<?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-01240729</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="2026-05-03T16:53:02+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Algebraic Diagonals and Walks</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-211984"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Louis</forename>
                <surname>Dumont</surname>
              </persName>
              <email type="md5">04628cd3ea4c15d064e1718e3abb20ac</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="numeric">973676</idno>
              <idno type="halauthorid" notation="string">949269-973676</idno>
              <affiliation ref="#struct-211984"/>
            </author>
            <author role="aut">
              <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-300009"/>
              <affiliation ref="#struct-178327"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Louis</forename>
                <surname>Dumont</surname>
              </persName>
              <email type="md5">04628cd3ea4c15d064e1718e3abb20ac</email>
              <email type="domain">inria.fr</email>
            </editor>
            <funder ref="#projanr-41196"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2015-12-14 08:18:46</date>
              <date type="whenModified">2025-10-24 17:40:02</date>
              <date type="whenReleased">2015-12-14 08:18:46</date>
              <date type="whenProduced">2015-07-06</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/1510.04080"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="327362">
                <persName>
                  <forename>Louis</forename>
                  <surname>Dumont</surname>
                </persName>
                <email type="md5">04628cd3ea4c15d064e1718e3abb20ac</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01240729</idno>
            <idno type="halUri">https://hal.science/hal-01240729</idno>
            <idno type="halBibtex">bostan:hal-01240729</idno>
            <idno type="halRefHtml">&lt;i&gt;ISSAC'15 International Symposium on Symbolic and Algebraic Computation&lt;/i&gt;, Jul 2015, Bath, United Kingdom. pp.77-84, &lt;a target="_blank" href="https://dx.doi.org/10.1145/2755996.2756663"&gt;&amp;#x27E8;10.1145/2755996.2756663&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">ISSAC'15 International Symposium on Symbolic and Algebraic Computation, Jul 2015, Bath, United Kingdom. pp.77-84, &amp;#x27E8;10.1145/2755996.2756663&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </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="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="INRIA-SACLAY-2015" corresp="UNIV-PARIS-SACLAY">INRIA-SACLAY-2015</idno>
            <idno type="stamp" n="INRIA-RENGRE">INRIA-RENGRE</idno>
            <idno type="stamp" n="INRIA-300009">Inria 300009</idno>
            <idno type="stamp" n="UDL">UDL</idno>
            <idno type="stamp" n="UNIV-LYON">Université de Lyon</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="GS-COMPUTER-SCIENCE">Graduate School Computer Science</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">Algebraic Diagonals and Walks</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-211984"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Louis</forename>
                    <surname>Dumont</surname>
                  </persName>
                  <email type="md5">04628cd3ea4c15d064e1718e3abb20ac</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="numeric">973676</idno>
                  <idno type="halauthorid" notation="string">949269-973676</idno>
                  <affiliation ref="#struct-211984"/>
                </author>
                <author role="aut">
                  <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-300009"/>
                  <affiliation ref="#struct-178327"/>
                </author>
              </analytic>
              <monogr>
                <meeting>
                  <title>ISSAC'15 International Symposium on Symbolic and Algebraic Computation</title>
                  <date type="start">2015-07-06</date>
                  <date type="end">2015-07-09</date>
                  <settlement>Bath</settlement>
                  <country key="GB">United Kingdom</country>
                </meeting>
                <imprint>
                  <publisher>ACM Press</publisher>
                  <biblScope unit="pp">77–84</biblScope>
                  <date type="datePub">2015-06</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1510.04080</idno>
              <idno type="doi">10.1145/2755996.2756663</idno>
              <ref type="publisher">http://issac-symposium.org/2015</ref>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">algorithms</term>
                <term xml:lang="en">walks</term>
                <term xml:lang="en">Diagonals</term>
              </keywords>
              <classCode scheme="acm" n="I.1.2.0">I.: Computing Methodologies/I.1: SYMBOLIC AND ALGEBRAIC MANIPULATION/I.1.2: Algorithms/I.1.2.0: Algebraic algorithms</classCode>
              <classCode scheme="halDomain" n="info.info-sc">Computer Science [cs]/Symbolic Computation [cs.SC]</classCode>
              <classCode scheme="halDomain" n="info.info-cc">Computer Science [cs]/Computational Complexity [cs.CC]</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>The diagonal of a multivariate power series F is the univariate power series Diag F generated by the diagonal terms of F. Diagonals form an important class of power series; they occur frequently in number theory, theoretical physics and enumerative combinatorics. We study algorithmic questions related to diagonals in the case where F is the Taylor expansion of a bivariate rational function. It is classical that in this case Diag F is an algebraic function. We propose an algorithm that computes an annihilating polynomial for Diag F. Generically, it is its minimal polynomial and is obtained in time quasi-linear in its size. We show that this minimal polynomial has an exponential size with respect to the degree of the input rational function. We then address the related problem of enumerating directed lattice walks. The insight given by our study leads to a new method for expanding the generating power series of bridges, excursions and meanders. We show that their first N terms can be computed in quasi-linear complexity in N, without first computing a very large polynomial equation.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <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="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="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="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>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-41196" status="VALID">
          <idno type="anr">ANR-14-CE25-0018</idno>
          <idno type="program">Fondements du numérique</idno>
          <orgName>Fast Relax</orgName>
          <desc>Approximation rapide et fiable</desc>
          <date type="start">2014</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>