Minimal Completely Factorable Annihilators

We propose an algorithm to construct the minimal annihilating operator of a function or a sequence, when the operator is completely factorable (i.e. can be decomposed in first order factors). The algorithm is designed in the frame of the Ore rings theory and can be used in the differential, difference and q-difference cases. We describe also a Maple implementation of the algorithm. 1 Introduction Constructing a linear ordinary differential operator annihilating a function (an annihilator of the function) is necessary when solving many computer algebra problems. We list some of these problems. P1. Expanding a function as a power series and subsequently investigating the expansion. An annihilator lets one construct the recurrence for the series coefficients and manipulate them ([14, 17]). P2. Solving linear inhomogeneous equations. Some methods use annihilators of the right-hand side ([4, 8]). P3. Integrating. If the minimal annihilator L; ord L = n, of f is given, then one can chec..