HPL, a Mathematica implementation of the harmonic polylogarithms

By Daniel Maître. Computer Physics Communications, 2005

397 citations recorded by the source corpus.

Abstract In this paper, we present an implementation of the harmonic polylogarithm of Remiddi and Vermaseren [E. Remiddi, J.A.M. Vermaseren, Int. J. Modern Phys. A 15 (2000) 725, hep-ph/9905237 ] for Mathematica. It contains an implementation of the product algebra, the derivative properties, series expansion and numerical evaluation. The analytic continuation has been treated carefully, allowing the user to keep the control over the definition of the sign of the imaginary parts. Many options enables the user to adapt the behavior of the package to his specific problem. Program summary Program title: HPL Catalogue identifier: ADWX Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWX Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Programming language: Mathematica No. of lines in distributed program, including test data, etc.: 13 310 No. of bytes in distributed program, including test data, etc.: 1 990 584 Distribution format: tar.gz Computer: all computers running Mathematica Operating systems: operating systems running Mathematica Nature of problem: Computer algebraic treatment of the harmonic polylogarithms which appear in the evaluation of Feynman diagrams Solution method: Mathematica implementation

Subfields: Geometry and Topology, Mathematical Physics, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/8ed91680233391454c30b421a7b64fc1affd17b6

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Citations in the corpus

Five-loop anomalous dimension of twist-two operators (2009, methodology): “With help of the SUMMER [40] and HARMPOL [61] packages for FORM [62] and the HPL package [63] for Mathematica, we have found”
Soft triple-real radiation for Higgs production at N3LO (2013, methodology): “This rational number can easily be determined by evaluating Ai1 numerically at a single point using any of the standard libraries to evaluate multiple polylogarithms [84,126–131], and running for”
Polylogarithms, multiple zeta values and superstring amplitudes (2013, result): “For example, at N = 5 one finds the term IregEx1 := 1 2 s223 ∫ 1 0 dz3 z3 − 1 ∫ z3 0 dz2 z2 (ln(z3 − z2)) 2 (5.12) = 1 2 s223 ∫ 1 0 dz3 z3 − 1 ∫ z3 0 dz2 z2 [ (ln(z3)) 2 + 2 lnz3 ln ( 1− z2 z3 ) + ( ln ( 1− z2 z3 ))2 ] 25This definition agrees with Remiddi and Vermaseren [42] and Maitre [43]. as par”
Space-time S-matrix and flux tube S-matrix II. Extracting and matching data (2013, methodology): “All the expressions in this appendix can be found in the compaying notebook Fnl.nb, where use is made of the notations of the HPL package [46].”
From polygons and symbols to polylogarithmic functions (2011, methodology): “higher order corrections to physical observables requires the analytical evaluation of Feynman integrals that can generally be expressed in terms of (special classes of) multiple polylogarithms, e.g. [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49,”
Bootstrapping the three-loop hexagon (2011, background): “The definition (8) includes logarithms and classical polylogarithms, as well as other iterated integrals, such as harmonic polylogarithms of one [58] or more [59, 60, 61, 62] variables.”