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TitleAn algebraist's view on border bases
Author(s) Achim Kehrein, Martin Kreuzer, Lorenzo Robbiano
TypeBook, Chapter in Book, Conference Proceeding
AbstractThis 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 {\em 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.
Keywordsborder basis, order ideal, Gröbner basis, commuting matrices, design of experiments
Length33
ISBN3-540-24326-7
File
LanguageEnglish
SeriesAlgorithms and Computation in Mathematics
Volume14
Chapter4
Pages160-202
PublisherSpringer Verlag
AddressHeidelberg
Year2005
EditorA. Dickenstein and I. Emiris
Edition0
Translation No
Refereed Yes
BookSolving Polynomial Equations: Foundations, Algorithms, and Applications
ConferencenameCIMPA School 2003 (Buenos Aires/Argentina)
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