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arXiv math/00041002000-04-15math.ACcs.NAmath-phmath.APmath.MPmath.NAmath.RA

关于Pommaret基与Janet基之间关系的探讨

On the Relation Between Pommaret and Janet Bases

Vladimir P. Gerdt

备注：: 15 pages. LaTeX, uses the Springer file lncse.cls. Submitted to CASC'2000, the Third International Workshop on Computer Algebra in Scientific Computing, October 5-9, Samarkand, Uzbekistan

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AI总结：

本文证明有限Pommaret基必为极小Janet基，改进Zharkov算法计算Janet基，并推广至线性微分理想。

摘要：

本文研究了多项式理想的Pommaret基与Janet基之间的关系。证明了若一个理想具有有限的Pommaret基，则该基是极小的Janet基。文中描述了由Zharkov最初设计的用于计算Janet基的相关算法的改进版本。对于具有有限Pommaret基的理想，该算法可计算出此基。否则，算法计算出的Janet基未必是极小的。所得结果被推广到线性微分理想。

英文摘要：

In this paper the relation between Pommaret and Janet bases of polynomial ideals is studied. It is proved that if an ideal has a finite Pommaret basis then the latter is a minimal Janet basis. An improved version of the related algorithm for computation of Janet bases, initially designed by Zharkov, is described. For an ideal with a finite Pommaret basis, the algorithm computes this basis. Otherwise, the algorithm computes a Janet basis which need not be minimal. The obtained results are generalized to linear differential ideals.

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