. We have extended the task management scheme for the parallel computer algebra package PACLIB. This extension supports "virtual tasks" (tasks that are not yet executable) which are created more efficiently than "real tasks" (tasks that are immediately scheduled for execution). Virtual tasks become real only when the system is idling or existing real tasks can be recycled. Consequently, the overhead for task creation and synchronization but also the memory requirements of a parallel program may be reduced. We analyze the system theoretically and experimentally and compare it with another virtual task package. 1 Introduction The purpose of this paper is twofold: first it reports the extension of the task management scheme for a parallel programming package developed at our institute. Second it carefully investigates the semantic and performance consequences of this modification and compares them with the results reported for a system that was developed elsewhere with similar objectives...

. This paper discusses the parallelisation and performance tuning of a typical computer algebra algorithm, LinSolv, using evaluation strategies. We present three steps in the parallelisation process starting with a naive parallel version. As this algorithm uses infinite data structures as intermediate values it is necessary to define very sophisticated strategies in order to improve parallel performance. We also compare the strategic parallel code with pre-strategy code. This comparison shows how evaluation strategies help to localise changes needed for parallelisation. In particular, the separation between algorithmic and parallel code makes the structure of the parallelism much clearer. 1 Introduction Tuning the performance of a parallel algorithm can be a long, tiresome process. A parallel programming model should aid the programmer especially in this stage, allowing him to experiment with different patterns of parallel behaviour. Based on our experiences with developing p...

In this work we describe the use of truncated p-adic expansion for handling rational numbers by parallel algorithms for symbolic computation. As a case study we propose a parallel implementation for solving linear systems over the rationals. The parallelization is based on a multiple homomorphic image technique and the result is recovered by a parallel version of the Chinese remainder algorithm. Using a MIMD machine, we compare the proposed implementation with the classical modular arithmetic, showing that truncated p-adic arithmetic is a feasible tool for solving systems of linear equations working directly over rational numbers. A safe algorithm for computing the p-adic division operation is proposed. The implementation leads to a speedup up to seven by ten processors with respect to the sequential implementation.