On the Relation between Pommaret and Janet Bases

Vladimir P. Gerdt
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Vladimir P. Gerdt: Joint Institute for Nuclear Research, Laboratory of Computing Techniques and Automation

A chapter in Computer Algebra in Scientific Computing, 2000, pp 167-181 from Springer

Abstract: 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.

Keywords: Polynomial Ideal; Hilbert Function; Differential Algebra; Initial Ideal; Linear Differential System (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57201-2_14

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DOI: 10.1007/978-3-642-57201-2_14

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