I use a Mathematica package to compute roots and weights (and other things) but the package gives me only the expression of the roots in $\omega$-basis (basis of fundamental weights) and in the $\alpha$-basis (basis of the simple roots). And the same for the weights. So my question is :
Let $V$ be a finite dimensional Euclidean vector space and a root system in $V$. As I said suppose I only have the roots expressed in the $\omega$-basis (or $\alpha$-basis) but I haven't the expression of the fundamental weights in an orthonormal basis of $V$ (nor the simple roots). How can I get the roots expressed in $V$ ? I mean, how can I plot this with the previous informations :
