'Add two roots together if and only if their sum is also a root
It takes as input two vectors which should be roots.  It then computes
their sum and checks if it is in the list of all possible roots.  If it
is, it returns the sum.  Otherwise it returns a string saying that the
sum is not a root.
Examples
>>> from sympy.liealgebras.root_system import RootSystem
>>> c = RootSystem("A3")
>>> c.add_as_roots([1, 0, -1, 0], [0, 0, 1, -1])
[1, 0, 0, -1]
>>> c.add_as_roots([1, -1, 0, 0], [0, 0, -1, 1])
\'The sum of these two roots is not a root\''

def add_as_roots(self, root1, root2):

    alpha = self.all_roots()
    newroot = []
    for entry in range(len(root1)):
        newroot.append((root1[entry] + root2[entry]))
    if (newroot in alpha.values()):
        return newroot
    else:
        return 'The    sum    of    these    two    roots    is    not    a    root'
