[Help-glpk] Re: Subsets in GNU MathProg

[Andrew Makhorin]

>I know there is a keyword named 'setof' (that maybe solve my problem),
>but I can't understand its behavior reading the documentation.
>
>When I do a
>
>set N := aa bb cc dd ee ff gg;
>set S := setof N;
>
>what happens exactly? With this syntax, will S be any subset of N (all
>the combinations)?
>

Consider an example:

   S := setof{i in I, (j,k) in J cross K: i+j <> k} (i+1, j, k-1);

In a procedural language (like Algol) the construction above could be
expressed as follows:

   S := empty set;
   for all i in I do
       for all (j,k) in J cross K do
           if i + j != k then
              S := S union { (i+1, j, k-1) };

Thus, the construction "set S := setof N" is syntactically invalid,
because there is missing an "integrand", i.e. a n-tuple which forms the
resultant set (as (i+1, j, k-1) in the example above).