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{
"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": []
}
],
"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
}
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