Details:
Title  Simple forms of higherorder linear differential systems and their applications in computing regular solutions  Author(s)  Carole El Bacha, M.A. Barkatou, Thomas Cluzeau  Type  Article in Journal  Abstract  We propose a direct algorithm for computing regular formal solutions of a given higherorder 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 nonsimple 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.  Keywords  Computer algebra, Higherorder linear differential systems, Singularities, Regular formal solutions, Matrix polynomials  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111000137 
Language  English  Journal  Journal of Symbolic Computation  Volume  46  Number  6  Pages  633  658  Year  2011  Edition  0  Translation 
No  Refereed 
No 
