Upload Artificial_Calc_Teacher_v7.7.ipynb

Artificial_Calc_Teacher_v7.7.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "raw",
+   "id": "59e65617",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "title: Calculus Problem Generator\n",
+    "description: Generates expressions for applying differential and integral calculus.\n",
+    "show-code: False\n",
+    "---"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 82,
+   "id": "c5197005",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# changelog: string spliced for easy copy/paste"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6bdf2faf",
+   "metadata": {},
+   "source": [
+    "# Solve with pen and paper:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "108761f9",
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [],
+   "source": [
+    "from sympy.simplify.fu import TR22,TR2i\n",
+    "from sympy import ln,exp,Function,Derivative,Eq,Integral,factor_terms, sqrt, Symbol,Limit\n",
+    "from sympy import sin,cos,tan,Rational,nsimplify\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)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
+   "id": "5ddcf6a5",
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\frac{d}{d z} \\frac{\\sqrt{z} \\left(z - 1\\right)}{z + 1} = ?$"
+      ],
+      "text/plain": [
+       "Eq(Derivative(sqrt(z)*(z - 1)/(z + 1), z), ?)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\int \\left(9 \\log{\\left(v \\right)} + 4\\right)\\, dv = ?$"
+      ],
+      "text/plain": [
+       "Eq(Integral(9*log(v) + 4, v), ?)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "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",
+    "lhs()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2393180e",
+   "metadata": {},
+   "source": [
+    "___________________________________________________________________________________________________________________\n",
+    "If LaTeX display breaks, refresh the page. Runtime is under a second if you run the Jupyter-Notebook locally.\n",
+    "\n",
+    "**Created by GitHub.com/NSC9  - Live @ https://nsc9.github.io/ - MIT License - v7.7**\n",
+    "\n",
+    "Latest version source code: https://github.com/NSC9/Sample_of_Work/tree/Main/Artificial_Calculus_Teacher\n",
+    "\n",
+    "Donate by sending Bitcoin (BTC) to address: **bc1qtawr2gw52ftufzu0r3r20pnj3vmynssxs0mjl4**\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 80,
+   "id": "15c3f34f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "For easy copy/paste into calculators below:\n",
+      "sqrt(z)*(z - 1)/(z + 1)\n",
+      "9*log(v) + 4\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"For easy copy/paste into calculators below:\")\n",
+    "keywords3 = {\"theta\"}\n",
+    "if any(kw in str(nsimplify(output1.lhs)) for kw in keywords3):\n",
+    "    print(str(nsimplify(output1.lhs))[11:-8])\n",
+    "else:\n",
+    "    print(str(nsimplify(output1.lhs))[11:-4])\n",
+    "    \n",
+    "if any(kw in str(nsimplify(output2.lhs)) for kw in keywords3):\n",
+    "    print(str(nsimplify(output2.lhs))[9:-8])\n",
+    "else:\n",
+    "    print(str(nsimplify(output2.lhs))[9:-4])    \n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "30b55c90",
+   "metadata": {},
+   "source": [
+    "https://www.derivative-calculator.net/\n",
+    "\n",
+    "https://www.integral-calculator.com/\n",
+    "___________________________________________________________________________________________________________________\n",
+    "\n",
+    "# Answers:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 81,
+   "id": "fbec286d",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\frac{d}{d z} \\frac{\\sqrt{z} \\left(z - 1\\right)}{z + 1} = - \\frac{\\sqrt{z} \\left(z - 1\\right)}{\\left(z + 1\\right)^{2}} + \\frac{\\sqrt{z}}{z + 1} + \\frac{z - 1}{2 \\sqrt{z} \\left(z + 1\\right)}$"
+      ],
+      "text/plain": [
+       "Eq(Derivative(sqrt(z)*(z - 1)/(z + 1), z), -sqrt(z)*(z - 1)/(z + 1)**2 + sqrt(z)/(z + 1) + (z - 1)/(2*sqrt(z)*(z + 1)))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\int \\left(9 \\log{\\left(v \\right)} + 4\\right)\\, dv = 9 v \\log{\\left(v \\right)} - 5 v$"
+      ],
+      "text/plain": [
+       "Eq(Integral(9*log(v) + 4, v), 9*v*log(v) - 5*v)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "rhs()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}