Feynman integral reduction by covariant differentiation

We show how a large class of Feynman integrals can be efficiently reduced to master integrals by suitable covariant differentiation on the vector space dual to the one spanned by the master integrals. The connections needed in the covariant derivatives have to be built only once for a given topology and then apply to any configuration of internal propagator masses. We implement our algorithm in the Mathematica code Method for Reduction of Loop Integrals (MERLIN).