Decide nontriviality of the zero-sum submodule M0 and construct its elements

Determine decision procedures to test whether the zero-sum submodule M0 = {h + △k(Ω) ∈ M | Σk h is zero for sufficiently large n} is trivial, and develop methods to explicitly construct nonzero elements of M0 in the creative telescoping module M = Ω/△k(Ω).

Background

The zero-sum submodule M0 captures components that sum to zero and thus do not contribute to recurrences for Σk h, explaining why minimal telescopers can exceed minimal recurrences.

Efficiently detecting and exploiting M0 early would avoid computing non-minimal telescopers and improve performance.