On the Relation Between Pommaret and Janet Bases
Vladimir P.Gerdt
在本文中,研究了庞马雷特和珍妮特多项式理想的基础之间的关系。 事实证明,如果一个理想有一个有限的Pommapret基础,那么后者是一个最小的珍妮特基础。 描述了最初由Zharkov设计的用于计算Janet碱基的相关算法的改进版本。 对于具有有限Pommaret基础的理想,该算法计算此基础。 否则,该算法计算一个不需要最小的Janet基础。 获得的结果被概括为线性差分理想。
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 general...