Standard bases of differential ideals View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1991

AUTHORS

François Ollivier

ABSTRACT

The aim of this paper is to introduce a new definition of standard bases of differential ideals, allowing more general orderings than the previous one, given by Giuseppa Carrá-Ferro, and following the general definition of standard bases, given in [O3], valid for algebraic ideals, canonical bases of subalgebras, etc. Differential standard bases, as canonical bases, suffer a great limitation: they can be infinite, even for ideals of finite type. Nevertheless, we can sometimes bound the order of intermediate computations, necessary to make some elements of special interest appear in the basis. As an illustration, we consider a differential rational map f: A F n →A F n , and show that if f is birational, then ord f −1≤n ord f. Partial standard bases computations provide then two algorithms to test the existence of f −1. The first one is also able to determine the inverse, if any. The second only determines existence, but we can provide a bound of complexity depending only of n, ord f and the number of derivatives. More... »

PAGES

304-321

Book

TITLE

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

ISBN

978-3-540-54195-0
978-3-540-47489-0

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/3-540-54195-0_60

DOI

http://dx.doi.org/10.1007/3-540-54195-0_60

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009172552


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