Comparative superiority of reduction-based telescoping approaches for D-finite functions

Determine which of the two competing approaches to reduction-based creative telescoping for D-finite functions—the approach based on Lagrange’s identity and the approach based on integral bases—is superior, in the sense intended by the authors’ remark that the superiority between these two methods remains unclear.

Background

Reduction-based creative telescoping is a modern technique for constructing telescopers by exploiting linear relations among reductions of derivatives or shifts of an integrand or summand. In the D-finite setting, two methodological lines have emerged: one derives telescopers using Lagrange’s identity, while the other leverages integral bases to normalize and reduce expressions.

The authors point out that both approaches are actively used and developed, yet they explicitly state that it is presently unclear which method is superior. Clarifying this would guide algorithm designers and practitioners in choosing methods for computing telescopers for D-finite functions in symbolic computation.