On the Relation Between Pommaret and Janet Bases

Details On the Relation Between Pommaret and Janet Bases On the Relation Between Pommaret and Janet Bases

2000-04-15

arxiv.org/abs/math/0004100v1

Mathematics

Commutative Algebra

15 pages. LaTeX, uses the Springer file lncse.cls. Submitted to CASC'2000, the Third International Workshop on Computer Algebr

Scientific paper

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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