On the Relation Between Pommaret and Janet Bases
Commutative Algebra
2025-10-20 v1 Numerical Analysis
Mathematical Physics
Analysis of PDEs
math.MP
Numerical Analysis
Rings and Algebras
Abstract
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.
Cite
@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}
}
Comments
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