Cartan integer (source code)

= Cartan integer
{c}
{title2=$\langle\beta,\alpha^\vee\rangle$}

The Cartan integer associated with two roots is
$$
\langle\beta,\alpha^\vee\rangle
=\frac{2(\beta,\alpha)}{(\alpha,\alpha)}.
$$
A crystallographic root system requires every Cartan integer to be an <integer>.