{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e5bdcfe3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/mercury+json": "{\n    \"widget\": \"App\",\n    \"title\": \"Calculus with button\",\n    \"description\": \"Generates expressions which students can apply differential and integral calculus to.\",\n    \"show_code\": false,\n    \"show_prompt\": false,\n    \"output\": \"app\",\n    \"schedule\": \"\",\n    \"notify\": \"{}\",\n    \"continuous_update\": true,\n    \"static_notebook\": false,\n    \"show_sidebar\": false,\n    \"full_screen\": true,\n    \"allow_download\": false,\n    \"model_id\": \"mercury-app\",\n    \"code_uid\": \"App.0.40.24.4-rand9623c2c5\"\n}",
      "text/html": [
       "<h3>Mercury Application</h3><small>This output won't appear in the web app.</small>"
      ],
      "text/plain": [
       "mercury.App"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import mercury as mr\n",
    " \n",
    "# set Application parameters\n",
    "app = mr.App(title=\"Calculus with button\",\n",
    "        description=\"Generates expressions which students can apply differential and integral calculus to.\",\n",
    "        show_code=False,\n",
    "        show_prompt=False,\n",
    "        continuous_update=True,\n",
    "        static_notebook=False,\n",
    "        show_sidebar=False,\n",
    "        full_screen=True,\n",
    "        allow_download=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6c291d72",
   "metadata": {},
   "outputs": [],
   "source": [
    "equation_count = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ed0119b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/mercury+json": "{\n    \"widget\": \"Button\",\n    \"label\": \"New equation\",\n    \"style\": \"primary\",\n    \"value\": false,\n    \"model_id\": \"d9b6141d235246f5a54aba97568bd28f\",\n    \"code_uid\": \"Button.0.40.11.1-randcb9ee30c\",\n    \"disabled\": false,\n    \"hidden\": false\n}",
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d9b6141d235246f5a54aba97568bd28f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "mercury.Button"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "generate = mr.Button(label=\"New equation\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b920c45c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\frac{7 t - 4}{- 6 t - 12} = ?$"
      ],
      "text/plain": [
       "Eq(Derivative((7*t - 4)/(-6*t - 12), t), ?)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int \\left(4 y + e^{y} - 2\\right)\\, dy = ?$"
      ],
      "text/plain": [
       "Eq(Integral(4*y + exp(y) - 2, y), ?)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\frac{7 t - 4}{- 6 t - 12} = \\frac{7}{- 6 t - 12} + \\frac{6 \\cdot \\left(7 t - 4\\right)}{\\left(- 6 t - 12\\right)^{2}}$"
      ],
      "text/plain": [
       "Eq(Derivative((7*t - 4)/(-6*t - 12), t), 7/(-6*t - 12) + 6*(7*t - 4)/(-6*t - 12)**2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int \\left(4 y + e^{y} - 2\\right)\\, dy = 2 y^{2} - 2 y + e^{y}$"
      ],
      "text/plain": [
       "Eq(Integral(4*y + exp(y) - 2, y), 2*y**2 - 2*y + exp(y))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy.simplify.fu import TR22,TR2i\n",
    "from sympy import *\n",
    "from sympy.abc import theta\n",
    "import random\n",
    "f = Function('f')\n",
    "g = Function('g')\n",
    "h = Function('h')\n",
    "theta = Symbol('theta')\n",
    "i = 0\n",
    "dkeywords = {\"polylog\",\"Ei\",\"gamma\",\"Piecewise\",\"li\",\"erf\",\"Si\",\"Ci\",\"hyper\",\"fresnel\",\"Li\",\"expint\",\"zoo\",\n",
    "\"nan\",\"oo\",\"abs\",\"re\",\"EulerGamma\", \"sinh\",\"tanh\", \"cosh\",'sign','abs','atan','csc','asin'} \n",
    "ikeywords = {\"polylog\",\"Ei\",\"gamma\",\"Piecewise\", \"li\", \"erf\", \"atan\", \"Si\",  \"Ci\",  \"hyper\",  \"fresnel\",  \"Li\", \n",
    "\"expint\",\"zoo\", \"nan\", \"oo\",\"EulerGamma\",\"sinh\",\"csc\",\"asin\"}\n",
    "keywords2 = {\"sin\",\"cos\",\"tan\"}\n",
    "def random_variable(i):\n",
    "    return Symbol(random.choice([i for i in ['v','t','x','z','y']]), real=True)\n",
    "def random_value(i):\n",
    "    return random.choice([i for i in range(-10,10) if i not in [0]])\n",
    "def power(a):      \n",
    "    return random_value(i)*a**int(random_value(i)/2)\n",
    "def scalar(a):       \n",
    "    return a*random_value(i) + random_value(i)\n",
    "def addSUBTR(a):     \n",
    "    return a+random_value(i)\n",
    "def dmain(a):\n",
    "    def random_math(a): \n",
    "        funs = [power,scalar,addSUBTR,power,scalar,addSUBTR,ln,exp,sin,cos,tan,sqrt]   \n",
    "        operations = [f(a)+g(a)+h(a),\n",
    "                      f(a)+g(a)-h(a),\n",
    "                      f(a)+g(a)*h(a),\n",
    "                      f(a)+g(a)/h(a),\n",
    "                      \n",
    "                      f(a)-g(a)+h(a),\n",
    "                      f(a)-g(a)-h(a),\n",
    "                      f(a)-g(a)*h(a),\n",
    "                      f(a)-g(a)/h(a),\n",
    "\n",
    "                      f(a)*g(a)+h(a),\n",
    "                      f(a)*g(a)-h(a),\n",
    "                      f(a)*g(a)*h(a),\n",
    "                      f(a)*g(a)/h(a),                    \n",
    "                      \n",
    "                      f(a)/g(a)+h(a),\n",
    "                      f(a)/g(a)-h(a),\n",
    "                      f(a)/g(a)*h(a),\n",
    "                      f(a)/g(a)/h(a),                      \n",
    "\n",
    "                      f(a)* ( g(a)+h(a) ),\n",
    "                      f(a)* ( g(a)-h(a) ),\n",
    "                      f(a)/ ( g(a)+h(a) ),\n",
    "                      f(a)/ ( g(a)-h(a) ),\n",
    "                      \n",
    "                      f(g(h(a))),\n",
    "                      f(h(a))+g(a),\n",
    "                      f(h(a))-g(a),\n",
    "                      f(h(a))*g(a),\n",
    "                      f(h(a))/g(a),\n",
    "                      f(a)/g(h(a))]\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",
    "    return random_math(a)\n",
    "def imain(a):\n",
    "    def random_math2(a):  \n",
    "        funs = [power,scalar,addSUBTR,power,scalar,addSUBTR,ln,exp,sin,cos,tan,sqrt]   \n",
    "        operations = [f(g(a)),f(a)+g(a),f(a)-g(a),f(a)/g(a),f(a)*g(a)]\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",
    "    return random_math2(a)\n",
    "derror = True\n",
    "def dtest():\n",
    "    global setup1\n",
    "    global derror\n",
    "    global practice1\n",
    "    a = random_variable(i)\n",
    "    setup1 = dmain(a)\n",
    "    practice1 = Derivative(setup1,a)       \n",
    "    p1eq = TR22(Eq(practice1,practice1.doit(),evaluate=False))\n",
    "    if any(kw in str(setup1) for kw in keywords2):\n",
    "        setup1 = setup1.replace(a,theta)\n",
    "        practice1 = Derivative(setup1,theta)   \n",
    "        p1eq = TR22(Eq(practice1,practice1.doit(),evaluate=False))\n",
    "    if p1eq.rhs != 0 and not any(kw in str(p1eq) for kw in dkeywords):\n",
    "        derror = False\n",
    "    return p1eq\n",
    "while derror == True: \n",
    "    output1 = dtest()\n",
    "ierror = True\n",
    "def itest():\n",
    "    global ierror\n",
    "    global practice2\n",
    "    global setup2\n",
    "    a = random_variable(i)\n",
    "    setup2 = imain(a)\n",
    "    practice2 = Integral(setup2,a)  \n",
    "    p2eq = TR22(Eq(practice2,practice2.doit(),evaluate=False))\n",
    "    if str(factor_terms(p2eq.lhs)) != str(factor_terms(p2eq.rhs)) and not any(kw in str(p2eq) for kw in ikeywords)\\\n",
    "    and str(p2eq.lhs) != str(-p2eq.rhs): \n",
    "        if any(kw in str(setup2) for kw in keywords2):\n",
    "            setup2 = setup2.replace(a,theta)\n",
    "            practice2 = Integral(setup2,theta)  \n",
    "            p2eq = TR22(Eq(practice2,practice2.doit(),evaluate=False))\n",
    "        ierror = False\n",
    "    return p2eq\n",
    "while ierror == True:\n",
    "    output2 = itest()\n",
    "questionmark = Symbol('?')\n",
    "def lhs():\n",
    "    return display(Eq(nsimplify(output1.lhs),questionmark),Eq(nsimplify(output2.lhs),questionmark)) \n",
    "def rhs():\n",
    "    return display(Eq(nsimplify(output1.lhs),nsimplify(output1.rhs)),Eq(nsimplify(output2.lhs),nsimplify(output2.rhs)))\n",
    "\n",
    "\n",
    "lhs()\n",
    "print(\"\\n\")\n",
    "print(\"\\n\")\n",
    "print(\"\\n\")\n",
    "rhs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "964a5275",
   "metadata": {},
   "outputs": [],
   "source": [
    "if generate.clicked:\n",
    "    equation_count += 1\n",
    "    print(f\"Equation count {equation_count}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "17c2d87c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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