sympy中abs()、sqrt()返回值无法与数值比较该如何解决？

报错的核心原因是：SymPy对包含abs()、sqrt()的表达式求导、代入数值后，返回的仍然是SymPy自定义的符号类型对象（而非Python原生数值类型），Python原生的比较运算符无法直接对这类对象做数值判断，因此抛出错误。

只需要对代入后的结果做两步处理即可：

• 求导后先调用sympy.simplify()化简表达式，消除残留的符号逻辑
• 代入数值后用float()强制转换为Python原生浮点数，再做大小比较

import sympy
import math
import numpy as np

def check_inc_des(f, x_min=-100, x_max=100, n_sample=100):
  x = sympy.symbols('x')
  expr = f(x)
  # 提前计算导数，避免循环里重复计算
  diff_expr = sympy.simplify(sympy.diff(expr, x))
  limit_expr = sympy.limit(expr, x, 0)
  b = ""
  d = ""
  if limit_expr == -math.inf or limit_expr == math.inf:
    for k in np.linspace(x_min, -0.5, n_sample):
        a = float(diff_expr.subs(x, k))
        if a < 0:
          b = "The function is decreasing in the interval (-oo;0)"
          break 
        if a > 0:
          b = "The function is increasing in the interval (-oo;0)"
          break
    for k in np.linspace(0.5, x_max, n_sample):
        a = float(diff_expr.subs(x, k))
        if a > 0:
          d = "The function is increasing in the interval (0;+oo)"
          break
        if a < 0:
          d = "The function is decreasing in the interval (0;+oo)"
          break
    return b + "\n" +" "+ d
  else:
    a_val = 0
    h_val = 0
    for k in np.linspace(x_min, -0.5, n_sample):
        a = float(diff_expr.subs(x, k))
        if a < 0:
          b = "The function is decreasing in the interval (-oo;0)"
          a_val = -1
          break 
        if a > 0:
          b = "The function is increasing in the interval (-oo;0)"
          a_val = 1
          break
    for k in np.linspace(0.5, x_max, n_sample):
        h = float(diff_expr.subs(x, k))
        if h > 0:
          d = "The function is increasing in the interval (0;+oo)"
          h_val = 1
          break
        if h < 0:
          d = "The function is decreasing in the interval (0;+oo)"
          h_val = -1
          break
    if a_val < 0 and h_val < 0:
      return "The function is decreasing in the Real number"
    if a_val > 0 and h_val > 0:
      return "The function is increasing in the Real number"
    return b + "\n"+" "+ d

def do_ex_3(fa):
    func_lst = [fa]
    for func in func_lst:
        print(check_inc_des(func))
    return

# 测试1：原测试用例x^(-5)
def f_3x_a(x):
    return x**(-5)
# 测试2：sqrt(abs(x))
def f_test2(x):
    return sympy.sqrt(sympy.abs(x))
# 测试3：1/(abs(x))
def f_test3(x):
    return 1/(sympy.abs(x))

print("测试x^(-5)：")
do_ex_3(f_3x_a)
print("\n测试sqrt(abs(x))：")
do_ex_3(f_test2)
print("\n测试1/(abs(x))：")
do_ex_3(f_test3)

测试x^(-5)：
The function is decreasing in the interval (-oo;0)
 The function is decreasing in the interval (0;+oo)

测试sqrt(abs(x))：
The function is decreasing in the interval (-oo;0)
 The function is increasing in the interval (0;+oo)

测试1/(abs(x))：
The function is increasing in the interval (-oo;0)
 The function is decreasing in the interval (0;+oo)

内容的提问来源于stack exchange，提问作者Znone