<?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-01350994</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="2026-05-20T08:02:32+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A short proof for the open quadrant problem</title>
            <author role="aut">
              <persName>
                <forename type="first">Fernando</forename>
                <forename type="middle">F</forename>
                <surname>José</surname>
              </persName>
              <idno type="halauthorid">1049668-0</idno>
              <affiliation ref="#struct-48181"/>
              <affiliation ref="#struct-118724"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Carlos</forename>
                <surname>Ueno</surname>
              </persName>
              <idno type="halauthorid">1049669-0</idno>
              <affiliation ref="#struct-123697"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Alain</forename>
                <surname>Monteil</surname>
              </persName>
              <email type="md5">8d58fc1b670b8074dd83e4a4c93d5914</email>
              <email type="domain">inria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2016-08-02 13:57:30</date>
              <date type="whenWritten">2015</date>
              <date type="whenModified">2025-04-14 14:24:03</date>
              <date type="whenReleased">2016-08-02 14:39:27</date>
              <date type="whenProduced">2015-06-15</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/1502.07866"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="102239">
                <persName>
                  <forename>Alain</forename>
                  <surname>Monteil</surname>
                </persName>
                <email type="md5">8d58fc1b670b8074dd83e4a4c93d5914</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01350994</idno>
            <idno type="halUri">https://inria.hal.science/hal-01350994</idno>
            <idno type="halBibtex">jose:hal-01350994</idno>
            <idno type="halRefHtml">&lt;i&gt;MEGA'2015 (Special Issue)&lt;/i&gt;, Jun 2015, Trento, Italy</idno>
            <idno type="halRef">MEGA'2015 (Special Issue), Jun 2015, Trento, Italy</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="MEGA">Effective Methods in Algebraic Geometry</idno>
            <idno type="stamp" n="MEGA2015" corresp="MEGA">MEGA 2015</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">25 pages, 3 figures. Comments welcome!</note>
            <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="0">No</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">A short proof for the open quadrant problem</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Fernando</forename>
                    <forename type="middle">F</forename>
                    <surname>José</surname>
                  </persName>
                  <idno type="halauthorid">1049668-0</idno>
                  <affiliation ref="#struct-48181"/>
                  <affiliation ref="#struct-118724"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Carlos</forename>
                    <surname>Ueno</surname>
                  </persName>
                  <idno type="halauthorid">1049669-0</idno>
                  <affiliation ref="#struct-123697"/>
                </author>
              </analytic>
              <monogr>
                <meeting>
                  <title>MEGA'2015 (Special Issue)</title>
                  <date type="start">2015-06-15</date>
                  <date type="end">2015-06-19</date>
                  <settlement>Trento</settlement>
                  <country key="IT">Italy</country>
                </meeting>
                <imprint/>
              </monogr>
              <idno type="arxiv">1502.07866</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">52A10</term>
                <term xml:lang="en">26C99</term>
                <term xml:lang="en">open quadrant 2000 MSC: 14P10</term>
                <term xml:lang="en">semialgebraic sets</term>
                <term xml:lang="en">Polynomial maps and images</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-ag">Mathematics [math]/Algebraic Geometry [math.AG]</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>In 2003 it was proved that the open quadrant Q := {x &gt; 0, y &gt; 0} of R 2 is a polynomial image of R 2. This result was the origin of an ulterior more systematic study of polynomial images of Euclidean spaces. In this article we provide a short proof of the previous fact that does not involve computer calculations, in contrast with the original one. The strategy here is to represent the open quadrant as the image of a polynomial map that can be expressed as the composition of three simple polynomial maps whose images can be easily understood.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-48181" status="VALID">
          <idno type="ROR">https://ror.org/02p0gd045</idno>
          <orgName>Universidad Complutense de Madrid =  Complutense University of Madrid  [Madrid]</orgName>
          <orgName type="acronym">UCM</orgName>
          <date type="start">2016-11-23</date>
          <desc>
            <address>
              <addrLine>Avda. de Séneca, 2, Ciudad Universitaria, 28040 Madrid</addrLine>
              <country key="ES"/>
            </address>
            <ref type="url">https://www.ucm.es/english</ref>
          </desc>
        </org>
        <org type="department" xml:id="struct-118724" status="VALID">
          <orgName>Departamento de Algebra [Madird]</orgName>
          <desc>
            <address>
              <country key="ES"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-48181" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-123697" status="VALID">
          <orgName>Dipartimento di Matematica [Pisa]</orgName>
          <desc>
            <address>
              <addrLine>L. Tonelli, 56127 Pisa, Largo Bruno Pontecorvo 5</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">http://www.dm.unipi.it/www2/user/sedi_u.php?id_sede=4&amp;language=0</ref>
          </desc>
          <listRelation>
            <relation active="#struct-366408" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-366408" status="VALID">
          <idno type="IdRef">026619385</idno>
          <idno type="ISNI">0000000417573729</idno>
          <idno type="ROR">https://ror.org/03ad39j10</idno>
          <idno type="Wikidata">Q645663</idno>
          <orgName>University of Pisa [Italy] = Università di Pisa [Italia] = Université de Pise [Italie]</orgName>
          <orgName type="acronym">UniPi</orgName>
          <date type="start">1343-01-01</date>
          <desc>
            <address>
              <addrLine>Lungarno Pacinotti 43 – 56126 Pisa – Italia</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">https://www.unipi.it/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>