000639595 001__ 639595
000639595 005__ 20251102034908.0
000639595 0247_ $$2INSPIRETeX$$aMaier:2024djk
000639595 0247_ $$2inspire$$ainspire:2828377
000639595 0247_ $$2arXiv$$aarXiv:2409.08757
000639595 0247_ $$2datacite_doi$$a10.3204/PUBDB-2025-04571
000639595 037__ $$aPUBDB-2025-04571
000639595 041__ $$aEnglish
000639595 082__ $$a530
000639595 088__ $$2arXiv$$aarXiv:2409.08757
000639595 088__ $$2DESY$$aDESY-24-138
000639595 1001_ $$0P:(DE-H253)PIP1029970$$aMaier, Andreas Martin$$b0$$eCorresponding author$$udesy
000639595 245__ $$aScaling up to multivariate rational function reconstruction
000639595 260__ $$c2025
000639595 3367_ $$0PUB:(DE-HGF)25$$2PUB:(DE-HGF)$$aPreprint$$bpreprint$$mpreprint$$s1761750549_3361113
000639595 3367_ $$2ORCID$$aWORKING_PAPER
000639595 3367_ $$028$$2EndNote$$aElectronic Article
000639595 3367_ $$2DRIVER$$apreprint
000639595 3367_ $$2BibTeX$$aARTICLE
000639595 3367_ $$2DataCite$$aOutput Types/Working Paper
000639595 500__ $$aComput. Phys. Commun. 317 (2025) 109827. 14 pages, no figures. Journal version with comparison to FireFly and FiniteFlow
000639595 520__ $$aI present an algorithm for the reconstruction of multivariate rational functions from black-box probes. The arguably most important application in high-energy physics is the calculation of multi-loop and multi-leg amplitudes, where rational functions appear as coefficients in the integration-by-parts reduction to basis integrals. I show that for a dense coefficient the algorithm is nearly optimal, in the sense that the number of required probes is close to the number of unknowns. PROGRAM SUMMARY Program title: rare CPC Library link to program files:https://doi.org/10.17632/wt228b57kw.1 Developer's repository link:https://github.com/a-maier/rare. Licensing provisions: GNU General Public License 3 Programming language: Rust Supplementary material: Comparison code to other programs is available under https://github.com/a-maier/scaling-rec and uses C++, Rust, and Wolfram Mathematica. Nature of problem: Straightforward computations of scattering amplitudes in perturbative quantum field theory suffer from large intermediate expressions. Hence, state-of-the-art approaches make heavy use of multivariate rational function reconstruction from probes in fields with a finite characteristic. In this way, only numbers with a bounded size are encountered in intermediate steps. This strategy requires efficient reconstruction algorithms. Solution method: The code provides a proof-of-concept implementation of a new rational reconstruction algorithm. The algorithm is particularly efficient for dense functions, where the number of required probes is close to the number of unknown coefficients. Additional comments including restrictions and unusual features: As customary for Rust libraries, the code is not intended for stand-alone installation, but for compilation as part of a larger program, e.g. using the Cargo package manager [1]. References: The code is compared to implementations of an algorithm by Cuyt and Lee [2,3] in FireFly[4–6] and FiniteFlow[7,8].
000639595 536__ $$0G:(DE-HGF)POF4-611$$a611 - Fundamental Particles and Forces (POF4-611)$$cPOF4-611$$fPOF IV$$x0
000639595 588__ $$aDataset connected to CrossRef, INSPIRE, Journals: bib-pubdb1.desy.de
000639595 693__ $$0EXP:(DE-MLZ)NOSPEC-20140101$$5EXP:(DE-MLZ)NOSPEC-20140101$$eNo specific instrument$$x0
000639595 8564_ $$uhttps://bib-pubdb1.desy.de/record/639595/files/2409.08757v2.pdf$$yOpenAccess
000639595 8564_ $$uhttps://bib-pubdb1.desy.de/record/639595/files/2409.08757v2.pdf?subformat=pdfa$$xpdfa$$yOpenAccess
000639595 909CO $$ooai:bib-pubdb1.desy.de:639595$$pdnbdelivery$$pdriver$$pVDB$$popen_access$$popenaire
000639595 9101_ $$0I:(DE-588b)2008985-5$$6P:(DE-H253)PIP1029970$$aDeutsches Elektronen-Synchrotron$$b0$$kDESY
000639595 9131_ $$0G:(DE-HGF)POF4-611$$1G:(DE-HGF)POF4-610$$2G:(DE-HGF)POF4-600$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$aDE-HGF$$bForschungsbereich Materie$$lMatter and the Universe$$vFundamental Particles and Forces$$x0
000639595 9141_ $$y2025
000639595 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess
000639595 915__ $$0LIC:(DE-HGF)CCBY4$$2HGFVOC$$aCreative Commons Attribution CC BY 4.0
000639595 915__ $$0StatID:(DE-HGF)0580$$2StatID$$aPublished
000639595 9201_ $$0I:(DE-H253)Z_ZPPT-20210408$$kZ_ZPPT$$lZeuthen Particle PhysicsTheory$$x0
000639595 980__ $$apreprint
000639595 980__ $$aVDB
000639595 980__ $$aUNRESTRICTED
000639595 980__ $$aI:(DE-H253)Z_ZPPT-20210408
000639595 9801_ $$aFullTexts