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Journal of Systems Science and Complexity

, Volume 32, Issue 1, pp 234–255 | Cite as

A Survey on Algorithms for Computing Comprehensive Gröbner Systems and Comprehensive Gröbner Bases

  • Dong LuEmail author
  • Yao Sun
  • Dingkang Wang
Article
First Online:

Abstract

Weispfenning in 1992 introduced the concepts of comprehensive Gröbner system/basis of a parametric polynomial system, and he also presented an algorithm to compute them. Since then, this research field has attracted much attention over the past several decades, and many efficient algorithms have been proposed. Moreover, these algorithms have been applied to many different fields, such as parametric polynomial equations solving, geometric theorem proving and discovering, quantifier elimination, and so on. This survey brings together the works published between 1992 and 2018, and we hope that this survey is valuable for this research area.

Keywords

Comprehensive Gröbner basis comprehensive Gröbner system discovering geometric theorems mechanically parametric polynomial system quantifier elimination 
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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.KLMM, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.SKLOIS, Institute of Information EngineeringChinese Academy of SciencesBeijingChina

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