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A New Library for Parallel Algebraic Computation
, 1993
"... 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, share ..."
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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, nondeterminism 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 finiteprecision (floating point) arithmetic and thus quickly yield approximative solutions. However, often one is also interested in certain qualitative aspects like s...
Industrial Applications of Computer Algebra: Climbing up a mountain, going down a hill
 In Proc. 3rd European Congress of Mathematics. Vol. 2, Progress in Mathematics
, 2001
"... Abstract. In this paper we present some personal experiences with Computer Algebra applications to industrial problems. In many cases the involved Computer Algebra problems seem as challenging as climbing up a difficult peak. Then one finds out that the trail leads up to a quite rugged hill... This ..."
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Abstract. In this paper we present some personal experiences with Computer Algebra applications to industrial problems. In many cases the involved Computer Algebra problems seem as challenging as climbing up a difficult peak. Then one finds out that the trail leads up to a quite rugged hill... This point of view will be illustrated with “real ” examples coming from robot kinematics and path planning, parametric CAD and shape design in automotive industry. 1. Considerations about the Nature of Computer Algebra Computer Algebra bounces back and forth, from Computer Science to Mathematics. As a scientific discipline Computer Algebra arises, in the 50’s, as a response to the difficulties posed by the first attempts to implement computer programs for analytical integration or differentiation (see the historical chapter in [10]). These programs were, in many cases, application oriented. The addressed difficulties were of various sorts, ranging from very mathematical —for instance, purely algebraic— to very computational, such as the need of a specific memory management policy. No matter how far from the implementation step could happen to be our research in Computer Algebra, we should not forget this: the success of so many symbolic computation programs that have been (and that are being) used to solve so many different problems, is the ultimate responsible for the existence, today, of Computer Algebra as a scientific discipline. There is not a “purely mathematical” Computer Algebra subfield. There are different levels of applicability, i.e. of proximity to an externally given goal... Thus, its achievement should measure the success of the application. This applies, in particular, to Computer Algebra industrial applications. Whether we agree totally, or just in part, or whether we disagree openly with the above statements, we will probably agree that the interest of Computer Algebra industrial applications should be primarily evaluated from the industrial partners ’ side of the picture. But they tend to be, for good or for bad, rather silent. They rarely spend time and energy writing papers, and they usually do not attend Computer Algebra conferences. A negative consequence of this state of things is that we do not have an objective way to provide a solid overview of