On the hyperfield or field-of-field concept

Abstract

This article introduces the concept of hyperfield as a recursive field-of-field structure using a Unified Modelling Language (UML) modelling approach in two different variants, the hyperfield instance and hyperfield template models. The recursive property defines a hyperfield of degree n as a representation of a relation between n locations in space, and where the normal field and constant value are special cases. Fields exposing vector space algebra may be used in the construction of a hyperfield of degree n. Inherent properties such as interpolation, dual appearance, fixed points and dual domain are discussed. There is also a description on how to implement the model in a generic programming language environment.