Subideal border bases

Kreuzer, Martin; Poulisse, Henk

doi:10.1090/S0025-5718-2010-02432-9

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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