MultivariateResidues: a Mathematica package for computing multivariate residues

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.

43 pages, 4 figures. Application to Cachazo-He-Yuan scattering equations added; journal version. The package MultivariateResidues can be downloaded from https://bitbucket.org/kjlarsen/multivariateresidues/raw/master/release/MultivariateResidues.zip

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• Refined swampland distance conjecture and exotic hybrid Calabi-Yaus
• Exact Stringy Microstates from Gauge Theories
• Intersection theory rules symbology
• Massive One-loop Conformal Feynman Integrals and Quadratic Transformations of Multiple Hypergeometric Series
• Multiple Mellin-Barnes integrals with straight contours
• Maximal transcendental weight contribution of scattering amplitudes
• Rings: an efficient Java/Scala library for polynomial rings
• BCJ Numerators from Differential Operator of Multidimensional Residue
• Hadronic Light by Light Corrections to the Muon Anomalous Magnetic Moment
• MultivariateResidues - a Mathematica package for computing multivariate residues