veryfy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#sympy와 비교 검증\n",
    "import sympy as sym\n",
    "import UncertaintyPy as upy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6 ± 1)x10"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(6 ± 1)x10"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "59 ± 9"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(9862735 ± 4)x10^4"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(0 ± 1)x10^2"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(0 ± 1)x10^2"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "5 ± 1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "7.1 ± 0.1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.0 ± 0.5"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.00 ± 0.03"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.00 ± 0.05"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.0 ± 0.1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2 ± 1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "upy.ufloat(59, 12)\n",
    "upy.ufloat(59, 10)\n",
    "upy.ufloat(59, 9)\n",
    "upy.ufloat(986.2735, 0.000358)\n",
    "upy.ufloat(36.5, 100)\n",
    "upy.ufloat(36.5, 100.1)\n",
    "upy.ufloat(4.5, 1)\n",
    "upy.ufloat(7.1278, 0.098)\n",
    "upy.ufloat(2, 0.5)\n",
    "upy.ufloat(2, 0.03)\n",
    "upy.ufloat(2, 0.05)\n",
    "upy.ufloat(2, 0.098)\n",
    "upy.ufloat(2, 0.98)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "a,b,c = sym.symbols(\"a b c\")\n",
    "u1 = upy.ufloat(1.5, 0.2, \"m\")\n",
    "u2 = upy.ufloat(3, 1.5, \"m\")\n",
    "u3 = upy.ufloat(7.78, 0.987)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a$"
      ],
      "text/plain": [
       "a"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b$"
      ],
      "text/plain": [
       "b"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c$"
      ],
      "text/plain": [
       "c"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(1.5 ± 0.2) m"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(3 ± 2) m"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "8 ± 1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a\n",
    "b\n",
    "c\n",
    "u1\n",
    "u2\n",
    "u3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a + b$"
      ],
      "text/plain": [
       "a + b"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(5 ± 2) m"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(5 ± 2) m"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.5132745950421556"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.5132745950421556"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#add\n",
    "func1 = upy.ufunc(a + b, [a, b])\n",
    "func1\n",
    "func1.f([u1, u2]).set_unit(\"m\")\n",
    "(u1 + u2).set_unit(\"m\")\n",
    "\n",
    "func1.f([u1, u2]).uncertainty\n",
    "(u1 + u2).uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a + b + c$"
      ],
      "text/plain": [
       "a + b + c"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(12 ± 2) m"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(12 ± 2) m"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.8067011374325306"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.8067011374325306"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "func2 = upy.ufunc(a + b + c, [a, b, c])\n",
    "func2\n",
    "func2.f([u1, u2, u3], \"m\")\n",
    "(u1 + u2 + u3).set_unit(\"m\")\n",
    "\n",
    "func2.f([u1, u2, u3], \"m\").uncertainty\n",
    "(u1 + u2 + u3).uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a - b$"
      ],
      "text/plain": [
       "a - b"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(-2 ± 2) m"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(-2 ± 2) m"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.5132745950421556"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.5132745950421556"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sub\n",
    "func3 = upy.ufunc(a - b, [a, b])\n",
    "func3\n",
    "func3.f([u1, u2]).set_unit(\"m\")\n",
    "(u1 - u2).set_unit(\"m\")\n",
    "\n",
    "func3.f([u1, u2]).uncertainty\n",
    "(u1 - u2).uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a b$"
      ],
      "text/plain": [
       "a*b"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "5 ± 2"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "5 ± 2"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.328626204439004"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.328626204439004"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#mul\n",
    "func4 = upy.ufunc(a*b, [a,b])\n",
    "func4\n",
    "func4.f([u1, u2])\n",
    "u1*u2\n",
    "\n",
    "func4.f([u1, u2]).uncertainty\n",
    "(u1*u2).uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a}{b}$"
      ],
      "text/plain": [
       "a/b"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.5 ± 0.3"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.5 ± 0.3"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.25873624493766706"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.25873624493766706"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#div\n",
    "func5 = upy.ufunc(a/b, [a,b])\n",
    "func5\n",
    "func5.f([u1, u2])\n",
    "u1/u2\n",
    "\n",
    "func5.f([u1, u2]).uncertainty\n",
    "(u1/u2).uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{3}$"
      ],
      "text/plain": [
       "a**3"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "3 ± 1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "3 ± 1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.35"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.35"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#pow\n",
    "func6 = upy.ufunc(a**3, [a])\n",
    "func6\n",
    "func6.f([u1])\n",
    "u1**3\n",
    "\n",
    "func6.f([u1]).uncertainty\n",
    "(u1**3).uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a b}{c}$"
      ],
      "text/plain": [
       "a*b/c"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.6 ± 0.3"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.6 ± 0.3"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.30817282579065397"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.308172825790654"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func7 = upy.ufunc(a*b/c, [a, b, c])\n",
    "func7\n",
    "func7.f([u1,u2,u3])\n",
    "u1*u2/u3\n",
    "\n",
    "func7.f([u1,u2,u3]).uncertainty\n",
    "(u1*u2/u3).uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{5 a}{b^{3}} - c$"
      ],
      "text/plain": [
       "5*a/b**3 - c"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "-8 ± 1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "-8 ± 1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.071985006062862"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.071985006062862"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func8 = upy.ufunc(5*a/b**3-c, [a, b, c])\n",
    "func8\n",
    "func8.f([u1, u2, u3])\n",
    "5*u1/u2**3-u3\n",
    "\n",
    "func8.f([u1, u2, u3]).uncertainty\n",
    "(5*u1/u2**3-u3).uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e^{a}$"
      ],
      "text/plain": [
       "exp(a)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "4.5 ± 0.9"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "4.5 ± 0.9"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.8963378140676129"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.8963378140676129"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([4.5 ± 0.9, (2 ± 3)x10, (2 ± 3)x10], dtype=object)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([4.5 ± 0.9, (2 ± 3)x10, (2 ± 2)x10^3], dtype=object)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#exp\n",
    "func9 = upy.ufunc(sym.exp(a), [a])\n",
    "func9\n",
    "func9.f([u1])\n",
    "upy.exp(u1)\n",
    "\n",
    "func9.f([u1]).uncertainty\n",
    "upy.exp(u1).uncertainty\n",
    "\n",
    "upy.exp([u1, u2, u2])\n",
    "upy.exp(upy.uarray([u1, u2, u3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\log{\\left(a \\right)}}{\\log{\\left(3 \\right)}}$"
      ],
      "text/plain": [
       "log(a)/log(3)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.4 ± 0.1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.4 ± 0.1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.12136523021691165"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.12136523021691166"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([0.4 ± 0.1, 1.1 ± 0.5, 2.1 ± 0.1], dtype=object)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#log base\n",
    "func10 = upy.ufunc(sym.log(a, 3), [a])\n",
    "func10\n",
    "func10.f([u1])\n",
    "upy.log(u1, 3)\n",
    "\n",
    "func10.f([u1]).uncertainty\n",
    "upy.log(u1, 3).uncertainty\n",
    "upy.log([u1, u2, u3], 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a \\log{\\left(b c \\right)}$"
      ],
      "text/plain": [
       "a*log(b*c)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "5 ± 1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "5 ± 1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.9978250958130539"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.9978250958130537"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func11 = upy.ufunc(a*sym.log(b*c), [a, b, c])\n",
    "func11\n",
    "func11.f([u1, u2, u3])\n",
    "u1*upy.log(u2*u3)\n",
    "\n",
    "func11.f([u1, u2, u3]).uncertainty\n",
    "(u1*upy.log(u2*u3)).uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{a}$"
      ],
      "text/plain": [
       "sqrt(a)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.22 ± 0.08"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.22 ± 0.08"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.08164965809277261"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.08164965809277261"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([1.22 ± 0.08, 1.7 ± 0.4, 2.8 ± 0.2], dtype=object)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sqrt\n",
    "func12 = upy.ufunc(sym.sqrt(a), [a])\n",
    "func12\n",
    "func12.f([u1])\n",
    "upy.sqrt(u1)\n",
    "\n",
    "func12.f([u1]).uncertainty\n",
    "upy.sqrt(u1).uncertainty\n",
    "upy.sqrt([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sin{\\left(a \\right)}$"
      ],
      "text/plain": [
       "sin(a)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.00 ± 0.01"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.00 ± 0.01"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.014147440333540581"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.014147440333540581"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([1.00 ± 0.01, 0 ± 1, 1.00 ± 0.07], dtype=object)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#trigonometry\n",
    "#sin\n",
    "func13 = upy.ufunc(sym.sin(a), [a])\n",
    "func13\n",
    "func13.f([u1])\n",
    "upy.sin(u1)\n",
    "\n",
    "func13.f([u1]).uncertainty\n",
    "upy.sin(u1).uncertainty\n",
    "upy.sin([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\cos{\\left(a \\right)}$"
      ],
      "text/plain": [
       "cos(a)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1 ± 0.2"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1 ± 0.2"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1994989973208109"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1994989973208109"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([0.1 ± 0.2, -1.0 ± 0.2, 0 ± 1], dtype=object)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#cos\n",
    "func14 = upy.ufunc(sym.cos(a), [a])\n",
    "func14\n",
    "func14.f([u1])\n",
    "upy.cos(u1)\n",
    "\n",
    "func14.f([u1]).uncertainty\n",
    "upy.cos(u1).uncertainty\n",
    "upy.cos([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\tan{\\left(a \\right)}$"
      ],
      "text/plain": [
       "tan(a)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(1 ± 4)x10"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(1 ± 4)x10"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "39.9700089052985"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "39.9700089052985"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([(1 ± 4)x10, 0 ± 2, (0 ± 2)x10^2], dtype=object)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#tan\n",
    "func15 = upy.ufunc(sym.tan(a), [a])\n",
    "func15\n",
    "func15.f([u1])\n",
    "upy.tan(u1)\n",
    "\n",
    "func15.f([u1]).uncertainty\n",
    "upy.tan(u1).uncertainty\n",
    "upy.tan([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\csc{\\left(a \\right)}$"
      ],
      "text/plain": [
       "csc(a)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.00 ± 0.01"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.00 ± 0.01"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.00 ± 0.01"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.014218586610461107"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.014218586610461107"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.014218586610461107"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([1.00 ± 0.01, (1 ± 7)x10, 1.00 ± 0.07], dtype=object)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#csc\n",
    "func16 = upy.ufunc(sym.csc(a), [a])\n",
    "func16\n",
    "func16.f([u1])\n",
    "upy.csc(u1)\n",
    "1/upy.sin(u1)\n",
    "\n",
    "func16.f([u1]).uncertainty\n",
    "upy.csc(u1).uncertainty\n",
    "(1/upy.sin(u1)).uncertainty\n",
    "upy.csc([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sec{\\left(a \\right)}$"
      ],
      "text/plain": [
       "sec(a)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(1 ± 4)x10"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(1 ± 4)x10"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "(1 ± 4)x10"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "39.86988349755466"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "39.86988349755466"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "39.86988349755466"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([(1 ± 4)x10, -1.0 ± 0.2, (0 ± 2)x10^2], dtype=object)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sec\n",
    "func17 = upy.ufunc(sym.sec(a), [a])\n",
    "func17\n",
    "func17.f([u1])\n",
    "upy.sec(u1)\n",
    "1/upy.cos(u1)\n",
    "\n",
    "func17.f([u1]).uncertainty\n",
    "upy.sec(u1).uncertainty\n",
    "(1/upy.cos(u1)).uncertainty\n",
    "upy.sec([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\cot{\\left(a \\right)}$"
      ],
      "text/plain": [
       "cot(a)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1 ± 0.2"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1 ± 0.2"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1 ± 0.2"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.2010057830284939"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.2010057830284939"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.20100578302849395"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([0.1 ± 0.2, (-1 ± 8)x10, 0 ± 1], dtype=object)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#cot\n",
    "func18 = upy.ufunc(sym.cot(a), [a])\n",
    "func18\n",
    "func18.f([u1])\n",
    "upy.cot(u1)\n",
    "1/upy.tan(u1)\n",
    "\n",
    "func18.f([u1]).uncertainty\n",
    "upy.cot(u1).uncertainty\n",
    "(1/upy.tan(u1)).uncertainty\n",
    "upy.cot([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4 ± 0.1"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.7 ± 0.3"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#inverse trigonometry function\n",
    "u4 = upy.ufloat(0.37, 0.1)\n",
    "u5 = upy.ufloat(0.7, 0.25)\n",
    "u4; u5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{asin}{\\left(a \\right)}$"
      ],
      "text/plain": [
       "asin(a)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.4 ± 0.1"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.4 ± 0.1"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1076389472867711"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1076389472867711"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([0.4 ± 0.1, 0.8 ± 0.4], dtype=object)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#asin\n",
    "func19 = upy.ufunc(sym.asin(a), [a])\n",
    "func19\n",
    "func19.f([u4])\n",
    "upy.asin(u4)\n",
    "\n",
    "func19.f([u4]).uncertainty\n",
    "upy.asin(u4).uncertainty\n",
    "upy.asin([u4, u5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{acos}{\\left(a \\right)}$"
      ],
      "text/plain": [
       "acos(a)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.2 ± 0.1"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.2 ± 0.1"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1076389472867711"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.1076389472867711"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([1.2 ± 0.1, 0.8 ± 0.4], dtype=object)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#acos\n",
    "func20 = upy.ufunc(sym.acos(a), [a])\n",
    "func20\n",
    "func20.f([u4])\n",
    "upy.acos(u4)\n",
    "\n",
    "func20.f([u4]).uncertainty\n",
    "upy.acos(u4).uncertainty\n",
    "upy.acos([u4, u5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{atan}{\\left(a \\right)}$"
      ],
      "text/plain": [
       "atan(a)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.35 ± 0.09"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.35 ± 0.09"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.08795848359574282"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.0879584835957428"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([0.35 ± 0.09, 0.6 ± 0.2], dtype=object)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#atan\n",
    "func21 = upy.ufunc(sym.atan(a), [a])\n",
    "func21\n",
    "func21.f([u4])\n",
    "upy.atan(u4)\n",
    "\n",
    "func21.f([u4]).uncertainty\n",
    "upy.atan(u4).uncertainty\n",
    "upy.atan([u4, u5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sinh{\\left(a \\right)}$"
      ],
      "text/plain": [
       "sinh(a)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.1 ± 0.5"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.1 ± 0.5"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.47048192304864944"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.47048192304864944"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([2.1 ± 0.5, (1 ± 2)x10, (1 ± 1)x10^3], dtype=object)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#hyperbolic function\n",
    "#sinh\n",
    "func22 = upy.ufunc(sym.sinh(a), [a])\n",
    "func22\n",
    "func22.f([u1])\n",
    "upy.sinh(u1)\n",
    "\n",
    "func22.f([u1]).uncertainty\n",
    "upy.sinh(u1).uncertainty\n",
    "upy.sinh([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\cosh{\\left(a \\right)}$"
      ],
      "text/plain": [
       "cosh(a)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.4 ± 0.4"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "2.4 ± 0.4"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.4258558910189635"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.4258558910189635"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([2.4 ± 0.4, (1 ± 2)x10, (1 ± 1)x10^3], dtype=object)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#cosh\n",
    "func23 = upy.ufunc(sym.cosh(a), [a])\n",
    "func23\n",
    "func23.f([u1])\n",
    "upy.cosh(u1)\n",
    "\n",
    "func23.f([u1]).uncertainty\n",
    "upy.cosh(u1).uncertainty\n",
    "upy.cosh([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\tanh{\\left(a \\right)}$"
      ],
      "text/plain": [
       "tanh(a)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.91 ± 0.04"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.91 ± 0.04"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.03614132778472971"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.03614132778472971"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([0.91 ± 0.04, 1.00 ± 0.01, (9999997 ± 7)x10^7], dtype=object)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#tanh\n",
    "func24 = upy.ufunc(sym.tanh(a), [a])\n",
    "func24\n",
    "func24.f([u1])\n",
    "upy.tanh(u1)\n",
    "\n",
    "func24.f([u1]).uncertainty\n",
    "upy.tanh(u1).uncertainty\n",
    "upy.tanh([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{csch}{\\left(a \\right)}$"
      ],
      "text/plain": [
       "csch(a)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.5 ± 0.1"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.5 ± 0.1"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.5 ± 0.1"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.10377138522978097"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.10377138522978098"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.10377138522978098"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([0.5 ± 0.1, 0.1 ± 0.2, (8 ± 8)x10^4], dtype=object)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#csch\n",
    "func25 = upy.ufunc(sym.csch(a), [a])\n",
    "func25\n",
    "func25.f([u1])\n",
    "upy.csch(u1)\n",
    "1/upy.sinh(u1)\n",
    "\n",
    "func25.f([u1]).uncertainty\n",
    "upy.csch(u1).uncertainty\n",
    "(1/upy.sinh(u1)).uncertainty\n",
    "upy.csch([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{sech}{\\left(a \\right)}$"
      ],
      "text/plain": [
       "sech(a)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.43 ± 0.08"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.43 ± 0.08"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.43 ± 0.08"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.07695498673187245"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.07695498673187245"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.07695498673187245"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([0.43 ± 0.08, 0.1 ± 0.1, (8 ± 8)x10^4], dtype=object)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sech\n",
    "func26 = upy.ufunc(sym.sech(a), [a])\n",
    "func26\n",
    "func26.f([u1])\n",
    "upy.sech(u1)\n",
    "1/upy.cosh(u1)\n",
    "\n",
    "func26.f([u1]).uncertainty\n",
    "upy.sech(u1).uncertainty\n",
    "(1/upy.cosh(u1)).uncertainty\n",
    "upy.sech([u1, u2, u3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\coth{\\left(a \\right)}$"
      ],
      "text/plain": [
       "coth(a)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.10 ± 0.04"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.10 ± 0.04"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "1.10 ± 0.04"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.044112804401647825"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.044112804401647825"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0.04411280440164782"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "undarray([0.1 ± 0.2, (-1 ± 8)x10, 0 ± 1], dtype=object)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#coth\n",
    "func27 = upy.ufunc(sym.coth(a), [a])\n",
    "func27\n",
    "func27.f([u1])\n",
    "upy.coth(u1)\n",
    "1/upy.tanh(u1)\n",
    "\n",
    "func27.f([u1]).uncertainty\n",
    "upy.coth(u1).uncertainty\n",
    "(1/upy.tanh(u1)).uncertainty\n",
    "upy.coth([u1, u2, u3])"
   ]
  }
 ],
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