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.

using namespace std; typedef complex z_type;
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)


 * 1) include "conto.cin"


 * 1) 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-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.

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

\end{picture} % \end{document} % %

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