SecRed: A program for sector-wise IBP reduction of Feynman integrals

Abstract

SecRed is a C++ program for the reduction of multi-loop Feynman integrals with integration-by-parts (IBP) identities. It reduces an integral family sector by sector for memory control and parallelism, and adds algorithms designed for that setting: an adaptive seed box with a corner cut, an optional seed truncation, a subsector level filter, and symmetry relations expanded only from the master integrals of a sector. A global stage assembles the retained equations and performs the finite-field reconstruction of the coefficients using FiniteFlow or FireFly, repeating the elimination over a sequence of primes. On the elimination side, a coefficient-free plan records the elimination order once and is replayed at each prime, so that only the arithmetic is repeated, and a head score orders the equations to reduce fill-in during the elimination. The program is demonstrated on a two-loop five-point non-planar family and on a four-loop cut family, where assembling the global equation system as a whole would exceed the memory of a single node.