def pade(T, n=1):
    """ 
    Create a linear system that approximates a delay.
    
    Return the numerator and denominator coefficients of the Pade approximation.
    
    Parameters
    ----------
    T : number
        time delay
    n : integer
        order of approximation
        
    Returns
    -------       
    num, den : array
        Polynomial coefficients of the delay model, in descending powers of s.
    
    Notes
    -----
    Based on an algorithm in Golub and van Loan, "Matrix Computation" 3rd.
    Ed. pp. 572-574.
    """
    if T == 0:
        num = [1,]
        den = [1,]
    else:
        num = [0. for i in range(n+1)]
        num[-1] = 1.
        den = [0. for i in range(n+1)]
        den[-1] = 1.
        c = 1.
        for k in range(1, n+1):
            c = T * c * (n - k + 1)/(2 * n - k + 1)/k
            num[n - k] = c * (-1)**k
            den[n - k] = c 
        num = [coeff/den[0] for coeff in num]
        den = [coeff/den[0] for coeff in den]
    return num, den