Efficiently find and work modulo a submodule of M0 early in the computation

Develop an algorithmic strategy to efficiently discover a nontrivial submodule of the zero-sum submodule M0 ⊂ M early in creative telescoping computations and to work modulo this submodule in order to avoid computing non-minimal telescopers or recurrences.

Background

When the minimal telescoper L is not the minimal recurrence Lmin, a nonzero submodule contained in M0 exists but may be identified only after computing L, which is too late to yield computational savings.

An early detection mechanism for such submodules would allow the algorithm to quotient them out and reduce complexity from the outset.