human
Solve the following python programming problem given the following code:
def Gram_matrix(self, F, F1, F2, lower, upper) : 
    '
        Return the Gram matrix of the vector of functions F with respect to the
        RKHS norm. The use of this function is limited to input_dim=1.

        :param F: vector of functions
        :type F: np.array
        :param F1: vector of derivatives of F
        :type F1: np.array
        :param F2: vector of second derivatives of F
        :type F2: np.array
        :param lower,upper: boundaries of the input domain
        :type lower,upper: floats
        ' 
    assert (self.input_dim == 1) 
    def L(x, i) : 
        return ((((3.0 / (self.lengthscale ** 2)) * F [i] (x)) + (((2 * np.sqrt (3)) / self.lengthscale) * F1 [i] (x))) + F2 [i] (x)) 
n = F.shape [0] 
    G = np.zeros ((n, n)) 
    for i in range (n) : 
        for j in range (i, n) : 
            G [(i, F)] = G [(j, i)] = integrate.quad ((lambda x : (L (x, i) * L (x, j))), lower, upper) [0] 
Flower = np.array ([f (lower) for f in F]) [:, None] 
    F1lower = np.array ([f (lower) for f in F1]) [:, None] 
    return (((((self.lengthscale ** 3) / ((12.0 * np.sqrt (3)) * self.variance)) * G) + ((1.0 / self.variance) * np.dot (Flower, Flower.T))) + (((self.lengthscale ** 2) / (3.0 * self.variance)) * np.dot (F1lower, F1lower.T))) 

    
    

    Fix the buggy line: G [(i, F)] = G [(j, i)] = integrate.quad ((lambda x : (L (x, i) * L (x, j))), lower, upper) [0]
assistant
#Here is Python program to fix the buggy line: G [(i, F)] = G [(j, i)] = integrate.

G [(i, j)] = G [(j, i)] = integrate.quad ((lambda x : (L (x, i) * L (x, j))), lower, upper) [0]