A practical criterion of irreducibility of multi-loop Feynman integrals

A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable (with zero gradient) points of a specially constructed polynomial. (c) 2006 Elsevier B.V. All rights reserved.