I was reading Wikipedia and came across the equation $e^Tx^2 + \frac{1}{T}xy + \sin(T)z-2=0$ and Wikipedia says that it is not a polynomial equation in the four variables $x,y,z$ and $T$ over the rational numbers(since sine, exponentiation, and $\frac{1}{T}$ aren't polynomial functions). However, it claims that it is a polynomial equation in the three variables $x,y$ and $z$ over the field of the elementary functions in the variable $T$.
Well, I don't have any idea to what it means by the latter sentence while former one is apparently clear. Would you kindly help me to grasp the meaning?
A polynomial in x,y,z over a field K is defined as a $\sum a_{i}\cdot x^{j}\cdot y^{l}\cdot z^{h}$ with $a_{k}$ elements of the Field and powers j,l,h as values of three $\mathbb{N}$-valued functions in i . If you now consider the Field of Elementary functions which can be seen as "all functions you could see in school and their compositions,sums and products", your function has exactly that form, because it is a sum of mixed powers of x,y,z weighted by elementary functions.