An Algorithm for Computing a Minimal Comprehensive Gr\"obner\, Basis of a Parametric Polynomial System
Abstract
An algorithm to generate a minimal comprehensive Gr\"obner\, basis of a parametric polynomial system from an arbitrary faithful comprehensive Gr\"obner\, system is presented. A basis of a parametric polynomial ideal is a comprehensive Gr\"obner\, basis if and only if for every specialization of parameters in a given field, the specialization of the basis is a Gr\"obner\, basis of the associated specialized polynomial ideal. The key idea used in ensuring minimality is that of a polynomial being essential with respect to a comprehensive Gr\"obner\, basis. The essentiality check is performed by determining whether a polynomial can be covered for various specializations by other polynomials in the associated branches in a comprehensive Gr\"obner\, system. The algorithm has been implemented and successfully tried on many examples from the literature.
Cite
@article{arxiv.2003.07957,
title = {An Algorithm for Computing a Minimal Comprehensive Gr\"obner\, Basis of a Parametric Polynomial System},
author = {Deepak Kapur and Yiming Yang},
journal= {arXiv preprint arXiv:2003.07957},
year = {2020}
}
Comments
8 pages