positiveRoots -- the positive (co)roots of a simple Lie algebra

Let R be an irreducible root system of rank m, and choose a base of simple roots $\Delta = \{\alpha_1,...,\alpha_m\}$. This function returns all the roots that are nonnegative linear combinations of the simple roots (expressed in the basis of fundamental weights). The formulas implemented here are taken from the tables following Bourbaki's Lie Groups and Lie Algebras Chapter 6.

In the example below, we see that for $sl_3$, the positive roots are $\alpha_1$, $\alpha_2$, and $\alpha_1+\alpha_2$.

Each positive root may be written $\alpha = \sum n_i \alpha_i$, where the coefficients $n_i$ are nonnegative integers. The sum $\sum n_i$ is called the level of $\alpha$. The positive roots are ordered first by the level, then lexicographically by their coefficients in the basis of simple roots.