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A finegrained parallel completion procedure
 IN ISSAC ’94: PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION
, 1994
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Parsac2: Parallel Computer Algebra On The DeskTop
, 1995
"... We give an introduction to programming methods, software systems, and algorithms, suitable for parallelizing Computer Algebra on modern multiprocessor workstations. As concrete examples we present multithreaded programming and its use in the PARSAC2 system for parallel symbolic computation, and we ..."
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We give an introduction to programming methods, software systems, and algorithms, suitable for parallelizing Computer Algebra on modern multiprocessor workstations. As concrete examples we present multithreaded programming and its use in the PARSAC2 system for parallel symbolic computation, and we present some examples of parallel algorithms useful for solving systems of polynomial equations.
A Parallel Gröbner Factorizer
, 1994
"... We report on some experience with a parallel version of the Gröbner basis algorithm with factorization, implemented in the REDUCE package CALI [4]. It is based on a coarse grain parallel masterslave model with distributed memory. This model was realized on an HP workstation cluster both with a disk ..."
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We report on some experience with a parallel version of the Gröbner basis algorithm with factorization, implemented in the REDUCE package CALI [4]. It is based on a coarse grain parallel masterslave model with distributed memory. This model was realized on an HP workstation cluster both with a disk remote connection based on (ordinary) REDUCE [9] and the special PVMbased parallel REDUCE version of H. Melenk and W. Neun [7]. Our considerations focus on a detailed study of the practical time behaviour of the parallelized improved Gröbner factorization algorithm [5]. For well splitting examples, where the number of intermediate subproblems is large compared to the number of parallel processes available on the system (only for such examples this approach makes sense), we've got almost always a good load balance. Since even for the relative slow disk remote connection the results are encouraging, we conclude that with a fast and stable communication hard and software one will obtain a serious speed up on such problems compared to the serial implementation.
COMPUTERALGEBRA ON A KSR1 PARALLEL COMPUTER
"... Abstract: We give a preliminary report on the implementation of the MAS computer algebra system on a KSR1 virtual shared memory parallel computer with 32 processors. The first topics discussed are dynamic memory management with garbage collection, a parallel integer product, and a parallel version o ..."
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Abstract: We give a preliminary report on the implementation of the MAS computer algebra system on a KSR1 virtual shared memory parallel computer with 32 processors. The first topics discussed are dynamic memory management with garbage collection, a parallel integer product, and a parallel version of Buchbergers Gröbner Basis algorithm. 1. Computer Algebra. Computer algebra software is concerned with exact and symbolic computation. E.g. with the computation of the following expressions. The computation of large numbers (e.g. 1000!), the expansion of polynomial expressions (e.g. (x+y)^20), the symbolic integration of functions (e.g. int(sin(x),x)) or the determination of all solutions to systems of algebraic equations (e.g. solve({x+2*y = 2, x^23*y = 10},{x,y})). Prominent products in this class of software are Maple, Mathematica, Reduce and Derive. With the availability of parallel computing hardware several attempts have been made to port computer algebra software to this machines. For an overview see the conference proceedings [3, 12] and the report [11]. It turned out that shared memory multiprocessor machines [7, 6] and also workstation clusters [10] are well suited for the implementation of computer algebra software.
Parallel Buchberger Algorithms on Virtual Shared Memory KSR1
, 1994
"... We develop parallel versions of Buchbergers Gröbner Basis algorithm for a virtual shared memory KSR1 computer. A coarse grain version does Spolynomial reduction concurrently and respects the same critical pair selection strategy as the sequential algorithm. A fine grain version parallelizes polynom ..."
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We develop parallel versions of Buchbergers Gröbner Basis algorithm for a virtual shared memory KSR1 computer. A coarse grain version does Spolynomial reduction concurrently and respects the same critical pair selection strategy as the sequential algorithm. A fine grain version parallelizes polynomial reduction in a pipeline and can be combined with the parallel Spolynomial reduction. The algorithms are designed for a virtual shared memory architecture and a dynamic memory management with concurrent garbage collection implemented in the MAS computer algebra system. We discuss the achieved speedup figures for up to 24 processors on some standard examples.
Relaxation and Hybrid Approaches for Efficient Polynomial Basis Computation on Distributed Memory Machines
, 1995
"... : Two new approaches to efficiently compute an important polynomial basis (Grobner basis) on distributed memory machines are presented. The first approach is based on relaxation of dependencies present in the sequential computation. For the relaxation approach, speculative parallelism is achieved. I ..."
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: Two new approaches to efficiently compute an important polynomial basis (Grobner basis) on distributed memory machines are presented. The first approach is based on relaxation of dependencies present in the sequential computation. For the relaxation approach, speculative parallelism is achieved. In the hybrid approach, a Grobner basis of a set of polynomials is computed in a treestructured fashion. The upper level nodes compute the Grobner basis using the relaxation approach. This hybrid approach takes advantages of both the treestructured computation and dependency relaxation at upper level nodes in the tree. The hybrid approach provides significant speedups for the examples considered in this paper. Both approaches exploit parallelism in an irregularly structured Grobner basis computation and provide encouraging speedups. A comparative study of both approaches along with some insights on their scalability is provided. The performance data provided in this paper results from experi...