Home | Quick Search | Advanced Search | Bibliography submission | Bibliography submission using bibtex | Bibliography submission using bibtex file | Links | Help | Internal

Details:

   
TitleGr\"obner bases for syzygy modules of border bases.
Author(s) Martin Kreuzer, Markus Kriegl
TypeArticle in Journal
AbstractGiven an order ideal 𝒪 and an 𝒪-border basis of a 0-dimensional polynomial ideal, it was shown by Huibregtse that the liftings of the neighbor syzygies (i.e. of the fundamental syzygies of neighboring border terms) form a system of generators for the syzygy module of the border basis. We elaborate on Huibregtse's proof and transform it into explicit algorithmic form. Based on this, we are able to exhibit explicit conditions on a module term ordering τ such that the liftings of the neighbor syzygies are in fact a τ-Gröbner basis. Finally, we construct term orderings satisfying these conditions in an explicit algorithmic way.
KeywordsBorder basis; syzygy module; Gröbner basis
ISSN0219-4988
URL http://www.worldscientific.com/doi/abs/10.1142/S0219498814500030
LanguageEnglish
JournalJ. Algebra Appl.
Volume13
Number6
Pages32
PublisherWorld Scientific, Singapore
Year2014
Edition0
Translation No
Refereed No
Webmaster