Journal of Systems Science and Complexity

, Volume 32, Issue 1, pp 287–316 | Cite as

Elimination Theory in Differential and Difference Algebra

  • Wei LiEmail author
  • Chun-Ming Yuan


Elimination theory is central in differential and difference algebra. The Wu-Ritt characteristic set method, the resultant and the Chow form are three fundamental tools in the elimination theory for algebraic differential or difference equations. In this paper, the authors mainly present a survey of the existing work on the theory of characteristic set methods for differential and difference systems, the theory of differential Chow forms, and the theory of sparse differential and difference resultants.


Differential Chow forms differential resultants sparse differential resultants Wu-Ritt characteristic sets 


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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.University of Chinese Academy of SciencesBeijingChina

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