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 socalled 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  07477171  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  683704  Publisher  Academic Press, Inc.  Address  Duluth, MN, USA  Year  1998  Month  June  Translation 
No  Refereed 
No  Organization 
Universität Leipzig 
