Scaling up to Multivariate Rational Function Reconstruction

Maier, Andreas

doi:10.1016/j.cpc.2025.109827

Typ	Amount	VAT	Currency	Share	Status	Cost centre
Hybrid-OA	2575.00	0.00	EUR	96.26 %	(DEAL)	9001010 / 476152
Payment fee	100.00	0.35	EUR	3.74 %	(Bestellt)	9001010 / 476152
Sum	2675.00	0.35	EUR
Total	2675.35

Journal Article

PUBDB-2024-05922

Scaling up to Multivariate Rational Function Reconstruction

Maier, A. (Corresponding author)Extern*DESY*

2025
North Holland Publ. Co. Amsterdam

Computer physics communications 317, 109827 (2025) [10.1016/j.cpc.2025.109827]

This record in other databases:

Please use a persistent id in citations: doi:10.1016/j.cpc.2025.109827 doi:10.3204/PUBDB-2024-05922

Report No.: DESY-24-138; arXiv:2409.08757

Abstract: I present an algorithm for the reconstruction of multivariate rational functions from black-box probes. The arguably most important application in high-energy physics is the calculation of multi-loop and multi-leg amplitudes, where rational functions appear as coefficients in the integration-by-parts reduction to basis integrals. I show that for a dense coefficient the algorithm is nearly optimal, in the sense that the number of required probes is close to the number of unknowns. PROGRAM SUMMARY Program title: rare CPC Library link to program files:https://doi.org/10.17632/wt228b57kw.1 Developer's repository link:https://github.com/a-maier/rare. Licensing provisions: GNU General Public License 3 Programming language: Rust Supplementary material: Comparison code to other programs is available under https://github.com/a-maier/scaling-rec and uses C++, Rust, and Wolfram Mathematica. Nature of problem: Straightforward computations of scattering amplitudes in perturbative quantum field theory suffer from large intermediate expressions. Hence, state-of-the-art approaches make heavy use of multivariate rational function reconstruction from probes in fields with a finite characteristic. In this way, only numbers with a bounded size are encountered in intermediate steps. This strategy requires efficient reconstruction algorithms. Solution method: The code provides a proof-of-concept implementation of a new rational reconstruction algorithm. The algorithm is particularly efficient for dense functions, where the number of required probes is close to the number of unknown coefficients. Additional comments including restrictions and unusual features: As customary for Rust libraries, the code is not intended for stand-alone installation, but for compilation as part of a larger program, e.g. using the Cargo package manager [1]. References: The code is compared to implementations of an algorithm by Cuyt and Lee [2,3] in FireFly[4–6] and FiniteFlow[7,8].

Classification:

ddc:530

Note: Comput. Phys. Commun. 317 (2025) 109827. 14 pages, no figures. Journal version with comparison to FireFly and FiniteFlow

Contributing Institute(s):

Zeuthen Particle PhysicsTheory (Z_ZPPT)

Research Program(s):

611 - Fundamental Particles and Forces (POF4-611) (POF4-611)

Experiment(s):

No specific instrument

Appears in the scientific report 2025

Database coverage:
Medline

;

;

; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; Nationallizenz