MultivariateResidues: a Mathematica package for computing multivariate residues

TL;DR

This paper introduces a Mathematica package that efficiently computes multivariate residues, crucial in physics and geometry, using algebraic geometry methods, including the global residue theorem for relations between residues.

Contribution

The paper presents a new Mathematica package that automates multivariate residue calculations with algebraic geometry techniques, including global residue relations.

Findings

Efficient computation of multivariate residues in physics and geometry.

Implementation of the global residue theorem within the package.

Facilitates residue evaluations at finite points and infinity.

Abstract

Multivariate residues appear in many different contexts in theoretical physics and algebraic geometry. In theoretical physics, they for example give the proper definition of generalized-unitarity cuts, and they play a central role in the Grassmannian formulation of the S-matrix by Arkani-Hamed et al. In realistic cases their evaluation can be non-trivial. In this paper we provide a Mathematica package for efficient evaluation of multidimensional residues based on methods from computational algebraic geometry. The package moreover contains an implementation of the global residue theorem, which produces relations between residues at finite locations and residues at infinity.