<?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-00008497</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="2026-05-16T10:51:09+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Rational, Replacement, and Local Invariants of a Group Action</title>
            <author role="aut">
              <persName>
                <forename type="first">Evelyne</forename>
                <surname>Hubert</surname>
              </persName>
              <email type="md5">9d69d5c405c782461017951d084cece0</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">ehubert</idno>
              <idno type="idhal" notation="numeric">1090</idno>
              <idno type="halauthorid" notation="string">569-1090</idno>
              <idno type="IDREF">https://www.idref.fr/057726477</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-1456-9524</idno>
              <affiliation ref="#struct-2451"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Irina</forename>
                <surname>Kogan</surname>
              </persName>
              <idno type="halauthorid">111014-0</idno>
              <affiliation ref="#struct-6988"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Evelyne</forename>
                <surname>Hubert</surname>
              </persName>
              <email type="md5">9d69d5c405c782461017951d084cece0</email>
              <email type="domain">inria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2005-09-06 17:23:17</date>
              <date type="whenWritten">2005</date>
              <date type="whenModified">2025-08-26 15:21:01</date>
              <date type="whenReleased">2005-09-06 17:23:17</date>
              <date type="whenProduced">2005</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/math.GM/0506574"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="102700">
                <persName>
                  <forename>Evelyne</forename>
                  <surname>Hubert</surname>
                </persName>
                <email type="md5">9d69d5c405c782461017951d084cece0</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00008497</idno>
            <idno type="halUri">https://hal.science/hal-00008497</idno>
            <idno type="halBibtex">hubert:hal-00008497</idno>
            <idno type="halRefHtml">2005</idno>
            <idno type="halRef">2005</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</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="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="DIEUDONNE-ATG" corresp="DIEUDONNE">Laboratoire J.A. Dieudonné - UMR 7351 - Algèbre, Topologie et Géométrie</idno>
            <idno type="stamp" n="UNIV-COTEDAZUR">Université Côte d'Azur</idno>
            <idno type="stamp" n="INRIA-ETATSUNIS">Copublications Inria-Etats-Unis</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">24 pages</note>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Rational, Replacement, and Local Invariants of a Group Action</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Evelyne</forename>
                    <surname>Hubert</surname>
                  </persName>
                  <email type="md5">9d69d5c405c782461017951d084cece0</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">ehubert</idno>
                  <idno type="idhal" notation="numeric">1090</idno>
                  <idno type="halauthorid" notation="string">569-1090</idno>
                  <idno type="IDREF">https://www.idref.fr/057726477</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-1456-9524</idno>
                  <affiliation ref="#struct-2451"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Irina</forename>
                    <surname>Kogan</surname>
                  </persName>
                  <idno type="halauthorid">111014-0</idno>
                  <affiliation ref="#struct-6988"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">math.GM/0506574</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="fr">invariants rationels et algébriques</term>
                <term xml:lang="fr">invariants differentiels</term>
                <term xml:lang="fr">action d'un groupe algébriques</term>
                <term xml:lang="fr">bases de Groebner</term>
                <term xml:lang="fr">méthode du repère mobile</term>
              </keywords>
              <classCode scheme="classification">AMS</classCode>
              <classCode scheme="halDomain" n="math.math-gm">Mathematics [math]/General Mathematics [math.GM]</classCode>
              <classCode scheme="halDomain" n="math.math-ac">Mathematics [math]/Commutative Algebra [math.AC]</classCode>
              <classCode scheme="halDomain" n="math.math-dg">Mathematics [math]/Differential Geometry [math.DG]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame method in differential geometry. The generating set of rational invariants appears as the coefficients of a Groebner basis, reduction with respect to which allows to express a rational invariant in terms of the generators. The replacement invariants, introduced in the paper, are tuples of algebraic functions of the rational invariants. Any invariant, whether rational, algebraic or local, can be can be rewritten terms of replacement invariants by a simple substitution.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-2451" status="OLD">
          <idno type="RNSR">200021385Z</idno>
          <orgName>Computer algebra and functional equations</orgName>
          <orgName type="acronym">CAFE</orgName>
          <date type="start">2000-04-17</date>
          <date type="end">2006-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-34586" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-6988" status="VALID">
          <orgName>Department of mathematics [North Carolina]</orgName>
          <desc>
            <address>
              <addrLine>255 Harrelson Hall Raleigh, North Carolina 27695</addrLine>
              <country key="US"/>
            </address>
            <ref type="url">http://www.math.ncsu.edu</ref>
          </desc>
          <listRelation>
            <relation active="#struct-306579" type="direct"/>
            <relation active="#struct-566986" type="indirect"/>
          </listRelation>
        </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-306579" status="VALID">
          <idno type="ISNI">0000 0001 2173 6074</idno>
          <idno type="ROR">https://ror.org/04tj63d06</idno>
          <orgName>North Carolina State University [Raleigh]</orgName>
          <orgName type="acronym">NC State</orgName>
          <desc>
            <address>
              <addrLine>Raleigh, NC 27695</addrLine>
              <country key="US"/>
            </address>
            <ref type="url">https://www.ncsu.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-566986" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-566986" status="VALID">
          <orgName>University of North Carolina System</orgName>
          <orgName type="acronym">UNC</orgName>
          <desc>
            <address>
              <country key="US"/>
            </address>
            <ref type="url">https://www.northcarolina.edu</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>