BibTeX
@MISC{Zippel96functionaldecomposition,
author = {Richard Zippel},
title = {Functional Decomposition},
year = {1996}
}
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Abstract
This paper presents a polynomial time algorithm for determining when a univariate rational function is the composition of two rational functions, and, if so, finds those rational functions. This algorithm is valid for rational functions over arbitrary fields and thus also resolves an outstanding problem: polynomial decomposition over fields of finite characteristic. In addition, we present a framework that unifies the previous work on polynomial and rational function decomposition and provides some guidance for future work. Contents 1 Introduction 2 2 Applications 3 3 A General Framework 4 3.1 Endomorphisms of A 1 (x) and P 1 (k) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Endomorphisms of A n (k) and P n (k) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 Endomorphisms of Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4 Preliminaries 8 4.1 Geometry . . . . . . . . . . . . . . . . . . . . ...
