from sympy import *


# 定义迭代函数
def exchange(i):
    x = symbols('x')
    eq = pow(x, 3)-85   # 定义初始函数 f(x) = 0 型
    dx = diff(eq, x)        # diff(a,b,c) 函数a对b求c阶导数
    if i == 1:  # 单根时
        c = x - eq / dx
        return c
    else:       # 多重根时
        d = eq/dx
        e = diff(d, x)
        f = x - d/e
        return f


change = exchange(1)
x0 = 4
n = 10
a = 0.5e-4
for k in range(1, n):
    x = change.evalf(subs={'x': x0})  # 把x等于x0 带入计算
    b = abs(x-x0)
    x0 = x
    print('k={:<4} Xk={:<{width}} 绝对误差为{:<{width}}'.format(k, x, b, width=20))
    if b < a:
        # print('k={:<4} Xk={:<{width}} 绝对误差为{:<{width}}'.format(k, x, b,width=20))
        break
    if k == n:
        print('迭代次数达到设置上限')