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TitleCharacterizations of border bases
Author(s) Achim Kehrein, Martin Kreuzer
TypeArticle in Journal
AbstractThis paper presents characterizations of border bases of zero-dimensional
polynomial ideals that are analogous to the known characterizations of
Gröbner bases. Based on a Border Division Algorithm, a variant of the
usual Division Algorithm, we characterize border bases as border prebases
with one of the following equivalent properties: special generation,
generation of the border form ideal, confluence of the corresponding
rewrite relation, reduction of S-polynomials to zero, and lifting of syzygies.
The last characterization relies on a detailed study of the relative position
of the border terms and their syzygy module. In particular, a border prebasis
is a border basis if and only if all fundamental syzygies of the
neighboring border terms lift; these liftings are easy to compute.
Keywordsborder basis, Gröbner basis, S-polynomial, lifting of syzygies, border term
Length23
File
LanguageEnglish
JournalJournal of Pure and Applied Algebra
Volume196
Pages251-270
Year2005
Edition0
Translation No
Refereed Yes
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