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    <article-meta>
      <title-group>
        <article-title>Better Answers to Real Questions</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Marek Kosta</string-name>
          <email>mkosta@mpi-inf.mpg.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Thomas Sturm</string-name>
          <email>sturm@mpi-inf.mpg.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Andreas Dolzmann</string-name>
          <email>andreas.dolzmann@dagstuhl.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Leibniz-Zentrum fur Informatik</institution>
          ,
          <addr-line>66041 Saarbrucken</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Max-Planck-Institut fur Informatik</institution>
          ,
          <addr-line>66123 Saarbrucken</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <abstract>
        <p />
      </abstract>
    </article-meta>
  </front>
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    <sec id="sec-1">
      <title>-</title>
      <p>We consider existential problems over the reals. Extended quanti er elimination
generalizes the concept of regular quanti er elimination by providing in addition answers, which
are descriptions of possible assignments for the quanti ed variables. Implementations of
extended quanti er elimination via virtual substitution have been successfully applied to
various problems in science and engineering. So far, the answers produced by these
implementations included in nitesimal and in nite numbers, which are hard to interpret in
practice. We introduce here a post-processing procedure to convert, for xed parameters,
all answers into standard real numbers. The relevance of our procedure is demonstrated
by applications of our implementation to various examples from the literature, where it
signi cantly improves the quality of the results.</p>
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