Introducing SummerTime: A package for high-precision computation of sums appearing in DRAp>1p> method

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• 作者：Roman N. Leep>ap>p> ; p>p>r.n.lee@inp.nsk.su" class="auth_mail" title="E-mail the corresponding authorp> ; Kirill T. Mingulovp>ap>p> ; p>p>bp>p> ; p>p>melkogotto@gmail.com" class="auth_mail" title="E-mail the corresponding authorp>
• 关键词：Multiloop calculations ; DRA method ; Hypergeometric sums
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：203
• 期：Complete
• 页码：255-267
• 全文大小：518 K

文摘

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.p>

Program summary

<p id="sp000020">Program title: SummerTimep><p id="sp000025">Catalogue identifier: AEZU_v1_0p><p id="sp000030">Program summary URL:pan id="ir000010" class="interref" data-locatorType="url" data-locatorKey="http://cpc.cs.qub.ac.uk/summaries/AEZU_v1_0.html">http://cpc.cs.qub.ac.uk/summaries/AEZU_v1_0.htmlpan>p><p id="sp000035">Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Irelandp><p id="sp000040">Licensing provisions: Standard CPC licence, pan id="ir000015" class="interref" data-locatorType="url" data-locatorKey="http://cpc.cs.qub.ac.uk/licence/licence.html">http://cpc.cs.qub.ac.uk/licence/licence.htmlpan>p><p id="sp000045">No. of lines in distributed program, including test data, etc.: 20950p><p id="sp000050">No. of bytes in distributed program, including test data, etc.: 333223p><p id="sp000055">Distribution format: tar.gzp><p id="sp000060">Programming language: Wolfram Mathematica.p><p id="sp000065">Computer: Any with Wolfram Mathematica installed.p><p id="sp000070">Operating system: Any supporting Wolfram Mathematica.p><p id="sp000075">RAM: Depending on the complexity of the problemp><p id="sp000080">Classification: 4.4, 4.7, 5.p><p id="sp000085">Nature of problem:p><p id="sp000090">Arbitrary-precision evaluation of the pan id="mmlsi12" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516300339&_mathId=si12.gif&_user=111111111&_pii=S0010465516300339&_rdoc=1&_issn=00104655&md5=83019743ed8840de4af06198ccf8e4cc" title="Click to view the MathML source">εpan>pan class="mathContainer hidden">pan class="mathCode">$\epsilon$pan>pan>pan>-expansion coefficients of the multiloop integrals obtained via DRA method [1]. Arbitrary-precision evaluation of the Goncharov’s polylogarithms and related function.p><p id="sp000095">Solution method:p><p id="sp000100">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.p><p id="sp000105">Restrictions:p><p id="sp000110">Depending on the complexity of the problem, limited by memory and CPU time.p><p id="sp000115">Running time:p><p id="sp000120">From a few seconds to a few hours, depending on the complexity of the problem.p><p id="sp000125">References:

[1]

<p id="p000005">R. Lee, Nuclear Physics B 830 (2010) 474.p>