$ The quasiGroup existence problem (CSP lib problem 3)
$
$ An m order quasigroup  is an mxm multiplication table of integers 1..m, 
$ where each element occurrs exactly once in each row and column and certain 
$ multiplication axioms hold (in this case, we want axiom 7 to hold). 
$
$ by Ian Miguel

ESSENCE' 1.0
given n : int(1..1000)
letting nDomain be domain int(0..n-1)

find quasiGroup : matrix indexed by [nDomain, nDomain] of nDomain
$find quasiGroupColumns : matrix indexed by [nDomain, nDomain] of nDomain

such that 
     
     $ assign the "reflected" quasigroup to qGColumns to access its columns
   $  forall row,col : nDomain .
     $    quasiGroupColumns[col,row] = quasiGroup[row,col],

     $ All rows have to be different
     forall row : nDomain . 
          allDifferent(quasiGroup[row,..]),

     $ all values in the diagonals
     forall i : nDomain . 
          (quasiGroup[i,i] = i), 

     $ All columns have to be different	       
     forall col : nDomain . 
          allDifferent(quasiGroup[..,col]),


     $ this strange constraint
     $ corresponds to:
     $ quasiGroup[i, quasiGroup[j,i]] = quasiGroup[quasiGroup[j,i], j]	
    $ forall i : nDomain .
    $      forall j : nDomain .	
    $          quasiGroup[i, quasiGroup[j,i]] = quasiGroup[quasiGroup[j,i],j],

     $ some implied? constraints		
     forall i : nDomain .
           quasiGroup[i,n-1] + 2 >= i