  Integration-by-parts reductions play a central role in perturbative QFT
calculations. They allow the set of Feynman integrals contributing to a given
observable to be reduced to a small set of basis integrals, and they moreover
facilitate the computation of those basis integrals. We introduce an efficient
new method for generating integration-by-parts reductions. This method
simplifies the task by making use of generalized-unitarity cuts and turns the
problem of finding the needed total derivatives into one of solving certain
polynomial (so-called syzygy) equations.
