Spaces:
Runtime error
Runtime error
Delete Artificial_Calc_Teacher_v9.ipynb
Browse files- Artificial_Calc_Teacher_v9.ipynb +0 -517
Artificial_Calc_Teacher_v9.ipynb
DELETED
|
@@ -1,517 +0,0 @@
|
|
| 1 |
-
{
|
| 2 |
-
"cells": [
|
| 3 |
-
{
|
| 4 |
-
"cell_type": "markdown",
|
| 5 |
-
"id": "0625835f",
|
| 6 |
-
"metadata": {},
|
| 7 |
-
"source": [
|
| 8 |
-
"*Credits to https://people.math.harvard.edu/~knill/teaching/math1a_2011/handouts/46-ai.pdf for inspiration*\n",
|
| 9 |
-
"\n",
|
| 10 |
-
"*Thanks to @smichr for .replace suggestion https://stackoverflow.com/a/73000728/17291132*\n",
|
| 11 |
-
"\n",
|
| 12 |
-
"**Notebook by github.com/nsc9 - MIT License**\n",
|
| 13 |
-
"\n",
|
| 14 |
-
"**Changelog:**\n",
|
| 15 |
-
"\n",
|
| 16 |
-
" Integrals are now filtered if answers are complicated or impossible. \n",
|
| 17 |
-
" \n",
|
| 18 |
-
"**Requested Features:**\n",
|
| 19 |
-
"\n",
|
| 20 |
-
" Program stops if it exceeds 2 second run-time.\n",
|
| 21 |
-
" \n",
|
| 22 |
-
"**Known Bugs**\n",
|
| 23 |
-
"\n",
|
| 24 |
-
" Still Rarely Crashes. Minimized by lowering \n",
|
| 25 |
-
" allowed_values = list(range(-5, 5)) -> -2,2"
|
| 26 |
-
]
|
| 27 |
-
},
|
| 28 |
-
{
|
| 29 |
-
"cell_type": "code",
|
| 30 |
-
"execution_count": 1,
|
| 31 |
-
"id": "108761f9",
|
| 32 |
-
"metadata": {
|
| 33 |
-
"scrolled": false
|
| 34 |
-
},
|
| 35 |
-
"outputs": [
|
| 36 |
-
{
|
| 37 |
-
"data": {
|
| 38 |
-
"text/latex": [
|
| 39 |
-
"$\\displaystyle \\frac{d}{d x} \\left(\\frac{\\log{\\left(x \\right)}}{3} + 1\\right) = \\frac{1}{3 x}$"
|
| 40 |
-
],
|
| 41 |
-
"text/plain": [
|
| 42 |
-
"Eq(Derivative(log(x)/3 + 1, x), 1/(3*x))"
|
| 43 |
-
]
|
| 44 |
-
},
|
| 45 |
-
"metadata": {},
|
| 46 |
-
"output_type": "display_data"
|
| 47 |
-
},
|
| 48 |
-
{
|
| 49 |
-
"data": {
|
| 50 |
-
"text/latex": [
|
| 51 |
-
"$\\displaystyle \\int \\cos{\\left(x \\right)}\\, dx = \\sin{\\left(x \\right)}$"
|
| 52 |
-
],
|
| 53 |
-
"text/plain": [
|
| 54 |
-
"Eq(Integral(cos(x), x), sin(x))"
|
| 55 |
-
]
|
| 56 |
-
},
|
| 57 |
-
"metadata": {},
|
| 58 |
-
"output_type": "display_data"
|
| 59 |
-
},
|
| 60 |
-
{
|
| 61 |
-
"data": {
|
| 62 |
-
"text/latex": [
|
| 63 |
-
"$\\displaystyle \\frac{d}{d x} \\cos^{\\frac{3}{2}}{\\left(x \\right)} = - \\frac{3 \\sin{\\left(x \\right)} \\sqrt{\\cos{\\left(x \\right)}}}{2}$"
|
| 64 |
-
],
|
| 65 |
-
"text/plain": [
|
| 66 |
-
"Eq(Derivative(cos(x)**(3/2), x), -3*sin(x)*sqrt(cos(x))/2)"
|
| 67 |
-
]
|
| 68 |
-
},
|
| 69 |
-
"metadata": {},
|
| 70 |
-
"output_type": "display_data"
|
| 71 |
-
},
|
| 72 |
-
{
|
| 73 |
-
"data": {
|
| 74 |
-
"text/latex": [
|
| 75 |
-
"$\\displaystyle \\int \\sin{\\left(x \\right)} \\tan{\\left(x \\right)}\\, dx = - \\frac{\\log{\\left(\\sin{\\left(x \\right)} - 1 \\right)}}{2} + \\frac{\\log{\\left(\\sin{\\left(x \\right)} + 1 \\right)}}{2} - \\sin{\\left(x \\right)}$"
|
| 76 |
-
],
|
| 77 |
-
"text/plain": [
|
| 78 |
-
"Eq(Integral(sin(x)*tan(x), x), -log(sin(x) - 1)/2 + log(sin(x) + 1)/2 - sin(x))"
|
| 79 |
-
]
|
| 80 |
-
},
|
| 81 |
-
"metadata": {},
|
| 82 |
-
"output_type": "display_data"
|
| 83 |
-
},
|
| 84 |
-
{
|
| 85 |
-
"data": {
|
| 86 |
-
"text/latex": [
|
| 87 |
-
"$\\displaystyle \\frac{d}{d x} \\frac{\\log{\\left(x \\right)}}{x} = \\frac{1 - \\log{\\left(x \\right)}}{x^{2}}$"
|
| 88 |
-
],
|
| 89 |
-
"text/plain": [
|
| 90 |
-
"Eq(Derivative(log(x)/x, x), (1 - log(x))/x**2)"
|
| 91 |
-
]
|
| 92 |
-
},
|
| 93 |
-
"metadata": {},
|
| 94 |
-
"output_type": "display_data"
|
| 95 |
-
},
|
| 96 |
-
{
|
| 97 |
-
"data": {
|
| 98 |
-
"text/latex": [
|
| 99 |
-
"$\\displaystyle \\int \\left(e^{x} - 1\\right)\\, dx = - x + e^{x}$"
|
| 100 |
-
],
|
| 101 |
-
"text/plain": [
|
| 102 |
-
"Eq(Integral(exp(x) - 1, x), -x + exp(x))"
|
| 103 |
-
]
|
| 104 |
-
},
|
| 105 |
-
"metadata": {},
|
| 106 |
-
"output_type": "display_data"
|
| 107 |
-
},
|
| 108 |
-
{
|
| 109 |
-
"data": {
|
| 110 |
-
"text/latex": [
|
| 111 |
-
"$\\displaystyle \\frac{d}{d x} \\cos{\\left(2 x \\right)} = - 2 \\sin{\\left(2 x \\right)}$"
|
| 112 |
-
],
|
| 113 |
-
"text/plain": [
|
| 114 |
-
"Eq(Derivative(cos(2*x), x), -2*sin(2*x))"
|
| 115 |
-
]
|
| 116 |
-
},
|
| 117 |
-
"metadata": {},
|
| 118 |
-
"output_type": "display_data"
|
| 119 |
-
},
|
| 120 |
-
{
|
| 121 |
-
"data": {
|
| 122 |
-
"text/latex": [
|
| 123 |
-
"$\\displaystyle \\int \\left(e^{\\sqrt[3]{x}} + \\frac{1}{x^{2}}\\right)\\, dx = \\frac{3 x \\left(x^{\\frac{2}{3}} - 2 \\sqrt[3]{x} + 2\\right) e^{\\sqrt[3]{x}} - 1}{x}$"
|
| 124 |
-
],
|
| 125 |
-
"text/plain": [
|
| 126 |
-
"Eq(Integral(exp(x**(1/3)) + x**(-2), x), (3*x*(x**(2/3) - 2*x**(1/3) + 2)*exp(x**(1/3)) - 1)/x)"
|
| 127 |
-
]
|
| 128 |
-
},
|
| 129 |
-
"metadata": {},
|
| 130 |
-
"output_type": "display_data"
|
| 131 |
-
},
|
| 132 |
-
{
|
| 133 |
-
"data": {
|
| 134 |
-
"text/latex": [
|
| 135 |
-
"$\\displaystyle \\frac{d}{d x} \\left(\\sqrt[3]{x} + e^{x}\\right) = e^{x} + \\frac{1}{3 x^{\\frac{2}{3}}}$"
|
| 136 |
-
],
|
| 137 |
-
"text/plain": [
|
| 138 |
-
"Eq(Derivative(x**(1/3) + exp(x), x), exp(x) + 1/(3*x**(2/3)))"
|
| 139 |
-
]
|
| 140 |
-
},
|
| 141 |
-
"metadata": {},
|
| 142 |
-
"output_type": "display_data"
|
| 143 |
-
},
|
| 144 |
-
{
|
| 145 |
-
"data": {
|
| 146 |
-
"text/latex": [
|
| 147 |
-
"$\\displaystyle \\int \\frac{1 - \\frac{x}{2}}{\\tan{\\left(x \\right)}}\\, dx = \\log{\\left(\\sin{\\left(x \\right)} \\right)} - \\frac{\\int \\frac{x}{\\tan{\\left(x \\right)}}\\, dx}{2}$"
|
| 148 |
-
],
|
| 149 |
-
"text/plain": [
|
| 150 |
-
"Eq(Integral((1 - x/2)/tan(x), x), log(sin(x)) - Integral(x/tan(x), x)/2)"
|
| 151 |
-
]
|
| 152 |
-
},
|
| 153 |
-
"metadata": {},
|
| 154 |
-
"output_type": "display_data"
|
| 155 |
-
},
|
| 156 |
-
{
|
| 157 |
-
"data": {
|
| 158 |
-
"text/latex": [
|
| 159 |
-
"$\\displaystyle \\frac{d}{d x} \\left(1 - \\cos{\\left(x \\right)}\\right) = \\sin{\\left(x \\right)}$"
|
| 160 |
-
],
|
| 161 |
-
"text/plain": [
|
| 162 |
-
"Eq(Derivative(1 - cos(x), x), sin(x))"
|
| 163 |
-
]
|
| 164 |
-
},
|
| 165 |
-
"metadata": {},
|
| 166 |
-
"output_type": "display_data"
|
| 167 |
-
},
|
| 168 |
-
{
|
| 169 |
-
"data": {
|
| 170 |
-
"text/latex": [
|
| 171 |
-
"$\\displaystyle \\int \\left(\\frac{\\log{\\left(x \\right)}}{2} - \\tan{\\left(x \\right)}\\right)\\, dx = \\frac{x \\log{\\left(x \\right)}}{2} - \\frac{x}{2} + \\log{\\left(\\cos{\\left(x \\right)} \\right)}$"
|
| 172 |
-
],
|
| 173 |
-
"text/plain": [
|
| 174 |
-
"Eq(Integral(log(x)/2 - tan(x), x), x*log(x)/2 - x/2 + log(cos(x)))"
|
| 175 |
-
]
|
| 176 |
-
},
|
| 177 |
-
"metadata": {},
|
| 178 |
-
"output_type": "display_data"
|
| 179 |
-
},
|
| 180 |
-
{
|
| 181 |
-
"data": {
|
| 182 |
-
"text/latex": [
|
| 183 |
-
"$\\displaystyle \\frac{d}{d x} \\left(\\sqrt{x - 1} + \\sin{\\left(x \\right)}\\right) = \\cos{\\left(x \\right)} + \\frac{1}{2 \\sqrt{x - 1}}$"
|
| 184 |
-
],
|
| 185 |
-
"text/plain": [
|
| 186 |
-
"Eq(Derivative(sqrt(x - 1) + sin(x), x), cos(x) + 1/(2*sqrt(x - 1)))"
|
| 187 |
-
]
|
| 188 |
-
},
|
| 189 |
-
"metadata": {},
|
| 190 |
-
"output_type": "display_data"
|
| 191 |
-
},
|
| 192 |
-
{
|
| 193 |
-
"data": {
|
| 194 |
-
"text/latex": [
|
| 195 |
-
"$\\displaystyle \\int \\left(- e^{x} + 1 + \\frac{1}{x}\\right)\\, dx = x - e^{x} + \\log{\\left(x \\right)}$"
|
| 196 |
-
],
|
| 197 |
-
"text/plain": [
|
| 198 |
-
"Eq(Integral(-exp(x) + 1 + 1/x, x), x - exp(x) + log(x))"
|
| 199 |
-
]
|
| 200 |
-
},
|
| 201 |
-
"metadata": {},
|
| 202 |
-
"output_type": "display_data"
|
| 203 |
-
},
|
| 204 |
-
{
|
| 205 |
-
"data": {
|
| 206 |
-
"text/latex": [
|
| 207 |
-
"$\\displaystyle \\frac{d}{d x} \\left(- x + \\sqrt[3]{\\cos{\\left(x \\right)}} - 1\\right) = - \\frac{\\sin{\\left(x \\right)}}{3 \\cos^{\\frac{2}{3}}{\\left(x \\right)}} - 1$"
|
| 208 |
-
],
|
| 209 |
-
"text/plain": [
|
| 210 |
-
"Eq(Derivative(-x + cos(x)**(1/3) - 1, x), -sin(x)/(3*cos(x)**(2/3)) - 1)"
|
| 211 |
-
]
|
| 212 |
-
},
|
| 213 |
-
"metadata": {},
|
| 214 |
-
"output_type": "display_data"
|
| 215 |
-
},
|
| 216 |
-
{
|
| 217 |
-
"data": {
|
| 218 |
-
"text/latex": [
|
| 219 |
-
"$\\displaystyle \\int \\left(\\sqrt[4]{x} - e^{x}\\right)\\, dx = \\frac{4 x^{\\frac{5}{4}}}{5} - e^{x}$"
|
| 220 |
-
],
|
| 221 |
-
"text/plain": [
|
| 222 |
-
"Eq(Integral(x**(1/4) - exp(x), x), 4*x**(5/4)/5 - exp(x))"
|
| 223 |
-
]
|
| 224 |
-
},
|
| 225 |
-
"metadata": {},
|
| 226 |
-
"output_type": "display_data"
|
| 227 |
-
},
|
| 228 |
-
{
|
| 229 |
-
"data": {
|
| 230 |
-
"text/latex": [
|
| 231 |
-
"$\\displaystyle \\frac{d}{d x} e^{- x} \\tan{\\left(x \\right)} = \\left(- \\tan{\\left(x \\right)} + \\frac{1}{\\cos^{2}{\\left(x \\right)}}\\right) e^{- x}$"
|
| 232 |
-
],
|
| 233 |
-
"text/plain": [
|
| 234 |
-
"Eq(Derivative(exp(-x)*tan(x), x), (-tan(x) + cos(x)**(-2))*exp(-x))"
|
| 235 |
-
]
|
| 236 |
-
},
|
| 237 |
-
"metadata": {},
|
| 238 |
-
"output_type": "display_data"
|
| 239 |
-
},
|
| 240 |
-
{
|
| 241 |
-
"data": {
|
| 242 |
-
"text/latex": [
|
| 243 |
-
"$\\displaystyle \\int \\left(x + e^{x}\\right)\\, dx = \\frac{x^{2}}{2} + e^{x}$"
|
| 244 |
-
],
|
| 245 |
-
"text/plain": [
|
| 246 |
-
"Eq(Integral(x + exp(x), x), x**2/2 + exp(x))"
|
| 247 |
-
]
|
| 248 |
-
},
|
| 249 |
-
"metadata": {},
|
| 250 |
-
"output_type": "display_data"
|
| 251 |
-
},
|
| 252 |
-
{
|
| 253 |
-
"data": {
|
| 254 |
-
"text/latex": [
|
| 255 |
-
"$\\displaystyle \\frac{d}{d x} \\left(- x - 1 + e^{- x}\\right) = -1 - e^{- x}$"
|
| 256 |
-
],
|
| 257 |
-
"text/plain": [
|
| 258 |
-
"Eq(Derivative(-x - 1 + exp(-x), x), -1 - exp(-x))"
|
| 259 |
-
]
|
| 260 |
-
},
|
| 261 |
-
"metadata": {},
|
| 262 |
-
"output_type": "display_data"
|
| 263 |
-
},
|
| 264 |
-
{
|
| 265 |
-
"data": {
|
| 266 |
-
"text/latex": [
|
| 267 |
-
"$\\displaystyle \\int 1\\, dx = x$"
|
| 268 |
-
],
|
| 269 |
-
"text/plain": [
|
| 270 |
-
"Eq(Integral(1, x), x)"
|
| 271 |
-
]
|
| 272 |
-
},
|
| 273 |
-
"metadata": {},
|
| 274 |
-
"output_type": "display_data"
|
| 275 |
-
},
|
| 276 |
-
{
|
| 277 |
-
"data": {
|
| 278 |
-
"text/latex": [
|
| 279 |
-
"$\\displaystyle \\frac{d}{d x} \\left(- \\frac{2 \\sin{\\left(x \\right)}}{\\sqrt[3]{x}}\\right) = \\frac{2 \\left(- 3 x \\cos{\\left(x \\right)} + \\sin{\\left(x \\right)}\\right)}{3 x^{\\frac{4}{3}}}$"
|
| 280 |
-
],
|
| 281 |
-
"text/plain": [
|
| 282 |
-
"Eq(Derivative(-2*sin(x)/x**(1/3), x), 2*(-3*x*cos(x) + sin(x))/(3*x**(4/3)))"
|
| 283 |
-
]
|
| 284 |
-
},
|
| 285 |
-
"metadata": {},
|
| 286 |
-
"output_type": "display_data"
|
| 287 |
-
},
|
| 288 |
-
{
|
| 289 |
-
"data": {
|
| 290 |
-
"text/latex": [
|
| 291 |
-
"$\\displaystyle \\int \\left(e^{x} + \\log{\\left(x \\right)}\\right)\\, dx = x \\log{\\left(x \\right)} - x + e^{x}$"
|
| 292 |
-
],
|
| 293 |
-
"text/plain": [
|
| 294 |
-
"Eq(Integral(exp(x) + log(x), x), x*log(x) - x + exp(x))"
|
| 295 |
-
]
|
| 296 |
-
},
|
| 297 |
-
"metadata": {},
|
| 298 |
-
"output_type": "display_data"
|
| 299 |
-
},
|
| 300 |
-
{
|
| 301 |
-
"data": {
|
| 302 |
-
"text/latex": [
|
| 303 |
-
"$\\displaystyle \\frac{d}{d x} \\sin{\\left(x \\right)} = \\cos{\\left(x \\right)}$"
|
| 304 |
-
],
|
| 305 |
-
"text/plain": [
|
| 306 |
-
"Eq(Derivative(sin(x), x), cos(x))"
|
| 307 |
-
]
|
| 308 |
-
},
|
| 309 |
-
"metadata": {},
|
| 310 |
-
"output_type": "display_data"
|
| 311 |
-
},
|
| 312 |
-
{
|
| 313 |
-
"data": {
|
| 314 |
-
"text/latex": [
|
| 315 |
-
"$\\displaystyle \\int \\left(- 2 x^{\\frac{5}{6}}\\right)\\, dx = - \\frac{12 x^{\\frac{11}{6}}}{11}$"
|
| 316 |
-
],
|
| 317 |
-
"text/plain": [
|
| 318 |
-
"Eq(Integral(-2*x**(5/6), x), -12*x**(11/6)/11)"
|
| 319 |
-
]
|
| 320 |
-
},
|
| 321 |
-
"metadata": {},
|
| 322 |
-
"output_type": "display_data"
|
| 323 |
-
},
|
| 324 |
-
{
|
| 325 |
-
"data": {
|
| 326 |
-
"text/latex": [
|
| 327 |
-
"$\\displaystyle \\frac{d}{d x} \\frac{\\log{\\left(x - 1 \\right)}}{\\sqrt{x}} = \\frac{x - \\frac{\\left(x - 1\\right) \\log{\\left(x - 1 \\right)}}{2}}{x^{\\frac{3}{2}} \\left(x - 1\\right)}$"
|
| 328 |
-
],
|
| 329 |
-
"text/plain": [
|
| 330 |
-
"Eq(Derivative(log(x - 1)/sqrt(x), x), (x - (x - 1)*log(x - 1)/2)/(x**(3/2)*(x - 1)))"
|
| 331 |
-
]
|
| 332 |
-
},
|
| 333 |
-
"metadata": {},
|
| 334 |
-
"output_type": "display_data"
|
| 335 |
-
},
|
| 336 |
-
{
|
| 337 |
-
"data": {
|
| 338 |
-
"text/latex": [
|
| 339 |
-
"$\\displaystyle \\int 1\\, dx = x$"
|
| 340 |
-
],
|
| 341 |
-
"text/plain": [
|
| 342 |
-
"Eq(Integral(1, x), x)"
|
| 343 |
-
]
|
| 344 |
-
},
|
| 345 |
-
"metadata": {},
|
| 346 |
-
"output_type": "display_data"
|
| 347 |
-
},
|
| 348 |
-
{
|
| 349 |
-
"data": {
|
| 350 |
-
"text/latex": [
|
| 351 |
-
"$\\displaystyle \\frac{d}{d x} \\frac{\\sin{\\left(x \\right)}}{\\sqrt[3]{x}} = \\frac{x \\cos{\\left(x \\right)} - \\frac{\\sin{\\left(x \\right)}}{3}}{x^{\\frac{4}{3}}}$"
|
| 352 |
-
],
|
| 353 |
-
"text/plain": [
|
| 354 |
-
"Eq(Derivative(sin(x)/x**(1/3), x), (x*cos(x) - sin(x)/3)/x**(4/3))"
|
| 355 |
-
]
|
| 356 |
-
},
|
| 357 |
-
"metadata": {},
|
| 358 |
-
"output_type": "display_data"
|
| 359 |
-
},
|
| 360 |
-
{
|
| 361 |
-
"data": {
|
| 362 |
-
"text/latex": [
|
| 363 |
-
"$\\displaystyle \\int \\left(\\log{\\left(\\sin{\\left(x \\right)} \\right)} - 1\\right)\\, dx = - x + \\int \\log{\\left(\\sin{\\left(x \\right)} \\right)}\\, dx$"
|
| 364 |
-
],
|
| 365 |
-
"text/plain": [
|
| 366 |
-
"Eq(Integral(log(sin(x)) - 1, x), -x + Integral(log(sin(x)), x))"
|
| 367 |
-
]
|
| 368 |
-
},
|
| 369 |
-
"metadata": {},
|
| 370 |
-
"output_type": "display_data"
|
| 371 |
-
},
|
| 372 |
-
{
|
| 373 |
-
"data": {
|
| 374 |
-
"text/latex": [
|
| 375 |
-
"$\\displaystyle \\frac{d}{d x} \\left(- \\frac{2}{x^{\\frac{3}{2}}}\\right) = \\frac{3}{x^{\\frac{5}{2}}}$"
|
| 376 |
-
],
|
| 377 |
-
"text/plain": [
|
| 378 |
-
"Eq(Derivative(-2/x**(3/2), x), 3/x**(5/2))"
|
| 379 |
-
]
|
| 380 |
-
},
|
| 381 |
-
"metadata": {},
|
| 382 |
-
"output_type": "display_data"
|
| 383 |
-
},
|
| 384 |
-
{
|
| 385 |
-
"data": {
|
| 386 |
-
"text/latex": [
|
| 387 |
-
"$\\displaystyle \\int \\log{\\left(x \\right)}\\, dx = x \\left(\\log{\\left(x \\right)} - 1\\right)$"
|
| 388 |
-
],
|
| 389 |
-
"text/plain": [
|
| 390 |
-
"Eq(Integral(log(x), x), x*(log(x) - 1))"
|
| 391 |
-
]
|
| 392 |
-
},
|
| 393 |
-
"metadata": {},
|
| 394 |
-
"output_type": "display_data"
|
| 395 |
-
},
|
| 396 |
-
{
|
| 397 |
-
"data": {
|
| 398 |
-
"text/latex": [
|
| 399 |
-
"$\\displaystyle \\frac{d}{d x} \\sin{\\left(\\log{\\left(\\cos{\\left(x \\right)} \\right)} \\right)} = - \\cos{\\left(\\log{\\left(\\cos{\\left(x \\right)} \\right)} \\right)} \\tan{\\left(x \\right)}$"
|
| 400 |
-
],
|
| 401 |
-
"text/plain": [
|
| 402 |
-
"Eq(Derivative(sin(log(cos(x))), x), -cos(log(cos(x)))*tan(x))"
|
| 403 |
-
]
|
| 404 |
-
},
|
| 405 |
-
"metadata": {},
|
| 406 |
-
"output_type": "display_data"
|
| 407 |
-
},
|
| 408 |
-
{
|
| 409 |
-
"data": {
|
| 410 |
-
"text/latex": [
|
| 411 |
-
"$\\displaystyle \\int \\left(- 2 \\sin{\\left(x \\right)}\\right)\\, dx = 2 \\cos{\\left(x \\right)}$"
|
| 412 |
-
],
|
| 413 |
-
"text/plain": [
|
| 414 |
-
"Eq(Integral(-2*sin(x), x), 2*cos(x))"
|
| 415 |
-
]
|
| 416 |
-
},
|
| 417 |
-
"metadata": {},
|
| 418 |
-
"output_type": "display_data"
|
| 419 |
-
},
|
| 420 |
-
{
|
| 421 |
-
"data": {
|
| 422 |
-
"text/latex": [
|
| 423 |
-
"$\\displaystyle \\frac{d}{d x} e^{2 x} = 2 e^{2 x}$"
|
| 424 |
-
],
|
| 425 |
-
"text/plain": [
|
| 426 |
-
"Eq(Derivative(exp(2*x), x), 2*exp(2*x))"
|
| 427 |
-
]
|
| 428 |
-
},
|
| 429 |
-
"metadata": {},
|
| 430 |
-
"output_type": "display_data"
|
| 431 |
-
},
|
| 432 |
-
{
|
| 433 |
-
"data": {
|
| 434 |
-
"text/latex": [
|
| 435 |
-
"$\\displaystyle \\int \\left(x - 2\\right) \\sqrt[3]{e^{x}}\\, dx = 3 \\left(x - 5\\right) \\sqrt[3]{e^{x}}$"
|
| 436 |
-
],
|
| 437 |
-
"text/plain": [
|
| 438 |
-
"Eq(Integral((x - 2)*exp(x)**(1/3), x), 3*(x - 5)*exp(x)**(1/3))"
|
| 439 |
-
]
|
| 440 |
-
},
|
| 441 |
-
"metadata": {},
|
| 442 |
-
"output_type": "display_data"
|
| 443 |
-
}
|
| 444 |
-
],
|
| 445 |
-
"source": [
|
| 446 |
-
"from sympy import sin,cos,log,exp,tan,Function,Derivative,Eq,Integral,Rational\n",
|
| 447 |
-
"from sympy import factor_terms,simplify, sqrt, cbrt\n",
|
| 448 |
-
"from sympy.abc import x\n",
|
| 449 |
-
"import random\n",
|
| 450 |
-
"f = Function('f')\n",
|
| 451 |
-
"g = Function('g')\n",
|
| 452 |
-
"h = Function('h')\n",
|
| 453 |
-
"def random_math(x):\n",
|
| 454 |
-
" allowed_values = list(range(-2, 2))\n",
|
| 455 |
-
" allowed_values.remove(0)\n",
|
| 456 |
-
" random_value = random.choice(allowed_values)\n",
|
| 457 |
-
" random_value2 = random.choice(allowed_values)\n",
|
| 458 |
-
" def power_function(x): \n",
|
| 459 |
-
" return x**(Rational(random_value,random_value2))\n",
|
| 460 |
-
" def scalar_function(x):\n",
|
| 461 |
-
" return x*random_value\n",
|
| 462 |
-
" def addSUBTR_function(x): \n",
|
| 463 |
-
" return x+random_value\n",
|
| 464 |
-
" funs = [sin,power_function,log,exp,cos,tan,sqrt,cbrt,\n",
|
| 465 |
-
" scalar_function,addSUBTR_function] \n",
|
| 466 |
-
" operations = [f(g(x)),f(x)+g(x),f(x)-g(x),f(x)/g(x),f(x)*g(x),\n",
|
| 467 |
-
" 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)]\n",
|
| 468 |
-
" operation = operations[random.randrange(0,len(operations))]\n",
|
| 469 |
-
" return [[[operation.replace(f, i) for i in funs][random.randrange(0,len(funs))].replace(g, i) for i in funs]\\\n",
|
| 470 |
-
"[random.randrange(0,len(funs))].replace(h, i) for i in funs][random.randrange(0,len(funs))]\n",
|
| 471 |
-
"\n",
|
| 472 |
-
"\n",
|
| 473 |
-
"for i in range(1,31): \n",
|
| 474 |
-
" practice1 = Derivative(simplify(random_math(x)),x)\n",
|
| 475 |
-
" practice2 = Integral(simplify(random_math(x)),x)\n",
|
| 476 |
-
" p1eq = Eq(practice1,practice1.doit().simplify(),evaluate=False)\n",
|
| 477 |
-
" p2eq = Eq(practice2,practice2.doit().simplify(),evaluate=False)\n",
|
| 478 |
-
" if str(factor_terms(p2eq.lhs)) != str(p2eq.rhs): \n",
|
| 479 |
-
" if str(p2eq).find(\"Ei\") == -1 and str(p2eq).find(\"gamma\") == -1 and str(p2eq).find(\"Piecewise\") == -1\\\n",
|
| 480 |
-
" and str(p2eq).find(\"li\") == -1 and str(p2eq).find(\"erf\") == -1 and str(p2eq).find(\"atan\") == -1\\\n",
|
| 481 |
-
" and str(p2eq).find(\"Si\") == -1 and str(p2eq).find(\"Ci\") == -1 and str(p2eq).find(\"hyper\") == -1\\\n",
|
| 482 |
-
" and str(p2eq).find(\"fresnel\") == -1 and str(p2eq).find(\"Li\") == -1: \n",
|
| 483 |
-
" if practice1.doit != 0: \n",
|
| 484 |
-
" display(p1eq)\n",
|
| 485 |
-
" display(p2eq)\n",
|
| 486 |
-
" else:\n",
|
| 487 |
-
" pass\n",
|
| 488 |
-
" #print(\"Error: Complex Integral\")\n",
|
| 489 |
-
" \n",
|
| 490 |
-
" else:\n",
|
| 491 |
-
" pass\n",
|
| 492 |
-
" # print(\"Error: Impossible Integral\") "
|
| 493 |
-
]
|
| 494 |
-
}
|
| 495 |
-
],
|
| 496 |
-
"metadata": {
|
| 497 |
-
"kernelspec": {
|
| 498 |
-
"display_name": "Python 3 (ipykernel)",
|
| 499 |
-
"language": "python",
|
| 500 |
-
"name": "python3"
|
| 501 |
-
},
|
| 502 |
-
"language_info": {
|
| 503 |
-
"codemirror_mode": {
|
| 504 |
-
"name": "ipython",
|
| 505 |
-
"version": 3
|
| 506 |
-
},
|
| 507 |
-
"file_extension": ".py",
|
| 508 |
-
"mimetype": "text/x-python",
|
| 509 |
-
"name": "python",
|
| 510 |
-
"nbconvert_exporter": "python",
|
| 511 |
-
"pygments_lexer": "ipython3",
|
| 512 |
-
"version": "3.8.10"
|
| 513 |
-
}
|
| 514 |
-
},
|
| 515 |
-
"nbformat": 4,
|
| 516 |
-
"nbformat_minor": 5
|
| 517 |
-
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|