论文标题
用于计算最小综合gröbner\的算法，参数多项式系统的基础
An Algorithm for Computing a Minimal Comprehensive Gröbner\, Basis of a Parametric Polynomial System
论文作者
论文摘要
从任意忠实的综合性gröbner\中提出了一种最小的综合性gröbner\的算法，这是参数多项式系统的基础。参数多项式理想的基础是一个综合的gröbner\，并且仅在给定字段中的每个参数专业化时，基础的专业化是一个相关专业的多项式理想的基础。确保最小性的关键思想是多项式对于全面的Gröbner\基础至关重要。通过确定是否可以在全面的gröbner\系统中相关分支中的其他多项式进行各种专业方面进行多项式检查，从而执行本质性检查。该算法已经实施并成功地在文献中的许多示例中进行了尝试。
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.
