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Mathematics of Computation

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Subideal border bases

Authors: Martin Kreuzer and Henk Poulisse
Journal: Math. Comp. 80 (2011), 1135-1154
MSC (2010): Primary 13P10; Secondary 41A10, 65D05, 14Q99
Published electronically: November 1, 2010
MathSciNet review: 2772116
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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

Henk Poulisse
Affiliation: Harkenkamp 1a, D-30851 Langenhagen, Germany

Keywords: Approximate vanishing ideal, Buchberger-Möller algorithm, border basis
Received by editor(s): May 7, 2009
Received by editor(s) in revised form: March 9, 2010
Published electronically: November 1, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.