Details:
Title  Parallel algorithms for Gr\"obnerbasis construction.  Author(s)  V.A. Mityunin, Eugeny V. Pankratiev  Type  Article in Journal  Abstract  The problem of the Gröbnerbasis construction is important both from the theoretical and applied points of view. As examples of applications of Gröbner bases, one can mention the consistency problem for systems of nonlinear algebraic equations and the determination of the number of solutions to a system of nonlinear algebraic equations. The Gröbner bases are actively used in the constructive theory of polynomial ideals and at the preliminary stage of numerical solution of systems of nonlinear algebraic equations. Unfortunately, many real examples cannot be processed due to the high computational complexity of known algorithms for computing the Gröbner bases. However, the efficiency of the standard basis construction can be significantly increased in practice. In this paper, we analyze the known algorithms for constructing the standard bases and consider some methods for increasing their efficiency. We describe a technique for estimating the efficiency of paralleling the algorithms and present some estimates.  ISSN  10723374; 15738795/e 
URL 
http://link.springer.com/article/10.1007%2Fs109580070136z 
Language  English  Journal  J. Math. Sci., New York  Volume  142  Number  4  Pages  22482266  Publisher  Springer US, New York, NY  Year  2007  Edition  0  Translation 
No  Refereed 
No 
