open Array;

     val n = 10;

     val M = array(n,array(n,0.0));

     val i = ref 1;

     while !i<n do (
         update(M,!i,array(n,0.0));
         i := !i + 1
     );

     i := 0;

     val j = ref 0;

     (* initialize M to be a particular matrix *)

     while !i<n do (
         while !j<n do (
             update(sub(M,!i),!j,1.0/real(!i + !j + 1));
             j := !j + 1
         );
         j := 0;
         i := !i + 1
     );

     i := 0;
     while !i<n-1 do (
         j := !i+1;
         while !j<n do
             let
                 val ratio = sub(sub(M,!j),!i)/sub(sub(M,!i),!i);
                 val k = ref (!i+1)
             in
                 update(sub(M,!j),!i,0.0);
                 while !k<n do (
                     update(sub(M,!j),!k,sub(sub(M,!j),!k) -
                             ratio*sub(sub(M,!i),!k));
                     k := !k + 1
                 );
                 j := !j + 1
             end;
         i := !i + 1
     );