FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(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 $\$\; \backslash mathfrak\; p\; \$$.
On the one hand, this generalizes our result about the Jacobi bound
for ordinary differential polynomials independent over a prime
differential ideal $\$\; \backslash mathfrak\; p\; \$$ and, on the other hand, the result by
Tomasovic, who proved the Jacobi bound for linear partial differential
polynomials.

Location: http://mech.math.msu.su/~fpm/eng/k08/k084/k08409h.htm

Last modified: February 26, 2009