Python math模块详解 - 标准库数学运算入门指南

# 方式一：导入整个模块（推荐）
import math

# 使用模块前缀调用函数
math.sqrt(16)       # 4.0
math.pi             # 3.141592653589793
math.ceil(3.2)      # 4

# 方式二：导入特定函数
from math import sqrt, pi, sin, cos

# 直接使用函数名调用
sqrt(16)            # 4.0
pi                  # 3.141592653589793

# 方式三：导入所有函数（不推荐，可能产生命名冲突）
from math import *

import math

# 数学常量一览
print(f"圆周率 pi  = {math.pi}")
print(f"自然常数 e  = {math.e}")
print(f"2*pi (tau) = {math.tau}")
print(f"正无穷 inf  = {math.inf}")
print(f"非数字 nan  = {math.nan}")

# 验证常量之间的关系
print(f"\n2 * pi == tau: {2 * math.pi == math.tau}")
print(f"e 的自然对数: {math.log(math.e)}")
print(f"pi / 2 的正弦值: {math.sin(math.pi / 2)}")

# 输出：
# 圆周率 pi  = 3.141592653589793
# 自然常数 e  = 2.718281828459045
# 2*pi (tau) = 6.283185307179586
# 正无穷 inf  = inf
# 非数字 nan  = nan
#
# 2 * pi == tau: True
# e 的自然对数: 1.0
# pi / 2 的正弦值: 1.0

import math

# 平方根与幂运算
print(f"sqrt(16)   = {math.sqrt(16)}")
print(f"pow(2, 10) = {math.pow(2, 10)}")
print(f"2 ** 10    = {2 ** 10}")  # 注意类型差异

# 对数运算
print(f"\nlog(e)      = {math.log(math.e)}")
print(f"log2(1024)  = {math.log2(1024)}")
print(f"log10(1000) = {math.log10(1000)}")

# 取整运算
print(f"\nceil(3.2)   = {math.ceil(3.2)}")
print(f"floor(3.8)  = {math.floor(3.8)}")
print(f"trunc(-3.8) = {math.trunc(-3.8)}")

# 绝对值与符号
print(f"\nfabs(-5.3)    = {math.fabs(-5.3)}")
print(f"copysign(3, -1) = {math.copysign(3, -1)}")

# 输出：
# sqrt(16)   = 4.0
# pow(2, 10) = 1024.0
# 2 ** 10    = 1024
#
# log(e)      = 1.0
# log2(1024)  = 10.0
# log10(1000) = 3.0
#
# ceil(3.2)   = 4
# floor(3.8)  = 3
# trunc(-3.8) = -3
#
# fabs(-5.3)    = 5.3
# copysign(3, -1) = -3.0

import math

# 阶乘运算
print(f"5!  = {math.factorial(5)}")
print(f"10! = {math.factorial(10)}")
print(f"0!  = {math.factorial(0)}")  # 0的阶乘为1

# 最大公约数
print(f"\ngcd(12, 8)   = {math.gcd(12, 8)}")
print(f"gcd(100, 75) = {math.gcd(100, 75)}")
print(f"gcd(17, 23)  = {math.gcd(17, 23)}")  # 互质

# 斜边长（勾股定理）
print(f"\nhypot(3, 4)    = {math.hypot(3, 4)}")
print(f"hypot(5, 12)   = {math.hypot(5, 12)}")

# 浮点数拆分
print(f"\nmodf(3.14)  = {math.modf(3.14)}")   # (小数部分, 整数部分)
print(f"frexp(8.0)  = {math.frexp(8.0)}")     # (0.5, 4) 即 0.5 * 2^4 = 8.0

# 近似相等判断
print(f"\nisclose(0.1 + 0.2, 0.3) = {math.isclose(0.1 + 0.2, 0.3)}")
print(f"0.1 + 0.2 == 0.3       = {0.1 + 0.2 == 0.3}")  # 浮点精度问题

# 输出：
# 5!  = 120
# 10! = 3628800
# 0!  = 1
#
# gcd(12, 8)   = 4
# gcd(100, 75) = 25
# gcd(17, 23)  = 1
#
# hypot(3, 4)    = 5.0
# hypot(5, 12)   = 13.0
#
# modf(3.14)  = (0.14000000000000012, 3.0)
# frexp(8.0)  = (0.5, 4)
#
# isclose(0.1 + 0.2, 0.3) = True
# 0.1 + 0.2 == 0.3       = False