2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57941For functions defined on C^n or (R_+)^n we construct a dequantization transform, which is closely related to the Maslov dequantization. The subdifferential at the origin of a dequantized polynomial coincides with its Newton polytope. For the semiring of polynomials with nonnegative coefficients, the dequantization transform is a homomorphism of this semiring to the idempotent semiring of convex polytopes with the well-known Minkowski operations. Using the dequantization transform we generalize these results to a wide class of functions and convex sets.7 pagesMathematical PhysicsAlgebraic Geometry81Q20, 14M25; 51P05, 52A20, 52B20text