Some examples for parallel computations using REDUCE

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 [7] and IMACS ACA 95 [12]. 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 Gröbner package for the calculation of Comprehensive Gröbner bases (defined in [6]). This package uses the also recently released REDLOG (“REDuce LOGic”) package (by Dolzmann and Sturm \cite[13] from Universität 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.