2020/03/17 by Kapur, Deepak, Yang, Yiming
#FOS: Computer and information sciences #Symbolic Computation (cs.SC)
paper · doi:10.48550/arxiv.2003.07957
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.