FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 1, PAGES 215-227

The ideal of separants in the ring of differential polynomials

D. V. Trushin

Abstract

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We obtained the criterion of existence of a quasi-liner polynomial in a differential ideal in the ordinary ring of differential polynomials over a field of characteristic zero. We generalized the "going up" and "going down" theorems onto the case of Ritt algebras. In particular, new finiteness criteria for differential standard bases and estimates that characterize calculation complexity were obtained.

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Last modified: December 21, 2006