Bounds for D-finite closure properties

TL;DR

This paper establishes bounds on the size, degree, and height of operators resulting from algorithms that perform closure operations on D-finite functions, highlighting how these bounds vary with operator order.

Contribution

It introduces bounds on operator size, degree, and height for D-finite closure algorithms, including order-degree curves for higher order operators.

Findings

Bounds on operator size for small order cases

Degree bounds parameterized by order for higher order operators

Higher order operators can have lower degrees, illustrating order-degree curves

Abstract

We provide bounds on the size of operators obtained by algorithms for executing D-finite closure properties. For operators of small order, we give bounds on the degree and on the height (bit-size). For higher order operators, we give degree bounds that are parameterized with respect to the order and reflect the phenomenon that higher order operators may have lower degrees (order-degree curves).