The open quadrant problem: A topological proof
| Autor: | Fernando, Jose F., Gamboa, J. M., Ueno, Carlos |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this work we present a new polynomial map $f:=(f_1,f_2):{\mathbb R}^2\to{\mathbb R}^2$ whose image is the open quadrant $\{x>0,y>0\}\subset{\mathbb R}^2$. The proof of this fact involves arguments of topological nature that avoid hard computer calculations. In addition each polynomial $f_i\in{\mathbb R}[{\tt x},{\tt y}]$ has degree $\leq16$ and only $11$ monomials, becoming the simplest known map solving the open quadrant problem. Comment: 13 pages, 7 figures |
| Databáze: | arXiv |
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