  Selberg-type integrals that can be turned into constant term identities for
Laurent polynomials arise naturally in conjunction with random matrix models in
statistical mechanics. Built on a recent idea of Karasev and Petrov we develop
a general interpolation based method that is powerful enough to establish many
such identities in a simple manner. The main consequence is the proof of a
conjecture of Forrester related to the Calogero--Sutherland model. In fact we
prove a more general theorem, which includes Aomoto's constant term identity at
the same time. We also demonstrate the relevance of the method in additive
combinatorics.
