Products of Ordinary Differential Operators by Evaluation and Interpolation

Abstract: It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than the previously-known one by a constant factor, and prove that in characteristic zero, multiplication of differential operators and of matrices are computationally equivalent problems. In positive characteristic, we show that differential operators can be multiplied in nearly optimal time. Theoretical results are validated by intensive experiments.