### 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.

Original language | English |
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Publisher | ArXiv |

Number of pages | 39 |

Publication status | Submitted - 30 Sep 2019 |

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### Keywords

- Supertropical algebra
- supertropical modules
- bilinear forms
- quadratic forms
- quadratic pairs
- ray spaces
- convex sets
- quasilinear sets
- Cauchy-Schwarz ratio
- Cauchy-Schwarz functions
- QL-stars