A short proof for the open quadrant problem. (March 2017)

• Record Type: Journal Article
• Authors: Fernando, José F.; Ueno, Carlos
• Is Part Of: Journal of symbolic computation. Volume 79(2017)Part 1
• Page Start: 57
• Page End: 64
• Publication Date: 2017-03
• Subjects: 14P10 -- 26C99 -- 52A10; Polynomial maps and images -- Semialgebraic sets -- Open quadrant; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.08.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In 2003 it was proved that the open quadrant Q : = { x > 0, y > 0 } of R 2 is a polynomial image of R 2 . This result was the origin of an ulterior more systematic study of polynomial images of Euclidean spaces. In this article we provide a short proof of the previous fact that does not involve computer calculations, in contrast with the original one. The strategy here is to represent the open quadrant as the image of a polynomial map that can be expressed as the composition of three simple polynomial maps whose images can be easily understood.