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@ARTICLE{Maier:639595,
      author       = {Maier, Andreas Martin},
      title        = {{S}caling up to multivariate rational function
                      reconstruction},
      reportid     = {PUBDB-2025-04571, arXiv:2409.08757. DESY-24-138},
      year         = {2025},
      note         = {Comput. Phys. Commun. 317 (2025) 109827. 14 pages, no
                      figures. Journal version with comparison to FireFly and
                      FiniteFlow},
      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].},
      cin          = {$Z_ZPPT$},
      ddc          = {530},
      cid          = {$I:(DE-H253)Z_ZPPT-20210408$},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611)},
      pid          = {G:(DE-HGF)POF4-611},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2409.08757},
      howpublished = {arXiv:2409.08757},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2409.08757;\%\%$},
      doi          = {10.3204/PUBDB-2025-04571},
      url          = {https://bib-pubdb1.desy.de/record/639595},
}