<?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-01968776v2</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="2026-05-15T21:14:31+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Computing the topology of a plane or space hyperelliptic curve</title>
            <author role="aut">
              <persName>
                <forename type="first">Juan</forename>
                <forename type="middle">Gerardo</forename>
                <surname>Alcázar</surname>
              </persName>
              <idno type="halauthorid">1491223-0</idno>
              <affiliation ref="#struct-79721"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jorge</forename>
                <surname>Caravantes</surname>
              </persName>
              <idno type="halauthorid">1491097-0</idno>
              <affiliation ref="#struct-79721"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Gema</forename>
                <forename type="middle">M</forename>
                <surname>Diaz-Toca</surname>
              </persName>
              <idno type="halauthorid">1491098-0</idno>
              <affiliation ref="#struct-213491"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Elias</forename>
                <surname>Tsigaridas</surname>
              </persName>
              <email type="md5">2574bcae9f1455fd6cf3833a1e5e5277</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">elias-tsigaridas</idno>
              <idno type="idhal" notation="numeric">690</idno>
              <idno type="halauthorid" notation="string">19773-690</idno>
              <affiliation ref="#struct-454669"/>
              <affiliation ref="#struct-1004976"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Elias</forename>
                <surname>Tsigaridas</surname>
              </persName>
              <email type="md5">2574bcae9f1455fd6cf3833a1e5e5277</email>
              <email type="domain">inria.fr</email>
            </editor>
            <funder ref="#projanr-42417"/>
            <funder ref="#projanr-37962"/>
            <funder>Supported by the Spanish Ministerio de Ciencia, Innovacion y Universidades and by he European Regional Development Fund (ERDF), under the project MTM2017-88796-P.Member of the Research Groupasynacs (Ref.ccee2011/r34).Partially  supported  by  a  Giner  de  los  Rıos  Grant  of  the  Universidad  de  Alcala, ANR JCJC GALOP (ANR-17-CE40-0009), a public grant as part of the Investissement d’avenir project reference ANR-11-LABX-0056-LMH LabEx LMH (PGMO ALMA), the PHC GRAPE, and from the 2232 International Fellowship for Outstanding Researchers Program from TUBITAK (Project No:  118C240)</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2019-01-03 11:40:10</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2020-02-27 21:23:42</date>
              <date type="whenModified">2025-10-15 11:44:02</date>
              <date type="whenReleased">2020-02-28 10:52:53</date>
              <date type="whenProduced">2020-02-25</date>
              <date type="whenEndEmbargoed">2020-02-27</date>
              <ref type="file" target="https://inria.hal.science/hal-01968776v2/document">
                <date notBefore="2020-02-27"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://inria.hal.science/hal-01968776v2/file/Topology-hyperelliptic-curves-paper-second-rev-versl-DEF.pdf" id="file-2493548-2369537">
                <date notBefore="2020-02-27"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="114831">
                <persName>
                  <forename>Elias</forename>
                  <surname>Tsigaridas</surname>
                </persName>
                <email type="md5">2574bcae9f1455fd6cf3833a1e5e5277</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01968776</idno>
            <idno type="halUri">https://inria.hal.science/hal-01968776</idno>
            <idno type="halBibtex">alcazar:hal-01968776</idno>
            <idno type="halRefHtml">&lt;i&gt;Computer Aided Geometric Design&lt;/i&gt;, 2020, &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.cagd.2020.101830"&gt;&amp;#x27E8;10.1016/j.cagd.2020.101830&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Computer Aided Geometric Design, 2020, &amp;#x27E8;10.1016/j.cagd.2020.101830&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-2493548-2369537"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <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="INRIA-ROCQ">INRIA Paris - Rocquencourt</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="IMJ" corresp="SORBONNE-UNIVERSITE">Institut de Mathématiques de Jussieu</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</idno>
            <idno type="stamp" n="SORBONNE-UNIV" corresp="SORBONNE-UNIVERSITE">Sorbonne Université 01/01/2018</idno>
            <idno type="stamp" n="SU-SCIENCES" corresp="SORBONNE-UNIVERSITE">Faculté des Sciences de Sorbonne Université</idno>
            <idno type="stamp" n="UNIV-PARIS">Université Paris Cité</idno>
            <idno type="stamp" n="UNIVERSITE-PARIS" corresp="UNIV-PARIS">Université Paris Cité</idno>
            <idno type="stamp" n="UP-SCIENCES">Université Paris Cité - Faculté des Sciences</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
            <idno type="stamp" n="INRIAARTDOI">INRIAARTDOI</idno>
            <idno type="stamp" n="SUPRA_MATHS_INFO">Mathématiques + Informatique</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Computing the topology of a plane or space hyperelliptic curve</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Juan</forename>
                    <forename type="middle">Gerardo</forename>
                    <surname>Alcázar</surname>
                  </persName>
                  <idno type="halauthorid">1491223-0</idno>
                  <affiliation ref="#struct-79721"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jorge</forename>
                    <surname>Caravantes</surname>
                  </persName>
                  <idno type="halauthorid">1491097-0</idno>
                  <affiliation ref="#struct-79721"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Gema</forename>
                    <forename type="middle">M</forename>
                    <surname>Diaz-Toca</surname>
                  </persName>
                  <idno type="halauthorid">1491098-0</idno>
                  <affiliation ref="#struct-213491"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Elias</forename>
                    <surname>Tsigaridas</surname>
                  </persName>
                  <email type="md5">2574bcae9f1455fd6cf3833a1e5e5277</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">elias-tsigaridas</idno>
                  <idno type="idhal" notation="numeric">690</idno>
                  <idno type="halauthorid" notation="string">19773-690</idno>
                  <affiliation ref="#struct-454669"/>
                  <affiliation ref="#struct-1004976"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">12012</idno>
                <idno type="issn">0167-8396</idno>
                <title level="j">Computer Aided Geometric Design</title>
                <imprint>
                  <publisher>Elsevier</publisher>
                  <date type="datePub">2020-02-25</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1016/j.cagd.2020.101830</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="info.info-sc">Computer Science [cs]/Symbolic Computation [cs.SC]</classCode>
              <classCode scheme="halDomain" n="info.info-cg">Computer Science [cs]/Computational Geometry [cs.CG]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational mapping of the plane or the space. We report on a Maple implementation of these algorithms, and present several examples. Complexity and certification issues are also discussed.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="department" xml:id="struct-79721" status="VALID">
          <orgName>Departamento de Física y Matematicas [Alcala]</orgName>
          <desc>
            <address>
              <addrLine>Alcalá de Henares</addrLine>
              <country key="ES"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-300498" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-213491" status="VALID">
          <orgName>Department of Information and Communications Engineering [Murcia]</orgName>
          <desc>
            <address>
              <addrLine>Department of Information and Communications Engineering, University of Murcia, Campus de Espinardo, 30100 Murcia, Spain</addrLine>
              <country key="ES"/>
            </address>
            <ref type="url">http://www.diic.um.es:8080/diic/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-309836" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-454669" status="VALID">
          <idno type="RNSR">201221216N</idno>
          <idno type="ROR">https://ror.org/01rrvyp50</idno>
          <orgName>OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs</orgName>
          <orgName type="acronym">OURAGAN</orgName>
          <date type="start">2016-01-01</date>
          <date type="end">2028-12-31</date>
          <desc>
            <address>
              <addrLine>4 place Jussieu 75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/ouragan</ref>
          </desc>
          <listRelation>
            <relation active="#struct-1004976" type="direct"/>
            <relation active="#struct-413221" type="indirect"/>
            <relation name="UMR7586" active="#struct-441569" type="indirect"/>
            <relation name="UMR_7586" active="#struct-557826" type="indirect"/>
            <relation active="#struct-1175218" type="direct"/>
            <relation active="#struct-454310" type="indirect"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1004976" status="VALID">
          <idno type="IdRef">084976330</idno>
          <idno type="ISNI">0000000110112151</idno>
          <idno type="RNSR">199712632Y</idno>
          <idno type="ROR">https://ror.org/03fk87k11</idno>
          <idno type="Wikidata">Q3152049</idno>
          <orgName>Institut de Mathématiques de Jussieu - Paris Rive Gauche</orgName>
          <orgName type="acronym">IMJ-PRG (UMR_7586)</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Sorbonne Université - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / Université Paris Diderot - Bât. Sophie Germain, case 7012</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.imj-prg.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413221" type="direct"/>
            <relation name="UMR7586" active="#struct-441569" type="direct"/>
            <relation name="UMR_7586" active="#struct-557826" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300498" status="VALID">
          <idno type="ISNI">0000 0004 1937 0239</idno>
          <idno type="ROR">https://ror.org/04pmn0e78</idno>
          <idno type="Wikidata">Q1243904</idno>
          <orgName>Universidad de Alcalá [Alcalá de Henares, España] = University of Alcalá [Alcalá de Henares, Spain] = Université d'Alcalá  [Alcalá de Henares, Espagne]</orgName>
          <orgName type="acronym">UAH</orgName>
          <desc>
            <address>
              <addrLine>Pza. San Diego, s/n, 28801 - Alcalá de Henares (Madrid)</addrLine>
              <country key="ES"/>
            </address>
            <ref type="url">http://www.uah.es/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-309836" status="VALID">
          <idno type="ROR">https://ror.org/03p3aeb86</idno>
          <orgName>Universidad de Murcia = University of Murcia</orgName>
          <desc>
            <address>
              <addrLine>Avda. Teniente Flomesta, 5 - 30003 - Murcia</addrLine>
              <country key="ES"/>
            </address>
            <ref type="url">http://www.um.es/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-413221" status="VALID">
          <idno type="IdRef">221333754</idno>
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Sorbonne Université</orgName>
          <orgName type="acronym">SU</orgName>
          <date type="start">2018-01-01</date>
          <desc>
            <address>
              <addrLine>21 rue de l’École de médecine - 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sorbonne-universite.fr/</ref>
          </desc>
        </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>
        <org type="institution" xml:id="struct-557826" status="VALID">
          <idno type="IdRef">236453505</idno>
          <idno type="ISNI">0000 0004 7885 7602</idno>
          <idno type="ROR">https://ror.org/05f82e368</idno>
          <orgName>Université Paris Cité</orgName>
          <orgName type="acronym">UPCité</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>85 boulevard Saint-Germain75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://u-paris.fr/</ref>
          </desc>
        </org>
        <org type="department" xml:id="struct-1175218" status="VALID">
          <idno type="ROR">https://ror.org/03cjm2544</idno>
          <orgName>Centre Inria de Sorbonne Université</orgName>
          <date type="start">2022-11-01</date>
          <desc>
            <address>
              <addrLine>48 Rue Barrault, 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-454310" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-454310" status="VALID">
          <idno type="IdRef">241614864</idno>
          <idno type="RNSR">196718247G</idno>
          <idno type="ROR">https://ror.org/05eyd5d35</idno>
          <orgName>Centre Inria de Paris</orgName>
          <date type="start">2016-03-10</date>
          <desc>
            <address>
              <addrLine>48 Rue Barrault, 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/paris</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>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-42417" status="VALID">
          <idno type="anr">ANR-17-CE40-0009</idno>
          <orgName>GALOP</orgName>
          <desc>Jeux à travers la lentille de algèbre et géométrie de l'optimisation</desc>
          <date type="start">2017</date>
        </org>
        <org type="anrProject" xml:id="projanr-37962" status="VALID">
          <idno type="anr">ANR-11-LABX-0056</idno>
          <idno type="program">Centres d'excellences</idno>
          <orgName>LMH</orgName>
          <desc>LabEx Mathématique Hadamard</desc>
          <date type="start">2011</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>