Details:
Title  On full rank differential systems with power series coefficients  Author(s)  S.A. Abramov, M.A. Barkatou, D.E. Khmelnov  Type  Article in Journal  Abstract  Abstract We consider the following problem: given a linear ordinary differential system of arbitrary order with formal power series coefficients, decide whether the system has nonzero Laurent series solutions, and find all such solutions if they exist (in a truncated form preserving the space dimension). If the series coefficients of the original systems are represented algorithmically then these problems are algorithmically undecidable. However, it turns out that they are decidable in the case when we know in advance that a given system is of full rank. We define the width of a given full rank system S with formal power series coefficients as the smallest nonnegative integer w such that any ltruncation of S with l ⩾ w is a full rank system. We prove that the value w exists for any full rank system and can be found algorithmically. We propose corresponding algorithms and their Maple implementation, and report some experiments.  Keywords  Differential system, Series coefficients, Laurent series solutions, System width  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717114000601 
Language  English  Journal  Journal of Symbolic Computation  Volume  68, Part 1  Number  0  Pages  120  137  Year  2015  Edition  0  Translation 
No  Refereed 
No 
