Python 数学计算模块详解

基本数学运算

常用数学计算和数值处理。

import math

def basic_math_operations():
    circle_area = math.pi * math.pow(5, 2)
    square_root = math.sqrt(16)
    natural_log = math.log(math.e)
    return circle_area, square_root, natural_log

def round_numbers(number):
    ceil_value = math.ceil(number)
    floor_value = math.floor(number)
    truncate_value = math.trunc(number)
    return ceil_value, floor_value, truncate_value

三角函数计算

角度与弧度的转换与计算。

def trigonometric_calculations(angle_degrees):
    angle_radians = math.radians(angle_degrees)

    sin_value = math.sin(angle_radians)
    cos_value = math.cos(angle_radians)
    tan_value = math.tan(angle_radians)

    return {
        "sin": sin_value,
        "cos": cos_value,
        "tan": tan_value
    }

def inverse_trigonometric(value):
    asin_value = math.degrees(math.asin(value))
    acos_value = math.degrees(math.acos(value))
    atan_value = math.degrees(math.atan(value))

    return {
        "asin": asin_value,
        "acos": acos_value,
        "atan": atan_value
    }

对数运算

不同底数的对数计算。

def logarithm_operations(number):
    natural_log = math.log(number)
    log2_value = math.log2(number)
    log10_value = math.log10(number)

    return {
        "ln": natural_log,
        "log2": log2_value,
        "log10": log10_value
    }

def custom_base_log(number, base):
    return math.log(number) / math.log(base)

数论函数

整数相关的数学运算。

def number_theory_operations(n, m):
    factorial_n = math.factorial(n)
    gcd_value = math.gcd(n, m)
    lcm_value = abs(n * m) // math.gcd(n, m)

    return {
        "factorial": factorial_n,
        "gcd": gcd_value,
        "lcm": lcm_value
    }

双曲函数

双曲线三角函数计算。

def hyperbolic_functions(x):
    sinh_value = math.sinh(x)
    cosh_value = math.cosh(x)
    tanh_value = math.tanh(x)

    return {
        "sinh": sinh_value,
        "cosh": cosh_value,
        "tanh": tanh_value
    }

数值精度处理

处理浮点数精度问题。

def handle_precision(value, precision=2):
    rounded = round(value, precision)
    formatted = format(value, f".{precision}f")

    return {
        "rounded": rounded,
        "formatted": formatted,
        "is_close": math.isclose(value, rounded,
                               rel_tol=1e-9)
    }

特殊函数

特殊数学函数计算。

def special_functions(x):
    gamma_value = math.gamma(x)
    erf_value = math.erf(x)

    return {
        "gamma": gamma_value,
        "error_function": erf_value
    }