Difference between revisions of "File:SuZexTay0testT.png"

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Agreement $A_{48}$ of the [[Taylor approximation]] of the [[SuZex]] at zero with highest term of 48th power;
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Importing image file
  
  +
  +
$\displaystyle \mathrm{SuZex}(z) \approx P_{48}(z)=\sum_{n=0}^{48} \,c_n\, z^n$
  +
  +
$\displaystyle A_{48}(z)= -\lg \left( \frac
  +
{|P_{48}(z) - \mathrm{SuZex}(z)|}
  +
{|P_{48}(z)| + |\mathrm{SuZex}(z)|}
  +
\right) $
  +
  +
==[[C++]] generator of curves==
  +
  +
// Files [[ado.cin]], [[conto.cin]] and
  +
  +
// should be loaded to the working directory 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++)
  +
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 "conto.cin"
  +
  +
// [[SuZex.cin]] below is the [[C++]] implementation of function [[SuZex]]
  +
// which is [[superfunction]] for the [[transfer function]] T(z)=[[zex]](z)= x exp(z)
  +
// Copyleft 2012 by Dmitrii Kouznetsov; I hope, files
  +
// [[SuZexCoef20.cin]], [[SuZexTay2008co.cin]], [[SuZexTay0co.cin]]
  +
// are already loaded to the working directory
  +
  +
z_type zex(z_type z) { return z*exp(z);}
  +
  +
z_type suzexo(z_type z){ int n,m; z_type L=log(-z); z_type c[20]; z_type s;
  +
#include "SuZexCoef20.cin"
  +
c[0]=-1.; c[1]=.5*L;
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for(n=2;n<21;n++){ s=a[n][n];
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for(m=n-1; m>=0; m--){ s*=L; s+=a[n][m]; }
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c[n]=s; }
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s=c[20]/z; for(n=19;n>=0;n--){ s+=c[n]; s/=z;}
  +
return s;
  +
}
  +
  +
z_type suzex2008t12(z_type z){ int n,m=80; z_type s;
  +
#include "SuZexTay2008co.cin"
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s=c[m]; for(n=m-1;n>=0;n--){ s*=z; s+=c[n];}
  +
return s;}
  +
  +
#include "SuZexTay0co.cin"
  +
z_type SuZexTay0(z_type z){ int n,m=96; z_type s;
  +
s=SuZexTay0co[m]; for(n=m-1;n>=0;n--){ s*=z; s+=SuZexTay0co[n];}
  +
return s;}
  +
  +
z_type SuZexTay0n48(z_type z){ int n,m=48; z_type s;
  +
s=SuZexTay0co[m]; for(n=m-1;n>=0;n--){ s*=z; s+=SuZexTay0co[n];}
  +
return s;}
  +
  +
z_type suzex(z_type z){int m,n; z_type s;
  +
if( abs(z) < 1.6 ) return SuZexTay0(z) ; // I made the Taylor expansion for this case
  +
if( Re(z)>0 && fabs(Im(z))<1.5){n=int(Re(z)+.5); s=SuZexTay0(z-(0.+n)); DO(m,n) s=zex(s); return s;}
  +
z+=-1.1259817765745026; // WARNING! ARGUEMENT CHANGES ITS VALUE!
  +
if( abs(z+12.) < 8.1 ) return suzex2008t12(z+12.) ; // I made the Taylor expansion for this case
  +
if( Re(z)<-12. || fabs(Im(z)) > 8. ) return suzexo(z); // definitely, |z|>8
  +
n= int(Re(z)+12.); s=suzex2008t12(z+12.-(0.+n)); DO(m,n) s=zex(s); return s;
  +
}
  +
  +
// Copyleft 2012 by Dmitrii Kouznetsov
  +
// [[Category:SuZex]]
  +
// [[Category:C++]]
  +
//The procedures above can be loaded also as [[SuZex.cin]]
  +
// #include "SuZex.cin"
  +
  +
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
  +
//DB x1=-1.1259817765745026; DO(n,8){ y=Re(suzex(x1)); x=y-1.; x1+=-1.2*x; printf("%18.16f %18.16f\n", x1,y);} getchar();
  +
int M=300,M1=M+1;
  +
int N=300,N1=N+1;
  +
DB X[M1],Y[N1];
  +
DB *g, *f, *w; // w is working array.
  +
g=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
  +
f=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
  +
w=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
  +
char v[M1*N1]; // v is working array
  +
FILE *o;o=fopen("SuZexTay0n48testSmallA.eps","w"); ado(o,602,602);
  +
fprintf(o,"301 301 translate\n 100 100 scale\n");
  +
fprintf(o,"1 setlinejoin 2 setlinecap\n");
  +
DO(m,M1) X[m]=-3.+.02*(m-.5);
  +
DO(n,N1) Y[n]=-3.+.02*(n-.5);
  +
//for(n=0;n<N1;n++) { Y[n]=1.09*sinh((3./200.)*(n-200)); printf("%3d %9.6f\n",n,Y[n]); }
  +
for(m=-3;m<4;m++){M(m,-3)L(m,3) }
  +
for(n=-3;n<4;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]=999;
  +
f[m*N1+n]=999;}
  +
DO(m,M1){x=X[m]; if(m/10*10==m) printf("x=%6.3f\n",x);
  +
DO(n,N1){y=Y[n]; z=z_type(x,y); //if(abs(z+2.)>.019)
  +
c=suzex(z);
  +
d=SuZexTay0n48(z);
  +
//c=suzex2008t12(z+(12.-1.1259817765745026));
  +
// c=suzexo(z-1.1259817765745026);
  +
// d=zex(suzex2008(z-1.));
  +
//d =suzexo(z);
  +
//d=zex(suzexo(z-1.));
  +
p=abs(c-d)/(abs(c)+abs(d)); p=-log(p)/log(10.); if(p>0 && p<27) g[m*N1+n]=p;
  +
// p=Re(c); q=Im(c); if(p>-19 && p<19 && ( x<2. || fabs(q)>1.e-12 && fabs(p)>1.e-12) ){ g[m*N1+n]=p;f[m*N1+n]=q;}
  +
}}
  +
fprintf(o,"1 setlinejoin 1 setlinecap\n");
  +
p=4.;q=.5;
  +
conto(o,g,w,v,X,Y,M,N, (1. ),-p,p); fprintf(o,".02 W .5 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N, (2. ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N, (3. ),-p,p); fprintf(o,".04 W 0 1 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N, (4. ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N, (5. ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N, (6. ),-p,p); fprintf(o,".04 W 0 1 1 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N, (7. ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N, (8. ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N, (9. ),-p,p); fprintf(o,".04 W 0 0 1 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N,(10. ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N,(11. ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N,(12. ),-p,p); fprintf(o,".04 W 1 0 1 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N,(13. ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N,(14. ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N,(15. ),-3,3); fprintf(o,".04 W 0 .4 0 RGB S\n");
  +
//conto(o,g,w,v,X,Y,M,N,(16 ),-4,4); fprintf(o,".02 W 0 0 0 RGB S\n");
  +
/*
  +
for(m=-8;m<8;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q,q);fprintf(o,".007 W 0 .6 0 RGB S\n");
  +
for(m=0;m<8;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);fprintf(o,".007 W .9 0 0 RGB S\n");
  +
for(m=0;m<8;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".007 W 0 0 .9 RGB S\n");
  +
for(m= 1;m<17;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".02 W .8 0 0 RGB S\n");
  +
for(m= 1;m<17;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".02 W 0 0 .8 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".02 W .5 0 .5 RGB S\n");
  +
for(m=-16;m<17;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".02 W 0 0 0 RGB S\n");
  +
*/
  +
// fprintf(o,"-12 0 8 10 350 arc 1 .3 0 RGB .06 W S\n");
  +
//#include "plofu.cin"
  +
// fprintf(o,"0 setlinejoin 0 setlinecap\n");
  +
fprintf(o,"showpage\n");
  +
fprintf(o,"%c%cTrailer\n",'%','%');
  +
fclose(o); free(f); free(g); free(w);
  +
system("epstopdf SuZexTay0n48testSmallA.eps");
  +
system( "open SuZexTay0n48testSmallA.pdf"); //for macintosh
  +
getchar(); system("killall Preview"); // For macintosh
  +
}
  +
  +
  +
==[[Latex]] generator of labels]]==
  +
  +
<nowiki> %<br>
  +
\documentclass[12pt]{article} % <br>
  +
\paperwidth 590px % <br>
  +
\paperheight 590px % <br>
  +
\textwidth 2394px % <br>
  +
\textheight 2300px % <br>
  +
\topmargin -110px % <br>
  +
\oddsidemargin -78px % <br>
  +
\usepackage{graphics} % <br>
  +
\usepackage{rotating} % <br>
  +
\newcommand \sx {\scalebox} % <br>
  +
\newcommand \rot {\begin{rotate}} % <br>
  +
\newcommand \ero {\end{rotate}} % <br>
  +
\newcommand \ing {\includegraphics} % <br>
  +
\newcommand \rmi {\mathrm{i}} % <br>
  +
\parindent 0pt
  +
\pagestyle{empty}
  +
\begin{document} % <br>
  +
\newcommand \zoomax { % <br>
  +
\put(20,580){\sx{3}{$y$}} % <br>
  +
\put(20,490){\sx{3}{$2$}} % <br>
  +
\put(20,390){\sx{3}{$1$}} % <br>
  +
\put(20,290){\sx{3}{$0$}} % <br>
  +
\put(-1,190){\sx{3}{$-\!1$}} % <br>
  +
\put(-1, 90){\sx{3}{$-\!2$}} % <br>
  +
\put(76, 20){\sx{3}{$-\!2$}} % <br>
  +
\put(176, 20){\sx{3}{$-\!1$}} % <br>
  +
\put(294, 20){\sx{3}{$0$}} % <br>
  +
\put(395, 20){\sx{3}{$1$}} % <br>
  +
\put(495, 20){\sx{3}{$2$}} % <br>
  +
\put(575, 22){\sx{3}{$x$}} % <br>
  +
} % <br>
  +
\parindent 0pt % <br>
  +
\sx{1}{\begin{picture}(600,600) % <br>
  +
%\put(40,20){\ing{b271tMap3}} % <br>
  +
%\put(40,20){\ing{ExpMap}} % <br>
  +
\put(0,0){\ing{SuZexTay0n48testSmallA}} % <br>
  +
%\put(0,0){\ing{SuZexMapSmall}} % <br>
  +
\put(415,516){\sx{4.6}{$A_{48}\!<\!1$}}
  +
\put(212,286){\sx{4.6}{$A_{48}\!>\!15$}}
  +
\zoomax % <br>
  +
\end{picture}} % <br>
  +
\end{document} % <br>
  +
</nowiki>
  +
  +
[[Category:SuZex]]
  +
[[Category:Zex]]
  +
[[Category:Superfunction]]
  +
[[Category:Regular iteration]]
  +
[[Category:Taylor approximation]]
  +
[[Category:Agreement map]]
  +
[[Category:C++]]
  +
[[Category:Latex]]

Latest revision as of 09:43, 21 June 2013

Agreement $A_{48}$ of the Taylor approximation of the SuZex at zero with highest term of 48th power;

$\displaystyle \mathrm{SuZex}(z) \approx P_{48}(z)=\sum_{n=0}^{48} \,c_n\, z^n$

$\displaystyle A_{48}(z)= -\lg \left( \frac

\right) $

C++ generator of curves

// Files ado.cin, conto.cin and

// should be loaded to the working directory 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++)
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 "conto.cin"

// SuZex.cin below is the C++ implementation of function SuZex
// which is superfunction for the transfer function T(z)=zex(z)= x exp(z)
// Copyleft 2012 by Dmitrii Kouznetsov; I hope, files  
// SuZexCoef20.cin, SuZexTay2008co.cin, SuZexTay0co.cin
// are already loaded to the working directory

z_type zex(z_type z) { return z*exp(z);}

z_type suzexo(z_type z){ int n,m; z_type L=log(-z); z_type c[20]; z_type s;
#include "SuZexCoef20.cin"
c[0]=-1.; c[1]=.5*L;
for(n=2;n<21;n++){ s=a[n][n]; 
                   for(m=n-1; m>=0; m--){ s*=L; s+=a[n][m]; }
                   c[n]=s; }
s=c[20]/z; for(n=19;n>=0;n--){ s+=c[n]; s/=z;}
return s;
}

 z_type suzex2008t12(z_type z){ int n,m=80; z_type s;
 #include "SuZexTay2008co.cin"
 s=c[m]; for(n=m-1;n>=0;n--){ s*=z; s+=c[n];}
 return s;}

 #include "SuZexTay0co.cin"
 z_type SuZexTay0(z_type z){ int n,m=96; z_type s;
 s=SuZexTay0co[m]; for(n=m-1;n>=0;n--){ s*=z; s+=SuZexTay0co[n];}
 return s;}

 z_type SuZexTay0n48(z_type z){ int n,m=48; z_type s;
 s=SuZexTay0co[m]; for(n=m-1;n>=0;n--){ s*=z; s+=SuZexTay0co[n];}
 return s;}

z_type suzex(z_type z){int m,n; z_type s;
if( abs(z) < 1.6 )                   return SuZexTay0(z) ; // I made the Taylor expansion for this case
if( Re(z)>0 && fabs(Im(z))<1.5){n=int(Re(z)+.5); s=SuZexTay0(z-(0.+n)); DO(m,n) s=zex(s); return s;}
 z+=-1.1259817765745026;     // WARNING! ARGUEMENT CHANGES ITS VALUE!
if( abs(z+12.) < 8.1 )               return suzex2008t12(z+12.) ; // I made the Taylor expansion for this case
if( Re(z)<-12. || fabs(Im(z)) > 8. ) return suzexo(z); // definitely, |z|>8
n= int(Re(z)+12.); s=suzex2008t12(z+12.-(0.+n)); DO(m,n) s=zex(s); return s;
} 

// Copyleft 2012 by Dmitrii Kouznetsov
//
//
//The procedures above can be loaded also as SuZex.cin
// #include "SuZex.cin"

main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
//DB x1=-1.1259817765745026; DO(n,8){ y=Re(suzex(x1)); x=y-1.; x1+=-1.2*x; printf("%18.16f %18.16f\n", x1,y);} getchar();
int M=300,M1=M+1;
int N=300,N1=N+1;
DB X[M1],Y[N1];
DB *g, *f, *w; // w is working array.
g=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
f=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
w=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
char v[M1*N1]; // v is working array
FILE *o;o=fopen("SuZexTay0n48testSmallA.eps","w");  ado(o,602,602);
fprintf(o,"301 301 translate\n 100 100 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");
DO(m,M1) X[m]=-3.+.02*(m-.5);
DO(n,N1) Y[n]=-3.+.02*(n-.5); 
//for(n=0;n<N1;n++) { Y[n]=1.09*sinh((3./200.)*(n-200)); printf("%3d %9.6f\n",n,Y[n]); }
for(m=-3;m<4;m++){M(m,-3)L(m,3) }
for(n=-3;n<4;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]=999;
                       f[m*N1+n]=999;}
DO(m,M1){x=X[m]; if(m/10*10==m) printf("x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y); //if(abs(z+2.)>.019)
c=suzex(z);
d=SuZexTay0n48(z);
//c=suzex2008t12(z+(12.-1.1259817765745026));
// c=suzexo(z-1.1259817765745026);
// d=zex(suzex2008(z-1.));
//d =suzexo(z);
//d=zex(suzexo(z-1.));
 p=abs(c-d)/(abs(c)+abs(d)); p=-log(p)/log(10.); if(p>0 && p<27) g[m*N1+n]=p;
// p=Re(c); q=Im(c); if(p>-19 && p<19 && ( x<2. ||  fabs(q)>1.e-12 && fabs(p)>1.e-12) ){ g[m*N1+n]=p;f[m*N1+n]=q;}
       }}
fprintf(o,"1 setlinejoin 1 setlinecap\n");
p=4.;q=.5;
 conto(o,g,w,v,X,Y,M,N, (1.  ),-p,p); fprintf(o,".02 W .5 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, (2.  ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, (3.  ),-p,p); fprintf(o,".04 W 0 1 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, (4.  ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, (5.  ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, (6.  ),-p,p); fprintf(o,".04 W 0 1 1 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, (7.  ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, (8.  ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N, (9.  ),-p,p); fprintf(o,".04 W 0 0 1 RGB S\n");
 conto(o,g,w,v,X,Y,M,N,(10.  ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N,(11.  ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N,(12.  ),-p,p); fprintf(o,".04 W 1 0 1 RGB S\n");
 conto(o,g,w,v,X,Y,M,N,(13.  ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N,(14.  ),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n");
 conto(o,g,w,v,X,Y,M,N,(15.  ),-3,3); fprintf(o,".04 W 0 .4 0 RGB S\n");
//conto(o,g,w,v,X,Y,M,N,(16  ),-4,4); fprintf(o,".02 W 0 0 0 RGB S\n");
/*
for(m=-8;m<8;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q,q);fprintf(o,".007 W 0 .6 0 RGB S\n");
for(m=0;m<8;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);fprintf(o,".007 W .9 0 0 RGB S\n");
for(m=0;m<8;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".007 W 0 0 .9 RGB S\n");
for(m= 1;m<17;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".02 W .8 0 0 RGB S\n");
for(m= 1;m<17;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".02 W 0 0 .8 RGB S\n");
               conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p); fprintf(o,".02 W .5 0 .5 RGB S\n");
for(m=-16;m<17;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".02 W 0 0 0 RGB S\n");
*/
//  fprintf(o,"-12 0 8 10 350 arc 1 .3 0 RGB .06 W S\n");
//#include "plofu.cin"
//  fprintf(o,"0 setlinejoin 0 setlinecap\n");
fprintf(o,"showpage\n");
fprintf(o,"%c%cTrailer\n",'%','%');
fclose(o);  free(f); free(g); free(w);
      system("epstopdf SuZexTay0n48testSmallA.eps"); 
      system(    "open SuZexTay0n48testSmallA.pdf"); //for macintosh
      getchar(); system("killall Preview"); // For macintosh
}


Latex generator of labels]]

 %<br> \documentclass[12pt]{article} % <br> \paperwidth 590px % <br> \paperheight 590px % <br> \textwidth 2394px % <br> \textheight 2300px % <br> \topmargin -110px % <br> \oddsidemargin -78px % <br> \usepackage{graphics} % <br> \usepackage{rotating} % <br> \newcommand \sx {\scalebox} % <br> \newcommand \rot {\begin{rotate}} % <br> \newcommand \ero {\end{rotate}} % <br> \newcommand \ing {\includegraphics} % <br> \newcommand \rmi {\mathrm{i}} % <br> \parindent 0pt \pagestyle{empty} \begin{document} % <br> \newcommand \zoomax { % <br> \put(20,580){\sx{3}{$y$}} % <br> \put(20,490){\sx{3}{$2$}} % <br> \put(20,390){\sx{3}{$1$}} % <br> \put(20,290){\sx{3}{$0$}} % <br> \put(-1,190){\sx{3}{$-\!1$}} % <br> \put(-1, 90){\sx{3}{$-\!2$}} % <br> \put(76, 20){\sx{3}{$-\!2$}} % <br> \put(176, 20){\sx{3}{$-\!1$}} % <br> \put(294, 20){\sx{3}{$0$}} % <br> \put(395, 20){\sx{3}{$1$}} % <br> \put(495, 20){\sx{3}{$2$}} % <br> \put(575, 22){\sx{3}{$x$}} % <br> } % <br> \parindent 0pt % <br> \sx{1}{\begin{picture}(600,600) % <br> %\put(40,20){\ing{b271tMap3}} % <br> %\put(40,20){\ing{ExpMap}} % <br> \put(0,0){\ing{SuZexTay0n48testSmallA}} % <br> %\put(0,0){\ing{SuZexMapSmall}} % <br> \put(415,516){\sx{4.6}{$A_{48}\!<\!1$}} \put(212,286){\sx{4.6}{$A_{48}\!>\!15$}} \zoomax % <br> \end{picture}} % <br> \end{document} % <br>

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