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I thank Loic Teyssier and Emil Jerabek who helped me to revise the two previous version This question is motivated by the following fact in complex variable:(I learned this fact from the book of ...

Updated: A polynomial $P(x,y)\in \mathbb{R}[x,y]$ is called an elliptic polynomial if its last homogeneous part does not vanish on $\mathbb{R}^2\setminus\{0\}$.The two answers to this post provide a ...