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

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