<?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 inria-00100984</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="2026-05-20T03:25:55+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">An environment for Symbolic and Numeric Computation</title>
            <author role="aut">
              <persName>
                <forename type="first">Gabriel</forename>
                <surname>dos Reis</surname>
              </persName>
              <idno type="halauthorid">143843-0</idno>
              <affiliation ref="#struct-62"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Bernard</forename>
                <surname>Mourrain</surname>
              </persName>
              <email type="md5">99d2b72427e88e39557fd123d18bb4ee</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">bernard-mourrain</idno>
              <idno type="idhal" notation="numeric">397</idno>
              <idno type="halauthorid" notation="string">15487-397</idno>
              <idno type="IDREF">https://www.idref.fr/050178725</idno>
              <affiliation ref="#struct-2461"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Philippe</forename>
                <surname>Trebuchet</surname>
              </persName>
              <email type="md5">33a21672b9c13f2c5a40e81168c1a9ca</email>
              <email type="domain">lip6.fr</email>
              <idno type="idhal" notation="numeric">833470</idno>
              <idno type="halauthorid" notation="string">142898-833470</idno>
              <idno type="IDREF">https://www.idref.fr/072245956</idno>
              <affiliation ref="#struct-408314"/>
              <affiliation ref="#struct-2461"/>
            </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-2364"/>
              <affiliation ref="#struct-408314"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Publications</forename>
                <surname>Loria</surname>
              </persName>
              <email type="md5">5ee6acd102a820bf4e187a1ec952273f</email>
              <email type="domain">loria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2006-09-26 14:53:19</date>
              <date type="whenModified">2025-11-04 11:58:29</date>
              <date type="whenReleased">2006-09-28 15:22:47</date>
              <date type="whenProduced">2002</date>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="108626">
                <persName>
                  <forename>Publications</forename>
                  <surname>Loria</surname>
                </persName>
                <email type="md5">5ee6acd102a820bf4e187a1ec952273f</email>
                <email type="domain">loria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">inria-00100984</idno>
            <idno type="halUri">https://inria.hal.science/inria-00100984</idno>
            <idno type="halBibtex">dosreis:inria-00100984</idno>
            <idno type="halRefHtml">&lt;i&gt;International Congress of Mathematical Software - ICMS'2002&lt;/i&gt;, 2002, Beijing, China. pp.239-249</idno>
            <idno type="halRef">International Congress of Mathematical Software - ICMS'2002, 2002, Beijing, China. pp.239-249</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNICE">Université Nice Sophia Antipolis</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="ENS-CACHAN">Ecole Normale Supérieure de Cachan</idno>
            <idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno>
            <idno type="stamp" n="INRIA-SOPHIA">INRIA Sophia Antipolis - Méditerranée</idno>
            <idno type="stamp" n="INRIASO">INRIA-SOPHIA</idno>
            <idno type="stamp" n="DIEUDONNE">Laboratoire Jean-Alexandre Dieudonné</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno>
            <idno type="stamp" n="LORIA2">Publications du LORIA</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="LIP6" corresp="SORBONNE-UNIVERSITE">Laboratoire d'Informatique de Paris 6</idno>
            <idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="LORIA">Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno>
            <idno type="stamp" n="UPMC_POLE_1" corresp="UPMC">UPMC Pôle 1</idno>
            <idno type="stamp" n="UNIV-COTEDAZUR">Université Côte d'Azur</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="CMLA">Centre de Mathématiques et de Leurs Applications</idno>
            <idno type="stamp" n="FARMAN">Institut Farman</idno>
            <idno type="stamp" n="ENS-PARIS-SACLAY">Ecole Normale Supérieure paris-Saclay</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">An environment for Symbolic and Numeric Computation</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Gabriel</forename>
                    <surname>dos Reis</surname>
                  </persName>
                  <idno type="halauthorid">143843-0</idno>
                  <affiliation ref="#struct-62"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Bernard</forename>
                    <surname>Mourrain</surname>
                  </persName>
                  <email type="md5">99d2b72427e88e39557fd123d18bb4ee</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">bernard-mourrain</idno>
                  <idno type="idhal" notation="numeric">397</idno>
                  <idno type="halauthorid" notation="string">15487-397</idno>
                  <idno type="IDREF">https://www.idref.fr/050178725</idno>
                  <affiliation ref="#struct-2461"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Philippe</forename>
                    <surname>Trebuchet</surname>
                  </persName>
                  <email type="md5">33a21672b9c13f2c5a40e81168c1a9ca</email>
                  <email type="domain">lip6.fr</email>
                  <idno type="idhal" notation="numeric">833470</idno>
                  <idno type="halauthorid" notation="string">142898-833470</idno>
                  <idno type="IDREF">https://www.idref.fr/072245956</idno>
                  <affiliation ref="#struct-408314"/>
                  <affiliation ref="#struct-2461"/>
                </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-2364"/>
                  <affiliation ref="#struct-408314"/>
                </author>
              </analytic>
              <monogr>
                <meeting>
                  <title>International Congress of Mathematical Software - ICMS'2002</title>
                  <date type="start">2002</date>
                  <settlement>Beijing</settlement>
                  <country key="CN">China</country>
                </meeting>
                <imprint>
                  <publisher>World Scientific</publisher>
                  <biblScope unit="pp">239-249</biblScope>
                  <date type="datePub">2002</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="fr">intégration logicielle</term>
                <term xml:lang="fr">applications</term>
                <term xml:lang="fr">calcul numérique</term>
                <term xml:lang="fr">calul symbolique</term>
                <term xml:lang="fr">numeric computations</term>
                <term xml:lang="fr">symbolic computations</term>
                <term xml:lang="fr">software integration</term>
              </keywords>
              <classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</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 describe the environment for symbolic and numeric computations, called SYNAPS (Symbolic and Numeric APplicationS) and developed in C++. Its aim is to provide a coherent platform integrating many of the nowadays freely available software in scientific computing. The approach taken here is inspired by the recent paradigm of software developments called active library. In this paper, we explain the design choices of the kernel and their impact on the development of generic and efficient codes for the treatment of algebraic objects, such as vectors, matrices, univariate and multivariate polynomials. Implementation details illustrate the performance of the approach. We describe the environment for symbolic and numeric computations, called SYNAPS (Symbolic and Numeric APplicationS) and developed in C++. Its aim is to provide a coherent platform integrating many of the nowadays freely available software in scientific computing. The approach taken here is inspired by the recent paradigm of software developments called active library. In this paper, we explain the design choices of the kernel and their impact on the development of generic and efficient codes for the treatment of algebraic objects, such as vectors, matrices, univariate and multivariate polynomials. Implementation details illustrate the performance of the approach.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-62" status="OLD">
          <orgName>Centre de Mathématiques et de Leurs Applications</orgName>
          <orgName type="acronym">CMLA</orgName>
          <date type="start">1990-01-01</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>ENS Cachan CNRS, PRES UniverSud, 61 Avenue du Pr´esident Wilson 94230 Cachan</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.cmla.ens-cachan.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-6862" type="direct"/>
            <relation name="UMR8536" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-2461" status="OLD">
          <idno type="RNSR">200218407D</idno>
          <orgName>Geometry, algebra, algorithms</orgName>
          <orgName type="acronym">GALAAD</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-34586" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-117617" type="direct"/>
            <relation name="UMR6621" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-408314" status="OLD">
          <orgName>Calcul formel</orgName>
          <orgName type="acronym">CALFOR</orgName>
          <date type="start">1997-01-01</date>
          <date type="end">2003-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-233" type="direct"/>
            <relation active="#struct-93591" type="indirect"/>
            <relation name="UMR7606" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-2364" status="OLD">
          <idno type="RNSR">200221401H</idno>
          <orgName>Solving problems through algebraic computation and efficient software</orgName>
          <orgName type="acronym">SPACES</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/spaces</ref>
          </desc>
          <listRelation>
            <relation active="#struct-2496" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-466633" type="direct"/>
            <relation active="#struct-300291" type="indirect"/>
            <relation active="#struct-300292" type="indirect"/>
            <relation active="#struct-300293" type="indirect"/>
            <relation name="UMR7503" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-6862" status="VALID">
          <orgName>École normale supérieure - Cachan</orgName>
          <orgName type="acronym">ENS Cachan</orgName>
          <desc>
            <address>
              <addrLine>61, avenue du Président Wilson - 94230 Cachan</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ens-cachan.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="laboratory" xml:id="struct-34586" status="VALID">
          <idno type="RNSR">198318250R</idno>
          <idno type="ROR">https://ror.org/01nzkaw91</idno>
          <orgName>Centre Inria d'Université Côte d'Azur</orgName>
          <desc>
            <address>
              <addrLine>2004 route des Lucioles BP 93 06902 Sophia Antipolis</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/sophia/</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="institution" xml:id="struct-117617" status="VALID">
          <idno type="IdRef">026403498</idno>
          <idno type="ISNI">0000000123372892</idno>
          <idno type="ROR">https://ror.org/02k9vew78</idno>
          <orgName>Université Nice Sophia Antipolis (1965 - 2019)</orgName>
          <orgName type="acronym">UNS</orgName>
          <date type="start">1965-10-23</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Parc Valrose, 06100 Nice</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://unice.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-233" status="OLD">
          <idno type="RNSR">199712651U</idno>
          <idno type="ROR">https://ror.org/05krcen59</idno>
          <orgName>Laboratoire d'Informatique de Paris 6</orgName>
          <orgName type="acronym">LIP6</orgName>
          <date type="start">1997-01-01</date>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>4 Place JUSSIEU 75252 PARIS CEDEX 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lip6.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-93591" type="direct"/>
            <relation name="UMR7606" active="#struct-441569" type="direct"/>
          </listRelation>
        </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="laboratory" xml:id="struct-2496" status="OLD">
          <orgName>INRIA 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/centre-de-recherche-inria/nancy-grand-est</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-466633" status="OLD">
          <orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
          <orgName type="acronym">LORIA</orgName>
          <date type="start">1997-01-01</date>
          <date type="end">2011-12-31</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-300291" type="direct"/>
            <relation active="#struct-300292" type="direct"/>
            <relation active="#struct-300293" type="direct"/>
            <relation name="UMR7503" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300291" status="OLD">
          <orgName>Université Henri Poincaré - Nancy 1</orgName>
          <orgName type="acronym">UHP</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300292" status="OLD">
          <orgName>Université Nancy 2</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300293" status="OLD">
          <orgName>Institut National Polytechnique de Lorraine</orgName>
          <orgName type="acronym">INPL</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>