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Artificial_Calc_Teacher_v7.8.ipynb
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "eefbb211",
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"metadata": {},
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"outputs": [],
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"source": [
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"import mercury as mr\n",
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" \n",
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"# set Application parameters\n",
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"app = mr.App(title=\"Calculus Problem Generator\",\n",
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" description=\"Generates expressions which students can apply differential and integral calculus to.\",\n",
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" show_code=False,\n",
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" show_prompt=False,\n",
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" continuous_update=True,\n",
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" static_notebook=False,\n",
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" show_sidebar=True,\n",
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" full_screen=True,\n",
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" allow_download=False)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "9258ca84",
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"metadata": {},
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"outputs": [],
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"source": [
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"equation_count = 0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "81f9af3c",
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"metadata": {},
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"outputs": [],
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"source": [
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"generate = mr.Button(label=\"New equation\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "c5197005",
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"metadata": {},
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"outputs": [],
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"source": [
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"# changelog: updated code to work with updated Mercury. (button works again!)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "6bdf2faf",
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"metadata": {},
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"source": [
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"# Solve with pen and paper:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"id": "108761f9",
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"metadata": {
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"scrolled": false
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},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\frac{d}{d \\theta} \\left(\\sin{\\left(\\theta \\right)} + \\tan{\\left(\\theta \\right)} + 2\\right) = ?$"
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],
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"text/plain": [
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"Eq(Derivative(sin(theta) + tan(theta) + 2, theta), ?)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\int \\left(- \\sqrt{y} + e^{y}\\right)\\, dy = ?$"
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],
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"text/plain": [
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"Eq(Integral(-sqrt(y) + exp(y), y), ?)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"Possible answers:\n"
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]
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\frac{d}{d \\theta} \\left(\\sin{\\left(\\theta \\right)} + \\tan{\\left(\\theta \\right)} + 2\\right) = \\cos{\\left(\\theta \\right)} + \\sec^{2}{\\left(\\theta \\right)}$"
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],
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"text/plain": [
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"Eq(Derivative(sin(theta) + tan(theta) + 2, theta), cos(theta) + sec(theta)**2)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\int \\left(- \\sqrt{y} + e^{y}\\right)\\, dy = - \\frac{2 y^{\\frac{3}{2}}}{3} + e^{y}$"
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],
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"text/plain": [
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"Eq(Integral(-sqrt(y) + exp(y), y), -2*y**(3/2)/3 + exp(y))"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"from sympy.simplify.fu import TR22,TR2i\n",
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"from sympy import *\n",
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"from sympy.abc import theta\n",
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"import random\n",
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"f = Function('f')\n",
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"g = Function('g')\n",
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"h = Function('h')\n",
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"theta = Symbol('theta')\n",
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"i = 0\n",
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"dkeywords = {\"polylog\",\"Ei\",\"gamma\",\"Piecewise\",\"li\",\"erf\",\"Si\",\"Ci\",\"hyper\",\"fresnel\",\"Li\",\"expint\",\"zoo\",\n",
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"\"nan\",\"oo\",\"abs\",\"re\",\"EulerGamma\", \"sinh\",\"tanh\", \"cosh\",'sign','abs','atan','csc','asin'} \n",
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"ikeywords = {\"polylog\",\"Ei\",\"gamma\",\"Piecewise\", \"li\", \"erf\", \"atan\", \"Si\", \"Ci\", \"hyper\", \"fresnel\", \"Li\", \n",
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"\"expint\",\"zoo\", \"nan\", \"oo\",\"EulerGamma\",\"sinh\",\"csc\",\"asin\"}\n",
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"keywords2 = {\"sin\",\"cos\",\"tan\"}\n",
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"def random_variable(i):\n",
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" return Symbol(random.choice([i for i in ['v','t','x','z','y']]), real=True)\n",
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"def random_value(i):\n",
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" return random.choice([i for i in range(-10,10) if i not in [0]])\n",
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"def power(a): \n",
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" return random_value(i)*a**int(random_value(i)/2)\n",
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"def scalar(a): \n",
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" return a*random_value(i) + random_value(i)\n",
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"def addSUBTR(a): \n",
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" return a+random_value(i)\n",
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"def dmain(a):\n",
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" def random_math(a): \n",
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" funs = [power,scalar,addSUBTR,power,scalar,addSUBTR,ln,exp,sin,cos,tan,sqrt] \n",
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" operations = [f(a)+g(a)+h(a),\n",
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" f(a)+g(a)-h(a),\n",
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" f(a)+g(a)*h(a),\n",
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" f(a)+g(a)/h(a),\n",
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" \n",
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" f(a)-g(a)+h(a),\n",
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" f(a)-g(a)-h(a),\n",
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" f(a)-g(a)*h(a),\n",
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" f(a)-g(a)/h(a),\n",
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"\n",
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" f(a)*g(a)+h(a),\n",
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" f(a)*g(a)-h(a),\n",
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" f(a)*g(a)*h(a),\n",
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" f(a)*g(a)/h(a), \n",
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" \n",
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" f(a)/g(a)+h(a),\n",
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" f(a)/g(a)-h(a),\n",
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" f(a)/g(a)*h(a),\n",
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" f(a)/g(a)/h(a), \n",
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"\n",
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" f(a)* ( g(a)+h(a) ),\n",
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" f(a)* ( g(a)-h(a) ),\n",
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" f(a)/ ( g(a)+h(a) ),\n",
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" f(a)/ ( g(a)-h(a) ),\n",
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" \n",
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" f(g(h(a))),\n",
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" f(h(a))+g(a),\n",
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" f(h(a))-g(a),\n",
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" f(h(a))*g(a),\n",
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" f(h(a))/g(a),\n",
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" f(a)/g(h(a))]\n",
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" operation = operations[random.randrange(0,len(operations))]\n",
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" return [[[operation.replace(f, i) for i in funs][random.randrange(0,len(funs))].replace(g, i) for i in funs]\\\n",
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" [random.randrange(0,len(funs))].replace(h, i) for i in funs][random.randrange(0,len(funs))]\n",
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" return random_math(a)\n",
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"def imain(a):\n",
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" def random_math2(a): \n",
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" funs = [power,scalar,addSUBTR,power,scalar,addSUBTR,ln,exp,sin,cos,tan,sqrt] \n",
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" operations = [f(g(a)),f(a)+g(a),f(a)-g(a),f(a)/g(a),f(a)*g(a)]\n",
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" operation = operations[random.randrange(0,len(operations))]\n",
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" return [[operation.replace(f, i) for i in funs][random.randrange(0,len(funs))].replace(g, i) for i in funs]\\\n",
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" [random.randrange(0,len(funs))]\n",
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" return random_math2(a)\n",
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"derror = True\n",
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"def dtest():\n",
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" global setup1\n",
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" global derror\n",
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" global practice1\n",
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" a = random_variable(i)\n",
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" setup1 = dmain(a)\n",
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" practice1 = Derivative(setup1,a) \n",
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" p1eq = TR22(Eq(practice1,practice1.doit(),evaluate=False))\n",
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" if any(kw in str(setup1) for kw in keywords2):\n",
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" setup1 = setup1.replace(a,theta)\n",
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" practice1 = Derivative(setup1,theta) \n",
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" p1eq = TR22(Eq(practice1,practice1.doit(),evaluate=False))\n",
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" if p1eq.rhs != 0 and not any(kw in str(p1eq) for kw in dkeywords):\n",
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" derror = False\n",
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" return p1eq\n",
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"while derror == True: \n",
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" output1 = dtest()\n",
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"ierror = True\n",
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"def itest():\n",
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" global ierror\n",
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" global practice2\n",
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" global setup2\n",
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" a = random_variable(i)\n",
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" setup2 = imain(a)\n",
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" practice2 = Integral(setup2,a) \n",
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" p2eq = TR22(Eq(practice2,practice2.doit(),evaluate=False))\n",
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" if str(factor_terms(p2eq.lhs)) != str(factor_terms(p2eq.rhs)) and not any(kw in str(p2eq) for kw in ikeywords)\\\n",
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" and str(p2eq.lhs) != str(-p2eq.rhs): \n",
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" if any(kw in str(setup2) for kw in keywords2):\n",
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" setup2 = setup2.replace(a,theta)\n",
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" practice2 = Integral(setup2,theta) \n",
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" p2eq = TR22(Eq(practice2,practice2.doit(),evaluate=False))\n",
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" ierror = False\n",
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" return p2eq\n",
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"while ierror == True:\n",
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" output2 = itest()\n",
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"questionmark = Symbol('?')\n",
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"def lhs():\n",
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" return display(Eq(nsimplify(output1.lhs),questionmark),Eq(nsimplify(output2.lhs),questionmark)) \n",
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"def rhs():\n",
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" return display(Eq(nsimplify(output1.lhs),nsimplify(output1.rhs)),Eq(nsimplify(output2.lhs),nsimplify(output2.rhs)))\n",
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"lhs()\n",
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"print(\"\\n\")\n",
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"print(\"\\n\")\n",
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"print(\"\\n\")\n",
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"print(\"\\n\")\n",
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"print(\"\\n\")\n",
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"print(\"Possible answers:\")\n",
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"rhs()\n",
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"if generate.clicked:\n",
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" equation_count += 1\n",
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" print(f\"Equation count {equation_count}\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2393180e",
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"metadata": {},
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"source": [
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"# Donate Bitcoin (BTC) to address: **bc1qtrjmtsfxhmjmu4wwdh03u92gpy662rnt3drlm7**\n",
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"\n",
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"**Created by https://github.com/NSC9 - Live @ https://nsc9.github.io/ - MIT License - v7.8**\n",
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"\n",
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"**Powered by https://huggingface.co & https://runmercury.com/**\n",
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"\n",
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"Latest version source code: https://github.com/NSC9/Sample_of_Work/tree/Main/Artificial_Calculus_Teacher\n",
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"\n",
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"**Below are the expressions in plain text format for easy copy/pasting into these calculus calculator websites if you get stuck:**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 30,
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"id": "15c3f34f",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Differentiate: sin(theta) + tan(theta) + 2\n",
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"Integrate: -sqrt(y) + exp(y)\n"
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]
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}
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],
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"source": [
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"keywords3 = {\"theta\"}\n",
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"if any(kw in str(nsimplify(output1.lhs)) for kw in keywords3):\n",
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" print(\"Differentiate:\",str(nsimplify(output1.lhs))[11:-8])\n",
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" p1 = \" \"+str(nsimplify(output1.lhs))[11:-8]\n",
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"else:\n",
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" print(\"Differentiate:\",str(nsimplify(output1.lhs))[11:-4])\n",
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" p1 = \" \"+str(nsimplify(output1.lhs))[11:-4]\n",
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" \n",
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"if any(kw in str(nsimplify(output2.lhs)) for kw in keywords3):\n",
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" print(\"Integrate:\",str(nsimplify(output2.lhs))[9:-8])\n",
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" p2 = \" \"+str(nsimplify(output2.lhs))[9:-8]\n",
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"else:\n",
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" print(\"Integrate:\",str(nsimplify(output2.lhs))[9:-4]) \n",
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" p2 = \" \"+str(nsimplify(output2.lhs))[9:-4]\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "30b55c90",
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"metadata": {},
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"source": [
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"**https://www.derivative-calculator.net/ -- https://www.integral-calculator.com/**"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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