Parallel Integral Multivariate Polynomial 
               Greatest Common Divisor Computation

              Mohamed Omar Rayes (mrayes@iupucs.iupui.edu)


	All of the existing computer algebra systems are sequential.
The underlying algorithms were written in sequential code regardless of
the machine architecture. Many of these algorithms perform poorly even
as processors become faster and storage become less expensive.

	It was the realization of the limited computing power of
uniprocessor computers that led the researchers to look for new ways to
achieve better performance. With the production of parallel computers
and with the dramatic performance of parallel numerical algorithms, it
was natural to investigate the possibility of designing computer
algebra systems that can exploit the collective computing power of
such computers.

	It is the goal of this research to design and implement parallel
algorithms for several computer algebra problems.  In particular, we
will discuss the design and implementation of parallel algorithms for
the multivariate polynomial greatest common divisor (GCD) problem. We
will study the current sequential algorithms and express them in forms
suitable for parallel machine implementation.  Actual programming
timings will be also given.

	In addition, we present a brand new GCD algorithm that is
suitable for parallel (MIMD) machine implementation. Actual programming
timings on the Sequent Balance will be given as well.