example_interview.ipynb 1.37 MB
 Theresa Pollinger committed Mar 08, 2018 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 { "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hello, freifrau! I am TheInterview, your partial differential equations and simulations expert. Let's set up a simulation together.\n", "\n", "To get explanations, enter \"explain \". \n", "To see a recap of what we know so far, enter \"recap \". \n",  Theresa Pollinger committed Mar 14, 2018 16  "To interact with the current theory graph, enter \"tgwiev \". \n",  Theresa Pollinger committed Mar 08, 2018 17  "Otherwise, you can always try and use LaTeX-type input.\n",  Theresa Pollinger committed Mar 14, 2018 18 19  "\n", "You can inspect the currently loaded MMT theories under http://localhost:34757\n",  Theresa Pollinger committed Mar 08, 2018 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114  "\n", "\n", "\n", "How many dimensions does your model have?\n", "I am just assuming it's 1, since that is all we can currently handle.\n", "\n", "\n", "What is the domain you would like to simulate for? Ω : type ❘ = [?;?], e.g. Ω = [0.0;1.0]\n", "By the way, you can always try and use LaTeX-type input.\n" ] } ], "source": [ "anything" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "we will just assume that the variable is called x for now.\n", "\n", "\n", "Which variable(s) are you looking for? / What are the unknowns in your model? u : Ω → ??, e.g., u : Ω → ℝ ?\n" ] } ], "source": [ "Ω = [0.0;1.0]" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ok, u : Ω → ℝ\n", "u : Ω → ℝ\n", "\n", "\n", "Would you like to name additional parameters like constants or functions (that are independent of your unknowns)? c : ℝ = ? or f : Ω → ℝ = ?\n" ] } ], "source": [ "u : Ω → ℝ" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ok, f = [ x : Ω] x\n", "Would you like to declare more parameters? [y/n]? \n" ] } ], "source": [ "f = x" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ok, α = [ x : Ω] -5.0\n", "Would you like to declare more parameters? [y/n]? \n" ] } ], "source": [ "\\alpha = -5.0" ] }, { "cell_type": "code",  115  "execution_count": 6,  Theresa Pollinger committed Mar 08, 2018 116 117 118 119 120 121 122 123 124 125 126 127 128 129  "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [] } ], "source": [ "y" ] }, { "cell_type": "code",  130  "execution_count": 7,  Theresa Pollinger committed Mar 08, 2018 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198  "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "I did not catch that. Could you please rephrase?\n", "Details: MMT server error: unbound token: ·.
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info.kwarc.mmt.api.SourceError of level 2
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unbound token: ·
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source error (object-parser) at http://mathhub.info/MitM/smglom/calculus#15.0.15:15.0.15\n", "\n", "
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\n", " info.kwarc.mmt.api.frontend.Logger.logGroup$(Log.scala:31)\n", " \n", " \n", " info.kwarc.mmt.api.parser.NotationBasedParser.logGroup(NotationBasedParser.scala:69)\n", " \n", " \n", " info.kwarc.mmt.api.parser.NotationBasedParser.apply(NotationBasedParser.scala:214)\n", " \n", " \n",  199  " info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:141)\n",  Theresa Pollinger committed Mar 08, 2018 200 201  " \n", " \n",  202  " info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:287)\n",  Theresa Pollinger committed Mar 08, 2018 203 204  " \n", " \n",  205  " info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:292)\n",  Theresa Pollinger committed Mar 08, 2018 206 207  " \n", " \n",  208  " info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:879)\n",  Theresa Pollinger committed Mar 08, 2018 209 210  " \n", " \n",  211  " info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:630)\n",  Theresa Pollinger committed Mar 08, 2018 212 213  " \n", " \n",  214  " info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:457)\n",  Theresa Pollinger committed Mar 08, 2018 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292  " \n", " \n", " info.kwarc.mmt.interviews.InterviewServer.parseDecl(InterviewServer.scala:102)\n", " \n", " \n", " info.kwarc.mmt.interviews.InterviewServer.apply(InterviewServer.scala:50)\n", " \n", " \n", " info.kwarc.mmt.api.web.Server.resolveExtension(Server.scala:95)\n", " \n", " \n", " info.kwarc.mmt.api.web.Server.resolve(Server.scala:76)\n", " \n", " \n", " info.kwarc.mmt.api.web.Server.handleRequest(Server.scala:53)\n", " \n", " \n", " info.kwarc.mmt.api.web.TiscafServerImplementation$RequestHandler$$anon1.act(TiscafServerImplementation.scala:49)\n", " \n", " \n", " tiscaf.HSimpleLet.aact(HLet.scala:166)\n", " \n", " \n", " tiscaf.HSimpleLet.aact(HLet.scala:165)\n", " \n", " \n", " info.kwarc.mmt.api.web.TiscafServerImplementationRequestHandler$$anon$1.aact(TiscafServerImplementation.scala:47)\n", " \n", " \n", " tiscaf.HAcceptor.talk(HAcceptor.scala:246)\n", " \n", " \n", " tiscaf.HSimplePeer.doTalkItself$1(HPeer.scala:101)\n", "
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\n", "\n" ] } ], "source": [ "k = x \\cdot x" ] }, { "cell_type": "code",  293  "execution_count": 8,  Theresa Pollinger committed Mar 08, 2018 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313  "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "f = x\n", "α = -5.0\n", "\n", "\n", "Let's talk about your partial differential equation(s). What do they look like? Δu = 0.0, or laplace_operator Ω ℝ u = f ?\n" ] } ], "source": [ "n" ] }, { "cell_type": "code",  314  "execution_count": 9,  Theresa Pollinger committed Mar 08, 2018 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377  "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ok, \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "These are all the PDEs needed.\n", "Let's discuss your boundary conditions. What do they look like? u(x) = f(x) or u(1.0) = \\alpha ?\n" ] } ], "source": [ "Δu = \\alpha" ] }, { "cell_type": "code",  378  "execution_count": 10,  Theresa Pollinger committed Mar 08, 2018 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400  "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ok \n", "\n", "\n", "These are all the boundary conditions needed.\n", "\n", "\n", "Do you know something about the operator Δ? Is it e.g. linear, or not elliptic ? \n" ] } ], "source": [ "u = f" ] }, { "cell_type": "code",  401  "execution_count": 11,  Theresa Pollinger committed Mar 08, 2018 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417  "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "do you know anything else?\n" ] } ], "source": [ "y" ] }, { "cell_type": "code",  418  "execution_count": 12,  Theresa Pollinger committed Mar 08, 2018 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435  "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK!\n", "do you know anything else?\n" ] } ], "source": [ "linear" ] }, { "cell_type": "code",  436  "execution_count": 13,  Theresa Pollinger committed Mar 08, 2018 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453  "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK!\n", "do you know anything else?\n" ] } ], "source": [ "elliptic" ] }, { "cell_type": "code",  454  "execution_count": 14,  Theresa Pollinger committed Mar 08, 2018 455 456 457 458 459 460 461 462  "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n",  Theresa Pollinger committed Mar 14, 2018 463  "Would you like to try and solve the PDE using the Finite Difference Method in ExaStencils?If yes, you can provide a configuration name, or we'll just use your name. [y/n]? \n"  Theresa Pollinger committed Mar 08, 2018 464 465 466 467 468 469 470 471 472  ] } ], "source": [ "n" ] }, { "cell_type": "code",  473  "execution_count": 15,  Theresa Pollinger committed Mar 08, 2018 474 475 476 477 478 479  "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [  Theresa Pollinger committed Mar 14, 2018 480 481  "Generated ExaStencils input; running ExaStencils\n", "Ran ExaStencils; preparing visualization\n"  Theresa Pollinger committed Mar 08, 2018 482  ]  Theresa Pollinger committed Mar 14, 2018 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511  }, { "data": { "text/html": [ "\n", " \n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" },  512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531  { "data": { "text/html": [ "\n", "\n", "\n", " \n", " \n", " my plot\n", " \n", "\n", " \n", "\n", "\n", " \n", " \n", " \n", "
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