A short proof for the open quadrant problem



Downloads per month over past year

Fernando Galván, José Francisco (2017) A short proof for the open quadrant problem. Journal of Symbolic Computation, 79 (1). pp. 57-64. ISSN 0747-7171

[thumbnail of 21libre.pdf] PDF
Restringido a Repository staff only

[thumbnail of 21.pdf]

Official URL: http://www.sciencedirect.com/science/article/pii/S0747717116300839


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.

Item Type:Article
Uncontrolled Keywords:Polynomial maps and images; Semialgebraic sets; Open quadrant
Subjects:Sciences > Mathematics > Algebra
ID Code:40540
Deposited On:02 Feb 2017 10:02
Last Modified:02 Feb 2017 11:45

Origin of downloads

Repository Staff Only: item control page