'The Cartan matrix for F_4
The Cartan matrix matrix for a Lie algebra is
generated by assigning an ordering to the simple
roots, (alpha[1], ...., alpha[l]).  Then the ijth
entry of the Cartan matrix is (<alpha[i],alpha[j]>).
Examples
>>> from sympy.liealgebras.cartan_type import CartanType
>>> c = CartanType(\'A4\')
>>> c.cartan_matrix()
Matrix([
[ 2, -1,  0,  0],
[-1,  2, -1,  0],
[ 0, -1,  2, -1],
[ 0,  0, -1,  2]])'

def cartan_matrix(self):

    m = Matrix(4, 4, [2, (-1), 0, 0, (-1), 2, (-2), 0, 0, (-1), 2, (-1), 0, 0, (-1), 2])
    return m
