Bounds for D-finite closure properties

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).

💡 Research Summary

The paper investigates the size of operators that arise when executing closure properties of D‑finite (holonomic) functions. A D‑finite function is defined as a solution of a non‑zero linear operator in an Ore algebra A = R