Basicness of semialgebraic sets
type: Item
instance of: scholarly article
title: Basicness of semialgebraic sets
zbMATH Open document ID: 0958.14040
DOI: 10.1023/A:1005123421867
author: Yanyan Li
published in: Geometriae Dedicata
publication date: 2000-02-07T00:00:00Z
review text: A semialgebraic subset in a real algebraic variety is called basic if it is the set of solutions to a system of polynomial inequalities. The main result of the paper is that the basicness of semialgebraic sets on an affine variety defined over the field of real algebraic numbers is decidable. Another result is an explicit recursive decision procedure for basicness, each time splitting the original problem to a finite number of similar ones in one dimension less by desingularizing the ambient variety and the boundary of the semialgebraic set and passing to this boundary.
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 03B25
zbMATH DE Number: 1384282
zbMATH Keywords: semialgebraic sets
zbMATH Keywords: decidability of basicness
zbMATH Keywords: fans
zbMATH Keywords: real prime divisors
zbMATH Keywords: recursive decision
reviewed by: Eugenii I. Shustin
MaRDI profile type: Publication
full work available at URL: a:1005123421867
OpenAlex ID: W1562477214
description: scientific article; zbMATH DE number 1384282