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

@article{Barkatou2011SimpleFO,
  title={Simple forms of higher-order linear differential systems and their applications in computing regular solutions},
  author={M. Barkatou and T. Cluzeau and Carole El Bacha},
  journal={J. Symb. Comput.},
  year={2011},
  volume={46},
  pages={633-658}
}
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… Expand
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