Efficient computation of Castelnuovo-Mumford regularity
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Abstract:
In 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.References
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Additional Information
- Amir Hashemi
- Affiliation: Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran
- Email: Amir.Hashemi@cc.iut.ac.ir
- Received by editor(s): April 7, 2008
- Received by editor(s) in revised form: January 4, 2011
- Published electronically: July 21, 2011
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 1163-1177
- MSC (2010): Primary 14Q20, 13P10
- DOI: https://doi.org/10.1090/S0025-5718-2011-02515-9
- MathSciNet review: 2869055