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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Subideal border bases
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by Martin Kreuzer and Henk Poulisse PDF
Math. Comp. 80 (2011), 1135-1154 Request permission

Abstract:

In modeling physical systems, it is sometimes useful to construct border bases of 0-dimensional polynomial ideals which are contained in the ideal generated by a given set of polynomials. We define and construct such subideal border bases, provide some basic properties and generalize a suitable variant of the Buchberger-Möller algorithm as well as the AVI-algorithm of Heldt, Kreuzer, Pokutta, and Poulisse to the subideal setting. The subideal version of the AVI-algorithm is then applied to an actual industrial problem.
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Additional Information
  • Martin Kreuzer
  • Affiliation: Fakultät für Informatik und Mathematik, Universität Passau, D-94030 Passau, Germany
  • Email: martin.kreuzer@uni-passau.de
  • Henk Poulisse
  • Affiliation: Harkenkamp 1a, D-30851 Langenhagen, Germany
  • Email: henk.poulisse@gmail.com
  • Received by editor(s): May 7, 2009
  • Received by editor(s) in revised form: March 9, 2010
  • Published electronically: November 1, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 1135-1154
  • MSC (2010): Primary 13P10; Secondary 41A10, 65D05, 14Q99
  • DOI: https://doi.org/10.1090/S0025-5718-2010-02432-9
  • MathSciNet review: 2772116