  A classical result from topology called Uryshon's lemma asserts the existence
of a continuous separator of two disjoint closed sets in a sufficiently regular
topological space. In this work we make a search for this separator
constructive and efficient in the context of real algebraic geometry. Namely,
given two compact disjoint basic semialgebraic sets which are contained in an
$n$-dimensional box, we provide an algorithm that computes a separating
polynomial greater than or equal to 1 on the first set and less than or equal
to 0 on the second one.
