Details:
Title  Characterizations of border bases  Author(s)  Achim Kehrein, Martin Kreuzer  Type  Article in Journal  Abstract  This paper presents characterizations of border bases of zerodimensional
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 Spolynomials 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.  Keywords  border basis, Gröbner basis, Spolynomial, lifting of syzygies, border term  Length  23 
File 
 Language  English  Journal  Journal of Pure and Applied Algebra  Volume  196  Pages  251270  Year  2005  Edition  0  Translation 
No  Refereed 
Yes 
