Logarithmic Hyperseries
Lou van den Dries, Joris van der Hoeven, Elliot Kaplan
TL;DR
This paper introduces the field of logarithmic hyperseries, defining its structure and natural calculus operations, and characterizes these operations through their fundamental properties.
Contribution
It constructs the field of logarithmic hyperseries and uniquely characterizes differentiation, integration, and composition within this framework.
Findings
Defined the field of logarithmic hyperseries
Constructed natural differentiation, integration, and composition operations
Established the fundamental properties and uniqueness of these operations
Abstract
We define the field of logarithmic hyperseries, construct on natural operations of differentiation, integration, and composition, establish the basic properties of these operations, and characterize these operations uniquely by such properties.
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Taxonomy
TopicsRings, Modules, and Algebras · Scheduling and Optimization Algorithms · Fuzzy Systems and Optimization