Constructive computation of generators for non-holonomic extension modules

Develop a constructive computer-algebra method for computing generators of non-holonomic modules ext¹_D(M,D) associated with differential-operator systems, so that suitable ghost-task columns can be obtained without heuristic enumeration of candidate operators.

Background

Theorem 3.1 guarantees the existence of ghost-task columns whose residue classes generate ext¹_D(M,D), but practical computation of a minimal generating set is a separate algorithmic problem. The paper explains that Macaulay2 can produce a cyclic generator in the holonomic case, whereas the authors resort to looping over candidate operators for non-holonomic extension modules and testing each candidate for torsion-freeness or projectivity.

A constructive method would replace this brute-force fallback and make ghost tasking more systematic for non-holonomic systems, including examples where the extension module is not covered by the available cyclic-generator procedure.