  An integer program (IP) with a finite number of feasible solutions may have
an unbounded linear programming relaxation if it contains irrational
parameters, due to implicit constraints enforced by the irrational numbers. We
show that those constraints can be obtained if the irrational parameters are
polynomials of roots of integers over the field of rational numbers, leading to
an equivalent rational formulation. We also establish a weaker result for IPs
involving the general class of algebraic irrational parameters, which extends
to IPs with a particular form of transcendental numbers.
