Applying parallel/distributed computing to advanced algebraic computations

PVM-based parallel/distributed computation tools have been designed, implemented, and applied to two important mathematical algorithms. The tools make PVM easier to use and applicable to a wider class of computations. The application shows how advanced algebraic algorithms can take advantage of modern parallel/distributed computing with the aid of such tools. The tools and interfaces described include PVM-ET (a set of enhancement tools for PVM), PvmJobs (a general bag of jobs library that works with any user created job structure in a master/slave paradigm), and SaclibPvm (a simple software package interfacing SACLIB to PVM). The ability to interface symbolic computing to PVM allows us to tackle the parallelization of the Grobner bases algorithm and the characteristic sets method, two very compute intensive algorithms important in algebraic computations. These algorithms, their parallelization, and experimental results are presented