The Maslov dequantization, idempotent and tropical mathematics: A brief introduction

Abstract

This paper is a brief introduction to idempotent and tropical mathematics. Tropical mathematics can be treated as a result of the so-called Maslov dequantization of the traditional mathematics over numerical fields as the Planck constant $\hslash$ tends to zero taking imaginary values.

English and Russian versions. This article, a result of a very considerable expansion of math.GM/0501038, is to appear in Journal of Mathematical Sciences (Notes of Scientific Seminars of the V.A. Steklov Mathematical Institute), see <http://tinyurl.com/a3ahc>. Dedicated to Anatoly Vershik with admiration and gratitude. Russian version to be published in "Zapiski Nauchnykh Seminarov POMI"

References in corpus (7)

• Factorization of polynomials in one variable over the tropical semiring
• The group law on a tropical elliptic curve
• Duality of Tropical Curves
• Toric degenerations of toric varieties and tropical curves
• Tropical Linear Spaces
• Kapranov rank vs. tropical rank
• Mixed toric residues and tropical degenerations