We give an overview on Paclib, a library for parallel algebraic computation on shared memory multiprocessors. Paclib is essentially a package of C functions that provide the basic objects and methods of computer algebra in a parallel context. The Paclib programming model supports concurrency, shared memory communication, non-determinism and speculative parallelism. The system is based on a heap management kernel with parallelized garbage collection that is portable among most Unix machines. We present the successful application of paclib for the parallelization of several algebraic algorithms and discuss the achieved results. 1 Introduction Scientific computing is a rich source of challenging problems such as the solution of systems of partial differential equations. Classical numerical methods operate with efficient finite-precision (floating point) arithmetic and thus quickly yield approximative solutions. However, often one is also interested in certain qualitative aspects like s...

We describe the design of a parallel algorithm for the exact solution of linear equation systems with integer coefficients and the implementation of this algorithm on a shared memory multiprocessor. An efficient solution of the original problem is difficult since the coefficients grow during the computation and arithmetic becomes very time-consuming. Therefore we transform the problem into a problem of determinant computation and apply a modular approach: the system is mapped into several finite fields where the determinants can be efficiently computed. The subresults are combined to yield the original determinants and to compute the solutions of the system. Several parallel versions of this algorithm have been developed and implemented on a shared memory multiprocessor. The programs are applied to equation systems of different characteristics and the results are analyzed and compared. Keywords: Parallel algorithms, scientific computing, computer algebra, shared memory machines. Fund...