imported>Dmitrii Kouznetsov |
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| == Summary == | | == Summary == |
| {{Image_Details|user
| | Importing file |
| |description = [[Iteration of function]] [[ArcLambertW]], id est [[zex]]<math>(z)=z\exp(z)~</math>. For various number <math>n</math> of iteration, <math>~y\!=\!\mathrm{zex}^n(x)~</math> is plottecd versus <math>x</math>.
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| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |date-created = 2012.11.11
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| |pub-country = Japan
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| |notes =
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| |versions = http://tori.ils.uec.ac.jp/TORI/index.php/File:ZexIteT.jpg
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| }}
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| ==[[C++]] Generator of curves==
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| // Files [[ado.cin]], [[Tania.cin]], [[LambertW.cin]], [[SuZex.cin]], [[AuZex.cin]] should be loaded to the working directory in order to compile the code below.
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|
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| #include <math.h>
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| #include <stdio.h>
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| #include <stdlib.h>
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| #define DB double
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| #define DO(x,y) for(x=0;x<y;x++)
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| using namespace std;
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| #include<complex>
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| typedef complex<double> z_type;
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| #define Re(x) x.real()
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| #define Im(x) x.imag()
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| #define I z_type(0.,1.)
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| #include "Tania.cin" // need for LambertW
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| #include "LambertW.cin" // need for AuZex
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| #include "SuZex.cin"
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| #include "AuZex.cin"
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| #include "ado.cin"
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| #define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
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| #define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
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| | |
| main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("ZexIte.eps","w"); ado(o,1204,1204);
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| fprintf(o,"2 2 translate\n 100 100 scale\n");
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| fprintf(o,"1 setlinejoin 2 setlinecap\n");
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| for(n=0;n<13;n++) {M(0,n)L(12,n)}
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| for(m=0;m<13;m++) {M(m,0)L(m,12)}
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| M(M_E,0)L(M_E,1) M(0,M_E)L(1,M_E) fprintf(o,".01 W S\n");
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|
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| DO(m,700){x=.01 +.02*m; y=Re(LambertW(LambertW(x)));if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;} fprintf(o,".033 W 1 0 1 RGB S\n");
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| DO(m,700){x=.01 +.02*m; y=Re(LambertW(x));if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;} fprintf(o,".04 W 1 0 1 RGB S\n");
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| M(0,0) L(12.03,12.03) fprintf(o,".03 W 0 1 0 RGB S\n");
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| DO(m,700){x=.01 +.02*m; y=Re(zex(x)); if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;} fprintf(o,".04 W 0 1 0 RGB S\n");
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| DO(m,700){x=.01 +.02*m; y=Re(zex(zex(x))); if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;} fprintf(o,".033 W 0 1 0 RGB S\n");
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| for(n=-10;n<11;n++){
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| DO(m,700){x=.01 +.02*m; y=Re(auzex(x)); y=Re(suzex(.1*n+y)); if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;}
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| fprintf(o,".023 W 0 0 0 RGB S\n");
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| }
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| fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o);
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| system("epstopdf ZexIte.eps");
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| system( "open ZexIte.pdf"); //for macintosh
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| getchar(); system("killall Preview"); // For macintosh
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| }
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| ==[[Latex]] generator of labels==
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| %<nowiki> %<br>
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| % file ZexIte.pdf should be generated with the code above in order to compile the Latex document below. %<br>
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| % Copyleft 2012 by Dmitrii Kouznetsov <br> %
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| \documentclass[12pt]{article} % <br>
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| \usepackage{geometry} % <br>
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| \usepackage{graphicx} % <br>
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| \usepackage{rotating} % <br>
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| \paperwidth 1208pt % <br>
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| \paperheight 1208pt % <br>
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| \topmargin -103pt % <br>
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| \oddsidemargin -73pt % <br>
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| \textwidth 1404pt % <br>
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| \textheight 1404pt % <br>
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| \pagestyle {empty} % <br>
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| \newcommand \sx {\scalebox} % <br>
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| \newcommand \rot {\begin{rotate}} % <br>
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| \newcommand \ero {\end{rotate}} % <br>
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| \newcommand \ing {\includegraphics} % <br>
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| \parindent 0pt% <br>
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| \pagestyle{empty} % <br>
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| \begin{document} % <br>
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| \begin{picture}(1202,1202) % <br>
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| %\put(10,10){\ing{IterPowPlot}} % <br>
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| %\put(10,10){\ing{IterEq2plot}} % <br>
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| \put(0,0){\ing{ZexIte}} % <br>
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| \put(11,1184){\sx{4.4}{$y$}} % <br>
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| \put(04,1090){\sx{4}{$11$}} % <br>
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| \put(04,990){\sx{4}{$10$}} % <br>
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| \put(11,890){\sx{4}{$9$}} % <br>
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| \put(11,790){\sx{4}{$8$}} % <br>
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| \put(11,690){\sx{4}{$7$}} % <br>
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| \put(11,590){\sx{4}{$6$}} % <br>
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| \put(11,490){\sx{4}{$5$}} % <br>
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| \put(11,390){\sx{4}{$4$}} % <br>
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| \put(11,290){\sx{4}{$3$}} % <br>
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| \put(11,190){\sx{4}{$2$}} % <br>
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| \put(11,090){\sx{4}{$1$}} % <br>
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| % <br>
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| \put(91,6){\sx{4}{$1$}} % <br>
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| \put(191,6){\sx{4}{$2$}} % <br>
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| \put(291,6){\sx{4}{$3$}} % <br>
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| \put(391,6){\sx{4}{$4$}} % <br>
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| \put(492,6){\sx{4}{$5$}} % <br>
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| \put(592,6){\sx{4}{$6$}} % <br>
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| \put(693,6){\sx{4}{$7$}} % <br>
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| \put(794,6){\sx{4}{$8$}} % <br>
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| \put(894,6){\sx{4}{$9$}} % <br>
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| \put(982,6){\sx{4}{$10$}} % <br>
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| \put(1082,6){\sx{4}{$11$}} % <br>
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| \put(1180,6){\sx{4.4}{$x$}} % <br>
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| % <br>
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|
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| \put(116,1058){\sx{5}{\rot{88}$n\!=\!2$\ero}} % <br>
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| \put(182,1058){\sx{5}{\rot{88}$n\!=\!1$\ero}} % <br>
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| \put(141,706){\sx{4.5}{\rot{86}$y\!=\!\mathrm{zex}(x)$\ero}} % <br>
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| %
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| \put(512,1030){\sx{5}{\rot{72}$n\!=\!0.3$\ero}} % <br>
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| \put(629,1032){\sx{5}{\rot{64}$n\!=\!0.2$\ero}} % <br>
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| \put(804,1037){\sx{5}{\rot{56}$n\!=\!0.1$\ero}} % <br>
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| % <br>
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| \put(1072,1052){\sx{5}{\rot{44}$n\!=\!0$\ero}} % <br>
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| \put(772,752){\sx{5}{\rot{44}$y\!=\!x$\ero}} % <br>
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| % <br>
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| \put(1028,762){\sx{5}{\rot{32}$n\!=\!-0.1$\ero}} % <br>
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| \put(1014,590){\sx{5}{\rot{23}$n\!=\!-0.2$\ero}} % <br>
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| \put(1006,470){\sx{5}{\rot{17}$n\!=\!-0.3$\ero}} % <br>
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| %
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| \put(510,108){\sx{4.3}{\rot{3}$y\!=\!\mathrm{LambertW}(x)$\ero}} % <br>
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| \put(1010,142){\sx{5}{\rot{2}$n\!=\!-1$\ero}} % <br>
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| \put(1010,83){\sx{5}{\rot{1}$n\!=\!-2$\ero}} % <br>
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| %<br>
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| \end{picture} % <br>
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| \end{document} % <br>
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| %</nowiki>
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| [[Category:Zex]]
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| [[Category:LambertW]]
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| [[Category:Iteration]]
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| [[Category:SuperFunction]]
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| [[Category:AbelFunction]]
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| [[Category:Explicit plot]]
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| [[Category:C++]]
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| [[Category:Latex]]
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| == Licensing ==
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| {{CC|by|3.0}}
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