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Preprint Number 821
821. Gal Binyamini Bezout-type Theorems for Differential Fields E-mail: Submission date: 13 January 2015. Abstract: We prove analogs of the Bezout and the Bernstein-Kushnirenko-Khovanskii
theorems for systems of algebraic differential conditions over
differentially
closed fields. Namely, given a system of algebraic conditions on the
first l
derivatives of an n-tuple of functions, which admits finitely many
solutions,
we show that the number of solutions is bounded by an appropriate constant
(depending singly-exponentially on n and l) times the volume of the
Newton
polytope of the set of conditions. This improves a doubly-exponential
estimate
due to Hrushovski and Pillay. Mathematics Subject Classification: 03C60, 11F03, 12H05, 14G05 Keywords and phrases: |

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