Compute invariant data directly from the module without constructing the telescoper

Develop an algorithm to compute invariant data—such as the characteristic polynomial or the p-curvature—directly from the isomorphism class of the D-module D/DL (or, in the example of Section 6, from the D-submodule N+ ≅ D/DL), without explicitly computing the telescoper operator L.

Background

In the submodule approach to creative telescoping, one often has access to the D-module structure D/DL that encodes the action of the shift operator on the relevant module, while explicitly computing the telescoper L itself can be expensive or undesirable.

The authors ask whether invariants of L that depend only on the isomorphism class of D/DL (e.g., characteristic polynomial, p-curvature) can be obtained directly from the module, thereby avoiding construction of L. This would provide theoretical and computational advantages when only the module structure is available.