Higher-Order Linear Differential Systems with Truncated Coefficients [chapter]

S. A. Abramov, M. A. Barkatou, E. Pflügel
2011 Lecture Notes in Computer Science  
We consider the following problem: given a linear differential system with formal Laurent series coefficients, we want to decide whether the system has non-zero Laurent series solutions, and find all such solutions if they exist. Let us also assume we need only a given positive integer number l of initial terms of these series solutions. How many initial terms of the coefficients of the original system should we use to construct what we need? Supposing that the series coefficients of the
more » ... l systems are represented algorithmically, we show that these questions are undecidable in general. However, they are decidable in the scalar case and in the case when we know in advance that a given system has an invertible leading matrix. We use our results in order to improve some functionality of the Maple [17] package ISOLDE [11] . ∞ i=0 Ξ u (i)x i is given. This is factually a model of computation. Our results can be represented without using this model (skipping the undecidability questions then), see Remark 1.
doi:10.1007/978-3-642-23568-9_2 fatcat:ktuedgckvfhszncafbuyefwwrq