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{
"cells": [
{
"cell_type": "raw",
"id": "8c69730d",
"metadata": {},
"source": [
"---\n",
"title: Calculus Problem Generator\n",
"description: Generates Derivative and Integral Expressions\n",
"show-code : False\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "c5197005",
"metadata": {},
"outputs": [],
"source": [
"# changelog: removes custom_ln cause i don't like it"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "108761f9",
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Solve\n"
]
},
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{d}{d x} x^{3} \\tan{\\left(x \\right)}$"
],
"text/plain": [
"Derivative(x**3*tan(x), x)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle \\int \\left(\\sqrt[3]{x} - e^{x}\\right)\\, dx$"
],
"text/plain": [
"Integral(x**(1/3) - exp(x), x)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"Solutions:\n"
]
},
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{d}{d x} x^{3} \\tan{\\left(x \\right)} = x^{3} \\sec^{2}{\\left(x \\right)} + 3 x^{2} \\tan{\\left(x \\right)}$"
],
"text/plain": [
"Eq(Derivative(x**3*tan(x), x), x**3*sec(x)**2 + 3*x**2*tan(x))"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle \\int \\left(\\sqrt[3]{x} - e^{x}\\right)\\, dx = \\frac{3 x^{\\frac{4}{3}}}{4} - e^{x}$"
],
"text/plain": [
"Eq(Integral(x**(1/3) - exp(x), x), 3*x**(4/3)/4 - exp(x))"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"-----------------------------------------------------------------------------------------------------------\n"
]
}
],
"source": [
"from sympy.simplify.fu import TR22\n",
"from sympy import sin,cos,ln,exp,tan,Function,Derivative,Eq,Integral,Rational\n",
"from sympy import factor_terms,simplify, sqrt\n",
"from sympy.abc import x\n",
"import random\n",
"f = Function('f')\n",
"g = Function('g')\n",
"h = Function('h')\n",
"def random_math(x):\n",
" allowed_values = list(range(2, 6))\n",
" random_value = random.choice(allowed_values)\n",
" random_value\n",
" def power_function(x): \n",
" return x**random_value\n",
" def scalar_function(x):\n",
" return x*random_value\n",
" def addSUBTR_function(x): \n",
" return x+random_value\n",
" funs = [sin,power_function,ln,exp,cos,tan,sqrt,\n",
" scalar_function,addSUBTR_function] \n",
" operations = [f(g(x)),f(x)+g(x),f(x)-g(x),f(x)/g(x),f(x)*g(x), f(x)/g(x)/h(x),f(x)*g(h(x)),\n",
" f(g(h(x))),f(h(x))+g(x),f(h(x))-g(x),f(h(x))/g(x),f(x)/g(h(x)),f(h(x))*g(x), f(x)*g(x)*h(x)]\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",
"\n",
"def random_math2(x):\n",
" allowed_values = list(range(2, 6))\n",
" random_value = random.choice(allowed_values)\n",
" random_value\n",
" def power_function(x): \n",
" return x**random_value\n",
" def scalar_function(x):\n",
" return x*random_value\n",
" def addSUBTR_function(x): \n",
" return x+random_value\n",
" funs = [sin,power_function,ln,exp,cos,tan,sqrt,\n",
" scalar_function,addSUBTR_function] \n",
" operations = [f(g(x)),f(x)+g(x),f(x)-g(x),f(x)/g(x),f(x)*g(x)]\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",
"setup1 = random_math(x)\n",
"setup2 = random_math2(x)\n",
"practice1 = Derivative(simplify(setup1),x)\n",
"practice2 = Integral(simplify(setup2),x)\n",
"p1eq = Eq(practice1,practice1.doit(),evaluate=False)\n",
"p2eq = Eq(practice2,practice2.doit().simplify(),evaluate=False)\n",
"print(\"Solve\")\n",
"display(p1eq.lhs)\n",
"if str(factor_terms(p2eq.lhs)) != str(p2eq.rhs): \n",
" if str(p2eq).find(\"Ei\") == -1 and str(p2eq).find(\"gamma\") == -1 and str(p2eq).find(\"Piecewise\") == -1\\\n",
" and str(p2eq).find(\"li\") == -1 and str(p2eq).find(\"erf\") == -1 and str(p2eq).find(\"atan\") == -1\\\n",
" and str(p2eq).find(\"Si\") == -1 and str(p2eq).find(\"Ci\") == -1 and str(p2eq).find(\"hyper\") == -1\\\n",
" and str(p2eq).find(\"fresnel\") == -1 and str(p2eq).find(\"Li\") == -1: \n",
" display(p2eq.lhs)\n",
" else:\n",
" print(\"Error: Complex Integral\")\n",
" pass\n",
"\n",
"else:\n",
" print(\"Error: Impossible Integral\") \n",
" pass\n",
" \n",
"for i in range(0,8):\n",
" print(\"\\n\")\n",
"print(\"Solutions:\")\n",
"display(TR22(p1eq))\n",
"display(TR22(p2eq))\n",
"print(\"-----------------------------------------------------------------------------------------------------------\")"
]
},
{
"cell_type": "markdown",
"id": "b3f5b9fb",
"metadata": {},
"source": [
"If LaTeX display breaks, refresh the page.\n",
"\n",
"Helpful resources: https://www.derivative-calculator.net/ & https://www.integral-calculator.com/ \n",
"\n",
"**Made by github.com/nsc9 - MIT License**\n",
"\n",
"Donate by sending Bitcoin (BTC) to address: **bc1qtawr2gw52ftufzu0r3r20pnj3vmynssxs0mjl4**"
]
}
],
"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": "3.8.10"
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"nbformat": 4,
"nbformat_minor": 5
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