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Preprint Number 821
821. Gal Binyamini
Bezout-type Theorems for Differential Fields
Submission date: 13 January 2015.
We prove analogs of the Bezout and the Bernstein-Kushnirenko-Khovanskii
theorems for systems of algebraic differential conditions over
closed fields. Namely, given a system of algebraic conditions on the
derivatives of an n-tuple of functions, which admits finitely many
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
polytope of the set of conditions. This improves a doubly-exponential
due to Hrushovski and Pillay.
Mathematics Subject Classification: 03C60, 11F03, 12H05, 14G05
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