/*Arithmetic Mean of a large number of Integers

   - or - solve a very large constraint matrix

          over 1 million rows and columns

   Nigel_Galloway@operamail.com

   March 18th., 2008.

 */

 param e := 20;

 /* set Sample := {-2**e..2**e-1}; */

 set Sample := {1..2**e-1};

 var Mean;

 var E{z in Sample};

 /* sum of variances is zero */

 zumVariance: sum{z in Sample} E[z] = 0;

 /* Mean + variance[n] = Sample[n] */

 variances{z in Sample}: Mean + E[z] = z;

 solve;

 printf "The arithmetic mean of the integers from 1 to %d is %f\n", 2**e-1, Mean;

 end;