Massively Parallel Methods for Free Resolutions

This paper describes work towards an approach to using massively parallel methods for computing syzygies and free resolutions of finitely generated modules over polynomial rings over fields. Our primary focus here is Schreyer’s resolution. Our method exploits the inherent parallelism of the algorithm, primarily utilizing Petri nets, within the GPI-Space [10] framework as our language for parallel workflows. GPI-Space is a task-based workflow management system that employs Petri nets as its coordination layer, while the computation is carried out by the computer algebra system Singular [9]. We outline how the algorithm is modeled through a Petri net, explaining the coordination of tasks and data structures within the parallel computing environment.