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.
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In memory of Prof. Eugeny Vasilievich Pankratiev
Deceased. (E. V. Pankratiev)
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 4, pp. 151–166, 2008.
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Kondratieva, M.V., Mikhalev, A.V. & Pankratiev, E.V. Jacobi’s bound for systems of algebraic differential equations. J Math Sci 163, 543–553 (2009). https://doi.org/10.1007/s10958-009-9692-8
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DOI: https://doi.org/10.1007/s10958-009-9692-8