The dequantization transform and generalized Newton polytopes

Details The dequantization transform and generalized Newton polytopes The dequantization transform and generalized Newton polytopes

2004-12-25

arxiv.org/abs/math-ph/0412090v2

"Idempotent Mathematics and Mathematical Physics", G. L. Litvinov, V. P. Maslov (eds.), AMS, Providence, 2005, ISBN 0-8218-353

Physics

Mathematical Physics

7 pages

Scientific paper

For 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.

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