/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 0.8.1 ] */

/* [wxMaxima: title   start ]
Collecting complete sets
   [wxMaxima: title   end   ] */

/* [wxMaxima: comment start ]
Finding the waiting time in order to collect a "complete set" by simulation. 
   [wxMaxima: comment end   ] */

/* [wxMaxima: comment start ]
Reference: J. Ziegenbalg: Algorithmen von Hammurapi bis Gödel,  
  Verlag Harri Deutsch, Frankfurt a.M. 2007, section 4.5   
   [wxMaxima: comment end   ] */

/* [wxMaxima: section start ]
Some tests with list operations
   [wxMaxima: section end   ] */

/* [wxMaxima: input   start ] */
L : makelist(j*j, j, 0, 6);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
L;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
L[4];
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
apply("+", L);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
rest(L);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
Some tests with the random generator
   [wxMaxima: section end   ] */

/* [wxMaxima: comment start ]
The commands  make_random_state  and  set_random_state  
serve the purpose of initializing the random number generator; 
cf. Maxima's help system. 
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
s1: make_random_state (654321) $
set_random_state (s1);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
make_random_state(true) $
random(1000);
L2 : []; for i:1 thru 12 do L2 : append(L2, [random(1000)]); L2;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
The collectors problem
   [wxMaxima: section end   ] */

/* [wxMaxima: input   start ] */
verbose : false    /* global variable to control printing */ $
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
collector() := 
  block([collector_array, r, i :0 ], 
    make_random_state(true), 
    collector_array : make_array(fixnum, 7), 
    fillarray(collector_array, makelist(0, j, 0, 6)), 
        /* fill collector_array with zeroes */ 
    if verbose then print(rest(listarray(collector_array))), 
    while is(apply("*", rest(listarray(collector_array))) = 0)    
    do (i : i+1 , 
        r : random(6)+1 ,
        collector_array[r] : collector_array[r]+1 , 
        if verbose then print(rest(listarray(collector_array))) ) ,
    [i, rest(listarray(collector_array))]  ) ;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
(verbose : true, collector() );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
collector_array_series(n) := 
  block(L : [],  
    for i:1 thru n do L : append(L, [collector()[1]]), 
    [L, float(apply("+",L)/length(L))]  );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
(verbose : false, collector_array_series(100) );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
collector_list() := 
  block([SL : [0,0,0,0,0,0], r, i :0 ], 
    make_random_state(true), 
    if verbose then print(SL), 
    while is(apply("*", SL) = 0)    
    do (i : i+1, 
        r : random(6)+1 ,
        SL[r] : SL[r]+1, 
        if verbose then print(SL) ) ,
    [i, SL]  );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
collector_list();
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
Some tests with the list operation "apply" 
   [wxMaxima: section end   ] */

/* [wxMaxima: input   start ] */
apply("*", [1,2,3,4]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
apply("*", []);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
collector_list_series(n) := 
  block(L : [],  
    for i:1 thru n do L : append(L, [collector_list()[1]]), 
    [L, float(apply("+",L)/length(L))]  );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
(verbose : false, collector_list_series(100) );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
timer(all);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
timer;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
timer_info();
/* [wxMaxima: input   end   ] */

/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$