File:Acosc1mapT.png

Complex map of function acosc1

The First branch of the inverse function ArcCosc

C++ generator of curves

Files acosc1.cin and ado.cin and conto.cin and plofu.cin should be loaded to the working directory in order to compile the C++ 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"

#include "acosc1.cin"

main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=401,M1=M+1;
int N=401,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("acosc1map.eps","w");ado(o,82,82);
fprintf(o,"41 41 translate\n 10 10 scale\n");
DO(n,200)Y[n]=-4.+.02*n;
      Y[200]=-.002;
      Y[201]= .002;
for(n=202;n<N1;n++) Y[n]=-4.+.02*(n-1.);
DO(m,M1)X[m]=Y[m];
for(m=-4;m<5;m++){if(m==0){M(m,-4.1)L(m,4.1)} else{M(m,-4)L(m,4)}}
for(n=-4;n<5;n++){     M(  -4,n)L(4,n)}
fprintf(o,".01 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("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
       c= acosc1(z);
 //      d= cosc(c);
 //    p=abs((z-d)/(z+d));  p=-log(p)/log(10.);
      p=Re(c);  q=Im(c);        
      if(p>-99. && p<99.
       &&     q>-99. && q<99 
      )
      {g[m*N1+n]=p; 
       f[m*N1+n]=q;
       }
                      }}
M(Tarao0,-4) L(Tarao0,4) M(Tarao1,-4) L(Tarao1,4)
fprintf(o,".002 W 0 0 0 RGB S\n");
// #include "plodi.cin"
   #include "plofu.cin"
M(Tarao0,0) L(-4,0)
M(Tarao1,0) L(4,0)
fprintf(o,"0 setlinecap .025 W 1 1 1 RGB S\n");
DO(m,37){x=Tarao0-.1*m; M(x,0) L(x-.05,0)}
DO(m,40){x=Tarao1+.1*m; M(x,0) L(x-.05,0)}
fprintf(o,".026 W 0 0 0 RGB S\n");
// 
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf acosc1map.eps");
      system(    "open acosc1map.pdf");            
      getchar(); system("killall Preview");//for mac
}

Latex generator of labels

File acosc1map.pdf should be generated with the code above in order to compile the Latex document below.

% %<br> \documentclass[12pt]{article} %<br> \paperheight 838px %<br> \paperwidth 844px %<br> \textwidth 1294px %<br> \textheight 1200px %<br> \topmargin -80px %<br> \oddsidemargin -80px %<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> \begin{document} %<br> \newcommand \zoomax { %<br> \put(16,820){\sx{4.4}{$y$}} %<br> \put(16,630){\sx{4}{$2$}} %<br> \put(16,430){\sx{4}{$0$}} %<br> \put(-4, 230){\sx{4}{$-\!2$}} %<br> \put(220, 5){\sx{4}{$-\!2$}} %<br> \put(441, 5){\sx{4}{$0$}} %<br> \put(642, 5){\sx{4}{$2$}} %<br> \put(831,6){\sx{4}{$x$}} %<br> } %<br> \parindent 0pt %<br> \begin{picture}(816,816) %<br> \put(40,30){\sx{10}{\ing{acosc1map}}} %<br> \zoomax %<br> \put(60,431){\sx{4}{\bf cut}} %<br> \put(660,431){\sx{4}{\bf cut}} %<br> \put(455,690){\sx{5}{\rot{78}$u\!=\!4$ \ero}} %<br> \put(650,584){\sx{5}{\rot{31}$u\!=\!5$ \ero}} %<br> \put(620,281){\sx{5}{\rot{-30}$u\!=\!5$ \ero}} %<br> \put(424,201){\sx{5}{\rot{-80}$u\!=\!4$ \ero}} %<br> \put(146,700){\sx{5}{\rot{-50}$u\!=\!3$ \ero}} %<br> \put(146,140){\sx{5}{\rot{50}$u\!=\!3$ \ero}} %<br> %<br> \put(280,590){\sx{5}{\rot{22}$v\!=\!3$ \ero}} %<br> \put(260,270){\sx{5}{\rot{-22}$v\!=\!-3$ \ero}} %<br> \end{picture} %<br> \end{document} %<br> %

Keywords

Cosc, Arccosc, Inverse funciton]], Sazae-san functions, Sazae-san constants

References