-
Notifications
You must be signed in to change notification settings - Fork 2
/
autocorrelation.nb
executable file
·476 lines (460 loc) · 19.1 KB
/
autocorrelation.nb
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
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
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
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
199
200
201
202
203
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
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
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
467
468
469
470
471
472
473
474
475
476
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 9.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 157, 7]
NotebookDataLength[ 18902, 467]
NotebookOptionsPosition[ 18268, 442]
NotebookOutlinePosition[ 18611, 457]
CellTagsIndexPosition[ 18568, 454]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{"Remove", "[", "\"\<Global`*\>\"", "]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"BCR", "[", "r_", "]"}], "=",
TagBox[GridBox[{
{"\[Piecewise]", GridBox[{
{"1",
RowBox[{
SuperscriptBox["r", "2"], "\[LessEqual]", "1"}]},
{"0", "True"}
},
AllowedDimensions->{2, Automatic},
Editable->True,
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {},
"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxItemSize->{
"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.84]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}},
Selectable->True]}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxItemSize->{
"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.35]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
"Piecewise",
DeleteWithContents->True,
Editable->False,
SelectWithContents->True,
Selectable->False]}], ";"}], "\[IndentingNewLine]",
RowBox[{"ConvolPair", "=",
RowBox[{"FullSimplify", "[",
RowBox[{"FunctionExpand", "[",
RowBox[{
RowBox[{"BCR", "[", "r", "]"}],
RowBox[{"BCR", "[",
RowBox[{"r", "-", "rp"}], "]"}]}], "]"}],
"]"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"F", "[", "\[Rho]_", "]"}], "=",
RowBox[{"FourierTransform", "[",
RowBox[{
RowBox[{"BCR", "[", "r", "]"}], ",",
RowBox[{"{", "r", "}"}], ",",
RowBox[{"{", "\[Rho]", "}"}]}], "]"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"FRT", "[", "\[Rho]_", "]"}], "=",
RowBox[{
RowBox[{"F", "[", "\[Rho]", "]"}],
RowBox[{"F", "[", "\[Rho]", "]"}]}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"RT", "[", "r_", "]"}], "=",
RowBox[{"FourierTransform", "[",
RowBox[{
RowBox[{"FRT", "[", "\[Rho]", "]"}], ",",
RowBox[{"{", "\[Rho]", "}"}], ",",
RowBox[{"{", "r", "}"}]}], "]"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"RT2", "[", "rp_", "]"}], "=",
RowBox[{"Integrate", "[",
RowBox[{"ConvolPair", " ", ",",
RowBox[{"{",
RowBox[{"r", ",",
RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "]"}]}],
"\[IndentingNewLine]", "\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"(*",
RowBox[{
RowBox[{
RowBox[{"AutoCor", "[", "r_", "]"}], ":=",
RowBox[{
RowBox[{
RowBox[{"NIntegrate", "[",
RowBox[{
RowBox[{
RowBox[{"BCR", "[", "r", "]"}],
RowBox[{"BCR", "[",
RowBox[{"r", "-", "rp"}], "]"}]}], ",",
RowBox[{"{",
RowBox[{"rp", ",",
RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "]"}],
"\[IndentingNewLine]", "plot"}], "=",
RowBox[{"Table", "[",
RowBox[{
RowBox[{"AutoCor", "[", "r", "]"}], ",",
RowBox[{"{",
RowBox[{"r", ",",
RowBox[{"-", "1"}], ",", "1", ",", ".01"}], "}"}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"ListPlot", "[", "plot", "]"}]}], "*)"}]}]}], "Input",
CellChangeTimes->{{3.5901839675814686`*^9, 3.5901840582389374`*^9},
3.5901841338194838`*^9, {3.590184405010785*^9, 3.5901844657684655`*^9}, {
3.590184506704664*^9, 3.590184508123844*^9}, {3.590184577740655*^9,
3.5901845963769903`*^9}, {3.590184710702469*^9, 3.5901847137168283`*^9}, {
3.5901847574593754`*^9, 3.590184831232692*^9}, {3.5901848634707704`*^9,
3.5901848913803387`*^9}, {3.590185094513999*^9, 3.590185097815428*^9}, {
3.5902284960292463`*^9, 3.590228584392511*^9}, {3.5902287081652856`*^9,
3.590228709132406*^9}, 3.590228889756424*^9, {3.5902289959169397`*^9,
3.5902291791172915`*^9}, {3.590229224512108*^9, 3.5902292777708783`*^9}, {
3.5902293219065037`*^9, 3.5902293525043926`*^9}, {3.5902300655002728`*^9,
3.5902301010497913`*^9}, {3.590230166868188*^9, 3.590230214093198*^9}, {
3.590243094148217*^9, 3.590243118022255*^9}, {3.590243488707511*^9,
3.5902434990448427`*^9}, {3.5902435335032263`*^9, 3.590243657782053*^9}, {
3.5902437629764585`*^9, 3.5902441030677986`*^9}, {3.590244184075141*^9,
3.5902442850540133`*^9}, {3.590244557708761*^9, 3.590244624528266*^9}, {
3.590244795240016*^9, 3.590244944355025*^9}}],
Cell[BoxData[
TagBox[GridBox[{
{"\[Piecewise]", GridBox[{
{"1",
RowBox[{
RowBox[{
RowBox[{"-", "1"}], "\[LessEqual]", "r", "\[LessEqual]", "1"}], "&&",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"r", "-", "rp"}], ")"}], "2"], "\[LessEqual]", "1"}]}]},
{"0",
TagBox["True",
"PiecewiseDefault",
AutoDelete->True]}
},
AllowedDimensions->{2, Automatic},
Editable->True,
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxItemSize->{
"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.84]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}},
Selectable->True]}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxItemSize->{
"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.35]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
"Piecewise",
DeleteWithContents->True,
Editable->False,
SelectWithContents->True,
Selectable->False]], "Output",
CellChangeTimes->{
3.5901844676287017`*^9, 3.5901845100280633`*^9, 3.590184597083075*^9,
3.5901847768638353`*^9, {3.5901848273362045`*^9, 3.5901848315857377`*^9},
3.590184892414443*^9, 3.5901851099789524`*^9, {3.5902285570780153`*^9,
3.590228585016569*^9}, {3.5902290668609858`*^9, 3.590229071363597*^9},
3.5902291796843596`*^9, 3.59022935325248*^9, {3.5902430951213427`*^9,
3.590243118412324*^9}, 3.5902435724871817`*^9, {3.5902436026750298`*^9,
3.5902436339110055`*^9}, {3.5902438563133497`*^9, 3.590243885087017*^9}, {
3.59024391760917*^9, 3.590243961226727*^9}, {3.59024406515397*^9,
3.5902441039489107`*^9}, 3.5902442859071016`*^9, {3.5902446173403473`*^9,
3.5902446249383097`*^9}, {3.590244820916295*^9, 3.5902449452531404`*^9}}],
Cell[BoxData[
FractionBox[
RowBox[{
SqrtBox[
FractionBox["2", "\[Pi]"]], " ",
RowBox[{"Sin", "[", "\[Rho]", "]"}]}], "\[Rho]"]], "Output",
CellChangeTimes->{
3.5901844676287017`*^9, 3.5901845100280633`*^9, 3.590184597083075*^9,
3.5901847768638353`*^9, {3.5901848273362045`*^9, 3.5901848315857377`*^9},
3.590184892414443*^9, 3.5901851099789524`*^9, {3.5902285570780153`*^9,
3.590228585016569*^9}, {3.5902290668609858`*^9, 3.590229071363597*^9},
3.5902291796843596`*^9, 3.59022935325248*^9, {3.5902430951213427`*^9,
3.590243118412324*^9}, 3.5902435724871817`*^9, {3.5902436026750298`*^9,
3.5902436339110055`*^9}, {3.5902438563133497`*^9, 3.590243885087017*^9}, {
3.59024391760917*^9, 3.590243961226727*^9}, {3.59024406515397*^9,
3.5902441039489107`*^9}, 3.5902442859071016`*^9, {3.5902446173403473`*^9,
3.5902446249383097`*^9}, {3.590244820916295*^9, 3.5902449454491663`*^9}}],
Cell[BoxData[
FractionBox[
RowBox[{"2", " ",
SuperscriptBox[
RowBox[{"Sin", "[", "\[Rho]", "]"}], "2"]}],
RowBox[{"\[Pi]", " ",
SuperscriptBox["\[Rho]", "2"]}]]], "Output",
CellChangeTimes->{
3.5901844676287017`*^9, 3.5901845100280633`*^9, 3.590184597083075*^9,
3.5901847768638353`*^9, {3.5901848273362045`*^9, 3.5901848315857377`*^9},
3.590184892414443*^9, 3.5901851099789524`*^9, {3.5902285570780153`*^9,
3.590228585016569*^9}, {3.5902290668609858`*^9, 3.590229071363597*^9},
3.5902291796843596`*^9, 3.59022935325248*^9, {3.5902430951213427`*^9,
3.590243118412324*^9}, 3.5902435724871817`*^9, {3.5902436026750298`*^9,
3.5902436339110055`*^9}, {3.5902438563133497`*^9, 3.590243885087017*^9}, {
3.59024391760917*^9, 3.590243961226727*^9}, {3.59024406515397*^9,
3.5902441039489107`*^9}, 3.5902442859071016`*^9, {3.5902446173403473`*^9,
3.5902446249383097`*^9}, {3.590244820916295*^9, 3.5902449454511647`*^9}}],
Cell[BoxData[
FractionBox[
RowBox[{
RowBox[{
RowBox[{"-", "2"}], " ",
RowBox[{"Sign", "[",
RowBox[{
RowBox[{"-", "2"}], "+", "r"}], "]"}]}], "+",
RowBox[{"r", " ",
RowBox[{"Sign", "[",
RowBox[{
RowBox[{"-", "2"}], "+", "r"}], "]"}]}], "-",
RowBox[{"2", " ", "r", " ",
RowBox[{"Sign", "[", "r", "]"}]}], "+",
RowBox[{"2", " ",
RowBox[{"Sign", "[",
RowBox[{"2", "+", "r"}], "]"}]}], "+",
RowBox[{"r", " ",
RowBox[{"Sign", "[",
RowBox[{"2", "+", "r"}], "]"}]}]}],
RowBox[{"2", " ",
SqrtBox[
RowBox[{"2", " ", "\[Pi]"}]]}]]], "Output",
CellChangeTimes->{
3.5901844676287017`*^9, 3.5901845100280633`*^9, 3.590184597083075*^9,
3.5901847768638353`*^9, {3.5901848273362045`*^9, 3.5901848315857377`*^9},
3.590184892414443*^9, 3.5901851099789524`*^9, {3.5902285570780153`*^9,
3.590228585016569*^9}, {3.5902290668609858`*^9, 3.590229071363597*^9},
3.5902291796843596`*^9, 3.59022935325248*^9, {3.5902430951213427`*^9,
3.590243118412324*^9}, 3.5902435724871817`*^9, {3.5902436026750298`*^9,
3.5902436339110055`*^9}, {3.5902438563133497`*^9, 3.590243885087017*^9}, {
3.59024391760917*^9, 3.590243961226727*^9}, {3.59024406515397*^9,
3.5902441039489107`*^9}, 3.5902442859071016`*^9, {3.5902446173403473`*^9,
3.5902446249383097`*^9}, {3.590244820916295*^9, 3.590244945494171*^9}}],
Cell[BoxData[
TagBox[GridBox[{
{"\[Piecewise]", GridBox[{
{"2",
RowBox[{"rp", "\[Equal]", "0"}]},
{
RowBox[{"2", "-", "rp"}],
RowBox[{"0", "<", "rp", "<", "2"}]},
{
RowBox[{"2", "+", "rp"}],
RowBox[{
RowBox[{"-", "2"}], "<", "rp", "<", "0"}]},
{"0",
TagBox["True",
"PiecewiseDefault",
AutoDelete->True]}
},
AllowedDimensions->{2, Automatic},
Editable->True,
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxItemSize->{
"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.84]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}},
Selectable->True]}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxItemSize->{
"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.35]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
"Piecewise",
DeleteWithContents->True,
Editable->False,
SelectWithContents->True,
Selectable->False]], "Output",
CellChangeTimes->{
3.5901844676287017`*^9, 3.5901845100280633`*^9, 3.590184597083075*^9,
3.5901847768638353`*^9, {3.5901848273362045`*^9, 3.5901848315857377`*^9},
3.590184892414443*^9, 3.5901851099789524`*^9, {3.5902285570780153`*^9,
3.590228585016569*^9}, {3.5902290668609858`*^9, 3.590229071363597*^9},
3.5902291796843596`*^9, 3.59022935325248*^9, {3.5902430951213427`*^9,
3.590243118412324*^9}, 3.5902435724871817`*^9, {3.5902436026750298`*^9,
3.5902436339110055`*^9}, {3.5902438563133497`*^9, 3.590243885087017*^9}, {
3.59024391760917*^9, 3.590243961226727*^9}, {3.59024406515397*^9,
3.5902441039489107`*^9}, 3.5902442859071016`*^9, {3.5902446173403473`*^9,
3.5902446249383097`*^9}, {3.590244820916295*^9, 3.590244945519207*^9}}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"RT2", "[", "\[Rho]", "]"}], ",",
RowBox[{"{",
RowBox[{"\[Rho]", ",",
RowBox[{
RowBox[{"-", "2"}], "\[Pi]"}], ",",
RowBox[{"2", "\[Pi]"}]}], "}"}]}], "]"}]], "Input",
CellChangeTimes->{{3.5902446317141747`*^9, 3.590244717444105*^9},
3.590244829286377*^9}],
Cell[BoxData[
GraphicsBox[{{{}, {},
{Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxTTMoPSmViYGBQB2IQ7eXJ5/xbUfIAAxRYb635wCGH4Osovp4rJoXg8/08
/sNQCMG/uKJxXQYTgh/B8VXy2iMJOD/9+O0PGxYj+C2uK+elqSL4hVd+CU0W
FofzT8VKvXgiLAbn/923aoOVpCic/3jTx4mBnCJwvtlCtiu93MJwvo3SJb3u
H4Jwvkw1X23PKwE4/8Icw4i0u/xw/vmMzc9Nd/PC+cs0L1oE7OWG8w1mXSgo
OskJ5ysa2N4SW80O57/a5crKtpEVzpfO3p1Y3sMM5/87JbT0QyEjnB84Q22r
eBaCvyTV6qhdEoLvxZD0tCcIwZ9mulFV0xjB113gvyzxCwOcH1Pas/xSGYK/
3mnB9p95CD6TwJbjCukI/opVt5/nhSP4X+5raXBbIPjua+0sjAwQ/FlVQR6R
Ggi+g2hVxnIJBH/yo96KcwII/rP1Czu+ciD4c0yjnpgg8QGP0o+O
"]], LineBox[CompressedData["
1:eJxlx31MzHEcwPHrwdbTPPS4ctolWqqpuO2qxecilYfSNcvM0tNauaxDDD1w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"]], LineBox[CompressedData["
1:eJxlx31MjAEAx/FnvXkLqRxmQzTTLkqYrTo/y9RRp6uulRin1HHamddmeamk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"]], LineBox[CompressedData["
1:eJxTTMoPSmViYGCwAGIQ7XOi+NlsTgYHBijoYNVUzBRE8BkaJk9jVkTwbfZ6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"]]}, {}}, {{}, {}, {}}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->True,
AxesLabel->{None, None},
AxesOrigin->{0, 0},
Method->{},
PlotRange->
NCache[{{(-2) Pi, 2 Pi}, {0., 1.997146590240257}}, {{-6.283185307179586,
6.283185307179586}, {0., 1.997146590240257}}],
PlotRangeClipping->True,
PlotRangePadding->{
Scaled[0.02],
Scaled[0.02]}]], "Output",
CellChangeTimes->{{3.590244663484242*^9, 3.590244686400144*^9}, {
3.5902448298004417`*^9, 3.590244875509267*^9}, {3.590244926356767*^9,
3.5902449476304436`*^9}}]
}, Open ]],
Cell[BoxData["."], "Input",
CellChangeTimes->{3.5902440671332197`*^9}]
},
WindowSize->{1264, 673},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (January 25, 2013)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[579, 22, 4929, 123, 269, "Input"],
Cell[5511, 147, 2494, 61, 46, "Output"],
Cell[8008, 210, 926, 16, 76, "Output"],
Cell[8937, 228, 964, 17, 52, "Output"],
Cell[9904, 247, 1401, 33, 51, "Output"],
Cell[11308, 282, 2475, 62, 72, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[13820, 349, 346, 10, 31, "Input"],
Cell[14169, 361, 4009, 75, 282, "Output"]
}, Open ]],
Cell[18193, 439, 71, 1, 31, "Input"]
}
]
*)
(* End of internal cache information *)