On the Relation Between Pommaret and Janet Bases
交换代数
2025-10-20 v1 数值分析
数学物理
偏微分方程分析
math.MP
数值分析
环与代数
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.
引用
@article{arxiv.math/0004100,
title = {On the Relation Between Pommaret and Janet Bases},
author = {Vladimir P. Gerdt},
journal= {arXiv preprint arXiv:math/0004100},
year = {2025}
}
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