Minimally generating ideals of rational parametric curves in polynomial time
type: Item
instance of: scholarly article
title: Minimally generating ideals of rational parametric curves in polynomial time
zbMATH Open document ID: 0980.14033
author: R. Smith
published in: Journal of Symbolic Computation
publication date: 2002-03-10T00:00:00Z
review text: In this paper, the authors present an algorithm for computing a minimal set of generators and the Hilbert function of the ideal of a rational parametric projective curve. The complexity of the algorithm is polynomial in the degree of the curve and in the minimal dimension of a linear variety containing the curve. This method is alternative to the Gröbner bases techniques and relies on previous algorithms which constructs minimal sets of generators of ideals of projective points in polynomial time. The efficiency of the algorithm is based on a bound for the Castelnuovo-Mumford regularity of the curves. This bound is also developed in this paper in the general case [for smooth curves, it was given by \textit{F. Orecchia}, J. Pure Appl. Algebra 155, 77-89 (2001; Zbl 1032.14015)]. The authors implemented their algorithms using C++. They compare this implementation with the Hilbert driven elimination algorithm included in CoCoA 3.6 and Singular 1.2 showing that, in many instances, this new algorithm gives significant improvements in timings.
reviewed by: Juan Sabia
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 14Q20
Mathematics Subject Classification ID: 68W40
Mathematics Subject Classification ID: 14-04
zbMATH DE Number: 1513054
zbMATH Keywords: ideal of projective curve
zbMATH Keywords: minimal set of generators
zbMATH Keywords: Hilbert function
zbMATH Keywords: complexity
zbMATH Keywords: algorithm
zbMATH Keywords: Gröbner bases
zbMATH Keywords: Castelnuovo-Mumford regularity
zbMATH Keywords: CoCoA
zbMATH Keywords: Singular
describes a project that uses: SINGULAR
describes a project that uses: CoCoA
MaRDI profile type: Publication
full work available at URL: jsco.1999.0354
OpenAlex ID: W1980725480
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DOI: 10.1006/JSCO.1999.0354
description: scientific article; zbMATH DE number 1513054