'Every lie algebra has a unique root system.
Given a root system Q, there is a subset of the
roots such that an element of Q is called a
simple root if it cannot be written as the sum
of two elements in Q.  If we let D denote the
set of simple roots, then it is clear that every
element of Q can be written as a linear combination
of elements of D with all coefficients non-negative.
This method returns the ith simple root for E_n.
Examples
>>> from sympy.liealgebras.cartan_type import CartanType
>>> c = CartanType("E6")
>>> c.simple_root(2)
[1, 1, 0, 0, 0, 0, 0, 0]'

def simple_root(self, i):

    n = self.n
    if (i == 1):
        root = ([(-0.5)] * 8)
        root[0] = 0.5
        root[7] = 0.5
        return root
    elif (i == 2):
        root = ([0] * 8)
        root[1] = 1
        root[0] = 1
        return root
    else:
        if ((i == 7) or ((i == 8) and (n == 6))):
            raise ValueError('E6    only    has    six    simple    roots!')
        if ((i == 8) and (n == 7)):
            raise ValueError('E7    has    only    7    simple    roots!')
        return self.basic_root((i - 3), (i - 2))
