Algorithms for determination of T-module structures on some extension groups

In their recent work the second and the third authors extended the methods of M. A. Papanikolas and N. Ramachandran and determined the t-module structure on [Formula: see text] where [Formula: see text] and [Formula: see text] were Anderson t-modules over [Formula: see text] of some specific types. This approach involved the concept of biderivation and certain reduction algorithm. In this paper, we generalize these results and present a complete algorithm for computation of t-module structure on [Formula: see text] for t-modules [Formula: see text] and [Formula: see text] such that [Formula: see text] The last condition is not sufficient for our algorithm to be executable. We show that it can be applied when the matrix at the biggest power of [Formula: see text] in [Formula: see text] is invertible. We also introduce a notion of [Formula: see text]-composition series which we find suitable for the additive category of t-modules and show that under certain assumptions on the composition series of [Formula: see text] and [Formula: see text] our algorithm is also executable.