Geodesic
The ideal of separants in the ring of differential polynomials
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 215-227

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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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     author = {D. V. Trushin},
     title = {The ideal of separants in the ring of differential polynomials},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_1_a12/}
}
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D. V. Trushin. The ideal of separants in the ring of differential polynomials. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 215-227. http://geodesic.mathdoc.fr/item/FPM_2007_13_1_a12/