File:Sunem0mdp.jpg

(* Coefficients of the asymptotic expansion of function SuNem can be computed with the Mathematica code below *)

T[z_] = z + z^3 + q z^4
P[m_, L_] := Sum[a[m, n] L^n, {n, 0, IntegerPart[m/2]}]
A[1, 0] = -q; A[1, 1] = 0;
a[2, 0] = 0; A[2, 0] = 0;
F[m_, z_] := 1/(-2 z)^(1/2) (1 - q/(-2 z)^(1/2) + Sum[P[n, Log[-z]]/(-2 z)^(n/2), {n, 2, m}])

m = 2; s[m] = Numerator[ Normal[Series[(T[F[m, -1/x^2]] - F[m, -1/x^2+1]) 2^((m+1)/2)/x^(m+2), {x,0,1}]]]
t[m] = Numerator[Coefficient[Normal[s[m]], x] ]
sub[m] = Extract[Solve[t[m] == 0, a[m, 1]], 1]
SUB[m] = Simplify[sub[m]]
f[m, z_] = ReplaceAll[F[m, z], SUB[m]]

m = 3
s[m] = Simplify[ ReplaceAll[ Series[(T[F[m, -1/x^2]] - F[m, -1/x^2+1]) 2^((m+3)/2)/x^(m+3), {x,0,0}], SUB[m-1]]];
t[m] = ReplaceAll[Normal[s[m]], Log[x] -> L];
u[m] = Table[ Coefficient[t[m] L, L^n] == 0, {n, 1, 1 + IntegerPart[m/2]}];
tab[m] = Table[a[m, n], {n, 0, IntegerPart[m/2]}];
sub[m] = Extract[Solve[u[m], tab[m]], 1]
SUB[m] = Join[SUB[m-1], sub[m]];

(* and the same for other m *)

Clear[m]; A[m_, n_] := ReplaceAll[a[m, n], sub[m]]

For[m = 1, m < 37,
 For[n = 0, n < (m + 1)/2,
  Print["A[", m, "][", n, "]=", CForm[N[ReplaceAll[HornerForm[A[m, n], q], {q^2 -> K, q -> Q}]]], ";"]; n++]; m++;]

#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 "conto.cin"

DB Q=0.;
z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); }
z_type nem1(z_type z){ return 1.+z*z*(3.+z*(4.*Q)); } // WARNING: Q is global!

#include "sune.cin"

DB SUNo=0; // should be reassigned
z_type sunem(z_type z){ return sune(z + SUNo);}

int main(){ int Max; int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
// DB rr,ti;
co(); // Evaluate soefficients of the expansion

x=0; DO(n,60) { y=Re(sune(x)); x-= y-1.; printf("%19.16lf %19.16lf\n", x,y);}
SUNo=x;
printf("A[2][0]= %9.5lf , A[2][1]=%9.5lf\n",A[2][0],A[2][1]);
printf("A[3][0]= %9.5lf , A[3][1]=%9.5lf\n",A[3][0],A[3][1]);
 int M=501,M1=M+1;
 int N=501,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
//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("sunem0md.eps","w");ado(o,1008,1008);
fprintf(o,"504 504 translate\n 100 100 scale 2 setlinecap\n");
DO(m,M1) X[m]=-5.+.02*(m-.5);
DO(n,N1) Y[n]=-5.+.02*(n-.5);
for(m=-5;m<6;m+=1){ M(m,-5)L(m,5)}
for(n=-5;n<6;n+=1){ M(-5,n)L(5,n)}
fprintf(o,".003 W 0 0 0 RGB 2 setlinecap S\n");

DO(m,M1)DO(n,N1){g[m*N1+n]=9999999; f[m*N1+n]=9999999;}
DO(m,M1){x=X[m]; if(m/10*10==m) printf("run at x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
c=sunem(z);
//d=sune(z);
//p=abs(c-d)/abs(c+d); p=-log(p)/log(10.);
        p=Re(c); q=Im(c);
//if(p>-85 && p<85) g[m*N1+n]=p;
        if(p>-1001 && p<1001 &&
        q >-1001 && q<1001 ) { g[m*N1+n]=p; f[m*N1+n]=q; }
        }}

//M(-2,0) L(0,0) M(tr,ti)L(0,0)L(tr,-ti)
//fprintf(o,".002 W 1 1 0 RGB 0 setlinecap S\n");

fprintf(o,"1 setlinejoin 1 setlinecap\n");
p=6.;q=.6;
//#include"plofu.cin"

for(m=-5;m<5;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q,q);
                                                fprintf(o,".01 W 0 .6 0 RGB S\n");
for(m=0;m<5;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);
                                                fprintf(o,".01 W .9 0 0 RGB S\n");
for(m=0;m<5;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);
                                                fprintf(o,".01 W 0 0 .9 RGB S\n");

for(m= 1;m<11;m++) conto(o,f,w,v,X,Y,M,N,(0.-m),-p,p);fprintf(o,".023 W .8 0 0 RGB S\n");
for(m= 1;m<11;m++) conto(o,f,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".023 W 0 0 .8 RGB S\n");
                   conto(o,f,w,v,X,Y,M,N,(0. ),-p,p);fprintf(o,".023 W .5 0 .5 RGB S\n");
for(m=-10;m<11;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".023 W 0 0 0 RGB S\n");

/*
conto(o,g,w,v,X,Y,M,N,15.5,-1,1);fprintf(o,".02 W 1 0 1 RGB S\n");
conto(o,g,w,v,X,Y,M,N,15.,-p,p);fprintf(o,".04 W 0 0 1 RGB S\n");
conto(o,g,w,v,X,Y,M,N,14.,-p,p);fprintf(o,".02 W 0 1 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,13.,-p,p);fprintf(o,".02 W 1 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,12.,-p,p);fprintf(o,".04 W 0 0 .7 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,10.,-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 .6 .8 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,7.,-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 .6 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,4.,-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 1 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,1.,-p,p);fprintf(o,".05 W .5 0 0 RGB S\n");
*/

//M(-2,0) L(0,0) M(tr,ti)L(0,0)L(tr,-ti)
//fprintf(o,".004 W 1 1 0 RGB 0 setlinecap S\n");

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
        system("epstopdf sunem0md.eps");
        system( "open sunem0md.pdf"); //mac

//for(m=-40;m<0;m++) {x=m; y=Re(sun(x)); t=Re(nem(sun(x-1.))); printf("%6.1lf %18.15lf %18.15lf %18.15lf\n", x,y,t,y-t);}
return 0;
}

%\documentclass[12pt]{article}
\documentclass{mcom-l}
 \usepackage{graphics}
 \paperwidth 1040pt
 \paperheight 1032pt
 \usepackage{geometry}
 \usepackage{rotating}
 \textwidth 1260pt
 \textheight 1260pt
 \topmargin -94pt
 \oddsidemargin -72pt
 \parindent 0pt
 \pagestyle{empty}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\begin{document}
\begin{picture}(1038,1030)
%\put(50,40){\ing{sunem10q10ma6s}}
%\put(24,20){\ing{nem120ma}}
\put(30,20){\ing{sunem0md}}
\put(11,1015){\sx{3.2}{$y$}}
\put(11,917){\sx{3}{$4$}}
\put(11,817){\sx{3}{$3$}}
\put(11,717){\sx{3}{$2$}}
\put(11,617){\sx{3}{$1$}}
\put(11,517){\sx{3}{$0$}}
\put(-6,417){\sx{3}{$-1$}}
\put(-6,317){\sx{3}{$-2$}}
\put(-6,217){\sx{3}{$-3$}}
\put(-6,117){\sx{3}{$-4$}}
\put(-6, 17){\sx{3}{$-5$}}
\put( 9, 0){\sx{3}{$-5$}}
\put(109, 0){\sx{3}{$-4$}}
\put(209, 0){\sx{3}{$-3$}}
\put(309, 0){\sx{3}{$-2$}}
\put(409, 0){\sx{3}{$-1$}}
\put(530, 0){\sx{3}{$0$}}
\put(630, 0){\sx{3}{$1$}}
\put(730, 0){\sx{3}{$2$}}
\put(830, 0){\sx{3}{$3$}}
\put(930, 0){\sx{3}{$4$}}
\put(1022,0){\sx{3.2}{$x$}}
%
\put(788,884){\sx{3}{\rot{57} $u\!=\!0.1$\ero}}
\put(620,998){\sx{3}{\rot{-73} $u\!=\!0.2$\ero}}
\put(150,929){\sx{3}{\rot{16} $u\!=\!0.3$\ero}}
\put(166,532){\sx{3}{\rot{79} $u\!=\!0.4$\ero}}
\put(308,536){\sx{3}{\rot{74} $u\!=\!0.5$\ero}}
\put(392,535){\sx{3}{\rot{70} $u\!=\!0.6$\ero}}
\put(446,531){\sx{3}{\rot{68} $u\!=\!0.7$\ero}}
\put(486,530){\sx{3}{\rot{68} $u\!=\!0.8$\ero}}
\put(538,526){\sx{3}{\rot{68} $u\!=\!1$\ero}}
%
\put(642,76){\sx{3}{\rot{72} $u\!=\!0.2$\ero}}
\put(784,148){\sx{3}{\rot{-59} $u\!=\!0.1$\ero}}
%
\put(664,876){\sx{3}{\rot{-9} $v\!=\!0.4$\ero}}
\put(520,946){\sx{3}{\rot{39} $v\!=\!0.3$\ero}}
\put(308,916){\sx{3}{\rot{-84} $v\!=\!0.2$\ero}}
\put(110,782){\sx{3}{\rot{-41} $v\!=\!0.1$\ero}}
\put(60,518){\sx{3}{\rot{0} $v\!=\!0$\ero}}
\put(846,518){\sx{3}{\rot{0} \bf huge values\ero}}
\put(100,236){\sx{3}{\rot{42} $v\!=\!-0.1$\ero}}
\put(321, 110){\sx{3}{\rot{82} $v\!=\!-0.2$\ero}}
%
\end{picture}
\end{document}