Unirational fields of transcendence degree one and functional decomposition
Jaime Gutierrez, Rosario Rubio, David Sevilla
TL;DR
This paper introduces algorithms for identifying unirational fields of transcendence degree one that contain specific rational functions and for decomposing multivariate rational functions into compositions of univariate and multivariate functions.
Contribution
It presents novel algorithms for computing unirational fields of transcendence degree one and for decomposing multivariate rational functions into simpler functional compositions.
Findings
Algorithm successfully computes all relevant unirational fields.
Effective decomposition of multivariate rational functions into g(h) form.
Enhanced understanding of the structure of rational functions in algebraic geometry.
Abstract
In this paper we present an algorithm to compute all unirational fields of transcendence degree one containing a given finite set of multivariate rational functions. In particular, we provide an algorithm to decompose a multivariate rational function f of the form f=g(h), where g is a univariate rational function and h a multivariate one.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Algebra and Logic · Polynomial and algebraic computation