Abstract
An algorithm to generate a minimal comprehensive Gröbner\, basis of a parametric polynomial system from an arbitrary faithful comprehensive Gröbner\, system is presented. A basis of a parametric polynomial ideal is a comprehensive Gröbner\, basis if and only if for every specialization of parameters in a given field, the specialization of the basis is a Gröbner\, 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 Gröbner\, 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 Gröbner\, system. The algorithm has been implemented and successfully tried on many examples from the literature.
Connections
Explore this paper’s authors, topics and related work.
Building this map preview
BZPEER is loading the nearby papers, people, topics and institutions for this page.
Reviews 0
Write a review
No reviews yet.
Discussion 0
Add a comment
No comments yet.