Quasi-optimal multiplication of linear differential operators

TL;DR

This paper demonstrates that linear differential operators with polynomial coefficients can be multiplied efficiently, achieving quasi-optimal computational complexity, thus resolving an open problem in the field.

Contribution

It provides a quasi-optimal multiplication algorithm for linear differential operators with polynomial coefficients, addressing a previously open question.

Findings

Achieves quasi-optimal multiplication time for differential operators.

Resolves an open problem posed by van der Hoeven.

Advances computational methods in symbolic algebra.

Abstract

We show that linear differential operators with polynomial coefficients over a field of characteristic zero can be multiplied in quasi-optimal time. This answers an open question raised by van der Hoeven.