Determine whether working modulo N helps when no proper right-factor exists

Determine whether and when working modulo a submodule N ⊂ M yields computational savings even in cases where Ann_D(m, M/N) equals Ann_D(m, M), i.e., where the right-factor equals the full telescoper and no proper factorization is obtained.

Background

The submodule method often accelerates computations by producing right-factors of the telescoper. However, when the telescoper is irreducible with respect to the chosen N, it is unclear whether reductions modulo N still provide a practical speedup.

Clarifying this would guide heuristic choices of N and inform implementation strategies.