Introducing SummerTime: A package for high-precision computation of sums appearing in DRA method

Abstract

We present the Mathematica package SummerTime for arbitrary-precision computation of sums appearing in the results of DRA method (Lee, 2010). So far these results include the following families of the integrals: 3-loop onshell massless vertices, 3-loop onshell mass operator type integrals, 4-loop QED-type tadpoles, 4-loop massless propagators (Lee et al., 2010; Lee and Smirnov, 2011; Lee et al., 2011, 2012). The package can be used for high-precision numerical computation of the expansion of the integrals from the above families around arbitrary space-time dimension. In addition, this package contains convenient tools for the calculation of multiple zeta values, harmonic polylogarithms and other transcendental numbers expressed in terms of nested sums with factorized summand. Program summaryProgram title: SummerTimeCatalogue identifier: AEZU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEZU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 20950No. of bytes in distributed program, including test data, etc.: 333223Distribution format: tar.gzProgramming language: Wolfram Mathematica.Computer: Any with Wolfram Mathematica installed.Operating system: Any supporting Wolfram Mathematica.RAM: Depending on the complexity of the problemClassification: 4.4, 4.7, 5.Nature of problem:Arbitrary-precision evaluation of the ε-expansion coefficients of the multiloop integrals obtained via DRA method [1]. Arbitrary-precision evaluation of the Goncharov’s polylogarithms and related function.Solution method:Multiple nested sums are calculated without nested loops using factorized form of the summand. Slowly convergent sums are treated using convergence acceleration. Required working precision, number of terms and similar parameters are determined by automatic analysis of the summand.Restrictions:Depending on the complexity of the problem, limited by memory and CPU time.Running time:From a few seconds to a few hours, depending on the complexity of the problem.