Elimination Theory in Differential and Difference Algebra  

作　　者：LI Wei YUAN Chun-Ming 

机构地区：[1]KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences [2]University of Chinese Academy of Sciences

出　　处：《Journal of Systems Science & Complexity》2019年第1期287-316,共30页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.11688101,11301519,11671014

摘　　要：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.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.

关 键 词：DIFFERENTIAL Chow FORMS DIFFERENTIAL RESULTANTS sparse DIFFERENTIAL RESULTANTS Wu-Ritt characteristic SETS 

分 类 号：O1[理学—数学]