{
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  {
   "cell_type": "raw",
   "id": "8cf32803",
   "metadata": {},
   "source": [
    "---\n",
    "title: Artificial Calculus Teacher\n",
    "description: Generates Derivative and Integral Expressions\n",
    "show-code : False\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "108761f9",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} \\left(- \\sqrt[3]{x} + \\sin{\\left(x \\right)}\\right)$"
      ],
      "text/plain": [
       "Derivative(-x**(1/3) + sin(x), x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int \\left(2 x + \\frac{1}{x^{2}}\\right)\\, dx$"
      ],
      "text/plain": [
       "Integral(2*x + x**(-2), x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} \\left(- \\sqrt[3]{x} + \\sin{\\left(x \\right)}\\right) = \\cos{\\left(x \\right)} - \\frac{1}{3 x^{\\frac{2}{3}}}$"
      ],
      "text/plain": [
       "Eq(Derivative(-x**(1/3) + sin(x), x), cos(x) - 1/(3*x**(2/3)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int \\left(2 x + \\frac{1}{x^{2}}\\right)\\, dx = \\frac{x^{3} - 1}{x}$"
      ],
      "text/plain": [
       "Eq(Integral(2*x + x**(-2), x), (x**3 - 1)/x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import sin,cos,log,exp,tan,Function,Derivative,Eq,Integral,Rational\n",
    "from sympy import factor_terms,simplify, sqrt, cbrt\n",
    "from sympy.abc import x\n",
    "import random\n",
    "f = Function('f')\n",
    "g = Function('g')\n",
    "h = Function('h')\n",
    "def random_math(x):\n",
    "    allowed_values = list(range(-2, 2))\n",
    "    allowed_values.remove(0)\n",
    "    random_value = random.choice(allowed_values)\n",
    "    random_value2 = random.choice(allowed_values)\n",
    "    def power_function(x):      \n",
    "        return x**(Rational(random_value,random_value2))\n",
    "    def scalar_function(x):\n",
    "        return x*random_value\n",
    "    def addSUBTR_function(x): \n",
    "        return x+random_value\n",
    "    funs = [sin,power_function,log,exp,cos,tan,sqrt,cbrt,\n",
    "            scalar_function,addSUBTR_function]     \n",
    "    operations = [f(g(x)),f(x)+g(x),f(x)-g(x),f(x)/g(x),f(x)*g(x),\n",
    "                 f(g(h(x))),f(h(x))+g(x),f(h(x))-g(x),f(h(x))/g(x),f(x)/g(h(x)),f(h(x))*g(x)]\n",
    "    operation = operations[random.randrange(0,len(operations))]\n",
    "    return [[[operation.replace(f, i) for i in funs][random.randrange(0,len(funs))].replace(g, i) for i in funs]\\\n",
    "[random.randrange(0,len(funs))].replace(h, i) for i in funs][random.randrange(0,len(funs))]\n",
    "\n",
    "setup1 = random_math(x)\n",
    "setup2 = random_math(x)\n",
    "practice1 = Derivative(simplify(setup1),x)\n",
    "practice2 = Integral(simplify(setup2),x)\n",
    "p1eq = Eq(practice1,practice1.doit(),evaluate=False)\n",
    "p2eq = Eq(practice2,practice2.doit().simplify(),evaluate=False)\n",
    "if  setup1 != 0: \n",
    "    display(p1eq.lhs)\n",
    "if str(factor_terms(p2eq.lhs)) != str(p2eq.rhs):    \n",
    "    if str(p2eq).find(\"Ei\") == -1 and str(p2eq).find(\"gamma\") == -1 and str(p2eq).find(\"Piecewise\") == -1\\\n",
    "    and str(p2eq).find(\"li\") == -1 and str(p2eq).find(\"erf\") == -1 and str(p2eq).find(\"atan\") == -1\\\n",
    "    and str(p2eq).find(\"Si\") == -1 and str(p2eq).find(\"Ci\") == -1 and str(p2eq).find(\"hyper\") == -1\\\n",
    "    and str(p2eq).find(\"fresnel\") == -1 and str(p2eq).find(\"Li\") == -1:  \n",
    "        display(p2eq.lhs)\n",
    "    else:\n",
    "        print(\"Error: Complex Integral\")\n",
    "        pass\n",
    "\n",
    "else:\n",
    "    print(\"Error: Impossible Integral\")  \n",
    "    pass\n",
    "    \n",
    "for i in range(0,5):\n",
    "    print(\"\\n\")\n",
    "display(p1eq)\n",
    "display(p2eq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "493bdcbe",
   "metadata": {},
   "source": [
    "*Credits to https://people.math.harvard.edu/~knill/teaching/math1a_2011/handouts/46-ai.pdf for inspiration*\n",
    "\n",
    "*Thanks to @smichr for .replace suggestion https://stackoverflow.com/a/73000728/17291132*\n",
    "\n",
    "**Notebook by github.com/nsc9   - MIT License**\n",
    "\n",
    "Donate by sending Bitcoin (BTC) to address: **bc1qtawr2gw52ftufzu0r3r20pnj3vmynssxs0mjl4**"
   ]
  }
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