FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 3, PAGES 747-756

W. Neun

Abstract

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In the last years, the parallel version of the computer algebra system
REDUCE using the Parallel Virtual Machine
(PVM, from Oak Ridge National Laboratory, USA) layer
has been successfully assembled
on almost all massively parallel systems on the market and for workstation
clusters. The general considerations and the system design
together with first results was presented
at the Rhine Workshop 94 and IMACS ACA 95.
This model for parallel computations is in particular well suited
to work for problems with coarse grain
parallelism in local memory environments on massively parallel system or
large networks, but the portable PVM layer allows
one to benefit from any special hardware and/or software features like very
fast networks or special, tuned implementations of PVM.
Nevertheless, on massively parallel system with fast connections and
dedicated nodes, one can apply fine-grain parallelism techniques, too.
Some typical applications which use this system are briefly summarized.
A recent application is an extension of the REDUCE
Gr\"obner package for the calculation of
Comprehensive Gr\"obner bases.
This package uses the also recently released REDLOG
(``REDuce LOGic'') package
(by Dolzmann and Sturm from Universit\"at Passau).
One of the aims of this paper is to further encourage attempts to parallelize
computer algebra algorithms (maybe even using this system). The parallel
version (for Unix) of REDUCE is freely available within the REDUCE
user community.
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