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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

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

## 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.

Item Type: | Article |
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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 |

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