Selected and satellite unknowns in linear differential systems

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• 作者：A.A. Panferov^a ; ^b ; ^{ast.a_s@mail.ru}
• 关键词：34A30 ; 68W30
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：85
• 期：Complete
• 页码：1-11
• 全文大小：301 K
• 卷排序：85

文摘

Consider the differential field K=Q‾(x) with derivation d/dxd/dx. Let some unknowns (components of the unknown vector y=(y1,…,yn)Ty=(y1,…,yn)T) of a linear homogeneous differential system S over K be selected. Denote this set of selected unknowns by s  . An unselected unknown yjyj of the system S is called satellite for s if the minimal subfield of a Picard–Vessiot extension over K for S, that contains all selected components of all solutions to S  , also contains yjyj component of any solution. We present an algorithm for constructing the set of satellite unknowns for a given linear homogeneous differential system with selected unknowns.