<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00777675v2</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-21T13:55:26+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Creative telescoping for rational functions using the Griffiths-Dwork method</title>
            <author role="aut">
              <persName>
                <forename type="first">Alin</forename>
                <surname>Bostan</surname>
              </persName>
              <email type="md5">09c400f106572c39c4362f555fd5c489</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="numeric">831654</idno>
              <idno type="halauthorid" notation="string">124926-831654</idno>
              <affiliation ref="#struct-65197"/>
              <affiliation ref="#struct-211984"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">Pierre</forename>
                <surname>Lairez</surname>
              </persName>
              <email type="md5">78569a64b6ab6fc14ac0964301526c4a</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">lairez</idno>
              <idno type="idhal" notation="numeric">792</idno>
              <idno type="halauthorid" notation="string">21566-792</idno>
              <idno type="IDREF">https://www.idref.fr/253134714</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-3756-0151</idno>
              <orgName ref="#struct-0"/>
              <affiliation ref="#struct-211984"/>
              <affiliation ref="#struct-65197"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">Bruno</forename>
                <surname>Salvy</surname>
              </persName>
              <email type="md5">8c1f42572a27360692d73379f494121b</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">bruno-salvy</idno>
              <idno type="idhal" notation="numeric">5843</idno>
              <idno type="halauthorid" notation="string">2801-5843</idno>
              <idno type="IDREF">https://www.idref.fr/034200274</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-4313-0679</idno>
              <orgName ref="#struct-0"/>
              <affiliation ref="#struct-178327"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Pierre</forename>
                <surname>Lairez</surname>
              </persName>
              <email type="md5">333a7447363587b1e71a14e03b5ad90d</email>
              <email type="domain">lairez.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2013-01-17 17:30:11</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2013-04-20 14:33:08</date>
              <date type="whenModified">2025-10-24 17:40:02</date>
              <date type="whenReleased">2013-04-21 08:22:29</date>
              <date type="whenProduced">2013-07-26</date>
              <date type="whenEndEmbargoed">2013-04-20</date>
              <ref type="file" target="https://inria.hal.science/hal-00777675v2/document">
                <date notBefore="2013-04-20"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://inria.hal.science/hal-00777675v2/file/arxiv.issac24p-bostan.pdf" id="file-816202-188735">
                <date notBefore="2013-04-20"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1301.4313"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="170878">
                <persName>
                  <forename>Pierre</forename>
                  <surname>Lairez</surname>
                </persName>
                <email type="md5">333a7447363587b1e71a14e03b5ad90d</email>
                <email type="domain">lairez.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00777675</idno>
            <idno type="halUri">https://inria.hal.science/hal-00777675</idno>
            <idno type="halBibtex">bostan:hal-00777675</idno>
            <idno type="halRefHtml">&lt;i&gt;ISSAC'13 - 38th International Symposium on Symbolic and Algebraic Computation&lt;/i&gt;, Northeastern University, Boston, Massachusetts, USA, Jul 2013, Boston, United States. pp.93-100, &lt;a target="_blank" href="https://dx.doi.org/10.1145/2465506.2465935"&gt;&amp;#x27E8;10.1145/2465506.2465935&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">ISSAC'13 - 38th International Symposium on Symbolic and Algebraic Computation, Northeastern University, Boston, Massachusetts, USA, Jul 2013, Boston, United States. pp.93-100, &amp;#x27E8;10.1145/2465506.2465935&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-816202-188735"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENS-LYON">École Normale Supérieure de Lyon</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="UNIV-LYON1">Université Claude Bernard - Lyon I</idno>
            <idno type="stamp" n="INRIA-RHA">INRIA Grenoble - Rhône-Alpes</idno>
            <idno type="stamp" n="INRIA-SACLAY" corresp="INRIA">INRIA Saclay - Ile de France</idno>
            <idno type="stamp" n="LIP" corresp="UNIV-LYON1">Laboratoire de l'Informatique du Parallélisme</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="INRIA-RENGRE">INRIA-RENGRE</idno>
            <idno type="stamp" n="UDL">UDL</idno>
            <idno type="stamp" n="UNIV-LYON">Université de Lyon</idno>
            <idno type="stamp" n="INRIA-ETATSUNIS">Copublications Inria-Etats-Unis</idno>
            <idno type="stamp" n="INRIA-ROYAUMEUNI">INRIA-ROYAUMEUNI</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="invited" n="0">No</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
            <note type="proceedings" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Creative telescoping for rational functions using the Griffiths-Dwork method</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Alin</forename>
                    <surname>Bostan</surname>
                  </persName>
                  <email type="md5">09c400f106572c39c4362f555fd5c489</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="numeric">831654</idno>
                  <idno type="halauthorid" notation="string">124926-831654</idno>
                  <affiliation ref="#struct-65197"/>
                  <affiliation ref="#struct-211984"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">Pierre</forename>
                    <surname>Lairez</surname>
                  </persName>
                  <email type="md5">78569a64b6ab6fc14ac0964301526c4a</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">lairez</idno>
                  <idno type="idhal" notation="numeric">792</idno>
                  <idno type="halauthorid" notation="string">21566-792</idno>
                  <idno type="IDREF">https://www.idref.fr/253134714</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-3756-0151</idno>
                  <orgName ref="#struct-0"/>
                  <affiliation ref="#struct-211984"/>
                  <affiliation ref="#struct-65197"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">Bruno</forename>
                    <surname>Salvy</surname>
                  </persName>
                  <email type="md5">8c1f42572a27360692d73379f494121b</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">bruno-salvy</idno>
                  <idno type="idhal" notation="numeric">5843</idno>
                  <idno type="halauthorid" notation="string">2801-5843</idno>
                  <idno type="IDREF">https://www.idref.fr/034200274</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-4313-0679</idno>
                  <orgName ref="#struct-0"/>
                  <affiliation ref="#struct-178327"/>
                </author>
              </analytic>
              <monogr>
                <meeting>
                  <title>ISSAC'13 - 38th International Symposium on Symbolic and Algebraic Computation</title>
                  <date type="start">2013-07-26</date>
                  <date type="end">2013-07-29</date>
                  <settlement>Boston</settlement>
                  <country key="US">United States</country>
                </meeting>
                <respStmt>
                  <resp>conferenceOrganizer</resp>
                  <name>Northeastern University, Boston, Massachusetts, USA</name>
                </respStmt>
                <imprint>
                  <biblScope unit="pp">93-100</biblScope>
                  <date type="datePub">2013</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1301.4313</idno>
              <idno type="doi">10.1145/2465506.2465935</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">algorithms</term>
                <term xml:lang="en">complexity</term>
                <term xml:lang="en">Picard-Fuchs equation</term>
                <term xml:lang="en">creative telescoping</term>
                <term xml:lang="en">Integration</term>
              </keywords>
              <classCode scheme="classification">Integration; creative telescoping; algorithms; complexity</classCode>
              <classCode scheme="halDomain" n="info.info-sc">Computer Science [cs]/Symbolic Computation [cs.SC]</classCode>
              <classCode scheme="halTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halOldTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halTreeTypology" n="COMM">Conference papers</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Creative telescoping algorithms compute linear differential equations satisfied by multiple integrals with parameters. We describe a precise and elementary algorithmic version of the Griffiths-Dwork method for the creative telescoping of rational functions. This leads to bounds on the order and degree of the coefficients of the differential equation, and to the first complexity result which is simply exponential in the number of variables. One of the important features of the algorithm is that it does not need to compute certificates. The approach is vindicated by a prototype implementation.</p>
            </abstract>
            <abstract xml:lang="fr">
              <p>Les algorithmes de création télescopique calculent les équations différentielles linéaires vérifiées par les intégrales multiples à paramètre. Nous décrivons, en utilisant la méthode de Griffiths-Dwork, un tel algorithme pour les fractions rationnelles. Cela permet d'obtenir des bornes sur l'ordre et le degré des coefficients des équations différentielles recherchées, ainsi qu'au premier résultat de complexité qui est simplement exponentiel en le nombre de variables. Un aspect important de l'algorithm est que le calcul du certificat n'est pas nécessaire. L'intérêt pratique de l'approche est démontré par une première implémentation.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-65197" status="VALID">
          <orgName>Microsoft Research - Inria Joint Centre</orgName>
          <orgName type="acronym">MSR - INRIA</orgName>
          <desc>
            <address>
              <addrLine>Parc Orsay Université 28, rue Jean Rostand 91893 Orsay Cedex FRANCE</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.msr-inria.inria.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-301681" type="direct"/>
            <relation active="#struct-379481" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-211984" status="OLD">
          <idno type="RNSR">201221067B</idno>
          <orgName>Symbolic Special Functions : Fast and Certified</orgName>
          <orgName type="acronym">SPECFUN</orgName>
          <date type="start">2012-11-01</date>
          <date type="end">2022-03-31</date>
          <desc>
            <address>
              <addrLine>Inria, Bâtiment Alan Turing 1 rue Honoré d'Estienne d'Orves Campus de l'École Polytechnique 91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/specfun</ref>
          </desc>
          <listRelation>
            <relation active="#struct-118511" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-178327" status="OLD">
          <idno type="RNSR">201221021B</idno>
          <orgName>Arithmetic and Computing</orgName>
          <orgName type="acronym">ARIC</orgName>
          <date type="start">2013-01-01</date>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>46 Allée d'Italie 69364 Lyon France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/aric</ref>
          </desc>
          <listRelation>
            <relation active="#struct-2497" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-35418" type="direct"/>
            <relation active="#struct-6818" type="indirect"/>
            <relation active="#struct-301088" type="indirect"/>
            <relation active="#struct-194495" type="indirect"/>
            <relation name="UMR5668 / URA1398" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-301681" status="VALID">
          <orgName>Microsoft Research Laboratory Cambridge</orgName>
          <desc>
            <address>
              <country key="GB"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-379481" status="VALID">
          <orgName>Microsoft Corporation [Redmond, Wash.]</orgName>
          <desc>
            <address>
              <country key="US"/>
            </address>
            <ref type="url">https://www.microsoft.com/fr-fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-118511" status="VALID">
          <idno type="RNSR">200818248E</idno>
          <idno type="ROR">https://ror.org/0315e5x55</idno>
          <orgName>Centre Inria de Saclay</orgName>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'OrvesBâtiment Alan TuringCampus de l'École Polytechnique91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/saclay</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-2497" status="VALID">
          <idno type="RNSR">199218244V</idno>
          <idno type="ROR">https://ror.org/00n8d6z93</idno>
          <orgName>Centre Inria de l'Université Grenoble Alpes</orgName>
          <desc>
            <address>
              <addrLine>Inovallée655 avenue de l'Europe38330 Montbonnot</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/grenoble</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-35418" status="VALID">
          <idno type="IdRef">191041289</idno>
          <idno type="ISNI">0000000104538607</idno>
          <idno type="RNSR">200317503S</idno>
          <idno type="ROR">04msnz457</idno>
          <orgName>Laboratoire de l'Informatique du Parallélisme</orgName>
          <orgName type="acronym">LIP</orgName>
          <date type="start">1990-01-01</date>
          <desc>
            <address>
              <addrLine>46 Allée d'Italie 69364 LYON CEDEX 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ens-lyon.fr/LIP/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-6818" type="direct"/>
            <relation active="#struct-301088" type="direct"/>
            <relation active="#struct-194495" type="direct"/>
            <relation active="#struct-300009" type="direct"/>
            <relation name="UMR5668 / URA1398" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-6818" status="VALID">
          <idno type="IdRef">149154992</idno>
          <idno type="ISNI">0000000123319856</idno>
          <idno type="ROR">https://ror.org/04zmssz18</idno>
          <idno type="Wikidata">Q10159</idno>
          <orgName>École normale supérieure de Lyon</orgName>
          <orgName type="acronym">ENS de Lyon</orgName>
          <date type="start">2010-01-01</date>
          <desc>
            <address>
              <addrLine>15 parvis René Descartes - BP 7000 - 69342 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ens-lyon.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301088" status="VALID">
          <idno type="ROR">https://ror.org/01rk35k63</idno>
          <orgName>Université de Lyon</orgName>
          <desc>
            <address>
              <addrLine>92 rue Pasteur - CS 30122, 69361 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-lyon.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-194495" status="VALID">
          <idno type="IdRef">026402823</idno>
          <idno type="ISNI">0000000121686185</idno>
          <idno type="ROR">https://ror.org/029brtt94</idno>
          <orgName>Université Claude Bernard Lyon 1</orgName>
          <orgName type="acronym">UCBL</orgName>
          <desc>
            <address>
              <addrLine>43, boulevard du 11 novembre 1918, 69622 Villeurbanne cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lyon1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>