Download instructions and   
      What is in this folder?

It is suggested that you download all the three zip files,
equ4genexe.zip, equ4genpas.zip, and equ4genelse.zip.
If your fire wall prohibits downloading the equ4genexe.zip because
it contains *.exe files, then there is no problem: download only the other
equ4genpas.zip file, which also contains the *.exe files so that they are 
renamed to *.fut   files. ("fut" is the Hungarian word for "run".) After
having the *.fut files, you can simply rename them to *.exe.
Note that your file explorer software should NOT hide the extensions
(like "exe", "txt", ...) of file names. (Such a software
prefers to hide these extensions by default, but you can change
the default setting.) The equ4genelse.zip consists of data files 
and Maple worksheets.


There are several programs here with the same core but with some
differences. (Search for "*** Program: " to see what they are.)
The most frequently used one is    equmgn. 
The names of these programs have been chosen according to the following
strategy: "equ"  is from "equivalence lattice", "gs" from "generating sets".
In the middle, "l" or "m" is for "little" or "medium". However, the most 
frequently uses "equmgn"  breaks the rule since  "n" in it stands for "new".

Important notes: 

- The programs output the numerical results on the screen and also into an
output file whose name is derived from the name of the input file (by
suffixing). If long lists are requested, then they are printed only into the
output files.  Input and output files are *.txt files that must obey strict
syntactical rules. 

- The programs surely run under Windows 10 (this has been 
tested), and they must run under some earlier version of Microsoft Windows
(but this has not been tested). However, the programs are not built on
the graphical interface of Windows; in particular, you you cannot start
them by a simple mouse click or mouse dragging! 

- You can either start one of these programs from 
a command line (but this is tedious and not
recommended), or you create a shortcut with the necessary parameters
(this is the recommended way). For example, if you put 
both the program equmgn.exe  and the data file 4.txt into 
a folder called C:\today's-work\,   then you can create a shortcut with content 
C:\today's-work\equmgn.exe 5.txt 1 10000 50 4
(Here 5.txt is the list of all partitions of the set {1,2,3,4,5}, which
has been obtained by the Maple worksheet listpartitions.mws, or with any
other program that outputs these partition following the same syntax.)
Now if you click on this shortcut, then equmgn.exe  performs 10000 random
test and prints a dot on the screen after every 50 tests; in each test,
a random 4-element subset is chosen and it is decided if this subset generates
Equ(5).  In order to create an appropriate shortcut, click on  equmgn.exe with
the right mouse button, create a shortcut. Then with a right-mouse-click on
the shortcut, select properties and add the parameters.





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*** Program: 
equmgn.pas, equmgn.exe    Purpose: perform random tests to decide
which portion of its g-element subsets generate Equ(n);
here  3<= n <= 9  and 3<g<=8. 
  1st parameter: the list of elements of Equ(n), i.e,
    the lexicographically ordered list of all partitions 
    on {1,2,...,n};  2<=n.  (Remark: n is not a parameter; the
    program figures out  n from the data file.)
  2nd parameter: 
     1, 2, or default: the program gives only the number of g-element generating sets.
     3 or larger: in addition to 1 above, the program prints all the selected g-element 
       subsets into a txt file, and for each subset, the size of the sublattice generated 
       by the subset in question is also printed. Subsets generating Equ(n) are listed 
       twice. (The elements, which are equivalences,  of the selected subsets are given by 
       their positions in the input txt file.)
  3rd parameter: the number of random subsets to be selected.  
  4th parameter: the number of selected subsets after which the program prints a dot on
        the screen. (This is to indicate that the program is still working.)
  5th parameter: the size of a randomly selected subset; permitted values: 3,4,...,8.      

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*** Program: 
equlgs.pas, equlgs.exe  : "l" is for "Little", 
 counts (and even lists) the 4-element generating sets of Equ(n), n<=6.

  1st parameter: the list of elements of Equ(n), i.e,
    the lexicographically ordered list of all partitions 
    on {1,2,...,n};  2<=n.

  2nd parameter: 
   1 (or default): gives only the number of 4-element generating sets.
   2: in addition to 1 above, gives these generating sets as well.
   3: in addition to 1 above, gives the first few elements of the
       "generation sequence" 4=|X0|, |X1|, |X2|, ...
   4: does both 2 and 3 above.

  3rd parameter:
   0 or default: the program runs without breaks (no break is allowed)
     For n=6, this is not recommended since the program runs for days.
     (If we want a break later, use "1" rather than "0".)
   i (any integer out of 1,2, ..., Bell(n)-3 ): the program 
     computes (and lists) from i1:=i, where
     i1 is the first partition (according to the file given
     in the first parameter), so the candidate generating
     sets are i1=i < i2 <i3 <i3. The program is allowed to
     stop only when a certain i1 (with all i2, i3 and i4)  
     is terminated. The results are saved into a new file
     named g-n-i-j.txt, where g is g, n is the size of the base
     set, i is the first value of i1 (from the 3rd parameter),
     and j is is its last value. E.g.,   g-6-5-13.txt  is such
     a file name.    To cause a termination of the program
     while it is running, press <alt><R>  (keeping the right
     <alt> key pressed, hit the <R> key). (In my system with
     Hungarian keyboard,  this key combination can also be used 
     to create an encircled dot in superscript position in 
     Microsoft Word. This key combination is rare enough
     to avoid that a parallel other running application terminates
     the program without intention.
     After that <alt><R> is pressed, the program acknowledges
     its notice with writing "<alt><R>", completes the remaining
     task with the actual value of i1 (this can take dozens of minutes),
     saves the results into the output files (see above), and 
     terminates --- do not switch the computer off before the 
     program terminates! 

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*** Program: 
ecompare.pas ecompare.exe ("e" comes from Equivalence-lattice-generating-sets)
  Counts and list those generating 4-sets that are NOT antichains; in particular,
  decides if there exists such.  The only parameter is  an integer n (n=3,4,5,6,...).
  The program takes its data from two input files:  n.txt   (which lists all
  equivalences of {1,2,...,n}) and n_r0.txt  (which is obtained from n.txt by
  means of equlgs.exe and lists all four-element generating sets.
  Even if n_r0.txt does not list ALL generating 4-sets, the program selects and
  counts the non-antichains out of them. The output is saved to n_comp.txt, 
  provided if there is no file with this name. (If there is, then the program
  halts without warning.)

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*** Program: opsequ
  The program takes its data from the input file  n.txt, listing all
  equivalences of {1,2,...,n}, and outputs the operation table of Part({1,...,n}).

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*** Program:   (out of date:)
equmgs.pas, equmgs.exe  ("m" comes from medium size)
  Picks many (but not all) 4-element subsets and count those 
  that generate the whole Equ(n); here n <= 10. (But the program
  is not enough efficient for n=10.) To do so,
  inputs the list of all partitions. Runs up to keypressed or
  up to a given number of experiments (given as the third parameter).
  The value of n (=ne in the program) is determined by the data file.
  - 4th parameter: dotoften ; after that many [X], a dot is printed on the 
    screen, default=0.
  The first three parameters: as above (but some of them may have no effect).
  Note that by the procedure "joinveeclosed", every join is computed only once.


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