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TitleEfficient computation of Castelnuovo-Mumford regularity.
Author(s) Amir Hashemi
TypeArticle in Journal
AbstractIn this paper, we introduce the notion of a homogeneous ideal in quasi stable position (QSP); a new definition for the notion of generic coordinates to compute efficiently the Castelnuovo-Mumford regularity of a homogeneous ideal. This definition is simple to check, because it is tested on the initial ideal for the degree reverse lexicographic ordering. It is explicit, because we provide an algorithm to decide whether a monomial ideal is in QSP or not. The main result of this paper is that the Castelnuovo-Mumford regularity of an ideal in QSP is the maximal degree of the elements of its reduced Gröbner basis with respect to the reverse lexicographic ordering. We have implemented an algorithm in (the distributed library noether.lib of) SINGULAR based on the above results for computing the Castelnuovo-Mumford regularity of a general ideal, and we evaluate its performance via some examples. - See more at: http://www.ams.org/journals/mcom/2012-81-278/S0025-5718-2011-02515-9/#sthash.30xQ5hgP.dpuf
ISSN0025-5718; 1088-6842/e
File
URL http://www.ams.org/journals/mcom/2012-81-278/S0025-5718-2011-02515-9/S0025-5718-2011-02515-9.pdf
LanguageEnglish
JournalMath. Comput.
Volume81
Number278
Pages1163--1177
PublisherAmerican Mathematical Society (AMS), Providence, RI
Year2012
Edition0
Translation No
Refereed No
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