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 Fundam. Prikl. Mat., 2008, Volume 14, Issue 4, Pages 109–120 (Mi fpm1128)

On the generalized Ritt problem as a computational problem

O. D. Golubitskya, M. V. Kondrat'evab, A. I. Ovchinnikovc

a University of Western Ontario
b M. V. Lomonosov Moscow State University
c University of Illinois at Chicago

Abstract: The Ritt problem asks if there is an algorithm that decides whether one prime differential ideal is contained in another one if both are given by their characteristic sets. We give several equivalent formulations of this problem. In particular, we show that it is equivalent to testing whether a differential polynomial is a zero divisor modulo a radical differential ideal. The technique used in the proof of this equivalence yields algorithms for computing a canonical decomposition of a radical differential ideal into prime components and a canonical generating set of a radical differential ideal. Both proposed representations of a radical differential ideal are independent of the given set of generators and can be made independent of the ranking.

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English version:
Journal of Mathematical Sciences (New York), 2009, 163:5, 515–522

Bibliographic databases:

UDC: 512.628

Citation: O. D. Golubitsky, M. V. Kondrat'eva, A. I. Ovchinnikov, “On the generalized Ritt problem as a computational problem”, Fundam. Prikl. Mat., 14:4 (2008), 109–120; J. Math. Sci., 163:5 (2009), 515–522

Citation in format AMSBIB
\Bibitem{GolKonOvc08} \by O.~D.~Golubitsky, M.~V.~Kondrat'eva, A.~I.~Ovchinnikov \paper On the generalized Ritt problem as a~computational problem \jour Fundam. Prikl. Mat. \yr 2008 \vol 14 \issue 4 \pages 109--120 \mathnet{http://mi.mathnet.ru/fpm1128} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2482036} \transl \jour J. Math. Sci. \yr 2009 \vol 163 \issue 5 \pages 515--522 \crossref{https://doi.org/10.1007/s10958-009-9689-3} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70649115365} 

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• http://mi.mathnet.ru/eng/fpm/v14/i4/p109

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Harrison-Trainor M., Klys J., Moosa R., “Nonstandard Methods for Bounds in Differential Polynomial Rings”, J. Algebra, 360 (2012), 71–86
2. Li W., Li Y.-H., “Computation of Differential Chow Forms For Ordinary Prime Differential Ideals”, Adv. Appl. Math., 72:SI (2016), 77–112
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