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A short proof for the open quadrant problem

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.
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Conference papers
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https://hal.inria.fr/hal-01350994
Contributor : Alain Monteil <>
Submitted on : Tuesday, August 2, 2016 - 1:57:30 PM
Last modification on : Tuesday, February 26, 2019 - 10:55:14 AM

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Distributed under a Creative Commons Attribution 4.0 International License

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  • HAL Id : hal-01350994, version 1
  • ARXIV : 1502.07866

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Fernando José, Carlos Ueno. A short proof for the open quadrant problem. MEGA'2015 (Special Issue), Jun 2015, Trento, Italy. ⟨hal-01350994⟩

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