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      Cauchy-Schwarz functions and convex partitions in the ray space of a supertropical quadratic form

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          Abstract

          Rays are classes of an equivalence relation on a module V over a supertropical semiring. They provide a version of convex geometry, supported by a "supertropical trigonometry" and compatible with quasilinearity, in which the CS-ratio takes the role of the Cauchy-Schwarz inequality. CS-functions which emerge from the CS-ratio are a useful tool that helps to understand the variety of quasilinear stars in the ray space Ray(V). In particular, these functions induce a partition of Ray(V) into convex sets, and thereby a finer convex analysis which includes the notions of median, minima, glens, and polars.

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          Supertropical semirings and supervaluations

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            Congruences and coordinate semirings of tropical varieties

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              Supertropical quadratic forms I

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                Author and article information

                Journal
                30 September 2019
                Article
                1909.13502
                08299643-bdfe-49f3-ac40-0c0610a607e4

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                39 pages
                math.RA math.AC

                Algebra
                Algebra

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