2 papers
math.MG2025
Convex geometry over ordered hyperfields
James Maxwell, Ben Smith
We initiate the study of convex geometry over ordered hyperfields. We define convex sets and halfspaces over ordered hyperfields, presenting structure theorems over hyperfields ari…
math.AG2024
Geometry of tropical extensions of hyperfields
James Maxwell, Ben Smith
We study the geometry of tropical extensions of hyperfields, including the ordinary, signed and complex tropical hyperfields. We introduce the framework of 'enriched valuations' as…