<!-- hamlet
<!-- copytar
examples/                                                                                           0040775 0001107 0000172 00000000000 05662451303 0014266 5                                                                                                    ustar 00zachary                         cs-teach                        377777770000630                                                                                                                                                                        examples/integrate.c                                                                                0100644 0001107 0000172 00000001440 05662451251 0016410 0                                                                                                    ustar 00zachary                         cs-teach                        377777770000630                                                                                                                                                                        #include <math.h>
#include <stdio.h>

/* The function that we will be integrating. */

float integrand(float t) {
  float V0 = 5.0;
  float K = 0.2;
  return V0 * exp(-K * t);
}


/* Computes the trapezoidal approximation to the integral of integrand, over
   the range (a,b), using N subintervals. */

float trapezoid (float a, float b, int N) {

  float sum, h;
  int i;

  sum = integrand(a)/2;
  h = (b-a) / N;

  for (i = 1; i < N; i = i+1) {
    sum = sum + integrand(a + i*h);
  }

  sum = sum + integrand(b)/2;
  return(sum*h);

}


/* Inputs a value for N and integrates integrand between 0 and 5. */

void main () {

  int N;
  float approx;

  printf("Enter N: ");
  scanf("%d", &N);

  approx = trapezoid(0, 5, N);

  printf("Trapezoidal approximation for N = %d is %g\n", N, approx);

}
                                                                                                                                                                                                                                examples/integrate.m                                                                                0100644 0001107 0000172 00000122714 05662251643 0016435 0                                                                                                    ustar 00zachary                         cs-teach                        377777770000630                                                                                                                                                                        5Òa 
 tubeplot       
 readlib     *    
 plots/tubeplot       
 plots/display    2  *  
 F        *  
 r        
 func         
 obj      
 objname      
 newobjs      
 newopts      
 plottype         
 tmp      
 plotopts         
 inseq        
 f        *  
 Copyright 1992 by the University of Waterloo         *  D  :  .     
 NULL        :  .     ˜–Û :  .    
 
 false       >    
 type        *  0       
 set     *  
 function        :  .     ,  *    
 op      *  ˜–ñ   ˜–ì *  ˜–ñ   
 list        ˜–÷ :  ˜–þ ˜–ñ $    ˜–ì *  ˜–ñ   ˜–ø   
 member      *    ˜— *        ˜–ñ 6  *  
 PLOT         
 PLOT3D       :  ˜–þ ,  ˜—   
 ERROR       *  
 first argument must be list, set, or PLOT structure      >  $  $  "       0        ˜–ì *    0 ÿÿÿÿ *       
 equation            
 lhs     *  ˜—V   
 insequence       D  :  ˜–ä   
 rhs     ˜—f >  &    ˜–ì *  ˜–ä 
 boolean       
 ERORR        *  
 insequence must be true or false.        :  .    	   ˜—W *  4       ˜—Q :  ˜—’   ˜—W *  4  ˜—Z ˜—Q :  .       
 map     *  2  *  
 x        ˜–Ö *  
 operator         
 arrow        ˜–Ö ˜—" ˜–Ö ˜–Ö 6  *    ˜— *  ˜–þ >    ˜—¤ 6  *    ˜—* D  :  .     ˜—* :  ˜–þ   ˜—§ *  2  ˜—¬ ˜–Ö ˜—± ˜–Ö     ˜–† *  
 print/PLOT       ˜— ˜–Ö ˜–Ö ˜–þ   ˜—¤ 6  *    ˜—. D  :  ˜—Î ˜—. :  ˜–þ   ˜—§ *  2  ˜—¬ ˜–Ö ˜—± ˜–Ö     ˜–† *  
 print/PLOT3D         ˜— ˜–Ö ˜–Ö ˜–þ   ˜—7 *  
 first argument must be a list of PLOT/PLOT3D structures      :  ˜–þ   ˜—§ *  
 plots/display/mvlocal        ˜–þ ˜–ä :  .       ˜—§ *  ˜— ˜–þ :  ˜—¤   
 intersect       *    
 convert     *    ˜—§ *  ˜—« ˜˜-   ˜–ô 
 plots/plot_objects       >    ˜—¤ 6  *    
 ANIMATE      D  :  .     2  ˜—¬ ˜–Ö *  
 Copyright 1993 by the University of Waterloo         ˜–Ö >    ˜—" ˜˜V 
 true        ˜–æ ˜–Ö ˜–Ö :  ˜—¤   
 select      *  ˜˜] ˜˜- >  &  ˜–ä :  ˜–Ù   
 plots/merge_animations       *    ˜— *  ˜—¤ :  ˜–Ù   ˜˜W *    ˜— *    ˜—§ *  ˜— ˜—¤   ˜— *  ˜˜V ˜—¤   ˜—7 *  
 Sorry, cannot display animation with dead plot.      <  .     ˜˜- ˜˜v D  :  .       ˜— *  ˜—% ˜˜¾ >    ˜— *  ˜˜Ä ˜˜J >    ˜˜Ä ˜˜V :  ˜–Ù *  ˜–Ù ˜˜¾   ˜— *  ˜˜Ä 
 plots/plot_options       :  ˜–à *  ˜–à ˜˜¾   ˜—7 *  
 Unknown plot object:         ˜˜Ä >  $  $  ˜–ä "  ˜—O   
 nops        *  ,  *  ˜–Ù     ˜— *  ˜—%   ˜–Ù *  ˜—O ˜˜V :  ˜–Ù   ˜˜W *    ˜— *    ˜—§ *  2  ˜—¬ ˜–Ö ˜—± ˜–Ö ˜—4 ˜–Ö ˜–Ö ˜™ :  ˜—¤ ˜–Û >    ˜—Î ˜—ì :  ˜—¤     ˜–† *  
 plot3d/options3d         *  ˜—’ :  ˜—¤     ˜–† *  
 plot/options2d       ˜™7   ˜—Î *      ˜–† *  
 plots/merge_options      *  ,  *  ˜–Ù ˜–à ,  ˜˜˜ ˜–Ö ˜–Ö 
 convert/name     2  *  ˜—­ *  *  
 Copyright 1993 by Waterloo Maple Software        ˜™e >    0            
          "       ˜™w       ˜™{   ˜™] *  0     
 ,          ˜™] *    0 ÿÿÿÿ *  4       ˜™w > *   ˜–ì *  ˜™‰ 
 string      ˜™‰   ˜–ì *  ˜™‰ 
 integer       ˜™{ ˜™‰   ˜–ì *  ˜™‰ 
 rational              ˜™{   ˜™] *    ˜— *  ˜™ ˜™‰ 
 /          ˜™] *    ˜— *  ˜™– ˜™‰   ˜–ì *  ˜™‰ 
 float         ˜™{   
 _convertnamefloat        ˜™ˆ   ˜–ì *  ˜™‰ 
 ^               
 (        ˜™» 
 )^(      ˜™Æ 
 )          ˜–ì *  ˜™‰ 
 *         
 _convertname*        ˜™ˆ   ˜–ì *  ˜™‰ 
 +         
 _convertname+        ˜™ˆ   ˜–ì *  ˜™‰ ˜—     
 [          ˜™] *    ˜— ˜™ˆ 
 ]          ˜–ì *  ˜™‰ ˜–ô     
 {        ˜š 
 }          ˜–ì *  ˜™‰ 
 indexed             ˜™{   ˜™] *    ˜— *  ˜™y ˜™‰ ˜š ˜š ˜š%   ˜–ì *  ˜™‰ ˜–ø         ˜™{ ˜šF ˜™ì ˜š ˜™ô   ˜–ì *  ˜™‰ 
 =             ˜™ë 
 )=(      ˜™Æ ˜™ô   ˜–ì *  ˜™‰ 
 ..            ˜™ë 
 )..(         ˜™Æ ˜™ô   ˜–ì *  ˜™‰ 
 <             ˜™ë 
 )<(      ˜™Æ ˜™ô   ˜–ì *  ˜™‰ 
 <=            ˜™ë 
 )<=(         ˜™Æ ˜™ô   ˜–ì *  ˜™‰ 
 <>            ˜™ë 
 )<>(         ˜™Æ ˜™ô   ˜–ì *  ˜™‰ 
 and           ˜™ë 
 ) and (      ˜™Æ ˜™ô   ˜–ì *  ˜™‰ 
 or            ˜™ë 
 ) or (       ˜™Æ ˜™ô   ˜–ì *  ˜™‰ 
 not         
  not (       ˜™» ˜™ô   ˜–ì *  ˜™‰ 
 .             ˜™ë 
 ).(      ˜™Æ ˜™ô   ˜—7 *  
 	unable to convert to name        ˜™e ˜™e 
 convert/set  2  *  
 a        *  *  ˜™g ˜› >    ˜–ì *  0     6  *  
 array       
 table         ˜—§ *  2  *  
 l        
 n        ˜› ˜› ˜›   0     *    ˜— *  ˜› ˜› ˜› 6  *    
 indices     ˜›/ ˜› 6  ˜›, ˜› ˜› 
 textplot       ˜–† *    
 plots/textplot       
 polygonplot3d      ˜–† *    
 plots/polygonplot3d      
 display3d      ˜–† *    ˜–’ 
 plots/getoptions     2  *  
 override         *  
 default      
 opts         
 t        *  ˜–È *  D  :  ˜–þ ˜–Û <  .       ˜—§ *  ˜— 6  *    ˜›6 *  
 plots/2dDefaults         ˜˜v >      ˜›“ *  ˜›ˆ   
 USERDEFAULT      :  ˜–þ *  ˜–þ   ˜›ˆ ˜› :  .         ˜–† *  ˜™? *  ˜–þ     ˜–† ˜™L *  ,  *  ˜˜- 0     ˜›‚ ˜›‚ 
 plots/merge_font     2  *  4  ˜› ˜–ø 4  
 b        ˜–ø *  
 font         ˜–¤ 
 alist        *  ˜›Þ D  >  &    
 has     *  0       
 FONT           
 RETURN      *  0     :  .       ˜— *    ˜˜€ *  2  *  ˜—­ ˜›Þ *  ˜—² ˜—· ˜›Þ $    ˜–ì *  ˜›õ   ˜–ø     ˜— *        ˜›õ ˜›ê ˜›Þ ˜›Þ ,  *    ˜— *  ˜›è :  .     ˜–Û <  .     ˜›õ ˜˜v >  &  $    ˜–ì *  ˜œ$ ˜–ø     ˜— *  ˜œ ˜œ$ ˜›ê :  ˜œ  *  ˜œ  ˜œ$   ˜œ *  ˜œ  ˜›ø ˜›Þ ˜›Þ 
 replot     ˜–† *    
 plots/replot         
 plot2d/axesstyles    8  *  ˜–æ J                                                                                                                                                                                                                                                                                             H  
 normal      
 NORMAL                                                                                                                                           H  
 BOX      ˜œÌ                 H  
 box      ˜œÌ                                                                                                                 H  
 frame        
 FRAME                                                                                                                                                                                                                                                        H  
 NONE         ˜;                                                                                                                                                                 H  ˜œú ˜œú                     H  
 boxed        ˜œÌ                     H  
 FRAMED       ˜œú                     H  
 framed       ˜œú                     H  ˜œ¦ ˜œ¦                     H  
 none         ˜;                     H  
 BOXED        ˜œÌ                                                                                                         
 cylinderplot       ˜–† *    
 plots/cylinder       
 contourplot    ˜–† *    
 plots/contplot       
 animate3d      ˜–† *    
 plots/animate3d      
 setoptions3d       ˜–† *    
 plots/setoptions3d       
 polarplot      ˜–† *    
 plots/polarplot      
 sphereplot     ˜–† *    
 plots/spherical      
 _plotDigits      
 
 polygonplot    ˜–† *    
 plots/polygonplot        
 _ARRAYINDEX  ˜—Z 
 odeplot    ˜–† *    
 plots/odeplot        
 plot/options2d   2  ˜œW *  
 s        ˜›} 
 dlabels      
 daxes        
 dstyle       
 dtitle       
 dscaling         
 dticks       
 dcolor       ˜–Ä 
 aa       
 bb       
 dview        
 dth      
 symb         
 dfont        
 dafont       
 dtfont       
 dlfont       
 ddashes      *  
 
Copyright 1992 by George Labahn      ˜œW D  :  .    
 2  ˜—¬ *  
 y        ˜–Ç ˜–Ö D  >  $    ˜–ì *  ˜–ñ 
 name        (    ˜–ñ   
 DEFAULT        ˜–ñ   ˜›u   ˜›ð ˜— :  ˜˜-   
 traperror       *    
 evalf       *  ˜–ñ      >    ˜–ì *  ˜˜- 
 numeric       ˜›ð *  ˜˜-   ˜—7 *  
 real constants expected in ranges        ˜–ñ ˜–Ö ˜–Ö :  .     ˜–Û :  .     ˜–Û :  .     ˜–Û :  .     ˜–Û :  .     ˜–Û :  .     ˜–Û :  .    	 ˜–Û :  .     ˜–Û :  .     ˜–Û :  .     ˜–Û :  .     ˜–Û :  .     ˜–Û :  .     ˜–Û :  .     ˜–Û :  .     ˜–Û <  .     0 ÿÿÿÿ ˜˜v D  >  &    ˜–ì *  ˜Ÿ0 ˜—\   ˜—7 *  
 bad argument         ˜Ÿ0 :  .       ˜— *       ˜Ÿ0 :  ˜Ÿ0   ˜— *       ˜Ÿ0 > ( $    ˜ŸH   
 title          ˜–ì *  ˜Ÿ0   ˜™ž :  ˜žø   
 TITLE        *  ˜Ÿ0   ˜ŸH   
 axes         D  >    
 assigned        *    ˜œP ˜Ÿn :  ˜Ÿ0 ˜Ÿ€ :  ˜žü   
 AXESSTYLE        ˜Ÿn (    ˜ŸH   
 color          ˜ŸH   
 colour       :  ˜Ÿ     ˜–† *    
 plot/color       ˜Ÿn $    ˜ŸH   
 labels         ˜–ì *  ˜Ÿ0 ,  *  ˜Ÿe ˜Ÿe :  ˜žô   
 AXESLABELS       *    ˜— ˜Ÿn   ˜ŸH   
 style        D  >    ˜Ÿz *    
 plot2d/plotstyles        ˜Ÿn :  ˜Ÿ0 ˜ŸÓ :  ˜Ÿ    
 STYLE        ˜Ÿn   ˜ŸH   
 scaling      D  >    ˜Ÿz *    
 plot2d/scalings      ˜Ÿn :  ˜Ÿ0 ˜Ÿó :  ˜Ÿ   
 SCALING      ˜Ÿn $    ˜ŸH   
 tickmarks          ˜–ì *  ˜Ÿ0 ,  *  
 anything        ˜  :  ˜Ÿ   
 subs        *    ˜›u ˜ž¸   
 AXESTICKS        ˜ŸÃ $    ˜ŸH   
 xtickmarks         ˜–ì *  ˜Ÿ0 ˜™§ >    ˜Ÿ ˜–Û :  ˜Ÿ   ˜ ' *  ˜Ÿ0 ˜ž· :  ˜Ÿ   ˜ ' *  ˜Ÿ0   ˜— *  ˜ŸU ˜Ÿ $    ˜ŸH   
 ytickmarks         ˜–ì *  ˜Ÿ0   ˜™§ >  ˜ < :  ˜Ÿ   ˜ ' *  ˜ž· ˜Ÿ0 :  ˜Ÿ   ˜ ' *    ˜— *  ˜ŸM ˜Ÿ ˜Ÿ0   ˜ŸH   
 view         >    ˜–ì *  ˜Ÿ0 ,  *  6  *  ˜ž° 4  
 constant        ˜ † ˜ ‚ D  :  .       ˜—§ *  ˜žŸ   ˜Ÿ0 *  ˜ŸM :  .       ˜—§ *  ˜žŸ   ˜Ÿ0 *  ˜ŸU >  (  $    ˜–ì *  ˜  ˜žÚ      ˜— *  ˜ŸU ˜    ˜— *  ˜ŸM ˜  $    ˜–ì *  ˜ š ˜žÚ      ˜— *  ˜ŸU ˜ š   ˜— *  ˜ŸM ˜ š   ˜—7 *  
 
view range must be non-empty         :  ˜Ÿ   
 VIEW         *  ˜  ˜ š   ˜—7 *  
 bad option view      ˜Ÿ0 $    ˜ŸH   
 thickness          ˜–ì *  ˜Ÿ0 
 nonnegint        :  ˜Ÿ   
 THICKNESS        ˜Ÿn $  (    ˜ŸH   
 line_style         ˜ŸH   
 linestyle        ˜ ò :  ˜Ÿ    
 LINESTYLE        ˜Ÿn   ˜ŸH   
 symbol       >    ˜Ÿz *    
 plot2d/symbols       ˜Ÿn :  ˜Ÿ   
 SYMBOL       ˜¡* :  ˜Ÿ   ˜¡6 ˜Ÿn   ˜ŸH   ˜›Õ >    ˜–ì *  ˜Ÿ0 ˜— :  ˜Ÿ   ˜›ë ˜ŸÃ   ˜—7 *  
 font specification must be a list        (    ˜ŸH   
 title_font         ˜ŸH   
 titlefont        >  ˜¡E :  ˜Ÿ, ˜¡L ˜¡O (    ˜ŸH   
 axes_font          ˜ŸH   
 axesfont         >  ˜¡E :  ˜Ÿ$ ˜¡L ˜¡O (    ˜ŸH   
 label_font         ˜ŸH   
 labelfont        >  ˜¡E :  ˜Ÿ( ˜¡L ˜¡O   ˜ŸH   
 resolution       ˜œW   ˜ŸH   
 numpoints        ˜œW   ˜—7 *  
 unknown or bad argument        ˜ŸH ˜Ÿ0 >  $    ˜Ÿ, ˜–Û   ˜žø ˜–Û :  ˜žø     ˜Ÿj *    ˜— *  ˜žø ˜Ÿ, >  $    ˜Ÿ( ˜–Û   ˜žô ˜–Û :  ˜žô     ˜Ÿ¾ *    ˜— *  ˜žô ˜Ÿ( >    ˜Ÿ$ ˜–Û >    ˜Ÿ ˜–Û :  ˜Ÿ     ˜ ' *    ˜— *  ˜Ÿ ˜Ÿ$ :  ˜Ÿ   ˜¡ó *  ˜ž· ˜ž· ˜Ÿ$ *  ˜žô ˜žø ˜žü ˜Ÿ  ˜Ÿ ˜Ÿ ˜Ÿ ˜Ÿ ˜Ÿ ˜Ÿ ˜Ÿ ˜Ÿ  ˜œW ˜œW 
 _convertnamefloat    2  *  ˜–Ä *  
 old      ˜žJ ˜™f ˜™e D  :  .     
 Digits       :  ˜¢&   
 max     *  ˜¢$     
 length      *    
 trunc       ˜™ˆ ˜™ ˜™ ˜™ >  "  ˜™‰ ˜™y :  .           
 -          ˜¢: *    ˜™‰      ˜šä   
 _convertnamefrac         *    
 frac        ˜¢Q :  ˜¢G       ˜™{ ˜¢9 ˜šä   ˜¢X *    ˜¢a ˜™ˆ :  ˜¢& ˜¢$   ˜›ð *  ˜¢G ˜™e ˜™e 
 plot/checkinftyticks     2  *  
 min     ˜¢- *  
 ticks        *  ˜–È *  D  :  .     ˜–Û >    0       
 infinity             :  ˜¢” *  ˜¢”          
 -infinity        >    0     ˜¢œ :  ˜¢” *  ˜¢”          ˜¢œ >    ˜¢” ˜–Û :  ˜¢”   ˜ž¸ :  ˜¢” ,  *  ˜¢”           
 0        ˜¢‘ ˜¢‘ 
 plots/plot_objects   6  * 	 ˜˜W 
 CURVES       
 GRID         
 POINTS       
 MESH         
 TEXT         
 POLYGONS         
 ISOSURFACE       
 plots/merge_options  2  *  
 objs         ˜›y *  ˜–« 
 v        
 vv       
 i        
 dimension        
 d        
 viewopt      
 uniq_options         
 new_uniq_opts        ˜—­ ˜ž° 
 numobjs      
 has_font_opts        *  ˜–È ˜›Þ D  >        ˜˜ý ˜›ô        ˜˜ý ˜œ ˜£A ˜œ   ˜›ð *  ˜–Û   ˜–† *  ˜–’ :  .     6  *  ˜›ê   ˜Ÿj   ˜    
 AMBIENTLIGHT           
 PROJECTION         ˜ Ø   ˜Ÿ‰   ˜Ÿ¾   ˜ '   
 CONTOURS           ˜¡   ˜ þ   ˜¡6   
 LIGHT          
 FUNCTION           
 COLOUR         ˜Ÿâ   
 GRIDSTYLE          
 LIGHTMODEL       :  .     6  *  ˜£V ˜£k ˜£m :  .     ˜–Û :  ˜›ø   ˜› *  4  ˜£A ˜£= :  .     ˜œ :  .    	   ˜› ˜›Þ :  .     ˜œ :  ˜œ    ˜› *  4  ˜—O ˜—˜ ,  *    ˜ž¸ ˜£Å ˜£Å <  .    
 ˜›õ ˜˜v >    ˜–ì *  ˜£Ê ˜–ø D  :  .       ˜— *  ˜œ ˜£Ê >    ˜£Ö ˜£g D  :  ˜£¸   ˜˜ý *  ˜£Ê :  ˜œ$ ˜£Ê <  .     ˜£A ˜£A ˜£¸ ˜˜v >  $    ˜–ì *    ˜œ  *  ˜£ì 
 range         ˜–ì *    ˜— *  ˜£ì ˜œ$ ˜£û :  ˜£÷ 4    ˜¢† *    ˜— *  ˜£A ˜£÷   ˜— *  ˜£A ˜¤   ˜¢- *    ˜— *       ˜£÷   ˜— *  ˜¤ ˜¤   ˜£÷ ˜£Å :  ˜£÷ ˜¤   ˜— *  ˜£Ö ˜£Q >  &    ˜Ÿz *    ˜£² *  ˜£Ö :  ˜¤6 ˜£Ê   ˜— *  ˜£Ö ˜£š :  ˜¤6   ˜›Ä *  ˜¤6 ˜£Ê D  :  ˜£®   ˜£® ˜£A ˜£A ˜£A :    ˜›ø *  ˜£® ˜£Ê <  ˜£Ê ˜›è ˜˜v >  ˜£Ï D  ˜£Õ >  ˜£Þ D  ˜£â ˜£è <  ˜£ì ˜£A ˜£A ˜£¸ ˜˜v >  (  ˜£ó ˜¤& ˜¤) ˜¤, >  $  $  ˜¤3 ˜¤= &    ˜›ä *  ˜£Ê ˜›ê :  ˜¤6   ˜›Ä *  ˜£Ê ˜¤6 ˜¤: ˜¤I >  "  ˜œ ˜£¸ :  ˜£¢   ˜ Ø *    
 seq     *    ˜œ  *  .       ˜¤• 4  ˜£A ˜£¸ ˜£¡ :  ˜£²   ˜— *    ˜—§ *  ˜— ,  *    
 entries     *  ˜£² :  ˜›ø   ˜¤Ž *    ˜›ø ˜¤”   ˜¤• 4  ˜£A ˜£® *  ˜›ø ˜£² ˜£¢ ˜›Þ ˜›Þ 
 conformal      ˜–† *    
 plots/conformal      
 plot2d/scalings  8  ˜œW ˜–æ J                                                                                                                                                                                                                                                                         H  
 UNCONSTRAINED        ˜¥                                                                                                                     H  
 unconstrained        ˜¥                                                                                             H  
 CONSTRAINED      ˜¥`                     H  
 constrained      ˜¥`                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
 pointplot      ˜–† *    
 plots/pointplot      
 _convertname*    2  ˜™c *  ˜£ ˜›} ˜™f ˜™e D  :  ˜¢G   ˜™ë ˜™ô <  ˜¢$ ˜™– ˜™   ˜˜ý ˜™ˆ ˜˜v :  ˜¢G         ˜™{ ˜¢G 
 *(         ˜™] *    ˜— *  ˜¢$ ˜™‰ ˜™ô ˜¢G ˜™e ˜™e 
 _convertname+    2  ˜™c ˜¦ ˜™f ˜™e D  ˜¦ <  ˜¢$ ˜™– ˜™ ˜¦' ˜˜v :  ˜¢G       ˜¦0 
 +(       ˜¦6 ˜™ô ˜¢G ˜™e ˜™e 
 plots/merge_animations   2  *  *  
 m        
 zip2         ˜›} 
 retval       *  ˜–È ˜¦j D  :  .     2  *  
 a1       
 a2       ˜¦j ˜¦x ˜¦j   ˜˜W *    ˜— *    
 zip     *  2  *  ˜—­ ˜ž¤ ˜¦j *  ˜—² ˜—· ˜¦j ,  *  ˜—   ˜— *  0     ˜¦j ˜¦j ˜—  ,  *  ˜¦¡ ,  ˜¦j ˜¦j ˜¦j >    ˜—Q       :  ˜˜Ä ˜–Û   ˜—Q      :  ˜˜Ä   0 ÿÿÿÿ *  ˜—O D  :  .       ˜¦} *  ˜¦¾ ˜—V <  ˜˜¾ ˜—” ˜˜v :  ˜¦Å   ˜¦} *  ˜¦Å ˜˜¾ :  ˜˜Ä ˜¦Å   ˜›ð *  ˜˜Ä ˜¦j ˜¦j 
 plot2d/symbols   8  ˜œW ˜–æ J                                                                                                                                                                                                                                                                                                                                                                                                                     H  ˜œÌ ˜œÌ                 H  ˜œÕ ˜œÌ                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         H  
 CROSS        ˜§ã                     H  
 CIRCLE       ˜§î                     H  
 cross        ˜§ã                     H  
 circle       ˜§î                     H  
 DIAMOND      ˜¨                     H  
 diamond      ˜¨                                                 
 surfdata       ˜–† *    
 plots/surfdata       
 plot/tolist  2  *  ˜—­ ˜¢‘ *  ˜˜c ˜¢‘ >    ˜–ì *  ˜¢™   
 vector         0 ÿÿÿþ *    ˜˜> *  ˜¢™   ˜—   ˜–ì *  ˜¢™   ˜› >  (        
 linalg      *  
 rowdim       *  ˜¢™ ˜¢º       ˜¨c *  
 coldim       ˜¨l ˜¢º   ˜˜> *    ˜˜> ˜¨G ˜¨V   ˜¨p        ˜˜> *  ˜¢™   
 listlist           ˜¨a ˜¨ƒ   ˜˜> *      ˜¨c *  
 transpose        ˜¨l ˜¨‰   ˜—7 *  
 do not know how to plot        ˜–ì *  ˜¢™   ˜¨V *  ˜¨I   ˜—§ *  ˜¨O ˜¢™ ˜¢™ ˜¢‘ ˜¢‘ 
 rect     2  *  ˜–  
 step         
 steps        
 lo       
 hi       *  ˜›# ˜—± ˜–Ö   
 plot        *  6  *  ,  *    ˜¤Ž *    
 onerect      *  0     ˜˜- ˜–ñ 0       ˜˜- 4  ˜—O 0       ˜¨ê ˜—O   ˜¨ð ˜—O ˜¨æ ˜—O ˜—O ˜—%   ˜–ñ ˜—¬   ˜—­ 4  ˜¨ê 0     ˜–Ö ˜–Ö 
 fieldplot3d    ˜–† *    
 plots/fieldplot3d        
 index/fill   2  *  
 T        
 iniv         *  
 ranges       
 nvals        ˜›# ˜£ *  ˜©. D  :  .     ,  *    ˜— *         
 eval        *  0     >      ˜˜ý *  ˜©2   0                ˜©L D  :    ˜©A *    0 ÿÿÿÿ *  4       ˜©J 0       ˜›ð ˜©. >  &    ˜–ì *  ˜©^ ˜—   ˜—7 *  
 initialization of arrays must be done with lists         :  .       ˜˜ý *  ˜©^ :  .         ˜— *  ˜©9   ˜©2 *    ˜©J ˜©L      ˜©L ˜©L   ˜— *  ˜©L ˜©‹ ˜©‘ ˜©L ˜©L >  "  ˜©„ ˜©}   ˜—7 *      
 a list with          ˜©„ 
  entries cannot be used to initialize the range      ˜©‹ <  .     ˜©L ˜©L ˜©} ˜˜v   0 ÿÿÿþ *  ˜©A   ˜©^ *  ˜©½ ˜©V   ˜©½ ˜©L ˜©‘ ˜©L ˜©• ˜©L ˜©. ˜©. 
 plot/transform   2  ˜¨> ˜¢‘ ˜¢ ˜¢‘ > 
   ˜¢™ ˜¢œ ˜¢º   ˜¢™   ˜¢œ   ˜¢¨ ˜¢Ì ˜¢¨ "       ˜¢™   ˜¢º ˜¢º   ˜¢™ ˜¢¨      "  ˜¢™        ˜¢¨ ˜¢º ˜©ô ˜©÷   ˜¢™   ˜¢º      ˜¢‘ ˜¢‘ 
 with/loaded  ,  *  
 plots       
 densityplot    ˜–† *    
 plots/densityplot        
 index/FillInitVals   2  *  
 tbl      ˜© *  ˜© 
 z        ˜£ *  
 Copyright 1994 Gaston Gonnet, Wissenschaftliches Rechnen, ETH Zurich         ˜©. D  :  ˜©2 ˜©A >    ˜–ì *  ˜©^ 6  *    ˜–ô *  ˜š`   ˜— ˜ªX <  ˜©} ˜©^ ˜˜v :    ˜©2 *    ˜— *  ˜©L ˜©}   ˜— *  ˜©9 ˜©}   ˜–ì *  ˜©2 ˜›   ˜© *  ˜©2 ˜©^   ˜–ì *  ˜©^ 6  *  ˜–ô ˜— <  ˜©„ ˜©L ˜©L ˜© ˜˜v :    ˜©2 *  ˜©„   ˜©^ ˜ªŠ   ˜—7 *  
 invalid initialization of table or array         ˜–Û ˜©. ˜©. 
 loglogplot     ˜–† *    
 plots/loglogplot         
 trap     2  ˜¨¿ ˜¨Ï ˜—± ˜–Ö   ˜¨Ô *  6  *  ,  *    ˜¤Ž *    
 onetrap      ˜¨å ˜¨ì ˜¨ò ˜—% ˜¨ü ˜¨ÿ ˜–Ö ˜–Ö 
 _COLOURARRAY     * 	 
 BLACK        
 RED      
 GREEN        
 YELLOW       
 BLUE         
 MAGENTA      
 CYAN         
 WHITE        
 plots/plot_options   6  *  
 COLOR        ˜£‡ ˜Ÿâ ˜›ë ˜¡6 ˜£| ˜  ˜Ÿj ˜ Ø ˜£[ ˜Ÿ¾ ˜Ÿ‰ ˜ ' ˜£p ˜£ ˜£Ž ˜£” ˜£b ˜ þ ˜¡ 
 onerect  2  *  
 h        ˜›# ˜–Ä ˜¨É ˜–Ö ˜—± ˜–Ö *    ˜¨ê ˜—O     ˜¨æ ˜—O ˜¢¡ ˜—O ˜—O ˜–ñ ˜—O ˜—O ˜—% ˜«#   ˜¨ð *    ˜¨ê ˜—O   ˜¨æ ˜—O ˜–ñ ˜—O ˜—O ˜–ñ        ˜¢¡   ˜¨ê ˜—O ˜«8 ˜—O ˜«2 ˜–Ö ˜–Ö 
 sparsematrixplot       ˜–† *    
 plots/smplot         
 gradplot3d     ˜–† *    
 plots/gradplot3d         
 plot2d/plotstyles    8  ˜œW ˜–æ J     H  
 LINE         ˜«v                     H  
 point        
 POINT                            H  ˜«… ˜«…                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     H  
 patch        
 PATCH                            H  ˜¬ ˜¬                     H  
 line         ˜«v                 
 plots/display/mvlocal    2  *  
 p        ˜–À *  ˜£ ˜›y ˜›} 
 col      
 obj1         ˜žJ ˜¦x ˜¦j D  :  ˜¦Å ˜–Û :  ˜¦} ˜–Û ˜¦µ ˜–Ø ˜–ß <  ˜˜¾ 0     ˜˜v >  $    ˜–ì *  ˜˜¾ ˜–ø   ˜— *  ˜˜Æ 6  *    ˜ªý   ˜£‡ :  ˜˜Ä ˜˜¾ $  ˜¬Ö   ˜— *  ˜˜Æ 6  *    ˜Ÿâ   ˜›ë   ˜¡6   ˜¡   ˜ þ ˜˜å ˜˜Õ >  (  (  ˜¦¤   ˜˜Ä ˜–Û   ,  *  ˜–à ˜¦¬ D  <  ˜˜¾ ˜™ ˜˜v >    ˜— *  ˜˜Æ ˜¢Ô :  ˜¦Å *  ˜¦Å   ˜˜Æ *    ˜— *  ˜˜¾ ˜˜Ä ˜–à :  ˜¦} *  ˜¦} ˜˜¾ >  $  ˜¦¤ &    ˜›ä *  ,  *  ˜¦Å ˜˜V   ˜—" *    ˜˜W *  ˜­, ˜¦}   ˜—" *  ˜¦Å ˜¦} ˜¬Ñ ˜¦j ˜¦j 
 display  ˜›b 
 implicitplot3d     ˜–† *    
 plots/iplot3d        
 _COLORRGB    * 	 ,  *  ˜—% ˜—% ˜—% ,  *    ˜ž ˜¢¡ ˜—% ˜—% ,  *  ˜¢Ì ˜­_ ˜¢Ì ,  *  ˜­_ ˜­_ ˜¢Ì ,  *  ˜¢Ì ˜¢Ì ˜­_ ,  *  ˜­_ ˜¢Ì ˜­_ ,  *  ˜¢Ì ˜­_ ˜­_ ,  *  ˜­_ ˜­_ ˜­_ 
 textplot3d     ˜–† *    
 plots/textplot3d         
 plots/2dDefaults     8  ˜›‚ ˜–æ J                                                                                                                                                         H  ˜¡®     1                                                                                                                                                                                                                                                                             H  ˜Ÿs ˜›¢                     H  ˜ŸÊ ˜›¢                                                                                     H  ˜ 
 ˜›¢                                         H  ˜Ÿ] ˜™{                                                                                                                                                                                         H  ˜¡¥     È                                                                                                     H  ˜ w ˜›¢                                                                                             H  ˜Ÿ¯ ,  *  ˜™{ ˜™{                                                                                                                                                                                     
 onetrap  2  ˜« ˜–Ö ˜—± ˜–Ö *  ˜«# ˜—% ˜«#   ˜¨ð *  ˜«# ˜«C   ˜¨ð *  ˜«C ˜–Ö ˜–Ö 
 _convertnamefrac     2  *  ˜– ˜™e ˜™f ˜™e >    ˜™‰ ˜™y ˜™{      ˜™ ˜¢T ˜™‰     ˜™{   ˜¢: *    ˜™‰     
   ˜®ç *    ˜™‰ ˜¯ ˜¯  ˜¢T   ˜¢Ï   ˜®ç ˜¯ ˜™e ˜™e 
 with/getpackage  2  *  4  
 A        6  *  ˜› ˜ž°   
 specfunc        *  ˜    ˜–† 
 procedure       4  
 initproc         ˜ž° *  ˜› ˜£ 
 idx      
 pkg      ˜ª+ 
 local_init       ˜›} *  
 remember         ˜˜c J                                                                                                                                                                                                                                                              H  *  ˜ª 
 initproc         8  *  ˜–æ J H  ˜ª¢ ˜ª¦ ˜­D ˜­I                                                                         H  
 matrixplot         ˜–† *    
 plots/matplot                                                                                                            H  ˜¦ ˜¦                         H  ˜ÿ ˜ž                     H  ˜ž! ˜ž%                         H  
 spacecurve         ˜–† *    
 plots/spacecurv                          H  ˜ž ˜ž                         H  ˜¨+ ˜¨/                     H  ˜›@ ˜›D                         H  ˜­‚ ˜­†                     H  ˜– ˜–…                         H  ˜Ó ˜×                                 H  ˜á ˜å                     H  ˜ª ˜ª                         H  ˜›^ ˜›b                     H  
 fieldplot          ˜–† *    
 plots/fieldplot                              H  ˜© ˜©                     H  
 gradplot           ˜–† *    
 plots/gradplot                                                               H  ˜¤Â ˜¤Æ                                                                         H  
 animate        ˜–† *    
 plots/animate                                                                                                        H  ˜«K ˜«Q                             H  ˜ž5 ˜ž8                                                                                                                                                                                             H  
 logplot        ˜–† *    
 plots/logplot                            H  ˜œC ˜œF                     H  ˜­@ ˜›b                     H  
 setoptions         ˜–† *    
 plots/setoptions                                                         H  ˜›N ˜›S                         H  
 polyhedraplot          ˜–† *    
 plots/polyhedraplot                                          H  ˜ï ˜ô                                                                                                                                                                                                                 H  ˜Ä ˜É                 H  ˜«[ ˜«_                                 H  
 implicitplot           ˜–† *    
 plots/iplot                                                                                                                                                                                                                                                                                                              D 	   
 userinfo        *       
 with        
 working on       0     :  .     
 FAIL        >    ˜›ä *  ˜²+ ˜¯- D    ˜² *       ˜²" 
 clearing readlibs        ˜²+ :  .       ˜©< *  ˜–ñ :  ˜²J ˜²+ >    ˜›ä *  ˜²J   ˜²J D    ˜² *  ˜²> ˜²" 
 unnamed procedure        ˜²+ :  .       ˜©< *  ˜²J   ˜–ì *  ˜²k 6  *    ˜›   
 package      D    ˜² *  ˜²> ˜²" 
 a table or procedure         ˜²+ :  ˜²i ˜²J D    ˜² *  ˜²> ˜²" 
 name case        ˜²k >    ˜–ì *  ˜²k ˜š: D    ˜² *       ˜²" 
 indexed name         ˜²k :  .     ,  *    ˜— ˜²m >  "         ˜˜ý *  ˜²¯ D  :  ˜²J   ˜— *        ˜²J <  .     ˜²¸ ˜²¸ ˜²º ˜˜v :  ˜²J   ˜²J *    ˜²¯ *  ˜²È >    ˜— *  ˜²Á ˜ª
 D    ˜² *  ˜²¤ ˜²" 
 looking for            ˜— *  ˜²¸ ˜²J :  ˜²i   0 ÿÿÿþ *  ˜²é   ˜². D    ˜² *  ˜²¤ ˜²" ˜²ã ˜²J :  .       ˜²ñ *  ˜²Á ˜²õ >  &    ˜Ÿz *    ˜³  *  ˜²é   ˜—7 *  
 undefined package        ˜²+ :  ˜²i   ˜²ñ *    ˜©< ˜³ ˜²õ D    ˜² *  ˜²> ˜²" 
 trying readlib       ˜²k :  ˜²i   ˜žÆ *    ˜–† ˜²m >    ˜²i 
 lasterror        :  ˜²i   ˜žÆ *    ˜–† *    
 cat     *  ˜²J ˜™Ã ˜²J   ˜² *       ˜²" 
 pkg =        ˜²i >    ˜–ì *  ,  *  ˜²i ,  *  ˜²w D  :  .       ˜žÆ *    ˜²i *    
 _InitFile        >  $    ˜³h ˜³< &    ˜›ä *  ˜³h ˜³p :  ˜².   ˜©< *  ˜³h :  ˜²i   ˜žÆ *    ˜²i *    
 _PackageTable        >  &    ˜–ì *  ˜³` ,  *  ˜²u   ˜—7 *  
 	procedure is not package         ˜²J ˜³— D  :  ˜¨æ ˜²0   ˜—7 *  
 undefined package        ˜²+ :  ˜¨æ   ˜©< *  ˜².   ˜›ð *    ˜©< ˜³a *  ˜³È 
 plots/setoptions     2  ˜–Ö *  
 e        
 ret      ˜–Ç ˜–Ö D  ˜›„ <  ˜˜- ,  *  ˜—W ˜˜v >    ˜–ì *  ˜˜- ˜—\ :    ˜­‘ *    ˜— *  ˜—O ˜˜-   ˜— *  ˜—Z ˜˜- >    ˜–þ ˜–Û   ˜—7 *  
 can only query one options at a time         :  ˜–þ   ˜­‘ ˜žà ˜–þ ˜–Ö ˜›’ 
 animrect     2  *  ˜–  ˜¨É ˜¨Ì 
 frames       *  ˜œö ˜—± ˜–Ö   ˜­@ *  ,  *    ˜¤Ž *    ˜¨» *  ˜–ñ     ˜¨ð ˜—O ˜¨æ ˜¢¡ ˜—O   ˜—Z ˜˜- ˜¢¡ ˜´6 ˜¨æ ˜¨ð   ˜˜- 4  ˜—O ˜¨ê   ˜—i ˜˜v   ˜Ÿ] 
 	Rectangular Approximation        ˜–Ö ˜–Ö 
 _NUMFUNEVALS         1 
 polyhedraplot    ˜±a 
 plot/untransform     2  ˜¨> ˜¢‘ ˜¢ ˜¢‘ > 
     ˜¢™ ˜¢º ˜¢¨ ˜¢º ˜¢Ì ˜¢œ     ˜¢™ ˜¢º ˜¢º ˜¢º ˜¢Ì ˜¢› "    ˜¢º ˜¨ƒ ˜¢™       ˜¢º ˜¢º ˜¢™ ˜¢¨ ˜¢¨ ˜¨ƒ "  ˜¢™   ˜¢¨ ˜¨ƒ     ˜´t ˜¢¨ ˜©÷   ˜¢™ ˜ª ˜¢‘ ˜¢‘ 
 spacecurve   ˜¯þ 
 animate  ˜°² 
 plot/jitter  ,  * f      Ä  Î           "‰  ± ˜´«      š   Ä ˜´«      ú   m ˜´«      ;  n ˜´«      )   | ˜´«      a   ˜´«         _ ˜´«      £   7 ˜´«      $  ð ˜´«      þ  3 ˜´«         - ˜´«      ä  ¹ ˜´«       ô  Ë ˜´«        » ˜´«      d  u ˜´«      0  Î ˜´«      ÷   Å ˜´«      #ˆ  n ˜´«      i    ˜´«      ›   œ ˜´«      	ö    ˜´«      -  © ˜´«      $   ì ˜´«       ï  Y ˜´«       W  ¹ ˜´«      
*  ì ˜´«      ø   Õ ˜´«      Ò    ˜´«      $Y  « ˜´«      "  w ˜´«      x   R ˜´«      T  ¾ ˜´«      &a   ¡ ˜´«      ,   i ˜´«      )   é ˜´«      í   ‡ ˜´«         ˜´«      _   J ˜´«           ˜´«      z   Ñ ˜´«      §  1 ˜´«      ¸  ¡ ˜´«      ¢   × ˜´«      P   ˜´«      Ù   † ˜´«      G  ­ ˜´«      ˜  Z ˜´«        A ˜´«      Ÿ   ˜´«       V   M ˜´«      ±  à ˜´«      %ª  ˜ ˜´«      Œ   ! ˜´«      d    ˜´«      s    ˜´«      Ò    ˜´«       ­  ® ˜´«      ¾   B ˜´«      s   ½ ˜´«      ò   Í ˜´«      ô  € ˜´«      $    ˜´«      ‰    ˜´«      Â   V ˜´«      "L  $ ˜´«      …   “ ˜´«      `  e ˜´«        Ä ˜´«      x   ð ˜´«      ×   ù ˜´«      !e  ¬ ˜´«      _   Ö ˜´«      ˆ   ð ˜´«      	®  V ˜´«      
   õ ˜´«       :  › ˜´«        q ˜´«      ø   a ˜´«      ß   ˜´«      B   J ˜´«      X  Ò ˜´«      É   M ˜´«      $B   # ˜´«      Ü   ì ˜´«        ‚ ˜´«      X  ¥ ˜´«      Y   ‡ ˜´«      '   ; ˜´«      ‚   p ˜´«      2   ˜´«       	   ó ˜´«        † ˜´«      X   Œ ˜´«         ê ˜´«      Ï   6 ˜´«      1  @ ˜´«      ª  Ð ˜´«      î  Â ˜´«      6  Ÿ ˜´«       6   ˜´« 
 fieldplot    ˜°b 
 plot/ptlist  2  *  
 pointlist        *  
 k        ˜›  ˜›# ˜£ 
 c        ˜›} 
 cc       *  ˜™g *  D  :  .       ˜žÍ *  0     >    ˜–ì *    ˜¶Ä *         ˜— :  ˜¶Ä   ˜—§ *  ˜— ˜¶Ä :  .       ˜˜ý *  ˜¶Ä >      
 irem        *  ˜¶Þ      ˜¶Ò   ˜—7 *  
 odd number of points given in point list         :  .     ˜–Û <  .     ˜¶Ò ˜¶í ˜¶Þ ˜˜v D  <  ˜¶Á ˜¶Ò ˜¶Ò ˜¶Á $  "  ˜· ˜¶Þ &  $    ˜–ì *    ˜¶Ä *  ˜· ˜žÚ   ˜–ì *    ˜¶Ä *    ˜· ˜¶Ò ˜¶Ò ˜¶Ò ˜žÚ :  ˜·   ˜· ˜¶Ò ˜¶í ˜¶Ò >  ˜· D  :  ˜· *  ˜· ˜· ˜·+ <  ˜¶Á ˜¶Ò ˜¶Ò ˜¶Á $  $  ˜· ˜· ˜· ˜·+ :  ˜· *  ˜·   ˜· ˜¶Ò      ˜¶Ò :  .     ˜–Û :  ˜· ,  *  ˜· :  ˜¶Þ   ˜˜ý ˜·W <  .     ˜¶Ò ˜¶Ò   ˜¶Þ   ˜¶Ò ˜¶í ˜˜v D  :  .     ,  *    ˜— *  4    ˜· *    ˜·_ ˜¶í ˜·M ˜¶Ò   ˜· *    ˜·_ ˜¶í ˜¶Ä :  ˜·Q *  ˜·Q ,  *    ˜¤Ž *  ,  *    ˜·k *    ˜· ˜¶í ˜·M ˜¶Ò   ˜·k *    ˜· ˜¶í   ˜· 4  ˜¶Ò     ˜˜ý *  ˜·k ˜·e :  ˜·Q   ˜¢Ý *  ˜·Q   ˜£‡ *  
 RGB        ˜— *    ˜­S *    ˜ž0 ˜¶Ò ˜¶Ò ˜¶Ò :  ˜ž0   
 mod      *  ˜·· 
 _HIGHESTINDEX        ˜·Q ˜¶Á *  ˜ž0 
 type/vector  2  *  ˜£
 ˜¶¸ *  ˜›Ð ˜£ *  ˜™g *  D  >  &    ˜–ì *  0     ˜›   ˜›ð *  ˜–æ >    ˜–ì *  ˜·â ˜ž° :  .     ,  *    ˜— *         ˜©< *  ˜·â :  ˜·ð ,  *    ˜— *  ˜·÷ ˜·â >  (      ˜˜ý *  ˜·ð          ˜— *  ˜¸   ˜·ð *  ˜¸ ˜¸ ˜·å >  (    0      ˜¸   0     ˜    ˜›ð *  ˜˜v <  .     ˜¸ ˜¸   ˜— *  ˜·÷ ˜¸ ˜˜v >  &    ˜–ì *  ,  *    ˜·â *  ˜¸) ,  *  ˜¸! ˜·å ˜˜v ˜·Û ˜·Û 
 _ANGLEBOUND    ˜—Z      
 gradplot     ˜°€ 
 print/PLOT   2  *  
 pin      *  
 rangex       
 rangey       ˜³Ó ˜£ 
 pnew         ˜¬³ 
 j        
 e2       
 enew         ˜¶² 
 axesstyle        
 opt      
 ticksx       
 ticksy       
 infinite         
 labelx       
 labely       
 axesx        
 axesy        *  ˜™g *  D  :  .       ˜—* *  0 ÿÿÿÿ :  .     ˜–æ :  .     ˜™{ :  .     ˜™{ :  .     ˜–Û :  .     ˜–Û <  .          ˜¸¾   ˜˜ý *  ˜¸  ˜˜v D  :  .       ˜— *  ˜¸¼ ˜¸  >    ˜–ì *  ˜¸È ˜–ø >      ˜— *        ˜¸È 
 RANGE        >      ˜— *  ˜¸¾ ˜¸È 
 HORIZONTAL       :  .       ˜— *       ˜¸È   ˜¸ã 
 VERTICAL         :  .     ˜¸ð   ˜¸× 
 AXIS         >  ˜¸â <  .     ˜¸ó ˜¸¾   ˜˜ý *  ˜¸È ˜˜v D  >      ˜— *  ˜¸Ú   ˜— *  ˜¹
 ˜¸È 
 LABEL        :  ˜¸¬   ˜— *    ˜— *  ˜¸¾ ˜¹ >    ˜¹ 
 SCALE        <  .    
 ˜¸¾ ˜¸¾   ˜˜ý *  ˜¹ ˜˜v >    ˜–ì *    ˜— *  ˜¹5 ˜¹   ˜™§ :  .     ˜¹B   ˜¹B 
 NONUMBER         :  ˜¹J ˜¸Ú   ˜¹B 
 INFINITY         :  ˜¸¨ ˜˜v ˜¸ö <  ˜¹
 ˜¸ó ˜¸¾ ˜¹ ˜˜v D  >  ˜¹ :  ˜¸° ˜¹% >  ˜¹. <  ˜¹5 ˜¸¾ ˜¸¾ ˜¹9 ˜˜v >  ˜¹? :  .     ˜¹B ˜¹M :  ˜¹y ˜¸Ú ˜¹W ˜¹^   ˜¸× 
 CURVE        D  :  .    	 ˜–Û <  ˜¹
 ˜¸¾ ˜¸¾ ˜¹ ˜˜v D  :  .     ˜¹ >    ˜–ì *  ˜¹• ˜— :  ˜¹Š   ˜¤Ž *  ,  *    ˜¹• *    ˜¹5 ˜¸ó      ˜¸¾   ˜¹• *    ˜¹5 ˜¸ó   ˜¹5 4  ˜¸¾   
 iquo        *    ˜˜ý *  ˜¹• ˜¸ó :  .     ˜–Û >    ˜›ä *  ˜¸È ˜ªÖ :  ˜¹Ä   ˜£‡ *  ˜·® ˜¸Ú ˜¸Ú ˜¸Ú >    ˜›ä *  ˜¸È ˜ªÚ :  ˜¹Ä   ˜£‡ *  ˜·®       
 ˜¹« ˜¸Ú ˜¸Ú >    ˜›ä *  ˜¸È ˜ªÝ :  ˜¹Ä   ˜£‡ *  ˜·® ˜¸Ú ˜¹â ˜¸Ú >    ˜›ä *  ˜¸È ˜ªá :  ˜¹Ä   ˜£‡ *  ˜·® ˜¹â ˜¹â ˜¸Ú >    ˜›ä *  ˜¸È ˜ªå :  ˜¹Ä   ˜£‡ *  ˜·® ˜¸Ú ˜¸Ú ˜¹â >    ˜›ä *  ˜¸È ˜ªé :  ˜¹Ä   ˜£‡ *  ˜·® ˜¹â ˜¸Ú ˜¹â >    ˜›ä *  ˜¸È ˜ªí :  ˜¹Ä   ˜£‡ *  ˜·® ˜¸Ú ˜¹â ˜¹â >    ˜›ä *  ˜¸È ˜ªñ :  ˜¹Ä   ˜£‡ *  ˜·® ˜¹â ˜¹â ˜¹â >    ˜›ä *  ˜¸È ˜«… :  ˜¸¸ *  ˜¸¸   ˜¢å *  ˜¹Š ˜¹Ä :  ˜¸¸ *  ˜¸¸   ˜¢Ý *  ,  *  ˜¹Š ˜¹Ä $    ˜¸× ˜Ÿj "  ˜¸Ú ˜¹ >  $    ˜–ì *  ˜¸ã ˜–ø     ˜— *  ˜¸Ú ˜¸ã ˜¢í :  ˜¸¸ *  ˜¸¸   ˜Ÿj *    ˜— *    ˜— ˜¹ :  ˜¸¸ *  ˜¸¸ ˜¸È   ˜¸× ˜¢å >    ˜–ì *  ˜¸ã     ˜— *    ˜ºŒ *    ˜  :  ˜¸¸ *  ˜¸¸   ˜¢å ˜ºw ˜º~   ˜¸× ˜Ÿ‰ :  ˜¸´   ˜  *      ˜¥   ˜œÌ ˜¸È   ˜¸× ˜Ÿâ :  ˜¸¸ *  ˜¸¸   ˜  *      
 WIREFRAME          ˜«v ˜¸È ˜º~ >    ˜–ì *  ˜¸þ ˜£û >  $    ˜–ì *  ˜¸î ˜£û   ˜¸î 4  
 undefined        ˜ºÏ :  ˜¸¸ *  ˜¸¸   ˜ Ø *  ˜¸î ˜¸þ :  ˜¸¸ *  ˜¸¸   ˜ Ø *  ˜ž¸ ˜¸þ >  ˜ºÆ :  ˜¸¸ *  ˜¸¸   ˜ Ø *  ˜¸î ˜ž¸ :  .     ˜ž¸ :  .     ˜ž¸ >    ˜¹J   ˜¹J :  ˜ºó ˜¹J >    ˜¹y   ˜¹y :  ˜º÷ ˜¹y >  ˜¸¨ D  >      ˜— *  ˜¸¾ ˜¸î ˜¸Ú :  ˜ºó ,  *    ˜¸Ú ˜¢Ï   ˜¸¾ 
 +infinity            ˜— *  ˜¸ó ˜¸î ˜¸Ú :  ˜ºó ,  *    ˜¹« ˜¢« ˜» :  ˜ºó ,  *  ˜». ˜» ˜» >    ˜¸þ   ˜¸þ :  ˜¸þ 4  ˜¹« ˜¸¾ >    ˜— *  ˜¸þ 6  *  ˜»@ 4  ˜¸Ú ˜¸¾ 4  ˜¹« ˜¸Ú >      ˜— *  ˜¸¾ ˜¸þ ˜¸Ú :  ˜º÷ ˜»     ˜— *  ˜¸ó ˜¸þ ˜¸Ú :  ˜º÷ ˜», :  ˜º÷ ˜»4 ˜»f >  (    ˜ºó ˜ž¸   ˜º÷ ˜ž¸ :  ˜¸¸ *  ˜¸¸   ˜ ' *  ˜ºó ˜º÷ >  (    ˜¸¬ ˜™{   ˜¸° ˜™{ :  ˜¸¸ *  ˜¸¸   ˜Ÿ¾ *  ˜¸¬ ˜¸°   ˜  *      ˜ºÏ   ˜²0   ˜—* *  ˜¸¸ ˜¸´ ˜¸ ˜¸ 
 _PARAM_ANGLE           b ˜©÷ 
 plot/makefunc    2  *  
 proctype         ˜–  
 funcparms        
 tform        *  *  ˜™g ˜»º >  0     >  $    0              ˜ž   
 evalhf      *  ˜¢&   ˜  *  6  *    
 _body        0       
 _transform       0     2  *  
 _parm        ˜»º ˜»º ˜»º D    ˜žÆ *    ˜»Ë *    ˜»× *  ˜»¿ >    ˜–ì *  
 "        ˜žÚ   ˜»Þ *  ˜»ý D    ˜žÆ *    ˜žÍ *  ˜»õ ˜ž >  ˜»ú ˜¼ ˜ºÏ ˜»º ˜»º ˜»Ã   ˜  *  ˜»Ô 2  ˜»æ ˜»º ˜»º ˜»º ˜¼ ˜»º ˜»º ˜»È   ˜  *  6  *  ˜»Ö 2  ˜»æ ˜»º ˜»º ˜»º D  ˜»ï >  ˜»ú ˜»ý D  ˜¼ >  ˜»ú ˜»ý ˜ºÏ ˜»º ˜»º   ˜  *  ˜¼% 2  ˜»æ ˜»º ˜»º ˜»º ˜¼2 ˜»º ˜»º >  ˜»Â   ˜  *  6  *  ˜»Ö ˜»Ý   ˜»ç 0     2  ˜»æ ˜»º ˜»º ˜»º D    ˜žÆ *    ˜»Ë *  ˜»× >  ˜»ú ˜¼ D    ˜žÆ *    ˜žÍ *  ˜»× ˜ž ˜¼ ˜»º ˜»º ˜»Ã   ˜  *  ˜¼K 2  ˜»æ ˜»º ˜»º ˜»º D    ˜žÆ *    ˜žÍ ˜¼^ ˜¼ ˜»º ˜»º ˜»È   ˜  *  6  *  ˜»Ö ˜¼O 2  ˜»æ ˜–Ö ˜–Ö ˜–Ö D  ˜¼Y >  ˜»ú ˜»ý D  ˜¼d ˜¼4 ˜–Ö ˜–Ö   ˜  *  ˜¼‡ 2  ˜»æ ˜»º ˜»º ˜»º ˜¼• ˜»º ˜»º ˜»º ˜»º 
 logplot  ˜± 
 type/lhsargs     ,  *  6  *  ˜£û 
 relation        
 animtrap     2  ˜´ ˜´ ˜—± ˜–Ö   ˜­@ *  ,  *    ˜¤Ž *    ˜ª± ˜´- ˜´= ˜´B   ˜Ÿ] 
 	Trapezoidal Approximation        ˜–Ö ˜–Ö 
 type/package     2  *  ˜–Ä *  ˜›} *  ˜˜c ˜³È D  ˜²I >  $    ˜–ì *  ˜²J   ˜¯/   ˜›ä *  ,  *    ˜— *       ˜²k ˜²w ˜˜v ˜–æ ˜³È ˜³È 
 _HIGHESTINDEX    ˜ª 
 implicitplot     ˜±Å 
 matrixplot   ˜¯» 
 plot/usual   2  *  ˜–Ä ˜›  ˜– ˜›# ˜žJ *  ˜£ ˜¸k ˜¶² ˜¨Á ˜—­ 
 xmin         
 xmax         ˜ž¤ 
 ymin         
 ymax         
 xlft         
 xmid         
 xrht         
 ylft         
 ymid         
 yrht         
 mid      
 minwidth         
 xrange       
 yrange       ˜¬³ 
 q        
 curves       
 NIL      ˜¦l 
 kk       
 angle        
 jitter       *  ˜™g *  D   :  .       ˜–† *    ˜´¡ :  .       ˜žÍ *  0     :  .       ˜žÍ *  0     :  .       ˜½Œ      ˜½„      >  "  ˜½”         ˜›ð *    0 ÿÿÿþ *  0     ˜½Œ ˜½„ 0     0     :  .    
   ˜½© *  ˜½Œ :  .    	 ˜½² :  .     ,  *  ,  *  ˜½Œ ˜½² .     :  .       ˜½” ˜½˜   ˜½­ ˜½˜ ˜½› ˜½˜ ˜½› <  .       ˜½­ ˜½˜      ˜½˜ ˜½› ˜½˜ ˜˜v D  >      ˜¶ç *  ˜½Ô      ˜½  :  .       ˜½„ ˜½˜   ˜½Ô ˜½˜ ˜½È ˜½˜ ˜½˜ :  ˜½ê   ˜½„ ˜½˜     ˜½Ô ˜½˜   ˜½| *      
 modp        *  ˜½Ô     e ˜½˜ ˜½˜ ˜½˜ ˜½˜ ˜½˜ ˜½È ˜½˜ ˜½˜ :  .       ˜½© *  ˜½ê :  ˜½½ ,  *  ,  *  ˜½ê ˜¾ ˜½½ > 	   ˜¾ ˜ºÏ ˜½y   ˜½¹ ˜ºÏ D  :  ˜½¹ ˜¾ :  ˜½² ˜¾ "  ˜½² ˜¾ ˜¾/ "  ˜¾ ˜½¹ ˜¾, :  ˜½ê ˜½„ ˜¾ ˜¾ ˜¾# :  ˜´R   ˜´R ˜½˜ ˜½­ ˜½˜ >  ˜¾(   ˜›ð ˜½y :  .       ˜½² ˜½˜ ˜½¹ ˜½› >    ˜¾M ˜½  :  ˜¾M ˜½˜ :  .         ˜½” ˜½˜ ˜½¯ ˜½›      :  .     ˜½˜ :    .     *  ˜—O   ˜½½ ˜¾n :  ˜½½   ˜½½ *  ˜¾d <  ˜½y ˜½˜ ˜½˜ ˜½y   ˜¾u ˜½Å D  :  .         ˜¾l *  ˜¾g ˜¾n :  .     ˜¾p ˜¾s :  .       ˜¾p ˜¾n :  .       ˜¾† ˜¾w :  .       ˜¾Œ ˜¾n :  .       ˜¾Œ ˜¾w :  .       ˜¾p ˜¾w :  .       ˜žÆ *    ˜»Ë *    
 abs     *          ˜¾£ ˜½˜ ˜¾— ˜½› ˜½˜   ˜¾ ˜½˜ ˜¾ƒ ˜½› ˜½› ˜½˜     ˜¾© ˜½˜ ˜¾£ ˜½› ˜½˜   ˜¾‘ ˜½˜ ˜¾ ˜½› ˜½› ˜½› ˜½˜   ˜¾‘ ˜½˜ ˜¾ƒ ˜½› ˜½˜ ˜¾M ˜½› >    ˜¾¯ ˜³< :  ˜¾¯   ˜žÍ ˜¾¶ >  "  ˜¾Û ˜¾\ D  :  ˜¾g   ˜¾g ˜½˜ ˜½˜ ˜½˜ :  ˜¾† ˜¾Œ $  $  $    ˜¾— ˜ºÏ   ˜¾£ ˜ºÏ   ˜¾© ˜ºÏ "  ˜¾¯ ˜¸E ˜¾ð $    ˜¾£ ˜ºÏ   ˜¾— ˜ºÏ ˜¾ð D    ˜² *  ˜¾d ˜¨Ô 
 subdividing interval         ˜¾† ˜¾Œ ˜¾p :  ˜´R   ˜´R ˜½˜ ˜½˜ ˜½˜ >  "  ˜¾Å ˜¾Ó D  :  ˜½ê   ˜¾   ˜½˜ ˜¾d ˜¾‘ ˜¿4 :  ˜½½ ,  *  ˜¾Œ ,  *  ,  *  ˜½ê ˜¾ ˜½½ D  :  ˜½ê   ˜¾ƒ ˜¿4 ˜¾ ˜¿4 :  ˜½½ ,  *  ˜¿@ ,  *  ˜¾Œ ˜½½ ˜¾ñ :  ˜¾† ˜¾p :  ˜½Ô ˜½˜ :  .     ˜–Û <  ˜½y ˜½˜ ˜½˜ ˜½y    ˜½Ô ˜¾g D  <  ˜½Ô ˜½Ô ˜½˜ ˜¾g       ˜¾l *  ˜½Ô ˜¾w ˜ºÏ ˜½y >  ˜¿f D  <  .     ˜½Ô ˜½˜ ˜¾g       ˜¾l *  ˜¿| ˜¾w ˜ºÏ ˜½y :  ˜½½ ,  *    
 $       *      ˜— *    ˜¾l *  .       ˜¿š 4  ˜½Ô   ˜¿| ˜½˜ ˜½› ˜½˜ :  ˜¿^ *  ˜¿^ ,  *    ˜¤Ž *  ,  *    ˜½½ *    .     ˜¾d ˜½› ˜½˜   ˜½½ *    ˜¿´ ˜¾d   ˜¿´ 4  ˜½˜     ˜˜ý *  ˜½½ ˜¿4 :  ˜½Ô ˜¿| :  ˜¿^   ˜¢Ý *  ˜¿^   ˜£‡ *    ˜·®   ˜— *    ˜­S *    ˜ž0 ˜½˜ ˜½˜ ˜½˜ :  ˜ž0   ˜·¿ *  ˜¿Ý ˜½ ˜¿^ ˜½y *  ˜´R ˜ž0 
 setoptions   ˜±:    …   “ ˜´«      `  e ˜´«        Äexamples/integrate.txt                                                                              0100644 0001107 0000172 00000007006 05662251617 0017015 0                                                                                                    ustar 00zachary                         cs-teach                        377777770000630                                                                                                                                                                        > with(plots);

  [animate, animate3d, conformal, contourplot, cylinderplot, densityplot,

      display, display3d, fieldplot, fieldplot3d, gradplot, gradplot3d,

      implicitplot, implicitplot3d, loglogplot, logplot, matrixplot, odeplot,

      pointplot, polarplot, polygonplot, polygonplot3d, polyhedraplot, replot,

      setoptions, setoptions3d, spacecurve, sparsematrixplot, sphereplot,

      surfdata, textplot, textplot3d, tubeplot]
--------------------------------------------------------------------------------
> onerect := (h, n, f, lo) -> (lo+(n-1)*h, 0, lo+(n-1)*h, f(lo + n*h - .5*h), lo+n*h, f(lo + n*h - .5*h));

          onerect := (h,n,f,lo) -> (lo + (n - 1) h, 0, lo + (n - 1) h,

              f(lo + n h - .5 h), lo + n h, f(lo + n h - .5 h))
--------------------------------------------------------------------------------
> rect := (func, step, steps, lo, hi) -> \
             plot({func(x), [seq(onerect(step, `n`, func, lo), `n`=1..steps), lo+steps*step, 0]}, x=lo..hi);
Warning, `n` is implicitly declared local


rect := (func,step,steps,lo,hi) -> local n; plot(

{[seq(onerect(step, n, func, lo), n = 1 .. steps), lo + steps step, 0], func(x)}
    ,

x = lo .. hi)
--------------------------------------------------------------------------------
> animrect := (func, lo, hi, frames) ->\
                    display([seq(rect(func, (hi-lo)/2^frame, 2^frame, lo, hi), frame=1..frames)],\
                                    insequence=true, title=`Rectangular Approximation`);
Warning, `frame` is implicitly declared local


      animrect := (func,lo,hi,frames) -> local frame; display(

                          hi - lo   frame
          [seq(rect(func, -------, 2     , lo, hi), frame = 1 .. frames)],
                            frame
                           2

          insequence = true, title = Rectangular Approximation)
--------------------------------------------------------------------------------
> onetrap := (h, n, f, lo) -> (lo+(n-1)*h, 0, lo+(n-1)*h, f(lo + (n-1)*h), lo+n*h, f(lo + n*h));

onetrap := (h,n,f,lo) ->

   (lo + (n - 1) h, 0, lo + (n - 1) h, f(lo + (n - 1) h), lo + n h, f(lo + n h))
--------------------------------------------------------------------------------
> trap := (func, step, steps, lo, hi) ->\
             plot({func(x), [seq(onetrap(step, n, func, lo), n=1..steps), lo+steps*step, 0]}, x=lo..hi);
Warning, `n` is implicitly declared local


trap := (func,step,steps,lo,hi) -> local n; plot(

{[seq(onetrap(step, n, func, lo), n = 1 .. steps), lo + steps step, 0], func(x)}
    ,

x = lo .. hi)
--------------------------------------------------------------------------------
> animtrap := (func, lo, hi, frames) ->\
                      display([seq(trap(func, (hi-lo)/2^frame, 2^frame, lo, hi), frame=1..frames)],\
                                    insequence=true,\
                                    title= `Trapezoidal Approximation`);
Warning, `frame` is implicitly declared local


      animtrap := (func,lo,hi,frames) -> local frame; display(

                          hi - lo   frame
          [seq(trap(func, -------, 2     , lo, hi), frame = 1 .. frames)],
                            frame
                           2

          insequence = true, title = Trapezoidal Approximation)
--------------------------------------------------------------------------------
> animrect(x->x^2, 0, 1, 5);
--------------------------------------------------------------------------------
> animtrap(x->x^2, 0, 1, 5);
--------------------------------------------------------------------------------
> 
      ˜¾l *  ˜¿| ˜¾w ˜ºÏ ˜½y :  ˜½½ ,  *    
 $       *      ˜— *    ˜¾l *  .       ˜¿š 4  ˜½Ô   ˜¿| ˜½˜ ˜½› ˜½˜ :  ˜¿^ *  ˜¿^ ,  *    ˜¤Ž *  ,  *    ˜½½ *    .     ˜¾d ˜½› ˜½˜   ˜½½ *    ˜¿´ ˜¾d   ˜¿´ 4  ˜½˜     ˜˜ý *  ˜½½ ˜¿4 :  ˜½Ô ˜¿| :  ˜¿^   ˜¢Ý *  ˜¿^   ˜£‡ *    ˜·®   ˜— *    ˜­S *    ˜ž0 ˜½˜ ˜½˜ ˜½˜ :  ˜ž0   ˜·¿ *  ˜¿Ý ˜½ ˜¿^ ˜½y *  ˜´R ˜ž0 
 setoptions   ˜±:    …   “ ˜´«      `  e ˜´«        Ä                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 ˜œú                     H  
 framed       ˜œú                     H  ˜œ¦ ˜œ¦                     H  
 none         ˜;                     H  
 BOXED        ˜œÌ                                                                                                         
 cylinderplot       ˜–† *    
 plots/cylinder       
 contourplot    ˜–† *    
 plots/contplot       
 animate3d      ˜–† *    
 plots/animate3d      
 setoptions3d       ˜–† *    
 plots/setoptions3d       
 