  Let n and d be positive integers, let k be a field and let P(n,d;k) be the
space of the polynomials in n variables of degree at most d with coefficients
in k. Let B(n,d) be the set of the Bernstein-Sato polynomials of all
polynomials in P(n,d;k) as k varies over all fields of characteristic 0. G.
Lyubeznik proved that B(n,d) is a finite set and asked if, for a fixed k, the
set of the polynomials corresponding to each element of B(n,d) is a
constructible subset of P(n,d;k).
  In this paper we give an affirmative answer to Lyubeznik's question by
showing that the set in question is indeed constructible and defined over Q,
i.e. its defining equations are the same for all fields k. Moreover, we
construct an algorithm that for each pair (n,d) produces a complete list of the
elements of B(n,d) and, for each element of this list, an explicit description
of the constructible set of polynomials having this particular Bernstein-Sato
polynomial.
