def simple_root(self, i):
        """The ith simple root of F_4

        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.

        Examples
        ========

        >>> from sympy.liealgebras.cartan_type import CartanType
        >>> c = CartanType("F4")
        >>> c.simple_root(3)
        [0, 0, 0, 1]

        """

        if i < 3:
            return basic_root(i-1, i)
        if i == 3:
            root = [0]*4
            root[3] = 1
            return root
        if i == 4:
            root = [Rational(-1, 2)]*4
            return root
dataset/ETHPy150Open sympy/sympy/sympy/liealgebras/type_f.py/TypeF.simple_root/original