File:PowPloT.jpg

Explicit plot of function Pow$_a$ for various real values of parameter $a$.

$y=\mathrm{Pow}_a(x)=\exp_x(a)=x^a$ versus $x$

C++ generator of curves
using namespace std; typedef complex z_type; //DB B=2.; //DB F(DB z) { return exp( exp( log(B)*z));} //DB G(DB z) { return log( log(z) )/log(B);} main{ int m,n; double z,x,y,t; FILE *o; o=fopen("PowPlo.eps","w"); ado(o,1010,1010); fprintf(o,"1 1 translate 100 100 scale\n"); for(m=0;m<11;m++) {M(m,0)L(m,10)} for(m=0;m<11;m++) {M(0,m)L(10,m)} fprintf(o,"2 setlinecap 1 setlinejoin .01 W S\n"); // DO(m,42){x=0.001+.1*m; y=exp(2.*log(x)); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 0 1 0 RGB S\n"); // DO(m,1002){x=0.001+.01*m; y=exp(.5*log(x)); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 1 0 1 RGB S\n"); // for(n=-31;n<31;n+=2){t=.1*n; DO(m,1002){x=.1+.02*m; y=exp(t*log(x)); if(m==0) M(x,y) else L(x,y); if(y>10.1)break;} } // fprintf(o,"1 setlinecap 1 setlinejoin\n"); // t=-3.; z=exp(log(10.05)/t); DO(m,1002){x=z+.02*m; y=exp(t*log(x)); if(m==0) M(x,y) else L(x,y); if(y>10.1)break;} fprintf(o,".02 W 1 0 0 RGB S\n"); t=-2.; z=exp(log(10.05)/t); DO(m,1002){x=z+.02*m; y=exp(t*log(x)); if(m==0) M(x,y) else L(x,y); if(y>10.1)break;} fprintf(o,".02 W 1 0 0 RGB S\n"); t=-1.; z=exp(log(10.05)/t); DO(m,1002){x=z+.02*m; y=exp(t*log(x)); if(m==0) M(x,y) else L(x,y); if(y>10.1)break;} fprintf(o,".02 W 1 0 0 RGB S\n"); t=1.; z=0; DO(m,1002){x=z+.02*m; y=exp(t*log(x)); if(m==0) M(x,y) else L(x,y); if(y>10.1)break;} fprintf(o,".02 W 0 0 1 RGB S\n"); t=2.; z=0; DO(m,1002){x=z+.02*m; y=exp(t*log(x)); if(m==0) M(x,y) else L(x,y); if(y>10.1)break;} fprintf(o,".02 W 0 0 1 RGB S\n"); t=3.; z=0; DO(m,1002){x=z+.02*m; y=exp(t*log(x)); if(m==0) M(x,y) else L(x,y); if(y>10.1)break;} fprintf(o,".02 W 0 0 1 RGB S\n"); for(n=-20;n<0;n+=2){t=.1*n; z=exp(log(10.05)/t); DO(m,1002){x=z+.01*m; y=exp(t*log(x)); if(m==0) M(x,y) else L(x,y); if(y>10.1)break;}} for(n=0;n<21;n+=2){t=.1*n; z=.005; DO(m,1002){x=z+.01*m; y=exp(t*log(x)); if(m==0) M(x,y) else L(x,y); if(y>10.1)break;}} fprintf(o,".01 W 0 0 0 RGB S\n"); fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf PowPlo.eps"); system(   "open PowPlo.pdf"); getchar; system("killall Preview"); }
 * 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 "ado.cin"
 * 1) define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
 * 2) define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);

Latex Generator of labels
% % % file PowPlo.pdf should be generated with the code above in order to compile the Latex document below. % % Copyleft 2012 by Dmitrii Kouznetsov % \documentclass[12pt]{article} % \usepackage{geometry} % \usepackage{graphicx} % \usepackage{rotating} % \paperwidth 1010pt % \paperheight 1010pt % \topmargin -94pt % \oddsidemargin -81pt % \textwidth 1100pt % \textheight 1100pt % \pagestyle {empty} % \newcommand \sx {\scalebox} % \newcommand \rot {\begin{rotate}} % \newcommand \ero {\end{rotate}} % \newcommand \ing {\includegraphics} % \parindent 0pt% \pagestyle{empty} % \begin{document} % \begin{picture}(1002,1002) % \put(10,10){\ing{PowPlo}} % \put(11,966){\sx{6}{$y\!=\!x^a$}} % \put(11,898){\sx{4}{$9$}} % \put(11,798){\sx{4}{$8$}} % \put(11,698){\sx{4}{$7$}} % \put(11,598){\sx{4}{$6$}} % \put(11,498){\sx{4}{$5$}} % \put(11,398){\sx{4}{$4$}} % \put(11,298){\sx{4}{$3$}} % \put(11,198){\sx{4}{$2$}} % \put(11,098){\sx{4}{$1$}} % % \put(100,16){\sx{4}{$1$}} % \put(200,16){\sx{4}{$2$}} % \put(301,16){\sx{4}{$3$}} % \put(401,16){\sx{4}{$4$}} % \put(502,16){\sx{4}{$5$}} % \put(602,16){\sx{4}{$6$}} % \put(703,16){\sx{4}{$7$}} % \put(803,16){\sx{4}{$8$}} % \put(903,16){\sx{4}{$9$}} % \put(990,16){\sx{4}{$x$}} % % \put(50,881){\sx{4}{\rot{-88}$a\!=\!-2$\ero}} % \put(204,774){\sx{4}{\rot{86}$a\!=\!3$\ero}} % \put(288,776){\sx{4}{\rot{81}$a\!=\!2$\ero}} % \put(423,838){\sx{4}{\rot{73}$a\!=\!1.6$\ero}} % \put(498,836){\sx{4}{\rot{68}$a\!=\!1.4$\ero}} % \put(636,851){\sx{4}{\rot{58}$a\!=\!1.2$\ero}} % % \put(826,831){\sx{4}{\rot{45}$a\!=\!1$\ero}} % % \put(880,580){\sx{4}{\rot{27}$a\!=\!0.8$\ero}} % \put(870,378){\sx{4}{\rot{14}$a\!=\!0.6$\ero}} % \put(864,250){\sx{4}{\rot{5}$a\!=\!0.4$\ero}} % \put(864,168){\sx{4}{\rot{2}$a\!=\!0.2$\ero}} % \put(864,114){\sx{4}{\rot{0}$a\!=\!0$\ero}} % \put(844,68){\sx{4}{\rot{-1}$a\!=\!-0.2$\ero}} % \end{picture} % \end{document} % %