Hilbert Stratification and Parametric Gröbner Bases

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• 作者：Laureano Gonzalez– ; Vega ; Carlo Traverso ; Alberto Zanoni
• 刊名：Lecture Notes in Computer Science
• 出版年：2005
• 出版时间：2005
• 年：2005
• 卷：3718
• 期：1
• 页码：p.220
• 全文大小：252 KB
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

In this paper we generalize a method to analyze inhomogeneous polynomial systems containing parameters. In particular, the Hilbert function is used as a tool to check that the specialization of a “generic” Gröbner basis of the parametric polynomial system (computed in a polynomial ring having both parameters and unknowns as variables) is a Gröbner basis of the specialized system. Extending the analysis, we can also build the so-called Hilbert stratification of the associated variety. We classify the possible specializations according to the value of the Hilbert function of the specialized system. Some computation examples with the PoSSoLib are reported.