问题归结为线性系统方程的解。处获得函数值的一个方程，并从导数方程中获得另外三个方程。那么，三阶多项式是合适的。$f(x_1)$

一种更暴力但不那么聪明的方法是使用计算机代数（例如 SymPy）来获得符号解决方案：

from sympy import *

N = 3 # degree of polynomial - for N + 1 'pieces of information', use a polynomial of degree N

known_x = symbols(["x_%i"%i for i in range(N)])  # create symbols for supporting points
known_derivs = symbols(["d_%i"%i for i in range(N)])  # create symbols for supporting points
y1 = Symbol("y_1")  # the single zeroth derivative we know

# create symbols for the independent variable and the coefficients:
x = Symbol("x")
a = [ Symbol("a_%i"%i) for i in range(N+1) ]

# generate polynomial and the derivative
p = sum([ coeff*x**i for i, coeff in enumerate(a) ])
p_prime = diff(p, x, 1)

# define the equations to solve:
eqns = [ p_prime.subs(x, xi) - d for xi, d in zip(known_x, known_derivs) ]  # equation for the first derivative
eqns.append(p.subs(x, known_x[0]) - y1)

# solve for the coefficients and print solution:
solution = solve(eqns, a)
pretty_sol = [ str(coeff) + " = " + str(value) + "\n"
               for coeff, value in zip(solution.keys(), solution.values()) ]
print("The coefficients are:\n" + "".join(pretty_sol))

这不是很优雅，但即使您为导数添加了另一个方程，这似乎也有效（因此可以对五个方程使用次数为“N = 4”的多项式）。