Balancing act: multivariate rational reconstruction for IBP. (English) Zbl 1529.81068
Summary: We address the problem of unambiguous reconstruction of rational functions of many variables. This is particularly relevant for recovery of exact expansion coefficients in integration-by-parts identites (IBPs) based on modular arithmetic. These IBPs are indispensable in modern approaches to evaluation of multiloop Feynman integrals by means of differential equations. Modular arithmetic is far more superior to algebraic implementations when one deals with high-multiplicity situations involving a large number of Lorentz invariants. We introduce a new method based on balanced relations which allows one to achieve the goal of a robust functional restoration with minimal data input. The technique is implemented as a Mathematica package Reconstruction.m in the FIRE6 environment and thus successfully demonstrates a proof of concept.
MSC:
| 81Q30 | Feynman integrals and graphs; applications of algebraic topology and algebraic geometry |
| 32C30 | Integration on analytic sets and spaces, currents |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 65Y15 | Packaged methods for numerical algorithms |
Software:
LiteRed; FIRE; Reduze; FireFly; Mathematica; Reconstruction.m; FiniteFlow; AIR; Kira; FOXBOXReferences:
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