Hi. Associated with a finite poset $P$, one can consider the poset $S(P)$, whose elements are the intervals of $P$, ordered by inclusion. (See http://mathoverflow.net/questions/73640 for some motivation why to look at this).
Does anyone know if there is an algorithm around which, given $P$, computes $S(P)$? I think it is not very difficult to come up with one, but I just want to know if it has already been implemented, say, in some computer algebra system, or studied in the literature.