Polynomial images of \(\mathbb{R}^n\)
type: Item
instance of: scholarly article
title: Polynomial images of \(\mathbb{R}^n\)
zbMATH Open document ID: 1042.14035
DOI: 10.1016/S0022-4049(02)00121-4
author: José F. Fernando
author: Jose Manuel Gamboa
published in: Journal of Pure and Applied Algebra
publication date: 2003-04-28T00:00:00Z
review text: The authors make a step towards a characterization of polynomial images of a real affine space (which are always semialgebraic according to the Tarski-Seidenberg theorem). The main result is that the complements of finite sets and the open convex polyhedral cones, defined by independent linear forms, in real \(n\)-space are polynomial images of real \(n\)-spaces. For the proof, the authors find explicit polynomial maps realizing the required images. The paper presents several examples and open questions related to the topic.
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 14Q99
Mathematics Subject Classification ID: 14R10
zbMATH DE Number: 1901783
zbMATH Keywords: real closed field
zbMATH Keywords: real semialgebraic set
zbMATH Keywords: polynomial map
reviewed by: Eugenii I. Shustin
MaRDI profile type: Publication
cites work: Q4889879
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full work available at URL: s0022-4049(02)00121-4
OpenAlex ID: W2118722249
description: scientific article; zbMATH DE number 1901783