File:Nemplot.jpg

Explicit plot of the Nemtsov function $\mathrm{Nem}_q(z)=z+z^3+qz^4$:

$y=\mathrm{Nem}_q(z)$ versus $x$ for various $q$.

C++ generator of the curves
File ado.cin, conto.cin should be loaded in order to compile the code below: //using namespace std; typedef std::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.)
 * 4) include "conto.cin"

//#include "aunem.cin"

int main{ int Max; int j,k,m,n; DB x,y, p,q, t,tr,ti; z_type z,c,d;

DB P=1 ; DB Q=.5; FILE *o;o=fopen("nemplo.eps","w");ado(o,402,1002); fprintf(o,"201 501 translate\n 100 100 scale 2 setlinecap\n"); for(m=-2;m<3;m++){M(m,-5)L(m,5)} for(n=-5;n<6;n++){M(-2,n)L(2,n)} fprintf(o,".006 W 0 0 0 RGB 2 setlinecap S 1 setlinejoin\n");

q=0.; DO(m,401){x=-2+.01*m; y=x*(1.+x*x*(1.+q*x)); if(m==0) M(x,y) else L(x,y) ; } fprintf(o,".02 W 0 0 0 RGB S\n"); q=.5; DO(m,401){x=-2+.01*m; y=x*(1.+x*x*(1.+q*x)); if(m==0) M(x,y) else L(x,y); if(x>0 && y>6) break; } fprintf(o,".02 W 1 0 0 RGB S\n"); q=1.; DO(m,401){x=-2+.01*m; y=x*(1.+x*x*(1.+q*x)); if(m==0) M(x,y) else L(x,y); if(x>0 && y>6) break; } fprintf(o,".02 W 0 .8 0 RGB S\n"); q=2.; DO(m,401){x=-1.5+.01*m; y=x*(1.+x*x*(1.+q*x)); if(m==0) M(x,y) else L(x,y) ; if(x>0 && y>6) break;} fprintf(o,".02 W 0 0 1 RGB S\n");

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

//getchar; system("killall Preview");// mac

return 0; }

Latex generator of labels
\documentclass[12pt]{article} \usepackage{graphics} \paperwidth 404pt \paperheight 1006pt \usepackage{geometry} \usepackage{rotating} \textwidth 1260pt \textheight 1260pt \topmargin -106pt \oddsidemargin -74pt \parindent 0pt \pagestyle{empty} \newcommand \ing {\includegraphics} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \begin{document} \begin{picture}(404,1004) %\put(24,20){\ing{arqne114}} %\put(50,40){\ing{sunem10q10ma6a}} %\put(50,40){\ing{sunem10q10ma6s}} %\put(24,20){\ing{aunem11mb}} \put(2,2){\ing{nemplo}} \put(176,990){\sx{3}{$y$}} \put(176,895){\sx{3}{$4$}} \put(176,795){\sx{3}{$3$}} \put(176,695){\sx{3}{$2$}} \put(176,595){\sx{3}{$1$}} \put(176,495){\sx{3}{$0$}} \put(156,395){\sx{3}{$-1$}} \put(156,295){\sx{3}{$-2$}} \put(156,195){\sx{3}{$-3$}} \put(156, 95){\sx{3}{$-4$}} %\put(156,395){\sx{3}{$-5$}} \put(82,476){\sx{3}{$-1$}} \put(196,476){\sx{3}{$0$}} \put(296,476){\sx{3}{$1$}} \put(385,476){\sx{3}{$x$}} \put(70,888){\sx{3}{\rot{-87} $q\!=\!2$\ero}} %\put(70,688){\sx{3}{\rot{-87} $q\!=\!2$\ero}} \put(40,490){\sx{3}{\rot{-79} $q\!=\!1$\ero}} \put(54,280){\sx{3}{\rot{60} $q\!=\!0.5$\ero}} %\put(90,108){\sx{3}{\rot{80} $q\!=\!0$\ero}} %\put(60,18){\sx{3}{\rot{80} $q\!=\!0$\ero}} \put(46,18){\sx{3}{\rot{80} $q\!=\!0$\ero}} % \put(294,916){\sx{3}{\rot{80} $q\!=\!2$\ero}} \put(368,916){\sx{3}{\rot{80} $q\!=\!0$\ero}} \end{picture} \end{document}