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  <doc>
    <id>1129</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2009-05-13</completedDate>
    <publishedDate>2009-05-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hyperdeterminants as integrable discrete systems</title>
    <abstract language="eng">We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A.~Cayley in 1845. We prove integrability (understood as $4d$-consistency) of a nonlinear difference equation defined by the $2 \times 2 \times 2$ - hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the $2\times 2\times 2\times 2$ - hyperdeterminant.</abstract>
    <identifier type="serial">09-17</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1178</identifier>
    <identifier type="doi">10.1088/1751-8113/42/45/454023</identifier>
    <identifier type="arxiv">0903.3864</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11292</identifier>
    <enrichment key="SourceTitle">Appeared in: J. Phys. A: Math. Theor., 42 (2009), 454023, 9 pages</enrichment>
    <author>Sergey Tsarev</author>
    <submitter>unknown unknown</submitter>
    <author>Thomas Wolf</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-17</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hyper determinants</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>integrable systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>large polynomial systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>computer algebra</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Form</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Reduce</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Singular</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="pacs" number="02.30.Ik">Integrable systems</collection>
    <collection role="pacs" number="02.70.Wz">Symbolic computation (computer algebra)</collection>
    <collection role="msc" number="52-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="52C99">None of the above, but in this section</collection>
    <collection role="institutes" number="sis">Digital Data and Information for Society, Science, and Culture</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1129/ZR_09_17.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1129/ZR_09_17.ps</file>
  </doc>
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