Minimally generating ideals of rational parametric curves in polynomial time
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.
scientific article; zbMATH DE number 1513054
scientific article