alpar@1: /*Arithmetic Mean of a large number of Integers
alpar@1:   - or - solve a very large constraint matrix
alpar@1:          over 1 million rows and columns
alpar@1:   Nigel_Galloway@operamail.com
alpar@1:   March 18th., 2008.
alpar@1: */
alpar@1: 
alpar@1: param e := 20;
alpar@1: /* set Sample := {-2**e..2**e-1}; */
alpar@1: set Sample := {1..2**e-1};
alpar@1: 
alpar@1: var Mean;
alpar@1: var E{z in Sample};
alpar@1: 
alpar@1: /* sum of variances is zero */
alpar@1: zumVariance: sum{z in Sample} E[z] = 0;
alpar@1: 
alpar@1: /* Mean + variance[n] = Sample[n] */
alpar@1: variances{z in Sample}: Mean + E[z] = z;
alpar@1: 
alpar@1: solve;
alpar@1: 
alpar@1: printf "The arithmetic mean of the integers from 1 to %d is %f\n", 2**e-1, Mean;
alpar@1: 
alpar@1: end;