Simple forms of higher-order linear differential systems and their applications in computing regular solutions

详细信息    查看全文

• 作者：Moulay A. Barkatou^a ; ^{moulay.barkatou@xlim.fr} ; Thomas Cluzeau^a ; ^{thomas.cluzeau@xlim.fr} ; Carole El Bacha¹ ; ^a ; ^{carole.el-bacha@xlim.fr}
• 关键词：Computer algebra ; Higher-order linear differential systems ; Singularities ; Regular formal solutions ; Matrix polynomials
• 刊名：Journal of Symbolic Computation
• 出版年：2011
• 出版时间：June 2011
• 年：2011
• 卷：46
• 期：6
• 页码：633-658
• 全文大小：418 K

文摘

We propose a direct algorithm for computing regular formal solutions of a given higher-order linear differential system near a singular point. With such a system, we associate a matrix polynomial and we say that the system is simple if the determinant of this matrix polynomial does not identically vanish. In this case, we show that the algorithm developed in Barkatou et al. (2009) can be applied to compute a basis of the regular formal solutions space. Otherwise, we develop an algorithm which, given a non-simple system, computes an auxiliary simple one from which the regular formal solutions space of the original system can be recovered. We also give the arithmetic complexity of our algorithms.