Algebraic structure behind Odrzywo{\l}ek's EML operator

TL;DR

This paper explores the algebraic structure of Odrzywo{ }lek's EML operator, revealing its underlying abelian group properties and functional inverse relationships, which facilitate the construction of various elementary functions.

Contribution

It uncovers the algebraic and group-theoretic foundations of the EML operator, providing new insights into its recursive application and functional capabilities.

Findings

The EML operator forms an abelian group structure.

Recursive application of the operator generates all elementary functions.

The operator's structure reveals a constructive path to diverse functional families.

Abstract

The binary EML operator yields all (transcendental) elementary functions by recursive application, or a binary tree. The structure of the operator itself carries two distinct ingredients: that of an abelian group, and of functional inverse, which reveal a constructive path to many distinct functional families.