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Elimination Theory in Differential and Difference Algebra

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Abstract

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.

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Authors and Affiliations

  1. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Wei Li & Chun-Ming Yuan

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Wei Li & Chun-Ming Yuan

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  1. Wei Li
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  2. Chun-Ming Yuan
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Correspondence to Wei Li.

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Dedicated to the memories of Professor Wen-Tsün Wu

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11688101, 11301519, 11671014.

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Li, W., Yuan, CM. Elimination Theory in Differential and Difference Algebra. J Syst Sci Complex 32, 287–316 (2019). https://doi.org/10.1007/s11424-019-8367-x

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