'Add two simple roots together
The function takes as input two integers, root1 and root2.  It then
uses these integers as keys in the dictionary of simple roots, and gets
the corresponding simple roots, and then adds them together.
Examples
>>> from sympy.liealgebras.root_system import RootSystem
>>> c = RootSystem("A3")
>>> newroot = c.add_simple_roots(1, 2)
>>> newroot
[1, 0, -1, 0]'

def add_simple_roots(self, root1, root2):

    alpha = self.simple_roots()
    if ((root1 > len(alpha)) or (root2 > len(alpha))):
        raise ValueError("You've    used    a    root    that    doesn't    exist!")
    a1 = alpha[root1]
    a2 = alpha[root2]
    newroot = []
    length = len(a1)
    for i in range(length):
        newroot.append((a1[i] + a2[i]))
    return newroot
