Abstract

In this paper, we consider the problem of constructing the first terms of formal Laurent series that act as solutions to a given component y_k (\(1 \leqslant k \leqslant m\)) of a vector of unknowns y for a differential system \(y{\kern 1pt} ' = Ay\), where \(y = {{({{y}_{1}}, \ldots ,{{y}_{m}})}^{T}}\) and A is an m × m matrix whose elements are d-truncations of formal Laurent series, i.e., their first terms up to the degree \(d \geqslant 0\) inclusive. An algorithm for solving this problem based on the truncated series Laurent solution (TSLS) algorithm is proposed. The first terms of the formal Laurent solutions for y_k constructed by the proposed algorithm are invariant to possible continuations of elements of the original system’s matrix.

中文翻译：

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截断微分系统的部分Laurent解的构造

摘要

在本文中，我们考虑构造一个形式上的Laurent级数的第一项的问题，该Laurent级数是对差分系统y的向量y的给定分量y _k（\（1 \ leqslant k \ leqslant m \））的求解\（y {\ kern 1pt}'= Ay \），其中\（y = {{（{{y} _ {1}}，\ ldots，{{y} _ {m}}）} ^ {T} } \）和阿是米×米矩阵，其元素为d -截短正式劳伦系列，即，它们的第一项到的程度\（d \ geqslant 0 \）包括的。提出了一种基于截断级数Laurent解（TSLS）算法的求解算法。由所提出的算法构造的y _k的形式Laurent解的第一项对于原始系统矩阵的元素的可能延续是不变的。