from fractions import Fraction
from decimal import Decimal
# 分?jǐn)?shù)運(yùn)算
a = Fraction(1, 3)  # 1/3
b = Fraction(1, 2)  # 1/2
print(a + b)  # 輸出: 5/6
# 高精度小數(shù)
c = Decimal('0.1') + Decimal('0.2')
print(c)  # 輸出: 0.3（避免浮點(diǎn)誤差）

import cmath
z = 1 + 2j
print(cmath.sqrt(z))  # 輸出: (1.272...+0.786...j)
print(cmath.phase(z))  # 輻角（弧度）

import numpy as np
# 矩陣運(yùn)算
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
print(A @ B)  # 矩陣乘法
# 特征值與特征向量
eigenvalues, eigenvectors = np.linalg.eig(A)

from scipy.integrate import quad
from scipy.optimize import minimize
# 數(shù)值積分
result, error = quad(lambda x: x**2, 0, 1)  # ∫x2 dx (0→1)
print(result)  # 輸出: 0.333...
# 優(yōu)化問題
res = minimize(lambda x: (x[0]-1)**2 + (x[1]-2)**2, x0=[0, 0])
print(res.x)  # 最優(yōu)解: [1.0, 2.0]

from sympy import symbols, diff, integrate, solve
x, y = symbols('x y')
expr = x**2 + 2*x + 1
# 求導(dǎo)
print(diff(expr, x))  # 輸出: 2*x + 2
# 積分
print(integrate(expr, x))  # 輸出: x**3/3 + x**2 + x
# 解方程
solution = solve(x**2 - 4, x)
print(solution)  # 輸出: [-2, 2]

import random
print(random.random())  # [0, 1) 隨機(jī)浮點(diǎn)數(shù)
print(random.randint(1, 10))  # 1~10 隨機(jī)整數(shù)

from statistics import mean, median, stdev
data = [1, 2, 3, 4, 5]
print(mean(data))  # 平均值: 3.0
print(stdev(data))  # 標(biāo)準(zhǔn)差: 1.581...