Details:

Title	The theory of involutive divisions and an application to Hilbert function computations
Author(s)	Joachim Apel
Type	Article in Journal
Abstract	Generalising the divisibility relation of terms we introduce the lattice of so-called involutive divisions and define the admissibility of such an involutive division for a given set of terms. Based on this theory we present a new approach for building a general theory of involutive bases of polynomial ideals. In particular, we give algorithms for checking the involutive basis property and for completing an arbitrary basis to an involutive one. It turns out that our theory is more constructive and more flexible than the axiomatic approach to general involutive bases due to Gerdt and Blinkov. Finally, we show that an involutive basis contains more structural information about the ideal of leading terms than a Grobner basis and that it is straightforward to compute the (affine) Hilbert function of an ideal I from an arbitrary involutive basis of al I.
Length	23
ISSN	0747-7171
Copyright	Academic Press
File
URL	http://dx.doi.org/10.1006/jsco.1997.0194
Language	English
Journal	Journal of Symbolic Computing
Volume	25
Number	6
Pages	683--704
Publisher	Academic Press, Inc.
Address	Duluth, MN, USA
Year	1998
Month	June
Translation	No
Refereed	No
Organization