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The Theory of Involutive Divisions and an Application to Hilbert Function Computations

✍ Scribed by Joachim Apel

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
600 KB
Volume
25
Category
Article
ISSN
0747-7171

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✦ Synopsis

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 GrΓΆbner basis and that it is straightforward to compute the (affine) Hilbert function of an ideal I from an arbitrary involutive basis of I.

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