Parallelization of matrix algorithms for Gröbner basis computation
✍ Scribed by D. E. Alexandrov; V. V. Galkin; A. I. Zobnin; M. V. Levin
- Publisher
- Springer US
- Year
- 2009
- Tongue
- English
- Weight
- 218 KB
- Volume
- 163
- Category
- Article
- ISSN
- 1573-8795
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Intermediate coefficient swell is a well-known difficulty with Buchberger's algorithm for computing Gröbner bases over the rational numbers. p-Adic and modular methods have been successful in limiting intermediate coefficient growth in other computations, and in particular in the Euclidian algorithm
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This paper reports our work on parallelizing an algorithm computing Gröbner bases on a distributed memory parallel machine. When computing Gröbner bases, the efficiency of computation is dominated by the total number of S-polynomials. To decrease the total number of S-polynomials it is necessary to