=ADD= =reftype= 14 =number= 03-11 =url= ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2003/03-11.ps.gz =year= 2003 =month= 11 =author= Athale; Rahul Ramesh + Lopez Diaz; Glauco Alfredo =title= Explaining Schwarz's \textsc{lodef} algorithm with examples =abstract= We study the Schwarz's \textsc{lodef} algorithm for factoring linear ordinary differential homogeneous operators with the help of examples. First, a simple example shows that additional steps, that are not explicitly mentioned in the algorithm, are necessary to get a solution. Second, we give step by step solution of the example mentioned in the original paper, by the application of the algorithm. =sponsor= Fonds zur F{\"o}rderung der wiss, project \textsc{det,}. Forschung, P16357-N04 =keywords= linear ordinary differential operators, factorization