数学math模块55个函数详解.ipynb

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   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数论与表示函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ceil\n",
    "描述：向上取整数，返回 x 的上限，即大于或者等于 x 的最小整数  \n",
    "语法：math.ceil(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
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     "execution_count": 4,
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   ],
   "source": [
    "math.ceil(5.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## copysign()\n",
    "描述：返回一个基于 x 的绝对值和 y 的符号的浮点数。在支持带符号零的平台上，copysign(1.0, -0.0) 返回 -1.0.  \n",
    "语法：math.copysign(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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     "end_time": "2020-05-18T07:46:04.340042Z",
     "start_time": "2020-05-18T07:46:04.335017Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.copysign(-14, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## fabs()\n",
    "描述：返回数字的绝对值  \n",
    "语法：math.fabs( x )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
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     "start_time": "2020-05-18T07:46:51.406917Z"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.0"
      ]
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     "execution_count": 7,
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     "execution_count": 7,
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   ],
   "source": [
    "math.fabs(12)\n",
    "math.fabs(-12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## factorial()\n",
    "描述：以一个整数返回 x 的阶乘。如果 x 不是整数或为负数时则将引发 ValueError。  \n",
    "语法：math.factorial( x )"
   ]
  },
  {
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   "execution_count": 9,
   "metadata": {
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     "data": {
      "text/plain": [
       "24"
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     "execution_count": 9,
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   ],
   "source": [
    "math.factorial(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## floor()\n",
    "描述：返回 x 的向下取整，小于或等于 x 的最大整数。如果 x 不是浮点数，则委托 x.__floor__() ，它应返回 Integral 值。  \n",
    "语法：math.floor( x )"
   ]
  },
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   "execution_count": 10,
   "metadata": {
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   ],
   "source": [
    "math.floor(1.2)\n",
    "math.floor(1.0)\n",
    "math.floor(-1.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## fmod()\n",
    "描述：返回余数，函数 fmod() 在使用浮点数时通常是首选，而Python的 x % y 在使用整数时是首选。  \n",
    "语法：math.fmod(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T07:48:51.848914Z",
     "start_time": "2020-05-18T07:48:51.843913Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
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     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
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    {
     "data": {
      "text/plain": [
       "1.0999999999999999"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.fmod(3, 2)\n",
    "math.fmod(2.3, 1.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## frexp()\n",
    "描述：返回 x 的尾数和指数作为对``(m, e)``。 m 是一个浮点数， e 是一个整数，正好是 x == m * 2**e 。如果 x 为零，则返回 (0.0, 0) ，否则返回 0.5 <= abs(m) < 1 。这用于以可移植方式“分离”浮点数的内部表示。  \n",
    "语法：math.frexp(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T07:50:06.539532Z",
     "start_time": "2020-05-18T07:50:06.535554Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.75, 4)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.frexp(12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## fsum()\n",
    "描述：对迭代器里的每个元素进行求和操作，返回迭代中的精确浮点值。通过跟踪多个中间部分和来避免精度损失  \n",
    "语法：math.fsum( x )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T07:51:36.568854Z",
     "start_time": "2020-05-18T07:51:36.563855Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.3"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.fsum([1, 3, 4, 0])\n",
    "math.fsum([1.1, 1.2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## gcd()\n",
    "描述：返回整数 a 和 b 的最大公约数。如果 a 或 b 之一非零，则 gcd(a, b) 的值是能同时整除 a 和 b 的最大正整数。gcd(0, 0) 返回 0。  \n",
    "语法：math.gcd( x,y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
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     "end_time": "2020-05-18T07:52:08.912277Z",
     "start_time": "2020-05-18T07:52:08.908248Z"
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       "6"
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     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "math.gcd(12, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## isclose()\n",
    "描述：若 a 和 b 的值比较接近则返回 True，否则返回 False。根据给定的绝对和相对容差确定两个值是否被认为是接近的。\n",
    "语法：math.isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)\n",
    "+ rel_tol 是相对容差 —— 它是 a 和 b 之间允许的最大差值，相对于 a 或 b 的较大绝对值。例如，要设置5％的容差，请传递 rel_tol=0.05 。默认容差为 1e-09，确保两个值在大约9位十进制数字内相同。 rel_tol 必须大于零。\n",
    "+ abs_tol 是最小绝对容差 —— 对于接近零的比较很有用。 abs_tol 必须至少为零。\n",
    "如果没有错误发生，结果将是：abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol) 。  \n",
    "\n",
    "IEEE 754特殊值 NaN ， inf 和 -inf 将根据IEEE规则处理。具体来说， NaN 不被认为接近任何其他值，包括 NaN 。inf 和 -inf 只被认为接近自己。"
   ]
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   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
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     "end_time": "2020-05-18T08:02:15.578408Z",
     "start_time": "2020-05-18T08:02:15.568404Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "True"
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     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.isclose(12, 12)\n",
    "math.isclose(12, 13)\n",
    "math.isclose(12, 13, abs_tol=10)\n",
    "math.isclose(12, 13, rel_tol=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## isfinite()\n",
    "描述：如果 x 既不是无穷大也不是NaN，则返回 True ，否则返回 False 。（注意 0.0 被认为 是 有限的。）  \n",
    "语法：math.isfinite(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T02:58:50.156769Z",
     "start_time": "2020-05-20T02:58:50.148771Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.isfinite(2)\n",
    "math.isfinite(math.nan)\n",
    "math.isfinite(math.inf)\n",
    "math.isfinite(-math.inf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## isinf()\n",
    "描述：如果 x 是正或负无穷大，则返回 True ，否则返回 False 。   \n",
    "语法：math.isinf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T02:59:31.093073Z",
     "start_time": "2020-05-20T02:59:31.084074Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.isinf(2)\n",
    "math.isinf(math.nan)\n",
    "math.isinf(math.inf)\n",
    "math.isinf(-math.inf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## isnan()\n",
    "描述：如果 x 是 NaN（不是数字），则返回 True ，否则返回 False 。  \n",
    "语法：math.isnan(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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     "start_time": "2020-05-20T03:00:18.571331Z"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.isnan(math.nan)\n",
    "math.isnan(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ldexp()\n",
    "描述：返回 x * (2**i) 。这基本上是函数 frexp() 的反函数。  \n",
    "语法：math.ldexp(x, i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:06:39.938022Z",
     "start_time": "2020-05-20T03:06:39.933022Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(0.5, 5)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.ldexp(0.5, 5)\n",
    "math.frexp(16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## modf()\n",
    "描述：返回 x 的小数和整数部分。两个结果都带有 x 的符号并且是浮点数。  \n",
    "语法：math.modf(x) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:07:11.511486Z",
     "start_time": "2020-05-20T03:07:11.507484Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.75, 3.0)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.modf(3.75)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## remainder()\n",
    "描述：返回 IEEE 754 风格的 x 相对于 y 的余数  \n",
    "语法：math.remainder(x, y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:08:49.957753Z",
     "start_time": "2020-05-20T03:08:49.948755Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "-2.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "-1.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.remainder(11, 5)\n",
    "math.remainder(12, 5)\n",
    "math.remainder(13, 5)\n",
    "math.remainder(14, 5)\n",
    "math.remainder(15, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## trunc()\n",
    "描述：返回 Real 值 x 截断为 Integral （通常是整数）  \n",
    "语法：math.trunc(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:09:35.238958Z",
     "start_time": "2020-05-20T03:09:35.235939Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.trunc(math.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 幂函数与对数函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exp()\n",
    "描述：返回 e 次 x 幂，其中 e = 2.718281... 是自然对数的基数。这通常比 math.e ** x 或 pow(math.e, x) 更精确。  \n",
    "语法：math.exp( x )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:10:48.906353Z",
     "start_time": "2020-05-20T03:10:48.900351Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.718281828459045"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "7.38905609893065"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.exp(1)\n",
    "math.exp(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## log()\n",
    "描述：使用一个参数，返回 x 的自然对数（底为 e ）。  \n",
    "语法：math.log(x[,base])\n",
    "参数：\n",
    "+ x -- 数值表达式。\n",
    "+ base -- 可选，底数，默认为 e。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:12:05.260201Z",
     "start_time": "2020-05-20T03:12:05.253175Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9999924078065106"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.log(7.389)\n",
    "math.log(10, 10)\n",
    "math.log(16, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## log1p()\n",
    "描述：返回 1+x (base e) 的自然对数。以对于接近零的 x 精确的方式计算结果。  \n",
    "语法：math.log1p(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:16:26.153118Z",
     "start_time": "2020-05-20T03:16:26.148147Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9999924078065106"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.9999924078065106"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.log1p(6.389)\n",
    "math.log(7.389)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## log2() / log10()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## pow()\n",
    "描述：返回 （x的y次方） 的值。与内置的 ** 运算符不同， math.pow() 将其参数转换为 float 类型。使用 ** 或内置的 pow() 函数来计算精确的整数幂。  \n",
    "语法：math.pow( x, y )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:17:36.868670Z",
     "start_time": "2020-05-20T03:17:36.861699Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.pow(2, 2)\n",
    "2 ** 2\n",
    "pow(2, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sqrt()\n",
    "描述：返回数字x的平方根。  \n",
    "语法：math.sqrt( x )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:17:58.167566Z",
     "start_time": "2020-05-20T03:17:58.164594Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.sqrt(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 三角函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## acos()\n",
    "描述：以弧度为单位返回 x 的反余弦值。  \n",
    "语法：math.acos(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:32:47.417887Z",
     "start_time": "2020-05-20T03:32:47.404889Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "6.123233995736766e-17"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.5707963267948966"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.5707963267948966"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.cos(math.pi)\n",
    "math.acos(-1) #pi\n",
    "math.cos(0) \n",
    "math.acos(1) #0\n",
    "math.cos(math.pi/2) # 0\n",
    "math.acos(0) # pi/2\n",
    "math.pi/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## asin()\n",
    "描述：以弧度为单位返回 x 的反正弦值。  \n",
    "语法：math.asin(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## atan()\n",
    "描述：以弧度为单位返回 x 的反正切值。  \n",
    "语法：math.atan(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## atan2()\n",
    "描述：以弧度为单位返回 atan(y / x) 。结果是在 -pi 和 pi 之间。从原点到点 (x, y) 的平面矢量使该角度与正X轴成正比。 atan2() 的点的两个输入的符号都是已知的，因此它可以计算角度的正确象限。例如， atan(1) 和 atan2(1, 1) 都是 pi/4 ，但 atan2(-1, -1) 是 -3*pi/4 。  \n",
    "语法：math.atan2(y, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:31:32.909942Z",
     "start_time": "2020-05-20T03:31:32.901941Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7853981633974483"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.7853981633974483"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "-2.356194490192345"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "-2.356194490192345"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.atan2(1, 1)\n",
    "math.pi/4\n",
    "math.atan2(-1, -1)\n",
    "-3 * math.pi / 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## cos()\n",
    "描述：返回 x 弧度的余弦值。  \n",
    "语法：math.cos(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:33:51.241020Z",
     "start_time": "2020-05-20T03:33:51.236045Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.cos(math.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## hypot()\n",
    "描述：返回欧几里德范数， sqrt(x*x + y*y) 。这是从原点到点 (x, y) 的向量长度。  \n",
    "语法：math.hypot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:34:28.316720Z",
     "start_time": "2020-05-20T03:34:28.310722Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.hypot(1, 1)\n",
    "math.hypot(3, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sin()\n",
    "描述：返回 x 弧度的正弦值。  \n",
    "语法：math.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:34:57.368942Z",
     "start_time": "2020-05-20T03:34:57.364942Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.sin(math.pi/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## tan()\n",
    "描述：返回 x 弧度的正切值。  \n",
    "语法：math.tan(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:35:21.895254Z",
     "start_time": "2020-05-20T03:35:21.891251Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999999"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.tan(math.pi/4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 角度转换"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## degrees()\n",
    "描述：将角度 x 从弧度转换为度数。  \n",
    "语法：math.degrees(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:36:26.266619Z",
     "start_time": "2020-05-20T03:36:26.262626Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "90.0"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.degrees(math.pi/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## radians()\n",
    "描述：将角度 x 从度数转换为弧度。  \n",
    "语法：math.radians(x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:37:39.071902Z",
     "start_time": "2020-05-20T03:37:39.068904Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.radians(180)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 双曲函数\n",
    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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## acosh()\n",
    "描述：返回 x 的反双曲余弦值。  \n",
    "语法：math.acosh(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## asinh()\n",
    "描述：返回 x 的反双曲正弦值。  \n",
    "语法：math.asinh(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## atanh()\n",
    "描述：返回 x 的反双曲正切值。  \n",
    "语法：math.atanh(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## cosh()\n",
    "描述：返回 x 的双曲余弦值。  \n",
    "语法：math.cosh(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sinh()\n",
    "描述：返回 x 的双曲正弦值。  \n",
    "语法：math.sinh(x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## tanh()\n",
    "描述：返回 x 的双曲正切值。  \n",
    "语法：math.tanh(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 特殊函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## erf()\n",
    "描述：返回 x 处的 error function 。  \n",
    "语法：math.erf(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:41:56.363431Z",
     "start_time": "2020-05-20T03:41:56.358431Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8427007929497149"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.erf(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## erfc()\n",
    "描述：返回 x 处的互补误差函数。 互补错误函数 定义为 1.0 - erf(x)。它用于 x 的大值，从其中减去一个会导致 有效位数损失。  \n",
    "语法：math.erfc(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:42:57.777740Z",
     "start_time": "2020-05-20T03:42:57.773739Z"
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   "outputs": [
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     "data": {
      "text/plain": [
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     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "math.erfc(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## gamma()\n",
    "描述：返回 x 处的 伽马函数 值。 \n",
    "语法：math.gamma(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:44:35.105580Z",
     "start_time": "2020-05-20T03:44:35.100581Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.gamma(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## lgamma()\n",
    "描述：返回Gamma函数在 x 绝对值的自然对数。  \n",
    "语法：math.lgamma(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-20T03:45:01.616967Z",
     "start_time": "2020-05-20T03:45:01.612992Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
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      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "math.lgamma(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 常量"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## pi\n",
    "描述：圆周率。数学常数 π = 3.141592...，精确到可用精度。  \n",
    "语法：math.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## e\n",
    "描述：数学常数 e = 2.718281...，精确到可用精度。  \n",
    "语法：math. e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## tau\n",
    "描述：数学常数 τ = 6.283185...，精确到可用精度。Tau 是一个圆周常数，等于 2π，圆的周长与半径之比  \n",
    "语法：math.tau "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## inf\n",
    "描述：浮点正无穷大。（对于负无穷大，使用 -math.inf 。）相当于``float('inf')`` 的输出。  \n",
    "语法：math.inf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## nan\n",
    "描述：浮点“非数字”（NaN）值。相当于 float('nan') 的输出。  \n",
    "语法：math.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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