HeightOfAPolynomial 2003-04-07 23:19:44 2003-04-07 23:19:44 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \PMlinkescapeword{height} Let $P = a_0 + a_1x + \ldots + a_nx^n \in \mathbb{C}[x]$ be a polynomial with complex coefficients. The height of $P$ is \begin{displaymath} H(P) = \operatorname{max}\{\mid a_0 \mid ,\mid a_1 \mid , \ldots , \mid a_n \mid\}. \end{displaymath}