|
237 | 237 | " data = f.read()\n", |
238 | 238 | "display_pretty(data, raw=True)" |
239 | 239 | ] |
| 240 | + }, |
| 241 | + { |
| 242 | + "cell_type": "markdown", |
| 243 | + "metadata": {}, |
| 244 | + "source": [ |
| 245 | + "## Reproduce Some bugs" |
| 246 | + ] |
| 247 | + }, |
| 248 | + { |
| 249 | + "cell_type": "code", |
| 250 | + "execution_count": 10, |
| 251 | + "metadata": {}, |
| 252 | + "outputs": [], |
| 253 | + "source": [ |
| 254 | + "Format()\n", |
| 255 | + "xyz_coords = x, y, z = symbols('x y z', real=True)\n", |
| 256 | + "o3d, ex, ey, ez = Ga.build('e', g=[1, 1, 1], coords=xyz_coords, norm=True)" |
| 257 | + ] |
| 258 | + }, |
| 259 | + { |
| 260 | + "cell_type": "code", |
| 261 | + "execution_count": 11, |
| 262 | + "metadata": {}, |
| 263 | + "outputs": [ |
| 264 | + { |
| 265 | + "data": { |
| 266 | + "text/latex": [ |
| 267 | + "$\\displaystyle \\left( \\left( 1\\right), \\ \\left( e_{x}, \\ e_{y}, \\ e_{z}\\right), \\ \\left( e^{e}_{x y}, \\ e^{e}_{x z}, \\ e^{e}_{y z}\\right), \\ \\left( e^{e e}_{x y z}\\right)\\right)$" |
| 268 | + ], |
| 269 | + "text/plain": [ |
| 270 | + "((1,), (eₓ, e_y, e_z), (e_x_y__e, e_x_z__e, e_y_z__e), (e_x_y_z__e__e,))" |
| 271 | + ] |
| 272 | + }, |
| 273 | + "execution_count": 11, |
| 274 | + "metadata": {}, |
| 275 | + "output_type": "execute_result" |
| 276 | + } |
| 277 | + ], |
| 278 | + "source": [ |
| 279 | + "# FIXME BUG: incorrect handling of \\wedge\n", |
| 280 | + "o3d.blades" |
| 281 | + ] |
| 282 | + }, |
| 283 | + { |
| 284 | + "cell_type": "code", |
| 285 | + "execution_count": 12, |
| 286 | + "metadata": {}, |
| 287 | + "outputs": [], |
| 288 | + "source": [ |
| 289 | + "def build_ga_from_solution(solution, norm=False):\n", |
| 290 | + " [metric, coordinate_set, _index_config, cosmological_constant] = solution\n", |
| 291 | + " return Ga('e', g=metric, coords=coordinate_set, norm=norm)\n", |
| 292 | + "\n", |
| 293 | + "g4coords = u, x, y, z = symbols(\"u x y z\")\n", |
| 294 | + "g = [\n", |
| 295 | + " [0, 0, -exp(-z), 0],\n", |
| 296 | + " [0, S.Half * u ** 2 * exp(4 * z), 0, 0],\n", |
| 297 | + " [-exp(-z), 0, 12 * exp(-2 * z), u * exp(-z)],\n", |
| 298 | + " [0, 0, u * exp(-z), S.Half * u ** 2],\n", |
| 299 | + "]\n", |
| 300 | + "g4 = build_ga_from_solution([g, g4coords, None, 0])" |
| 301 | + ] |
| 302 | + }, |
| 303 | + { |
| 304 | + "cell_type": "code", |
| 305 | + "execution_count": 13, |
| 306 | + "metadata": {}, |
| 307 | + "outputs": [ |
| 308 | + { |
| 309 | + "data": { |
| 310 | + "text/plain": [ |
| 311 | + "(e_u, e_x, e_y, e_z)" |
| 312 | + ] |
| 313 | + }, |
| 314 | + "execution_count": 13, |
| 315 | + "metadata": {}, |
| 316 | + "output_type": "execute_result" |
| 317 | + } |
| 318 | + ], |
| 319 | + "source": [ |
| 320 | + "# FIXME BUG: should be LaTeX\n", |
| 321 | + "g4.mv()" |
| 322 | + ] |
| 323 | + }, |
| 324 | + { |
| 325 | + "cell_type": "code", |
| 326 | + "execution_count": 14, |
| 327 | + "metadata": {}, |
| 328 | + "outputs": [ |
| 329 | + { |
| 330 | + "data": { |
| 331 | + "text/plain": [ |
| 332 | + "(-10*e_u - exp(z)*e_y + 2*e_z/u,\n", |
| 333 | + " 2*exp(-4*z)*e_x/u**2,\n", |
| 334 | + " -exp(z)*e_u,\n", |
| 335 | + " 2*e_u/u + 2*e_z/u**2)" |
| 336 | + ] |
| 337 | + }, |
| 338 | + "execution_count": 14, |
| 339 | + "metadata": {}, |
| 340 | + "output_type": "execute_result" |
| 341 | + } |
| 342 | + ], |
| 343 | + "source": [ |
| 344 | + "# FIXME BUG: should be LaTeX\n", |
| 345 | + "g4.mvr()" |
| 346 | + ] |
| 347 | + }, |
| 348 | + { |
| 349 | + "cell_type": "code", |
| 350 | + "execution_count": 15, |
| 351 | + "metadata": {}, |
| 352 | + "outputs": [ |
| 353 | + { |
| 354 | + "data": { |
| 355 | + "text/latex": [ |
| 356 | + "$\\displaystyle \\left( \\left( 1\\right), \\ \\left( e_{u}, \\ e_{x}, \\ e_{y}, \\ e_{z}\\right), \\ \\left( e^{e}_{u x}, \\ e^{e}_{u y}, \\ e^{e}_{u z}, \\ e^{e}_{x y}, \\ e^{e}_{x z}, \\ e^{e}_{y z}\\right), \\ \\left( e^{e e}_{u x y}, \\ e^{e e}_{u x z}, \\ e^{e e}_{u y z}, \\ e^{e e}_{x y z}\\right), \\ \\left( e^{e e e}_{u x y z}\\right)\\right)$" |
| 357 | + ], |
| 358 | + "text/plain": [ |
| 359 | + "((1,), (eᵤ, eₓ, e_y, e_z), (e_u_x__e, e_u_y__e, e_u_z__e, e_x_y__e, e_x_z__e, \n", |
| 360 | + "e_y_z__e), (e_u_x_y__e__e, e_u_x_z__e__e, e_u_y_z__e__e, e_x_y_z__e__e), (e_u_\n", |
| 361 | + "x_y_z__e__e__e,))" |
| 362 | + ] |
| 363 | + }, |
| 364 | + "execution_count": 15, |
| 365 | + "metadata": {}, |
| 366 | + "output_type": "execute_result" |
| 367 | + } |
| 368 | + ], |
| 369 | + "source": [ |
| 370 | + "# FIXME BUG: incorrect handling of \\wedge\n", |
| 371 | + "g4.blades" |
| 372 | + ] |
| 373 | + }, |
| 374 | + { |
| 375 | + "cell_type": "code", |
| 376 | + "execution_count": 16, |
| 377 | + "metadata": {}, |
| 378 | + "outputs": [ |
| 379 | + { |
| 380 | + "data": { |
| 381 | + "text/latex": [ |
| 382 | + "$\\displaystyle e^{e e e}_{u x y z}$" |
| 383 | + ], |
| 384 | + "text/plain": [ |
| 385 | + "e_u_x_y_z__e__e__e" |
| 386 | + ] |
| 387 | + }, |
| 388 | + "execution_count": 16, |
| 389 | + "metadata": {}, |
| 390 | + "output_type": "execute_result" |
| 391 | + } |
| 392 | + ], |
| 393 | + "source": [ |
| 394 | + "# FIXME BUG: incorrect handling of \\wedge\n", |
| 395 | + "# This is the root cause of the above\n", |
| 396 | + "g4.e.obj" |
| 397 | + ] |
240 | 398 | } |
241 | 399 | ], |
242 | 400 | "metadata": { |
|
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