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.
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© 2005 Springer-Verlag Berlin Heidelberg
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Kehrein, A., Kreuzer, M., Robbiano, L. (2005). An algebraist’s view on border bases. In: Bronstein, M., et al. Solving Polynomial Equations. Algorithms and Computation in Mathematics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27357-3_4
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DOI: https://doi.org/10.1007/3-540-27357-3_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24326-7
Online ISBN: 978-3-540-27357-8
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