The dequantization transform and generalized Newton polytopes

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dc.creatorLitvinov, G. L.
dc.creatorShpiz, G. B.
dc.date2004-12-25
dc.date2005-01-09
dc.date.accessioned2026-07-07T04:31:46Z
dc.date.available2026-07-07T04:31:46Z
dc.descriptionFor 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.
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0412090
dc.identifierhttp://arxiv.org/abs/math-ph/0412090
dc.identifier"Idempotent Mathematics and Mathematical Physics", G. L. Litvinov, V. P. Maslov (eds.), AMS, Providence, 2005, ISBN 0-8218-3538-6, p. 181-186
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57941
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.subject81Q20, 14M25; 51P05, 52A20, 52B20
dc.titleThe dequantization transform and generalized Newton polytopes
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