<?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-00992634</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="2026-05-18T22:04:05+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Improved algorithm for computing separating linear forms for bivariate systems</title>
            <author role="aut">
              <persName>
                <forename type="first">Yacine</forename>
                <surname>Bouzidi</surname>
              </persName>
              <email type="md5">8a4cc55dab9d8f222e4214c073f56a83</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="numeric">897265</idno>
              <idno type="halauthorid" notation="string">547093-897265</idno>
              <affiliation ref="#struct-205129"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Sylvain</forename>
                <surname>Lazard</surname>
              </persName>
              <email type="md5">803278b692333378439119bae9f2aea9</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">sylvain-lazard</idno>
              <idno type="idhal" notation="numeric">2334</idno>
              <idno type="halauthorid" notation="string">13654-2334</idno>
              <idno type="IDREF">https://www.idref.fr/179326554</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-6032-0802</idno>
              <affiliation ref="#struct-205129"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Guillaume</forename>
                <surname>Moroz</surname>
              </persName>
              <email type="md5">04f97a7bb703021727e505e7ead17efd</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">guillaume-moroz</idno>
              <idno type="idhal" notation="numeric">9582</idno>
              <idno type="halauthorid" notation="string">24353-9582</idno>
              <idno type="IDREF">https://www.idref.fr/137961456</idno>
              <affiliation ref="#struct-205129"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Marc</forename>
                <surname>Pouget</surname>
              </persName>
              <email type="md5">74b972461bd244cb3a048752a20e0d6a</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">marc-pouget</idno>
              <idno type="idhal" notation="numeric">378</idno>
              <idno type="halauthorid" notation="string">21834-378</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-8085-4134</idno>
              <idno type="IDREF">https://www.idref.fr/094973768</idno>
              <affiliation ref="#struct-205129"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Fabrice</forename>
                <surname>Rouillier</surname>
              </persName>
              <email type="md5">dba73af70e5a5e5ba0bdd73b6574aed7</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">fabrice-rouillier</idno>
              <idno type="idhal" notation="numeric">2066</idno>
              <idno type="halauthorid" notation="string">15516-2066</idno>
              <idno type="IDREF">https://www.idref.fr/076629481</idno>
              <idno type="ORCID">https://orcid.org/0009-0004-2972-822X</idno>
              <affiliation ref="#struct-22"/>
              <affiliation ref="#struct-206119"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Marc</forename>
                <surname>Pouget</surname>
              </persName>
              <email type="md5">74b972461bd244cb3a048752a20e0d6a</email>
              <email type="domain">inria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2014-05-19 10:08:38</date>
              <date type="whenModified">2025-11-04 12:00:29</date>
              <date type="whenReleased">2014-05-19 16:31:24</date>
              <date type="whenProduced">2014-07-23</date>
              <date type="whenEndEmbargoed">2014-05-19</date>
              <ref type="file" target="https://inria.hal.science/hal-00992634v1/document">
                <date notBefore="2014-05-19"/>
              </ref>
              <ref type="file" subtype="greenPublisher" n="1" target="https://inria.hal.science/hal-00992634v1/file/separating_element_curve.pdf" id="file-992634-771749">
                <date notBefore="2014-05-19"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1405.4740"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="113334">
                <persName>
                  <forename>Marc</forename>
                  <surname>Pouget</surname>
                </persName>
                <email type="md5">74b972461bd244cb3a048752a20e0d6a</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00992634</idno>
            <idno type="halUri">https://inria.hal.science/hal-00992634</idno>
            <idno type="halBibtex">bouzidi:hal-00992634</idno>
            <idno type="halRefHtml">&lt;i&gt;ISSAC - 39th International Symposium on Symbolic and Algebraic Computation&lt;/i&gt;, Jul 2014, Kobe, Japan</idno>
            <idno type="halRef">ISSAC - 39th International Symposium on Symbolic and Algebraic Computation, Jul 2014, Kobe, Japan</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-992634-771749"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-PARIS7" corresp="UNIV-PARIS">Université Denis Diderot - Paris VII</idno>
            <idno type="stamp" n="UPMC" corresp="SORBONNE-UNIVERSITE">Université Pierre et Marie Curie</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="INRIA-ROCQ">INRIA Paris - Rocquencourt</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="LORIA2">Publications du LORIA</idno>
            <idno type="stamp" n="IMJ" corresp="SORBONNE-UNIVERSITE">Institut de Mathématiques de Jussieu</idno>
            <idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="LORIA-ALGO-TEST5">LORIA-ALGO-TEST5  </idno>
            <idno type="stamp" n="LORIA">Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno>
            <idno type="stamp" n="LORIA-ALGO" corresp="LORIA">Department of Algorithms, Computation, Image and Geometry</idno>
            <idno type="stamp" n="NANCY-2014">NANCY 2014</idno>
            <idno type="stamp" n="UPMC_POLE_1" corresp="UPMC">UPMC Pôle 1</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</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="UP-SCIENCES">Université Paris Cité - Faculté des Sciences</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
            <idno type="stamp" n="AM2I-UL">Pôle scientifique Automatique, Mathématiques, Informatique et leurs Intéractions de l'Université de Lorraine</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">Improved algorithm for computing separating linear forms for bivariate systems</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Yacine</forename>
                    <surname>Bouzidi</surname>
                  </persName>
                  <email type="md5">8a4cc55dab9d8f222e4214c073f56a83</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="numeric">897265</idno>
                  <idno type="halauthorid" notation="string">547093-897265</idno>
                  <affiliation ref="#struct-205129"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Sylvain</forename>
                    <surname>Lazard</surname>
                  </persName>
                  <email type="md5">803278b692333378439119bae9f2aea9</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">sylvain-lazard</idno>
                  <idno type="idhal" notation="numeric">2334</idno>
                  <idno type="halauthorid" notation="string">13654-2334</idno>
                  <idno type="IDREF">https://www.idref.fr/179326554</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-6032-0802</idno>
                  <affiliation ref="#struct-205129"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Guillaume</forename>
                    <surname>Moroz</surname>
                  </persName>
                  <email type="md5">04f97a7bb703021727e505e7ead17efd</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">guillaume-moroz</idno>
                  <idno type="idhal" notation="numeric">9582</idno>
                  <idno type="halauthorid" notation="string">24353-9582</idno>
                  <idno type="IDREF">https://www.idref.fr/137961456</idno>
                  <affiliation ref="#struct-205129"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Marc</forename>
                    <surname>Pouget</surname>
                  </persName>
                  <email type="md5">74b972461bd244cb3a048752a20e0d6a</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">marc-pouget</idno>
                  <idno type="idhal" notation="numeric">378</idno>
                  <idno type="halauthorid" notation="string">21834-378</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-8085-4134</idno>
                  <idno type="IDREF">https://www.idref.fr/094973768</idno>
                  <affiliation ref="#struct-205129"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Fabrice</forename>
                    <surname>Rouillier</surname>
                  </persName>
                  <email type="md5">dba73af70e5a5e5ba0bdd73b6574aed7</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">fabrice-rouillier</idno>
                  <idno type="idhal" notation="numeric">2066</idno>
                  <idno type="halauthorid" notation="string">15516-2066</idno>
                  <idno type="IDREF">https://www.idref.fr/076629481</idno>
                  <idno type="ORCID">https://orcid.org/0009-0004-2972-822X</idno>
                  <affiliation ref="#struct-22"/>
                  <affiliation ref="#struct-206119"/>
                </author>
              </analytic>
              <monogr>
                <meeting>
                  <title>ISSAC - 39th International Symposium on Symbolic and Algebraic Computation</title>
                  <date type="start">2014-07-23</date>
                  <date type="end">2014-07-25</date>
                  <settlement>Kobe</settlement>
                  <country key="JP">Japan</country>
                </meeting>
                <imprint>
                  <date type="datePub">2014-07</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1405.4740</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="info.info-cg">Computer Science [cs]/Computational Geometry [cs.CG]</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>We address the problem of computing a linear separating form of a system of two bivariate polynomials with integer coefficients, that is a linear combination of the variables that takes different values when evaluated at the distinct solutions of the system. The computation of such linear forms is at the core of most algorithms that solve algebraic systems by computing rational parameterizations of the solutions and this is the bottleneck of these algorithms in terms of worst-case bit complexity. We present for this problem a new algorithm of worst-case bit complexity $\sOB(d^7+d^6\tau)$ where $d$ and $\tau$ denote respectively the maximum degree and bitsize of the input (and where $\sO$ refers to the complexity where polylogarithmic factors are omitted and $O_B$ refers to the bit complexity). This algorithm simplifies and decreases by a factor $d$ the worst-case bit complexity presented for this problem by Bouzidi et al. \cite{bouzidiJSC2014a}. This algorithm also yields, for this problem, a probabilistic Las-Vegas algorithm of expected bit complexity $\sOB(d^5+d^4\tau)$.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-205129" status="OLD">
          <idno type="RNSR">200518305E</idno>
          <orgName>Effective Geometric Algorithms for Surfaces and Visibility</orgName>
          <orgName type="acronym">VEGAS</orgName>
          <date type="start">2005-08-01</date>
          <date type="end">2016-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/vegas</ref>
          </desc>
          <listRelation>
            <relation active="#struct-129671" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-423083" type="direct"/>
            <relation active="#struct-206040" type="indirect"/>
            <relation active="#struct-411575" type="indirect"/>
            <relation active="#struct-413289" type="indirect"/>
            <relation name="UMR7503" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-22" status="OLD">
          <orgName>Institut de Mathématiques de Jussieu</orgName>
          <orgName type="acronym">IMJ</orgName>
          <desc>
            <address>
              <addrLine>2, place Jussieu 75251 Paris Cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.institut.math.jussieu.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-93591" type="direct"/>
            <relation active="#struct-300301" type="direct"/>
            <relation name="UMR7586" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-206119" status="OLD">
          <idno type="RNSR">201221216N</idno>
          <orgName>OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs</orgName>
          <orgName type="acronym">OURAGAN</orgName>
          <date type="start">2012-01-01</date>
          <date type="end">2015-12-31</date>
          <desc>
            <address>
              <addrLine>8 Pl. Aurélie Nemours75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/ouragan</ref>
          </desc>
          <listRelation>
            <relation active="#struct-86790" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-129671" status="VALID">
          <idno type="RNSR">198618246Y</idno>
          <idno type="ROR">https://ror.org/03fcjvn64</idno>
          <orgName>Centre Inria de l'Université de Lorraine</orgName>
          <desc>
            <address>
              <addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/nancy</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="department" xml:id="struct-423083" status="VALID">
          <orgName>Department of Algorithms, Computation, Image and Geometry</orgName>
          <orgName type="acronym">LORIA - ALGO</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.loria.fr/en/research/departments/algorithms-computation-image-and-geometry/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-206040" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-411575" type="indirect"/>
            <relation active="#struct-413289" type="indirect"/>
            <relation name="UMR7503" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-206040" status="VALID">
          <idno type="IdRef">067077927</idno>
          <idno type="ISNI">0000000121795429</idno>
          <idno type="RNSR">198912571S</idno>
          <idno type="IdUnivLorraine">[UL]RSI--</idno>
          <idno type="ROR">https://ror.org/02vnf0c38</idno>
          <orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
          <orgName type="acronym">LORIA</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.loria.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-411575" type="direct"/>
            <relation active="#struct-413289" type="direct"/>
            <relation name="UMR7503" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-411575" status="VALID">
          <idno type="IdRef">184443237</idno>
          <idno type="ROR">https://ror.org/019tcpt25</idno>
          <orgName>CentraleSupélec</orgName>
          <desc>
            <address>
              <addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.centralesupelec.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-413289" status="VALID">
          <idno type="IdRef">157040569</idno>
          <idno type="IdUnivLorraine">[UL]100--</idno>
          <idno type="ROR">https://ror.org/04vfs2w97</idno>
          <orgName>Université de Lorraine</orgName>
          <orgName type="acronym">UL</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lorraine.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-93591" status="OLD">
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Université Pierre et Marie Curie - Paris 6</orgName>
          <orgName type="acronym">UPMC</orgName>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>4 place Jussieu - 75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.upmc.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300301" status="OLD">
          <idno type="IdRef">027542084</idno>
          <idno type="ISNI">0000000121514068</idno>
          <idno type="ROR">https://ror.org/02n7qrg46</idno>
          <orgName>Université Paris Diderot - Paris 7</orgName>
          <orgName type="acronym">UPD7</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>5 rue Thomas-Mann - 75205 Paris cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-paris-diderot.fr</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-86790" status="OLD">
          <orgName>Inria Paris-Rocquencourt</orgName>
          <date type="end">2016-03-30</date>
          <desc>
            <address>
              <addrLine>INRIA Rocquencourt : Domaine de Voluceau, Rocquencourt B.P. 105 78153 le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/paris-rocquencourt</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>