(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 4, PAGES 151-166

## Jacobi's bound for systems of algebraic differential equations

M. V. Kondratieva
A. V. Mikhalev
E. V. Pankratiev

Abstract

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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.

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