Invited speaker: I will attend ACA 2022 in Instanbul, Turkey. I will give a talk for the session about ``D-finite Functions and Beyond: Algorithms, Combinatorics, and Arithmetic''.
Some commands added to FPS: AddHolonomicDE, MulHolonomicDE, and SelfOpHolonomicDE. We are still in the univariate case. Assume you have n (valued positive integer) holonomic DEs DE1, ..., DEn, in the dependent variables y1(t), ...,yn(t), respectively. Then you can compute a differential equation for the sum z(t)=y1(t)+y2(t)+...+yn(t) as follows:
Similarly for the product z(t)=y1(t)*y2(t)*...*yn(t), one uses
Now, if you have a differential equation DE in the dependent variable y(t), and you want to compute a differential equation for a polynomial expression z=p(y(t)), you can proceed as follows: