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JOURNALS // Fundamentalnaya i Prikladnaya Matematika // Archive

Fundam. Prikl. Mat., 2008 Volume 14, Issue 4, Pages 151–166 (Mi fpm1131)

This article is cited in 2 papers

Jacobi's bound for systems of algebraic differential equations

M. V. Kondrat'eva, A. V. Mikhalev, E. V. Pankratiev

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 512.628


 English version:
Journal of Mathematical Sciences (New York), 2009, 163:5, 543–553

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