'Generate all the positive roots of A_n
This is half of all of the roots of A_n; by multiplying all the
positive roots by -1 we get the negative roots.
Examples
>>> from sympy.liealgebras.cartan_type import CartanType
>>> c = CartanType("A3")
>>> c.positive_roots()
{1: [1, -1, 0, 0], 2: [1, 0, -1, 0], 3: [1, 0, 0, -1], 4: [0, 1, -1, 0],
5: [0, 1, 0, -1], 6: [0, 0, 1, -1]}'

def positive_roots(self):

    roots = {1: [0, 1, (-1)], 2: [1, (-2), 1], 3: [1, (-1), 0], 4: [1, 0, 1], 5: [1, 1, (-2)], 6: [2, (-1), (-1)]}
    return roots
