Jacobi's bound for systems of algebraic differential equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 151-166
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This review paper is devoted to the Jacobi bound for systems of partial differential polynomials. We prove the conjecture for the system of $n$ partial differential equations in $n$ differential variables which are independent over a prime differential ideal $\mathfrak p$. On the one hand, this generalizes our result about the Jacobi bound for ordinary differential polynomials independent over a prime differential ideal $\mathfrak p$ and, on the other hand, the result by Tomasovic, who proved the Jacobi bound for linear partial differential polynomials.
@article{FPM_2008_14_4_a9,
author = {M. V. Kondrat'eva and A. V. Mikhalev and E. V. Pankratiev},
title = {Jacobi's bound for systems of algebraic differential equations},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {151--166},
publisher = {mathdoc},
volume = {14},
number = {4},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a9/}
}
TY - JOUR AU - M. V. Kondrat'eva AU - A. V. Mikhalev AU - E. V. Pankratiev TI - Jacobi's bound for systems of algebraic differential equations JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2008 SP - 151 EP - 166 VL - 14 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a9/ LA - ru ID - FPM_2008_14_4_a9 ER -
%0 Journal Article %A M. V. Kondrat'eva %A A. V. Mikhalev %A E. V. Pankratiev %T Jacobi's bound for systems of algebraic differential equations %J Fundamentalʹnaâ i prikladnaâ matematika %D 2008 %P 151-166 %V 14 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a9/ %G ru %F FPM_2008_14_4_a9
M. V. Kondrat'eva; A. V. Mikhalev; E. V. Pankratiev. Jacobi's bound for systems of algebraic differential equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 151-166. http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a9/