# On k-simple forms of first-order linear differential systems and their computation

@article{Barkatou2013OnKF, title={On k-simple forms of first-order linear differential systems and their computation}, author={M. Barkatou and Carole El Bacha}, journal={J. Symb. Comput.}, year={2013}, volume={54}, pages={36-58} }

In this paper, we develop a direct method for computing a k-simple form (see Pflugel, 2000) of a singular linear differential system of first-order. The k-simple forms give information on the integer slopes of the Newton polygon of the system and are useful in the construction of its formal solutions (see Barkatou and Pflugel, 1998; Pflugel, 2000). We study the arithmetic complexity of our algorithm which has been implemented in Maple and we illustrate it with some examples. Finally, we show… Expand

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