A short proof for the open quadrant problem

2015/02/27 by José F. Fernando, Jose F. Fernando, Fernando, Jose F. +2
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Mathematics and Applications #Polynomial and algebraic computation #math.AG #msc:14P10 #msc:26C99 #msc:52A10

paper · pdf · doi:10.48550/arxiv.1502.07866

8 pages, 1 figure, 1 table

arxiv created 2015/02/27 · arxiv updated 2015/03/02

Abstract

In 2003 it was proved that the open quadrant \x>0,y>0\ of \mathbb R² is a polynomial image of \mathbb R². 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.

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