Formal reduction of singular linear differential systems using eigenrings: A refined approach. (January 2021) - Barkatou, Moulay A.; Saade, Joelle; Weil, Jacques-Arthur
Abstract: This paper provides a new algorithm for the formal reduction of linear differential systems with Laurent series coefficients. We show how to obtain a decomposition of Balser, Jurkat and Lutz using eigenring techniques. This allows us to establish structural information on the obtained indecomposable subsystems and retrieve information on their invariants such as ramification. We show why classical algorithms then perform well on these subsystems. We also give precise estimates of the precision on the power series which is required in each step of our algorithm. The algorithm is implemented in Maple and examples are given in Saade (2018) .