'Generate the simple roots of the Lie algebra
The rank of the Lie algebra determines the number of simple roots that
it has.  This method obtains the rank of the Lie algebra, and then uses
the simple_root method from the Lie algebra classes to generate all the
simple roots.
Examples
>>> from sympy.liealgebras.root_system import RootSystem
>>> c = RootSystem("A3")
>>> roots = c.simple_roots()
>>> roots
{1: [1, -1, 0, 0], 2: [0, 1, -1, 0], 3: [0, 0, 1, -1]}'

def simple_roots(self):

    n = self.cartan_type.rank()
    roots = {}
    for i in range(1, (n + 1)):
        root = self.cartan_type.simple_root(i)
        roots[i] = root
    return roots
