Suppose $f\in C^{\infty}(\mathbb{R}^n)$ and $f(x)=\sum_{|\alpha|=0}^{\infty}a_{\alpha} x^{\alpha}$ for all $x\in\mathbb{R}^n$. Moreover we know a priori that $f$ is algebraic. Is $f$ necessarily a polynomial?If not what are typical counterexamples?