example_interview.ipynb 55.6 KB
 Theresa Pollinger committed Mar 08, 2018 1 2 3 { "cells": [ {  4  "cell_type": "markdown",  Theresa Pollinger committed Mar 08, 2018 5 6  "metadata": {}, "source": [  Theresa Pollinger committed Apr 06, 2018 7  "**Hello, user! I am TheInterview, your partial differential equations and simulations expert.**\n",  8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  "Let's set up a model and simulation together.\n", "\n", "To get explanations, enter explain . \n", "To see a recap of what we know so far, enter recap . \n", "To interactively visualize ther current theory graph, enter tgwiev or tgview mpd. \n", "Otherwise, you can always answer with LaTeX-type input.\n", "\n", "\n", "How many dimensions does your model have?\n", "\n", "\n", "I am just assuming it's 1, since that is all we can currently handle.\n", "\n", "\n", "\n", "\n", "What is the domain you would like to simulate for? Ω : type ❘ = [?;?], e.g. \\Omega = [0.0;1.0]\n", "By the way, you can always try and use LaTeX-type input.\n"  Theresa Pollinger committed Mar 08, 2018 26 27 28 29  ] }, { "cell_type": "code",  30  "execution_count": 1,  Theresa Pollinger committed Mar 08, 2018 31  "metadata": {},  32  "outputs": [  Theresa Pollinger committed Apr 10, 2018 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54  { "name": "stdout", "output_type": "stream", "text": [ "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephdomain\n", "\n", "Ω = [0.0;1.0]❙\n", "http://localhost:55537/:interview/infer?cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephdomain\n", "\n", "Ω\n", "http://localhost:55537/:query\n", "\n", "\n", "http://localhost:55537/:interview/new?view=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephdomainASmDomain&from=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FmDomain&to=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephdomain\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephdomainASmDomain\n", "\n", "domain = Ω❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephdomainASmDomain\n", "\n", "boundary = Ω❙\n" ] },  55  {  56 57 58 59 60  "data": { "text/markdown": [ "we will just assume that the variable is called x for now.\n", "\n", "\n",  Theresa Pollinger committed Apr 06, 2018 61 62  "\n", "Which variable(s) are you looking for? / What are the unknowns in your model? u : Ω ⟶ ??, e.g., u : Ω ⟶ ℝ ?\n"  63 64 65 66  ] }, "metadata": {}, "output_type": "display_data"  67 68  } ],  Theresa Pollinger committed Mar 08, 2018 69  "source": [  Theresa Pollinger committed Apr 10, 2018 70  "Ω = [0.0;1.0]\n"  Theresa Pollinger committed Mar 08, 2018 71 72 73 74  ] }, { "cell_type": "code",  75  "execution_count": 2,  Theresa Pollinger committed Mar 08, 2018 76  "metadata": {},  77  "outputs": [  Theresa Pollinger committed Apr 10, 2018 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119  { "name": "stdout", "output_type": "stream", "text": [ "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FT&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FT\n", "\n", "include http://mathhub.info/MitM/Foundation?Strings❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FT\n", "\n", "include ?ephdomain❙\n", "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FT_to_go_to_trash&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FT_to_go_to_trash\n", "\n", "include http://mathhub.info/MitM/Foundation?Strings❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FT_to_go_to_trash\n", "\n", "include ?ephdomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FT_to_go_to_trash\n", "\n", "T : Ω ⟶ ℝ❙\n", "http://localhost:55537/:interview/infer?cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FT_to_go_to_trash\n", "\n", "T\n", "http://localhost:55537/:query\n", "\n", "\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FT\n", "\n", "myUnkType = Ω ⟶ ℝ❙\n", "http://localhost:55537/:interview/new?view=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FTASmUnknown&from=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FmUnknown&to=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FT\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FTASmUnknown\n", "\n", "include ?mDomain = ?ephdomainASmDomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FTASmUnknown\n", "\n", "ucodomain = ℝ❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FTASmUnknown\n", "\n", "unknowntype = myUnkType❙\n" ] },  120  {  121 122  "data": { "text/markdown": [  Theresa Pollinger committed Apr 06, 2018 123 124  "Ok, T : Ω ⟶ ℝ\n", "\n",  125 126  "\n", "\n",  Theresa Pollinger committed Apr 06, 2018 127  "Would you like to name additional parameters like constants or functions (that are independent of your unknowns)? c : ℝ = ? or f : Ω ⟶ ℝ = ?\n"  128 129 130 131  ] }, "metadata": {}, "output_type": "display_data"  132 133  } ],  Theresa Pollinger committed Mar 08, 2018 134  "source": [  Theresa Pollinger committed Apr 06, 2018 135  "T : Ω ⟶ ℝ"  Theresa Pollinger committed Mar 08, 2018 136 137 138 139  ] }, { "cell_type": "code",  140  "execution_count": 3,  Theresa Pollinger committed Mar 08, 2018 141  "metadata": {},  142  "outputs": [  Theresa Pollinger committed Apr 10, 2018 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  { "name": "stdout", "output_type": "stream", "text": [ "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Ff&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Ff\n", "\n", "include http://mathhub.info/MitM/smglom/arithmetics?RealArithmetics❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Ff\n", "\n", "include ?ephdomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Ff\n", "\n", "include http://mathhub.info/MitM/Foundation?Math❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Ff\n", "\n", "f = [ x : Ω] x❘ role Quantity❙\n", "http://localhost:55537/:query\n", "\n", "\n", "http://localhost:55537/:interview/infer?cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Ff\n", "\n", "f\n", "http://localhost:55537/:interview/new?view=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FfASmParameter&from=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FmParameter&to=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Ff\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FfASmParameter\n", "\n", "include ?mDomain = ?ephdomainASmDomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FfASmParameter\n", "\n", "include ?mUnknown = ?TASmUnknown❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FfASmParameter\n", "\n", "ptype = { : Ω } Ω❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FfASmParameter\n", "\n", "param = f❙\n" ] },  181  {  182 183 184  "data": { "text/markdown": [ "Ok, f = [ x : Ω] x\n",  Theresa Pollinger committed Apr 06, 2018 185 186 187  "\n", "\n", "\n",  188 189 190 191 192  "Would you like to declare more parameters?\n" ] }, "metadata": {}, "output_type": "display_data"  193 194  } ],  Theresa Pollinger committed Mar 08, 2018 195 196 197 198 199 200  "source": [ "f = x" ] }, { "cell_type": "code",  201  "execution_count": 4,  Theresa Pollinger committed Mar 08, 2018 202  "metadata": {},  203  "outputs": [  Theresa Pollinger committed Apr 10, 2018 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247  { "name": "stdout", "output_type": "stream", "text": [ "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1\n", "\n", "include http://mathhub.info/MitM/smglom/arithmetics?RealArithmetics❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1\n", "\n", "include ?ephdomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1\n", "\n", "include http://mathhub.info/MitM/Foundation?Math❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1\n", "\n", "include ?f❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1\n", "\n", "α = [ x : Ω] -5.0❘ role Quantity❙\n", "http://localhost:55537/:query\n", "\n", "\n", "http://localhost:55537/:interview/infer?cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1\n", "\n", "α\n", "http://localhost:55537/:interview/new?view=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1ASmParameter&from=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FmParameter&to=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1ASmParameter\n", "\n", "include ?mDomain = ?ephdomainASmDomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1ASmParameter\n", "\n", "include ?mUnknown = ?TASmUnknown❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1ASmParameter\n", "\n", "include ?mParameter = ?fASmParameter❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1ASmParameter\n", "\n", "ptype = { : Ω } ℝ❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3F%CE%B1ASmParameter\n", "\n", "param = α❙\n" ] },  248  {  249 250 251  "data": { "text/markdown": [ "Ok, α = [ x : Ω] -5.0\n",  Theresa Pollinger committed Apr 06, 2018 252 253 254  "\n", "\n", "\n",  255 256 257 258 259  "Would you like to declare more parameters?\n" ] }, "metadata": {}, "output_type": "display_data"  260 261  } ],  Theresa Pollinger committed Mar 08, 2018 262 263 264 265 266 267  "source": [ "\\alpha = -5.0" ] }, { "cell_type": "code",  268  "execution_count": 5,  Theresa Pollinger committed Mar 08, 2018 269  "metadata": {},  270 271  "outputs": [ {  272 273 274 275 276  "data": { "text/markdown": [] }, "metadata": {}, "output_type": "display_data"  277 278  } ],  Theresa Pollinger committed Mar 08, 2018 279 280 281 282 283 284  "source": [ "y" ] }, { "cell_type": "code",  285  "execution_count": 6,  286 287 288 289 290  "metadata": { "scrolled": true }, "outputs": [ {  Theresa Pollinger committed Apr 10, 2018 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466  "name": "stdout", "output_type": "stream", "text": [ "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fk&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fk\n", "\n", "include http://mathhub.info/MitM/smglom/arithmetics?RealArithmetics❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fk\n", "\n", "include ?ephdomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fk\n", "\n", "include http://mathhub.info/MitM/Foundation?Math❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fk\n", "\n", "include ?f❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fk\n", "\n", "include ?α❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fk\n", "\n", "k = [ x : Ω] x · x❘ role Quantity❙\n" ] }, { "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/differentialequations#15.0.15:15.0.15\n", "\n", "
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\n", " info.kwarc.mmt.api.parser.NotationBasedParser.makeError(NotationBasedParser.scala:93)\n", "
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\n", " info.kwarc.mmt.api.parser.NotationBasedParser.makeTerm(NotationBasedParser.scala:321)\n", "
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\n", " info.kwarc.mmt.api.parser.NotationBasedParser.$anonfun$makeTerm$5(NotationBasedParser.scala:345)\n", " \n", " \n", " scala.collection.immutable.List.map(List.scala:287)\n", " \n", " \n", " info.kwarc.mmt.api.parser.NotationBasedParser.makeTerm(NotationBasedParser.scala:345)\n", " \n", " \n", " info.kwarc.mmt.api.parser.NotationBasedParser.doFoundContent$1(NotationBasedParser.scala:437)\n", "
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\n", " info.kwarc.mmt.api.parser.NotationBasedParser.$anonfun$makeTermFromMatchedList$14(NotationBasedParser.scala:496)\n", " \n", " \n", " info.kwarc.mmt.api.parser.NotationBasedParser.$anonfun$makeTermFromMatchedList$14$adapted(NotationBasedParser.scala:493)\n", " \n", " \n", " scala.collection.immutable.List.foreach(List.scala:389)\n", " \n", " \n", " info.kwarc.mmt.api.parser.NotationBasedParser.makeTermFromMatchedList(NotationBasedParser.scala:493)\n", " \n", " \n", " info.kwarc.mmt.api.parser.NotationBasedParser.makeTerm(NotationBasedParser.scala:329)\n", " \n", " \n", " info.kwarc.mmt.api.parser.NotationBasedParser.makeTerm(NotationBasedParser.scala:335)\n", " \n", " \n", " info.kwarc.mmt.api.parser.NotationBasedParser.$anonfun$apply$10(NotationBasedParser.scala:214)\n", "
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\n", " info.kwarc.mmt.api.frontend.Logger.logGroup(Log.scala:34)\n", "
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\n", " info.kwarc.mmt.api.frontend.Logger.logGroup$(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", " info.kwarc.mmt.api.parser.KeywordBasedParser.puCont(StructureParser.scala:141)\n", " \n", " \n", " info.kwarc.mmt.api.parser.KeywordBasedParser.readParsedObject(StructureParser.scala:287)\n", " \n", " \n", " info.kwarc.mmt.api.parser.KeywordBasedParser.doComponent(StructureParser.scala:292)\n", " \n", " \n", " info.kwarc.mmt.api.parser.KeywordBasedParser.readConstant(StructureParser.scala:880)\n", " \n", " \n", " info.kwarc.mmt.api.parser.KeywordBasedParser.readInModuleAux(StructureParser.scala:630)\n", " \n", " \n", " info.kwarc.mmt.api.parser.KeywordBasedParser.readInModule(StructureParser.scala:457)\n", " \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$1(HPeer.scala:101)\n", "
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\n", " tiscaf.HSimplePeer.$anonfun$readChannel$1(HPeer.scala:114)\n", " \n", " \n", " scala.runtime.java8.JFunction0$mcV$sp.apply(JFunction0$mcV$sp.java:12)\n", " \n", " \n", " scala.concurrent.Future$.$anonfun$apply$1(Future.scala:653)\n", " \n", " \n", " scala.util.Success.$anonfun$map$1(Try.scala:251)\n", "
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\n", " scala.concurrent.impl.Promise.$anonfun$transform$1(Promise.scala:29)\n", " \n", " \n", " scala.concurrent.impl.CallbackRunnable.run(Promise.scala:60)\n", " \n", " \n", " tiscaf.sync.SyncQuExecutionContext$$anon$1.run(SyncQuExecutionContext.scala:69)\n", "
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\n", "\n" ]  467 468  } ],  Theresa Pollinger committed Mar 08, 2018 469 470 471 472 473 474  "source": [ "k = x \\cdot x" ] }, { "cell_type": "code",  475  "execution_count": 7,  Theresa Pollinger committed Mar 08, 2018 476  "metadata": {},  477 478  "outputs": [ {  479 480 481 482 483 484  "data": { "text/markdown": [ "f = x\n", "α = -5.0\n", "\n", "\n",  Theresa Pollinger committed Apr 06, 2018 485  "\n",  486 487 488 489 490  "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" ] }, "metadata": {}, "output_type": "display_data"  491 492  } ],  Theresa Pollinger committed Mar 08, 2018 493 494 495 496 497 498  "source": [ "n" ] }, { "cell_type": "code",  499  "execution_count": 8,  Theresa Pollinger committed Mar 21, 2018 500 501 502  "metadata": { "scrolled": true },  503  "outputs": [  Theresa Pollinger committed Apr 10, 2018 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624  { "name": "stdout", "output_type": "stream", "text": [ "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", "include ?mDifferentialOperators❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", "include ?T❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", "include ?f❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", "include ?α❙\n", "http://localhost:55537/:interview/infer?cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", " α\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", "include ?T❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", "include ?f❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", "include ?α❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", " mylhs = [ anyT : Ω ⟶ ℝ ] Δ anyT ❙\n", "http://localhost:55537/:query\n", "\n", "\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", " myrhs = α❙\n", "http://localhost:55537/:query\n", "\n", "\n", "http://localhost:55537/:interview/new?view=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1ASmPDE&from=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FmPDE&to=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1ASmPDE\n", "\n", "include ?mDomain = ?ephdomainASmDomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1ASmPDE\n", "\n", "include ?mUnknown = ?TASmUnknown❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1ASmPDE\n", "\n", "include ?mParameter = ?fASmParameter❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1ASmPDE\n", "\n", "include ?mParameter = ?αASmParameter❙\n", "http://localhost:55537/:interview/infer?cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", "mylhs\n", "http://localhost:55537/:interview/infer?cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", "myrhs\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1ASmPDE\n", "\n", "eqtype = ℝ❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1ASmPDE\n", "\n", "lhs = mylhs❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1ASmPDE\n", "\n", "rhs = myrhs❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1ASmPDE\n", "\n", "pde = [u](mylhs u) ≐ myrhs❙\n", "http://localhost:55537/:query\n", "\n", "\n", "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs\n", "\n", "include ?ephdomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs\n", "\n", "include ?mLinearity❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs\n", "\n", "include ?mDifferentialOperators❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs\n", "\n", "include http://mathhub.info/MitM/smglom/arithmetics?RealArithmetics❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs\n", "\n", "include ?T❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs\n", "\n", "structure T_boundary_types : ?mBCTypes =include ?mUnknown = ?TASmUnknown❙include ?mDifferentialOperators = ?mDifferentialOperators❙❚\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs\n", "\n", "include ?f❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs\n", "\n", "include ?α❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs\n", "\n", "include ?ephpde1❙\n", "http://localhost:55537/:interview/new?view=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephbcsASmBCsRequired&from=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FmBCsRequired&to=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephbcs\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephbcsASmBCsRequired\n", "\n", "include ?mDomain = ?ephdomainASmDomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephbcsASmBCsRequired\n", "\n", "include ?mUnknown = ?TASmUnknown❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephbcsASmBCsRequired\n", "\n", "include ?mParameter = ?fASmParameter❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephbcsASmBCsRequired\n", "\n", "include ?mParameter = ?αASmParameter❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephbcsASmBCsRequired\n", "\n", "include ?mPDE = ?ephpde1ASmPDE❙\n" ] },  625  {  626 627 628 629 630 631 632  "data": { "text/markdown": [ "Ok, \n", " \n", " \n", " \n", " \n",  Theresa Pollinger committed Apr 06, 2018 633  " \n",  634 635 636  " \n", " \n", " \n",  Theresa Pollinger committed Apr 06, 2018 637  " \n",  638 639 640 641 642 643 644 645 646 647  " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n",  Theresa Pollinger committed Apr 06, 2018 648  " \n",  649 650 651 652 653  " \n", " \n", " \n", " \n", " \n",  Theresa Pollinger committed Apr 06, 2018 654  " \n",  655 656 657 658 659 660 661 662  " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n",  Theresa Pollinger committed Apr 06, 2018 663  " \n",  664 665 666 667 668 669 670 671 672 673  " \n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n",  Theresa Pollinger committed Apr 06, 2018 674  "\n",  675 676 677 678 679 680  "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" ] }, "metadata": {}, "output_type": "display_data"  681 682  } ],  Theresa Pollinger committed Mar 08, 2018 683  "source": [  Theresa Pollinger committed Apr 06, 2018 684  "ΔT = \\alpha"  Theresa Pollinger committed Mar 08, 2018 685 686 687 688  ] }, { "cell_type": "code",  689  "execution_count": 9,  Theresa Pollinger committed Mar 08, 2018 690  "metadata": {},  691  "outputs": [  Theresa Pollinger committed Apr 10, 2018 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756  { "name": "stdout", "output_type": "stream", "text": [ "http://localhost:55537/:interview/infer?cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", " [ anyT : Ω ⟶ ℝ ] anyT \n", "http://localhost:55537/:interview/infer?cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3Fephpde1\n", "\n", " f\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephbcsASmBCsRequired\n", "\n", "firstBC = T_boundary_types/DirichletBCfun f❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephbcsASmBCsRequired\n", "\n", "secondBC = T_boundary_types/DirichletBCfun f❙\n", "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem\n", "\n", "include ?mLinearity❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem\n", "\n", "include http://mathhub.info/MitM/Foundation?Strings❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem\n", "\n", "include ?T❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem\n", "\n", "include ?f❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem\n", "\n", "include ?α❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem\n", "\n", "include ?ephpde1❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem\n", "\n", "include ?ephbcs❙\n", "http://localhost:55537/:interview/new?view=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem&from=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FmEllipticLinearDirichletBoundaryValueProblem&to=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem\n", "\n", "include ?mDomain = ?ephdomainASmDomain❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem\n", "\n", "include ?mUnknown = ?TASmUnknown❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem\n", "\n", "include ?mParameter = ?fASmParameter❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem\n", "\n", "include ?mParameter = ?αASmParameter❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem\n", "\n", "include ?mPDE = ?ephpde1ASmPDE❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem\n", "\n", "include ?mBCsRequired = ?ephbcsASmBCsRequired❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem\n", "\n", "include ?mDifferentialOperators = ?mDifferentialOperators❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem\n", "\n", "include ?mLinearity = ?mLinearity❙\n" ] },  757  {  758 759  "data": { "text/markdown": [  Theresa Pollinger committed Apr 10, 2018 760 761 762 763 764 765 766 767 768  "Ok \n", "\n", "\n", "\n", "These are all the boundary conditions needed.\n", "\n", "\n", "\n", "Do you know something about the operator Δ? Is it e.g. linear, or not elliptic ? \n"  769 770 771 772  ] }, "metadata": {}, "output_type": "display_data"  773 774  } ],  Theresa Pollinger committed Mar 08, 2018 775  "source": [  Theresa Pollinger committed Apr 06, 2018 776  "T = f"  Theresa Pollinger committed Mar 08, 2018 777 778 779 780  ] }, { "cell_type": "code",  781  "execution_count": 10,  Theresa Pollinger committed Mar 08, 2018 782  "metadata": {},  783  "outputs": [  Theresa Pollinger committed Apr 10, 2018 784 785 786 787 788 789 790 791 792 793 794 795  { "name": "stdout", "output_type": "stream", "text": [ "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem\n", "\n", "user_linear : ⊦ linear mylhs ❘= sketch \"user knowledge\" ❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem\n", "\n", "isLinear = user_linear❙\n" ] },  796  {  797 798  "data": { "text/markdown": [  Theresa Pollinger committed Apr 10, 2018 799 800  "OK!\n", "do you know anything else?\n"  801 802 803 804  ] }, "metadata": {}, "output_type": "display_data"  805 806  } ],  Theresa Pollinger committed Mar 08, 2018 807 808 809 810 811 812  "source": [ "linear" ] }, { "cell_type": "code",  813  "execution_count": 11,  Theresa Pollinger committed Mar 08, 2018 814  "metadata": {},  815  "outputs": [  Theresa Pollinger committed Apr 10, 2018 816 817 818 819 820 821 822 823 824 825 826 827  { "name": "stdout", "output_type": "stream", "text": [ "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblem\n", "\n", "user_elliptic : ⊦ elliptic mylhs ❘= sketch \"user knowledge\" ❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem\n", "\n", "isElliptic = user_elliptic❙\n" ] },  828  {  829 830  "data": { "text/markdown": [  Theresa Pollinger committed Apr 10, 2018 831 832  "OK!\n", "do you know anything else?\n"  833 834 835 836  ] }, "metadata": {}, "output_type": "display_data"  837 838  } ],  Theresa Pollinger committed Mar 08, 2018 839 840 841 842 843 844  "source": [ "elliptic" ] }, { "cell_type": "code",  845  "execution_count": 12,  Theresa Pollinger committed Mar 08, 2018 846  "metadata": {},  847 848  "outputs": [ {  849 850  "data": { "text/markdown": [  Theresa Pollinger committed Apr 10, 2018 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904  "\n", "\n", "\n", "These are the things we know so far about your problem:\n", "\n", "\n", "\n", "\n", "\n", "\n", "domain: {'name': 'Ω', 'theoryname': 'ephdomain', 'axes': OrderedDict([('x', '[0.0;1.0]')]), 'from': '0.0', 'to': '1.0', 'boundary_name': 'Ω', 'viewname': 'ephdomainASmDomain'}\n", "\n", "\n", "\n", "\n", "\n", "\n", "unknowns: OrderedDict([('T', {'theoryname': 'T', 'string': 'T : Ω ⟶ ℝ', 'type': 'Ω ⟶ ℝ', 'codomain': 'ℝ', 'viewname': 'TASmUnknown'})])\n", "\n", "\n", "\n", "\n", "\n", "\n", "parameters: OrderedDict([('f', {'theoryname': 'f', 'string': 'f = x', 'parsestring': 'f = [ x : Ω] x', 'type': '{ : Ω } Ω', 'viewname': 'fASmParameter'}), ('α', {'theoryname': 'α', 'string': 'α = -5.0', 'parsestring': 'α = [ x : Ω] -5.0', 'type': '{ : Ω } ℝ', 'viewname': 'αASmParameter'})])\n", "\n", "\n", "\n", "\n", "\n", "\n", "pdes: {'pdes': [{'theoryname': 'ephpde1', 'string': 'ΔT = α', 'lhsstring': 'ΔT', 'rhsstring': 'α', 'rhsstring_expanded': '-5.0', 'viewname': 'ephpde1ASmPDE', 'op': 'Δ', 'lhsparsestring': ' [ anyT : Ω ⟶ ℝ ] Δ anyT ', 'rhsparsestring': ' α'}]}\n", "\n", "\n", "\n", "\n", "\n", "\n", "bcs: {'theoryname': 'ephbcs', 'bcs': [{'name': 'bc0', 'string': 'T = f', 'lhsstring': 'T', 'rhsstring': 'f', 'rhsstring_expanded': 'x', 'type': ('Dirichlet',), 'on': ('x',), 'measure': (2,)}], 'viewname': 'ephbcsASmBCsRequired', 'measure_given': 2}\n", "\n", "\n", "\n", "\n", "\n", "\n", "props: {'theoryname': 'ephBoundaryValueProblem', 'viewname': 'ephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem', 'ops': [{'name': 'Δ', 'props': ['elliptic'], 'linear': True}]}\n", "\n", "\n", "\n", "\n", "\n", "\n", "sim: {'type': None}\n", "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.\n"  905 906 907 908  ] }, "metadata": {}, "output_type": "display_data"  909 910  } ],  Theresa Pollinger committed Mar 08, 2018 911 912 913 914 915 916  "source": [ "n" ] }, { "cell_type": "code",  Theresa Pollinger committed Mar 21, 2018 917  "execution_count": null,  Theresa Pollinger committed Mar 08, 2018 918  "metadata": {},  Theresa Pollinger committed Mar 21, 2018 919  "outputs": [],  920 921 922 923  "source": [] }, { "cell_type": "code",  Theresa Pollinger committed Apr 10, 2018 924  "execution_count": null,  925 926 927 928 929  "metadata": { "scrolled": false }, "outputs": [ {  Theresa Pollinger committed Apr 10, 2018 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973  "name": "stdout", "output_type": "stream", "text": [ "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_T&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_T\n", "\n", "include ?T❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_T\n", "\n", "T : Ω ⟶ ℝ❘ role Quantity❙\n", "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_f&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_f\n", "\n", "include ?f❙\n", "http://localhost:55537/:query\n", "\n", "\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_f\n", "\n", "proof_f : ⊦ f ≐ [ x : Ω] x❘ role Law❙\n", "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_%CE%B1&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_%CE%B1\n", "\n", "include ?α❙\n", "http://localhost:55537/:query\n", "\n", "\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_%CE%B1\n", "\n", "proof_α : ⊦ α ≐ [ x : Ω] -5.0❘ role Law❙\n", "http://localhost:55537/:interview/new?theory=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_ephpde1&meta=http%3A//mathhub.info/MitM/Foundation%3FLogic\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_ephpde1\n", "\n", "include ?ephpde1❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_ephpde1\n", "\n", "include ?MPD_T❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_ephpde1\n", "\n", "include ?f❙\n", "http://localhost:55537/:interview/new?decl=d&cont=http%3A//mathhub.info/MitM/smglom/calculus/differentialequations%3FMPD_ephpde1\n", "\n", "include ?α❙\n" ]  974 975  } ],  976  "source": [  977  "tgview mpd"  978 979 980 981  ] }, { "cell_type": "code",  982  "execution_count": 14,  983  "metadata": {},  984 985  "outputs": [ {  986 987  "data": { "text/markdown": [  Theresa Pollinger committed Apr 06, 2018 988 989 990 991 992 993 994  "These are the things we know so far about your problem:\n", "\n", "\n", "\n", "\n", "\n", "\n",  995  "domain: {'name': 'Ω', 'theoryname': 'ephdomain', 'axes': OrderedDict([('x', '[0.0;1.0]')]), 'from': '0.0', 'to': '1.0', 'boundary_name': 'Ω', 'viewname': 'ephdomainASmDomain'}\n",  Theresa Pollinger committed Apr 06, 2018 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008  "\n", "\n", "\n", "\n", "\n", "\n", "unknowns: OrderedDict([('T', {'theoryname': 'T', 'string': 'T : Ω ⟶ ℝ', 'type': 'Ω ⟶ ℝ', 'codomain': 'ℝ', 'viewname': 'TASmUnknown'})])\n", "\n", "\n", "\n", "\n", "\n", "\n",  1009  "parameters: OrderedDict([('f', {'theoryname': 'f', 'string': 'f = x', 'parsestring': 'f = [ x : Ω] x', 'type': '{ : Ω } Ω', 'viewname': 'fASmParameter'}), ('α', {'theoryname': 'α', 'string': 'α = -5.0', 'parsestring': 'α = [ x : Ω] -5.0', 'type': '{ : Ω } ℝ', 'viewname': 'αASmParameter'})])\n",  Theresa Pollinger committed Apr 06, 2018 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022  "\n", "\n", "\n", "\n", "\n", "\n", "pdes: {'pdes': [{'theoryname': 'ephpde1', 'string': 'ΔT = α', 'lhsstring': 'ΔT', 'rhsstring': 'α', 'rhsstring_expanded': '-5.0', 'viewname': 'ephpde1ASmPDE', 'op': 'Δ', 'lhsparsestring': ' [ anyT : Ω ⟶ ℝ ] Δ anyT ', 'rhsparsestring': ' α'}]}\n", "\n", "\n", "\n", "\n", "\n", "\n",  Theresa Pollinger committed Apr 10, 2018 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037  "bcs: {'theoryname': 'ephbcs', 'bcs': [{'name': 'bc0', 'string': 'T = f', 'lhsstring': 'T', 'rhsstring': 'f', 'rhsstring_expanded': 'x', 'type': ('Dirichlet',), 'on': ('x',), 'measure': (2,)}], 'viewname': 'ephbcsASmBCsRequired', 'measure_given': 2}\n", "\n", "\n", "\n", "\n", "\n", "\n", "props: {'theoryname': 'ephBoundaryValueProblem', 'viewname': 'ephBoundaryValueProblemASmEllipticLinearDirichletBoundaryValueProblem', 'ops': [{'name': 'Δ', 'props': ['elliptic'], 'linear': True}]}\n", "\n", "\n", "\n", "\n", "\n", "\n", "sim: {'type': None}\n"  1038 1039 1040 1041  ] }, "metadata": {}, "output_type": "display_data"  1042 1043  } ],  Theresa Pollinger committed Mar 14, 2018 1044  "source": [  1045  "recap"  Theresa Pollinger committed Mar 14, 2018 1046  ]  1047  },  1048 1049  { "cell_type": "code",  1050  "execution_count": 15,  1051  "metadata": {},  1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082  "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{\n", " \"stdin_port\": UNKNOWN,\n", " \"shell_port\": UNKNOWN,\n", " \"iopub_port\": UNKNOWN,\n", " \"hb_port\": UNKNOWN,\n", " \"ip\": \"UNKNOWN\",\n", " \"key\": \"UNKNOWN\",\n", " \"signature_scheme\": \"UNKNOWN\",\n", " \"transport\": \"UNKNOWN\"\n", "}\n", "\n", "Paste the above JSON into a file, and connect with:\n", " $> ipython --existing \n", "or, if you are local, you can connect with just:\n", "$> ipython --existing UNKNOWN\n", "\n", "or even just:\n", " \$> ipython --existing\n", "if this is the most recent Jupyter session you have started.\n", "\n" ] } ], "source": [ "%connect_info" ]  1083  },  Theresa Pollinger committed Apr 06, 2018 1084 1085  { "cell_type": "code",  Theresa Pollinger committed Apr 10, 2018 1086  "execution_count": 16,  Theresa Pollinger committed Apr 06, 2018 1087  "metadata": {},  Theresa Pollinger committed Apr 10, 2018 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117  "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tgview" ]  Theresa Pollinger committed Apr 06, 2018 1118  },  Theresa Pollinger committed Mar 08, 2018 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128  { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": {  1129  "display_name": "TheInterview",  Theresa Pollinger committed Mar 08, 2018 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147  "language": "text", "name": "interview" }, "language_info": { "file_extension": ".txt", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/plain", "name": "text" } }, "nbformat": 4, "nbformat_minor": 2 }