A factorization algorithm for linear ordinary differential equations

The reducibility and factorization of linear homogeneous differential equations are of great theoretical and practical importance in mathematics. Although it has been known for a long time that factorization is in principle a decision procedure, its use in an automatic differential equation solver requires a more detailed analysis of the various steps involved. Especially important are certain auxiliary equations, the so-called associated equations. An upper bound for the degree of its coefficients is derived. Another important ingredient is the computation of optimal estimates for the size of polynomial and rational solutions of certain differential equations with rational coefficients. Applying these results, the design of the factorization algorithm LODEF and its implementation in the Scratchpad II Computer Algebra System is described.