotating} |
\usepackage{rotating} |
||
\usepackage{geometry} |
\usepackage{geometry} |
||
− | \paperwidth |
+ | \paperwidth 378px |
%\paperheight 134px |
%\paperheight 134px |
||
− | \paperheight |
+ | \paperheight 180px |
− | \topmargin - |
+ | \topmargin -104pt |
\oddsidemargin -94pt |
\oddsidemargin -94pt |
||
\pagestyle{empty} |
\pagestyle{empty} |
||
Line 175: | Line 217: | ||
\newcommand \ero {\end{rotate}} |
\newcommand \ero {\end{rotate}} |
||
+ | \sx{2.2}{\begin{picture}(90,80) |
||
− | \newcommand \tafiax { |
||
− | \put( |
+ | %\put(0,0){\includegraphics{figsexpF4}} |
− | %\put( |
+ | %\put(0,0){\includegraphics{figcf4small}} |
− | + | \put(0,0){\includegraphics{vladi08a}} |
|
+ | \put(5,68){\sx{.45}{$\Im(z)$}} |
||
\put(7,59){\sx{.5}{$5$}} |
\put(7,59){\sx{.5}{$5$}} |
||
\put(7,49){\sx{.5}{$4$}} |
\put(7,49){\sx{.5}{$4$}} |
||
Line 185: | Line 228: | ||
\put(7,19){\sx{.5}{$1$}} |
\put(7,19){\sx{.5}{$1$}} |
||
\put(7, 9){\sx{.5}{$0$}} |
\put(7, 9){\sx{.5}{$0$}} |
||
− | \put( |
+ | \put(70 , 6){\sx{.45}{$\Re(z)$}} |
− | \put( |
+ | \put(60 , 6){\sx{.5}{$2$}} |
− | \put(27 ,6){\sx{.5}{$-\!1$}} |
||
\put(40 , 6){\sx{.5}{$0$}} |
\put(40 , 6){\sx{.5}{$0$}} |
||
− | \put( |
+ | \put(17 ,6){\sx{.5}{$-\!2$}} |
+ | \put(25,62){\sx{.5}{$D\!>\!14$}} |
||
+ | \put(55,60){\sx{.5}{$12\!<\!D\!<\!14$}} |
||
+ | \put(68,20){\sx{.5}{$D\!<\!1$}} |
||
+ | \end{picture}} |
||
+ | \sx{2.2}{\begin{picture}(80,80) |
||
+ | %\put(0,0){\includegraphics{figsexpF5}} |
||
+ | %\put(0,0){\includegraphics{figcf5small}} |
||
+ | \put(0,0){\includegraphics{vladi08b}} |
||
+ | \put(5,68){\sx{.45}{$\Im(z)$}} |
||
+ | \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(70 , 6){\sx{.45}{$\Re(z)$}} |
||
\put(60 , 6){\sx{.5}{$2$}} |
\put(60 , 6){\sx{.5}{$2$}} |
||
− | + | \put(40 , 6){\sx{.5}{$0$}} |
|
− | + | \put(17 ,6){\sx{.5}{$-\!2$}} |
|
− | \put( |
+ | \put(31,56){\sx{.5}{$D\!>\!14$}} |
+ | \put(68,20){\sx{.5}{$D\!<\!1$}} |
||
− | } |
||
− | %\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{picture}} |
||
\end{document} |
\end{document} |
||
</nowiki></nomathjax></poem> |
</nowiki></nomathjax></poem> |
||
+ | |||
[[Category:Agreement]] |
[[Category:Agreement]] |
||
[[Category:Book]] |
[[Category:Book]] |
||
[[Category:Agreement]] |
[[Category:Agreement]] |
||
− | [[Category:Complex map]] |
||
[[Category:BookMap]] |
[[Category:BookMap]] |
||
[[Category:Tetration]] |
[[Category:Tetration]] |
Latest revision as of 08:56, 1 December 2018
Agreement of approximations of tetration by elementary functions with the original representation through the Cauchi integral is shown in the left hand side map.
The similar map at the right hand side represents the comparison to the similar representation through the Cauchi integral, but the contour of integration is displaced for 1/2 to the left.
Levels $D=\mathrm{const}$ are drawn with step 2, but the exception is dome for level $D=1$, this level is drawn with thick lines.
$\displaystyle {\rm fse}(z)=\left\{ \begin{array}{ccrcccr} {\rm fima}(z) &,& 4.5& \!<\! &\Im(z) \\ {\rm tai}(z) &,& 1.5& \!<\! &\Im(z) &\!\le\!& 4.5 \\ {\rm maclo}(z) &,& -1.5& \le &\Im(z) &\!\le\!& 1.5 \\ {\rm tai}(z^{*})^{*} &,& -4.5& \le &\Im(z) &\!<\!&\!\! -1.5 \\ {\rm fima}(z^{*})^{*} &,& & &\Im(z) &\!<\!&\!\! -4.5 \end{array} \right.$
Mnemonics for the name of the approximation: Fast Super Exponent.
The agreement plotted is
$\displaystyle D=D_{8}(z)=-\lg\left( \frac
Contents
Refereces
- ↑
http://www.ams.org/mcom/2009-78-267/S0025-5718-09-02188-7/home.html
http://www.ils.uec.ac.jp/~dima/PAPERS/2009analuxpRepri.pdf
http://mizugadro.mudns.jp/PAPERS/2009analuxpRepri.pdf D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670. - ↑
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 8.
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;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
//#include "superex.cin"
#include "fsexp.cin"
#include "f4natu.cin"
//z_type FSEXP(z_type z){DB y=Im(z);
z_type fsexp(z_type z){DB y=Im(z);
if(y> 4.5) return fima(z);
if(y> 1.5) return tai3(z);
if(y>-1.5) return maclo(z);
if(y>-4.5) return conj(tai3(conj(z)));
return conj(fima(conj(z)));
}
//#include "superlo.cin"
#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
z_type Zo=z_type(.31813150520476413, 1.3372357014306895);
z_type Zc=z_type(.31813150520476413,-1.3372357014306895);
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("figcf4small.eps","w");ado(o,0,0,82,82);
FILE *o;o=fopen("vladi08a.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=fsexp(z);
d=F4natu(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"
//M(-2,0)L(-3.1,0) fprintf(o,".04 W 0 0 0 RGB [.1 .1] 1 setdash S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
// system( "gv fig08a.eps");
system("epstopdf vladi08a.eps");
system( "open vladi08a.pdf"); // for linux
// getchar(); system("killall Preview");// for macintosh
}
C++ generator of the second picture
vladif5c.cin also should be loaded
#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;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
//#include "superex.cin"
#include "fsexp.cin"
//#include "f4natu.cin"
#include "vladif5c.cin"
//z_type FSEXP(z_type z){DB y=Im(z);
z_type fsexp(z_type z){DB y=Im(z);
if(y> 4.5) return fima(z);
if(y> 1.5) return tai3(z);
if(y>-1.5) return maclo(z);
if(y>-4.5) return conj(tai3(conj(z)));
return conj(fima(conj(z)));
}
//#include "superlo.cin"
#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
z_type Zo=z_type(.31813150520476413, 1.3372357014306895);
z_type Zc=z_type(.31813150520476413,-1.3372357014306895);
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("figcf5small.eps","w");ado(o,0,0,82,82);
FILE *o;o=fopen("vladi08b.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=fsexp(z);
d=F5(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"
//M(-2,0)L(-3.1,0) fprintf(o,".04 W 0 0 0 RGB [.1 .1] 1 setdash S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
system("epstopdf vladi08b.eps");
system( "open vladi08b.pdf");//linux
//getchar(); system("killall Preview");
}
Latex combiner
\documentclass[12pt]{article}
\usepackage{graphicx}
\usepackage{rotating}
\usepackage{geometry}
\paperwidth 378px
%\paperheight 134px
\paperheight 180px
\topmargin -104pt
\oddsidemargin -94pt
\pagestyle{empty}
\begin{document}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\sx{2.2}{\begin{picture}(90,80)
%\put(0,0){\includegraphics{figsexpF4}}
%\put(0,0){\includegraphics{figcf4small}}
\put(0,0){\includegraphics{vladi08a}}
\put(5,68){\sx{.45}{$\Im(z)$}}
\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(70 , 6){\sx{.45}{$\Re(z)$}}
\put(60 , 6){\sx{.5}{$2$}}
\put(40 , 6){\sx{.5}{$0$}}
\put(17 ,6){\sx{.5}{$-\!2$}}
\put(25,62){\sx{.5}{$D\!>\!14$}}
\put(55,60){\sx{.5}{$12\!<\!D\!<\!14$}}
\put(68,20){\sx{.5}{$D\!<\!1$}}
\end{picture}}
\sx{2.2}{\begin{picture}(80,80)
%\put(0,0){\includegraphics{figsexpF5}}
%\put(0,0){\includegraphics{figcf5small}}
\put(0,0){\includegraphics{vladi08b}}
\put(5,68){\sx{.45}{$\Im(z)$}}
\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(70 , 6){\sx{.45}{$\Re(z)$}}
\put(60 , 6){\sx{.5}{$2$}}
\put(40 , 6){\sx{.5}{$0$}}
\put(17 ,6){\sx{.5}{$-\!2$}}
\put(31,56){\sx{.5}{$D\!>\!14$}}
\put(68,20){\sx{.5}{$D\!<\!1$}}
\end{picture}}
\end{document}
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