Upload calculus.ipynb

calculus.ipynb

@@ -0,0 +1,283 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "f78791d5",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/mercury+json": "{\n    \"widget\": \"App\",\n    \"title\": \"Calculus Problem Generator\",\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-randf482e104\"\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 Problem Generator\",\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": 8,
+   "id": "46df7f52",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/mercury+json": "{\n    \"widget\": \"Button\",\n    \"label\": \"New equation\",\n    \"style\": \"primary\",\n    \"value\": false,\n    \"model_id\": \"924849ab8db145cf8e9f7bc75f38bb23\",\n    \"code_uid\": \"Button.0.40.11.1-randd017f351\",\n    \"disabled\": false,\n    \"hidden\": false\n}",
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "924849ab8db145cf8e9f7bc75f38bb23",
+       "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": 10,
+   "id": "3a7db45a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\frac{d}{d \\theta} \\left(- \\sqrt{\\theta} + \\sin{\\left(\\theta \\right)} + \\cos{\\left(\\theta \\right)}\\right) = ?$"
+      ],
+      "text/plain": [
+       "Eq(Derivative(-sqrt(theta) + sin(theta) + cos(theta), theta), ?)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\int \\left(z - 3\\right) \\left(6 z - 10\\right)\\, dz = ?$"
+      ],
+      "text/plain": [
+       "Eq(Integral((z - 3)*(6*z - 10), z), ?)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n"
+     ]
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\frac{d}{d \\theta} \\left(- \\sqrt{\\theta} + \\sin{\\left(\\theta \\right)} + \\cos{\\left(\\theta \\right)}\\right) = - \\sin{\\left(\\theta \\right)} + \\cos{\\left(\\theta \\right)} - \\frac{1}{2 \\sqrt{\\theta}}$"
+      ],
+      "text/plain": [
+       "Eq(Derivative(-sqrt(theta) + sin(theta) + cos(theta), theta), -sin(theta) + cos(theta) - 1/(2*sqrt(theta)))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\int \\left(z - 3\\right) \\left(6 z - 10\\right)\\, dz = 2 z^{3} - 14 z^{2} + 30 z$"
+      ],
+      "text/plain": [
+       "Eq(Integral((z - 3)*(6*z - 10), z), 2*z**3 - 14*z**2 + 30*z)"
+      ]
+     },
+     "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",
+    "if generate.clicked:\n",
+    "    lhs()\n",
+    "    print(\"\\n\")\n",
+    "    print(\"\\n\")\n",
+    "    print(\"\\n\")\n",
+    "    rhs()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "08e768e2",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "menv",
+   "language": "python",
+   "name": "menv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}