New results about super-irreducible forms of a linear differential system. (Q2386089)

This paper is concerned with the study of some formal transformations of matrices \( M=M(x)\) whose elements are complex polynomials in \(x\). Such transformations are mainly concerned to the formal solution of linear differential systems with polynomial coefficients \( Y'(x)= M(x) Y(x)\) by application of successive changes of variables. After introducing a lengthy list of notations and definitions, the author establishes some properties of the so called Newton polygons and certain ``super-irreducible'' forms. He claims that these properties can be useful to improve the efficiency of the formal algorithms such as those proposed in the DESIR package (http://www-lmc.imag.fr/MOSAIC/LOGICIELS/desir\_maple/desir2.html) to solve linear differential systems but no examples and practical applications are given.