On k-simple forms of first-order linear differential systems and their computation
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 how using this algorithm one can find the minimal Poincare-rank and the formal invariants of the system. (C) 2013 Elsevier B.V. All rights reserved.
k-simple forms first-order linear differential systems newton polygon formal solutions minimal poincare-rank super-reduction local invariants regular/irregular singularities