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An algebraist’s view on border bases. (English) Zbl 1152.13304

Dickenstein, Alicia (ed.) et al., Solving polynomial equations. Foundations, algorithms, and applications. Berlin: Springer (ISBN 3-540-24326-7/hbk). Algorithms and Computation in Mathematics 14, 169-202, 393-418 (2005).
Summary: This chapter is devoted to laying the algebraic foundations for border bases of ideals. Using an order ideal \({\mathcal O}\), we describe a zero-dimensional ideal from the outside. The first and higher borders of \({\mathcal O}\) can be used to measure the distance of a term from \({\mathcal O}\) and to define \({\mathcal O}\)-border bases. We study their existence and uniqueness, their relation to Gröbner bases, and their characterization in terms of commuting matrices. Finally, we use border bases to solve a problem coming from statistics.
For the entire collection see [Zbl 1061.12001].

MSC:

13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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