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   "source": [
    "---\n",
    "title: Artificial Calculus Teacher\n",
    "description: Generates Derivative and Integral Expressions\n",
    "show-code : False\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c5197005",
   "metadata": {},
   "outputs": [],
   "source": [
    "# changelog: title, removed cbrt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "108761f9",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solve\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} \\left(x + 2\\right) \\tan{\\left(x \\right)}$"
      ],
      "text/plain": [
       "Derivative((x + 2)*tan(x), x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int \\left(\\sqrt{x} + 2 x\\right)\\, dx$"
      ],
      "text/plain": [
       "Integral(sqrt(x) + 2*x, x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "Solutions:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} \\left(x + 2\\right) \\tan{\\left(x \\right)} = \\left(x + 2\\right) \\sec^{2}{\\left(x \\right)} + \\tan{\\left(x \\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative((x + 2)*tan(x), x), (x + 2)*sec(x)**2 + tan(x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int \\left(\\sqrt{x} + 2 x\\right)\\, dx = \\frac{2 x^{\\frac{3}{2}}}{3} + x^{2}$"
      ],
      "text/plain": [
       "Eq(Integral(sqrt(x) + 2*x, x), 2*x**(3/2)/3 + x**2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----------------------------------------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "from sympy.simplify.fu import TR22\n",
    "from sympy import sin,cos,ln,exp,tan,Function,Derivative,Eq,Integral\n",
    "from sympy import factor_terms,simplify, sqrt\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, 6))\n",
    "    random_value = random.choice(allowed_values)\n",
    "    random_value\n",
    "    def power_function(x):      \n",
    "        return x**random_value\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,ln,exp,cos,tan,sqrt,\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), f(x)/g(x)/h(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), f(x)*g(x)*h(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",
    "def random_math2(x):\n",
    "    allowed_values = list(range(2, 6))\n",
    "    random_value = random.choice(allowed_values)\n",
    "    random_value\n",
    "    def power_function(x):      \n",
    "        return x**random_value\n",
    "    def scalar_function(x):\n",
    "        return x*random_value\n",
    "    def addSUBTR_function(x): \n",
    "        return x+random_value\n",
    "    \n",
    "    funs = [sin,power_function,ln,exp,cos,tan,sqrt,\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",
    "    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))]\n",
    "setup1 = random_math(x)\n",
    "setup2 = random_math2(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",
    "print(\"Solve\")\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(0,6):\n",
    "    print(\"\\n\")\n",
    "print(\"Solutions:\")\n",
    "display(TR22(p1eq))\n",
    "display(TR22(p2eq))\n",
    "print(\"                                                                  \")\n",
    "print(\"                                                                  \")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3f5b9fb",
   "metadata": {},
   "source": [
    "If LaTeX display breaks, refresh the page and run again.\n",
    "\n",
    "Helpful resources: https://www.derivative-calculator.net/ & https://www.integral-calculator.com/ \n",
    "\n",
    "**Made by github.com/nsc9   - MIT License**\n",
    "\n",
    "Donate by sending Bitcoin (BTC) to address: **bc1qtawr2gw52ftufzu0r3r20pnj3vmynssxs0mjl4**"
   ]
  }
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