Polynomial/Field/n variables/Directly/Definition

A polynomial ${\displaystyle {}F}$ in the variables ${\displaystyle {}X_{1},\ldots ,X_{n}}$ over a field ${\displaystyle {}K}$ is a finite linear combination of monomials

${\displaystyle {}F=\sum _{\nu }c_{\nu }X^{\nu }\,,}$

where ${\displaystyle {}c_{\nu }\in K}$.