This article mentions the degree and the order of a polynomial in two variables (over $\mathbb{R}$ or over $\mathbb{C}$). I certainly know what is the degree of a polynomial (actually, in any finite number of variables), but I am not familiar with the definition of the order of a polynomial.
I guess the definition of the order of a polynomial is a known notion in algebraic geometry (perhaps I am wrong, and this notion belongs to other mathematical topic than algebraic geometry).
Can someone please explain what is the definition of an order used in the above article?
Perhaps the fourth definition here is the definition I am looking for?
Thank you very much!