Degree of rational mappings, and the theorems of Sturm and Tarski
type: Item
instance of: scholarly article
title: Degree of rational mappings, and the theorems of Sturm and Tarski
zbMATH Open document ID: 1159.14032
published in: Journal of Fixed Point Theory and Applications
publication date: 2008-09-08T00:00:00Z
review text: The paper is an extended version of lecture notes (taken by the second author) of a course given by the first author at the University of Toronto. It gives an algorithm for computing the mapping degree of a rational mapping \(\mathbb{R}\mathbb{P}^1\to\mathbb{R}\mathbb{P}^1,\) which serves as a basic tool for proving Sturm's theorem. The latter in turn is used to prove Tarski's theorem on semialgebraicity of the image of a real semialgebraic set under a polynomial mapping, and the theorem on constructibility of the image of a complex constructible set under a polynomial mapping. References to other modern algorithmic treatments of the latter classical results are missing in the paper -- we can recommend e.g. [\textit{S.~Basu, R.~Pollack} and \textit{M.-F.~Roy}, Algorithms in real algebraic geometry. 2nd ed. Berlin: Springer (2006; Zbl 1102.14041)].
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 14P25
zbMATH DE Number: 5322581
zbMATH Keywords: mapping degree
zbMATH Keywords: semialgebraic set
zbMATH Keywords: Tarski's theorem
zbMATH Keywords: Sturm's theorem
author: A. G. Khovanskii
author: Yuri Burda
reviewed by: Dmitrii V. Pasechnik
MaRDI profile type: Publication
full work available at URL: s11784-008-0065-6
OpenAlex ID: W2082925666
DOI: 10.1007/S11784-008-0065-6
description: scientific article; zbMATH DE number 5322581