-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathcotransportmatrix.nb
2275 lines (2211 loc) · 116 KB
/
cotransportmatrix.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
477
478
479
480
481
482
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
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
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
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
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
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
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
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
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 12.3' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 118534, 2267]
NotebookOptionsPosition[ 115565, 2223]
NotebookOutlinePosition[ 115957, 2239]
CellTagsIndexPosition[ 115914, 2236]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"Needs", "[", "\"\<PlotLegends`\>\"", "]"}],
"\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ua", " ", "=", " ", "1000"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"uap", " ", "=", " ", "100"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"wa", " ", "=", " ", "100"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"wb", " ", "=", " ", "100"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ub", " ", "=", " ", "1000"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ubp", " ", "=", " ", "200"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"x", " ", "=", " ", "1"}], ";"}],
"\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"g", " ", "=", " ", "1"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Clear", "[",
RowBox[{
"ua", ",", " ", "ub", ",", " ", "uap", ",", " ", "ubp", ",", " ", "wa",
",", " ", "wb", ",", " ", "g", ",", " ", "x"}], "]"}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"Clear", "[", "ubp", "]"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"Clear", "[",
RowBox[{
"p", ",", " ", "s", ",", " ", "g", ",", " ", "x", ",", " ", "c", ",", " ",
"t", ",", " ", "q", ",", " ", "w", ",", " ", "b"}], "]"}],
"*)"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"mat", " ", "=", " ",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"-",
RowBox[{"(",
RowBox[{
RowBox[{"g", "*", "x"}], "+", "wa"}], ")"}]}], " ", ",",
RowBox[{"g", "/", "x"}], " ", ",", "0", ",", "0", ",", "0", ",", "ua",
",", " ", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"g", "*", "x"}], " ", ",",
RowBox[{"-",
RowBox[{"(",
RowBox[{
RowBox[{"g", "/", "x"}], "+",
RowBox[{"wa", "/", "x"}]}], " ", ")"}]}], ",",
RowBox[{"uap", "*", "x"}], ",", "0", ",", "0", ",", "0", ",", " ",
"0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"wa", "/", "x"}], ",",
RowBox[{"-",
RowBox[{"(",
RowBox[{"g", "+",
RowBox[{"uap", "*", "x"}], "+",
RowBox[{"ubp", "*", "x"}]}], ")"}]}], ",",
RowBox[{"wb", "/", "x"}], ",", "0", ",", "g", ",", " ", "0"}], "}"}],
",",
RowBox[{"{",
RowBox[{"0", ",", "0", ",",
RowBox[{"ubp", "*", "x"}], ",",
RowBox[{"-",
RowBox[{"(",
RowBox[{
RowBox[{"wb", "/", "x"}], " ", "+", " ",
RowBox[{"g", " ", "/", "x"}]}], ")"}]}], ",",
RowBox[{"g", "*", "x"}], ",", "0", ",", " ", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0", ",", "0", ",",
RowBox[{"g", "/", "x"}], " ", ",",
RowBox[{"-",
RowBox[{"(",
RowBox[{"wb", " ", "+", " ",
RowBox[{"g", "*", "x"}]}], ")"}]}], ",", "ub", ",", " ", "0"}],
"}"}], ",",
RowBox[{"{",
RowBox[{"wa", ",", "0", ",", "g", ",", "0", ",", "wb", ",",
RowBox[{"-", " ",
RowBox[{"(",
RowBox[{"g", " ", "+", " ", "ua", " ", "+", " ", "ub"}], ")"}]}],
",", " ", "0"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{
"1", ",", " ", "1", ",", " ", "1", ",", " ", "1", ",", " ", "1", ",",
" ", "1", ",", " ", "1"}], "}"}]}], "}"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"Transpose", "[", "mat", "]"}], " ", "//", " ", "MatrixForm"}],
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"mat", " ", "//", " ",
RowBox[{"MatrixForm", "\[IndentingNewLine]",
RowBox[{"Det", "[", "mat", "]"}]}]}], "*)"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"solmat", " ", "=",
RowBox[{"RowReduce", "[", "mat", "]"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"solmat", " ", "//", " ", "MatrixForm"}],
"*)"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"pone", " ", "=", " ",
RowBox[{"solmat", "[",
RowBox[{"[",
RowBox[{"1", ",", " ", "7"}], "]"}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ptwo", " ", "=", " ",
RowBox[{"solmat", "[",
RowBox[{"[",
RowBox[{"2", ",", " ", "7"}], "]"}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"pthree", " ", "=", " ",
RowBox[{"solmat", "[",
RowBox[{"[",
RowBox[{"3", ",", " ", "7"}], "]"}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"pfour", " ", "=", " ",
RowBox[{"solmat", "[",
RowBox[{"[",
RowBox[{"4", ",", " ", "7"}], "]"}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"pfive", " ", "=", " ",
RowBox[{"solmat", "[",
RowBox[{"[",
RowBox[{"5", ",", "7"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"psix", " ", "=", " ",
RowBox[{"solmat", "[",
RowBox[{"[",
RowBox[{"6", ",", " ", "7"}], "]"}], "]"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"sugarflowrate", " ", "=", " ",
RowBox[{
RowBox[{
RowBox[{"g", " ", "/", "x"}], " ", "*", " ", "pfour"}], " ", "-", " ",
RowBox[{"g", " ", "*", "x", " ", "*", " ", "pfive"}]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{"Numerator", "[",
RowBox[{"Simplify", " ", "[",
RowBox[{"Numerator", "[",
RowBox[{
RowBox[{"g", "*", "x", "*", "pfive"}], " ", "-", " ",
RowBox[{
RowBox[{"g", "/", "x"}], "*", "pfour"}]}], "]"}], "]"}],
"]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"aflowrate", " ", "=", " ",
RowBox[{
RowBox[{"g", " ", "*", " ", "x", " ", "*", " ", "pone"}], " ", "-", " ",
RowBox[{"g", " ", "*", " ", "x", " ", "*", " ", "ptwo"}]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{"sol1", " ", "=", " ",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{"sugarflowrate", " ", "==", " ",
RowBox[{"0.5", " ", "*", " ", "aflowrate"}]}], ",", " ", "ubp"}],
"]"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"sol2", " ", "=", " ",
RowBox[{"x", " ", "/.", " ",
RowBox[{"sol1", "[",
RowBox[{"[", "2", "]"}], "]"}]}]}], " ",
"\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"p1", " ", "=", " ",
RowBox[{"Plot", "[",
RowBox[{"pone", ",", " ",
RowBox[{"{",
RowBox[{"x", ",", " ", "0", ",", " ", "6"}], "}"}], ",", " ",
RowBox[{"PlotStyle", "\[Rule]", "Red"}], ",", " ",
RowBox[{"PlotRange", " ", "->", " ", "Full"}], ",", " ",
RowBox[{"AxesLabel", " ", "->", " ", "Automatic"}]}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"p2", " ", "=", " ",
RowBox[{"Plot", "[",
RowBox[{"ptwo", ",", " ",
RowBox[{"{",
RowBox[{"x", ",", " ", "0", ",", " ", "6"}], "}"}], ",", " ",
RowBox[{"PlotStyle", "\[Rule]", "Orange"}], ",", " ",
RowBox[{"PlotRange", " ", "->", " ", "Full"}], ",", " ",
RowBox[{"AxesLabel", " ", "->", " ", "Automatic"}]}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"p3", " ", "=", " ",
RowBox[{"Plot", "[",
RowBox[{"pthree", ",", " ",
RowBox[{"{",
RowBox[{"x", ",", " ", "0", ",", " ", "6"}], "}"}], ",", " ",
RowBox[{"PlotStyle", "\[Rule]", " ", "Yellow"}], ",", " ",
RowBox[{"PlotRange", " ", "->", " ", "Full"}], ",", " ",
RowBox[{"AxesLabel", " ", "->", " ", "Automatic"}]}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{"p4", "=", " ",
RowBox[{"Plot", "[",
RowBox[{"pfour", ",", " ",
RowBox[{"{",
RowBox[{"x", ",", " ", "0", ",", " ", "6"}], "}"}], ",", " ",
RowBox[{"PlotStyle", "\[Rule]", " ", "Green"}], ",", " ",
RowBox[{"PlotRange", " ", "->", " ", "Full"}], ",", " ",
RowBox[{"AxesLabel", " ", "->", " ", "Automatic"}]}],
"]"}]}], "\[IndentingNewLine]",
RowBox[{"p5", " ", "=", " ",
RowBox[{"Plot", "[",
RowBox[{"pfive", ",", " ",
RowBox[{"{",
RowBox[{"x", ",", " ", "0", ",", " ", "6"}], "}"}], ",",
RowBox[{"PlotStyle", " ", "->", " ", "Blue"}], ",", " ",
RowBox[{"PlotRange", " ", "->", " ", "Full"}], ",", " ",
RowBox[{"AxesLabel", " ", "->", " ", "Automatic"}]}],
"]"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"p6", " ", "=", " ",
RowBox[{"Plot", "[",
RowBox[{"psix", ",", " ",
RowBox[{"{",
RowBox[{"x", ",", " ", "0", ",", " ", "6"}], "}"}], ",", " ",
RowBox[{"PlotStyle", "\[Rule]", " ", "Purple"}], ",", " ",
RowBox[{"PlotRange", " ", "->", " ", "Full"}], ",", " ",
RowBox[{"AxesLabel", " ", "->", " ", "Automatic"}]}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{"p7", " ", "=", " ",
RowBox[{"Plot", "[",
RowBox[{"aflowrate", ",", " ",
RowBox[{"{",
RowBox[{"wb", ",", " ", "10", ",", "500"}], "}"}], ",",
RowBox[{"PlotStyle", " ", "->", " ", "Blue"}], ",", " ",
RowBox[{"PlotRange", " ", "->", " ", "Full"}], ",", " ",
RowBox[{"AxesLabel", " ", "->", " ", "Automatic"}]}],
"]"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"p8", " ", "=", " ",
RowBox[{"Plot", "[",
RowBox[{"sugarflowrate", ",", " ",
RowBox[{"{",
RowBox[{"wb", ",", " ", "10", ",", " ", "500"}], "}"}], ",", " ",
RowBox[{"PlotStyle", "\[Rule]", " ", "Purple"}], ",", " ",
RowBox[{"PlotRange", " ", "->", " ", "Full"}], ",", " ",
RowBox[{"AxesLabel", " ", "->", " ", "Automatic"}]}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"Show", "[",
RowBox[{
"p1", ",", " ", "p2", ",", " ", "p3", ",", " ", "p4", ",", " ", "p5", ",",
" ", "p6", ",", " ",
RowBox[{"PlotRange", " ", "->", " ",
RowBox[{"{",
RowBox[{"0", ",", " ", ".6"}], "}"}]}], ",", " ",
RowBox[{"AxesLabel", " ", "->", " ",
RowBox[{"{",
RowBox[{"x", ",", " ", "\"\<Prob\>\""}], "}"}]}]}], "]"}],
"*)"}]}], "\[IndentingNewLine]",
RowBox[{"Show", "[",
RowBox[{"p7", ",", " ", "p8", ",", " ",
RowBox[{"AxesLabel", " ", "->", " ",
RowBox[{"{",
RowBox[{"x", ",", " ", "\"\<Prob\>\""}], "}"}]}], ",", " ",
RowBox[{"PlotRange", " ", "->", " ", "Full"}]}],
"]"}], "\[IndentingNewLine]",
RowBox[{"Close", "[", "\"\<PycharmProjects/cotransport/solutiontext.txt\>\"",
"]"}], "\[IndentingNewLine]",
RowBox[{"Close", "[", "\"\<PycharmProjects/cotransport/sugar.txt\>\"",
"]"}], "\[IndentingNewLine]",
RowBox[{"str", " ", "=", " ",
RowBox[{
"OpenWrite", "[", "\"\<PycharmProjects/cotransport/solutiontext.txt\>\"",
"]"}]}], "\[IndentingNewLine]",
RowBox[{"str2", " ", "=", " ",
RowBox[{
"OpenWrite", "[", "\"\<PycharmProjects/cotransport/sugar.txt\>\"",
"]"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Write", "[",
RowBox[{"str", ",", " ", "\"\<Hello\>\""}], "]"}],
";"}], "\[IndentingNewLine]",
RowBox[{"For", " ", "[",
RowBox[{
RowBox[{"ubp", " ", "=", " ", "100"}], ",", " ",
RowBox[{"ubp", " ", "<", " ", "1000"}], ",",
RowBox[{"ubp", "+=", " ", "5"}], ",", "\[IndentingNewLine]",
RowBox[{
RowBox[{"thing", " ", "=", " ",
RowBox[{"ToString", "[",
RowBox[{"N", "[",
RowBox[{"{",
RowBox[{"wa", ",", " ",
RowBox[{"{",
RowBox[{
"psix", ",", " ", "pone", ",", " ", "ptwo", ",", " ", "pthree", ",",
" ", "pfour", ",", " ", "pfive"}], "}"}]}], "}"}], "]"}], "]"}]}],
";", " ", "\[IndentingNewLine]",
RowBox[{"Write", "[",
RowBox[{"str", ",", " ", "thing"}], "]"}], ";", "\[IndentingNewLine]",
RowBox[{"Write", "[",
RowBox[{"str2", ",", " ",
RowBox[{"ToString", "[",
RowBox[{"N", "[",
RowBox[{"{",
RowBox[{
RowBox[{"ub", "/", "ubp"}], ",", " ", "aflowrate", ",", " ",
"sugarflowrate"}], "}"}], "]"}], "]"}]}], "]"}], ";"}]}],
"]"}], "\[IndentingNewLine]",
RowBox[{"Close", "[", "\"\<PycharmProjects/cotransport/solutiontext.txt\>\"",
"]"}], "\[IndentingNewLine]",
RowBox[{"Close", "[", "\"\<PycharmProjects/cotransport/sugar.txt\>\"",
"]"}]}], "Input",
CellChangeTimes->{{3.833558778536768*^9, 3.833558781715734*^9}, {
3.8335588306519957`*^9, 3.833558832838896*^9}, {3.83355886364544*^9,
3.833558872344499*^9}, {3.833625047352909*^9, 3.833625049601701*^9}, {
3.833626021953487*^9, 3.833626055255522*^9}, {3.833626108126762*^9,
3.833626111415339*^9}, {3.833631545912269*^9, 3.83363154783976*^9}, {
3.8336316697942467`*^9, 3.833631703702785*^9}, {3.833631783788254*^9,
3.8336317963053713`*^9}, {3.83363192322447*^9, 3.833631942058517*^9}, {
3.833632516112563*^9, 3.833632637324567*^9}, {3.833632685422181*^9,
3.8336328829120693`*^9}, {3.833909163848475*^9, 3.8339093789274683`*^9}, {
3.8339094113142433`*^9, 3.8339094765551643`*^9}, {3.8339112342954063`*^9,
3.8339112469090137`*^9}, {3.8339118250655537`*^9,
3.8339119155809193`*^9}, {3.833911968550735*^9, 3.833911991492496*^9}, {
3.833912343418994*^9, 3.833912361394697*^9}, {3.8339710875325747`*^9,
3.833971150275408*^9}, {3.833971276828862*^9, 3.833971278125572*^9}, {
3.8339718308658247`*^9, 3.833971846929681*^9}, {3.83397188543712*^9,
3.833971931455361*^9}, {3.8339764383420057`*^9, 3.833976451632606*^9}, {
3.833976753564452*^9, 3.833976767403885*^9}, 3.83397951952295*^9, {
3.8339796443388557`*^9, 3.833979654798254*^9}, {3.833979691046111*^9,
3.833979712366714*^9}, 3.8339799701734056`*^9, {3.833981469984501*^9,
3.833981476763188*^9}, {3.8339816820833387`*^9, 3.833981686556402*^9}, {
3.833981830326207*^9, 3.833981852616699*^9}, {3.8339820189088993`*^9,
3.833982033996705*^9}, {3.833984815957055*^9, 3.833984818194213*^9},
3.833984864781271*^9, {3.833984945457007*^9, 3.833984957421159*^9},
3.833989681091338*^9, 3.833993649143404*^9, {3.834059972798246*^9,
3.834059978375574*^9}, {3.83406051806779*^9, 3.834060520319778*^9}, {
3.834060851563449*^9, 3.834060869088923*^9}, {3.834061121098526*^9,
3.834061121203751*^9}, 3.834061189919057*^9, 3.8340613145359917`*^9, {
3.834062180596882*^9, 3.8340622069485817`*^9}, {3.834062307342167*^9,
3.834062327843563*^9}, {3.8340628163107843`*^9, 3.8340628322049227`*^9}, {
3.834062905068619*^9, 3.834063001469742*^9}, {3.834063118606118*^9,
3.834063181716977*^9}, {3.834063232219273*^9, 3.8340632586781073`*^9}, {
3.834063300204877*^9, 3.8340633004915257`*^9}, {3.83406337923359*^9,
3.834063400936212*^9}, {3.834063442318509*^9, 3.834063445580668*^9}, {
3.834063589818206*^9, 3.8340636451560497`*^9}, {3.834063846169467*^9,
3.834063975034464*^9}, {3.834064075696528*^9, 3.834064108659293*^9}, {
3.834064143038946*^9, 3.834064143392943*^9}, {3.834064604632422*^9,
3.834064604998376*^9}, {3.834069780020686*^9, 3.834069789114244*^9}, {
3.834069839910925*^9, 3.834069947119088*^9}, {3.8340701220622263`*^9,
3.8340701495961523`*^9}, {3.8340701808974743`*^9, 3.834070183403986*^9}, {
3.83407025285013*^9, 3.834070294125021*^9}, {3.834070325506939*^9,
3.834070373522051*^9}, {3.8340707434293633`*^9, 3.83407074366741*^9}, {
3.834164555240901*^9, 3.8341645596641893`*^9}, {3.8344908415904093`*^9,
3.834490853887995*^9}, {3.834585051963139*^9, 3.834585100308578*^9}, {
3.8345909332946863`*^9, 3.8345909641240263`*^9}, {3.834591315515442*^9,
3.8345913317774343`*^9}, {3.8345914010128183`*^9, 3.834591401336873*^9}, {
3.834591648853401*^9, 3.834591669761034*^9}, {3.8345917388184967`*^9,
3.8345918158025303`*^9}, {3.834591859557523*^9, 3.834591864110712*^9}, {
3.834592246702157*^9, 3.834592259967113*^9}, {3.834592679690034*^9,
3.834592735592236*^9}, {3.834592933951188*^9, 3.834592955958531*^9}, {
3.83459303871819*^9, 3.834593040471417*^9}, {3.834593084282482*^9,
3.834593090132518*^9}, {3.83459411149279*^9, 3.834594133657237*^9}, {
3.834594859752927*^9, 3.834594905181789*^9}, {3.8345949542231903`*^9,
3.834594955336399*^9}, {3.834595894941009*^9, 3.8345959140053663`*^9},
3.834595954364149*^9, {3.83459603252487*^9, 3.834596077880878*^9}, {
3.8345971449081297`*^9, 3.8345971526293163`*^9}, {3.8345971837835197`*^9,
3.8345973098971367`*^9}, {3.834597370904903*^9, 3.834597418448522*^9}, {
3.834597448769237*^9, 3.834597448899334*^9}, {3.834597860085129*^9,
3.83459792864951*^9}, {3.834598486535668*^9, 3.83459852121344*^9}, {
3.834598638167334*^9, 3.8345987325570307`*^9}, {3.834598764743869*^9,
3.8345988296205473`*^9}, {3.834598871390684*^9, 3.834598906935705*^9}, {
3.8345989519510603`*^9, 3.83459895574492*^9}, {3.8345990351846523`*^9,
3.834599071171496*^9}, {3.834599428853902*^9, 3.834599446425104*^9}, {
3.8345994805401917`*^9, 3.834599481677312*^9}, 3.834599898858253*^9, {
3.834663428732141*^9, 3.834663429703177*^9}, {3.834665155062619*^9,
3.834665170614341*^9}, {3.8346652084944563`*^9, 3.83466521634133*^9}, {
3.834665264301*^9, 3.834665270935624*^9}, {3.8346654083237753`*^9,
3.8346654391780024`*^9}, {3.834665603212287*^9, 3.8346656066306143`*^9}, {
3.8346656738794117`*^9, 3.8346656873493547`*^9}, {3.834665874724599*^9,
3.834665889607114*^9}, {3.8346659260417423`*^9, 3.834665927901456*^9}, {
3.8346659714443903`*^9, 3.834665984549171*^9}, {3.8346661093768187`*^9,
3.834666129226796*^9}, {3.834666162201231*^9, 3.834666181497999*^9}, {
3.834666233089096*^9, 3.834666241081312*^9}, {3.8346663800108557`*^9,
3.834666405438613*^9}, {3.8346664498219967`*^9, 3.8346664506840773`*^9}, {
3.834666706912736*^9, 3.834666720940435*^9}, {3.834666770120009*^9,
3.8346667751533947`*^9}, {3.834666818968152*^9, 3.834666895487185*^9}, {
3.8346669693169003`*^9, 3.834666993538198*^9}, {3.834667731723484*^9,
3.834667739542177*^9}, {3.834668289037128*^9, 3.834668356628997*^9}, {
3.834668389300403*^9, 3.83466847849087*^9}, {3.834676266780799*^9,
3.83467636768192*^9}, {3.834676425491321*^9, 3.834676455545927*^9}, {
3.834677592447637*^9, 3.8346776079679813`*^9}, {3.834677954356059*^9,
3.834677958384231*^9}, {3.834678122560234*^9, 3.834678216292715*^9},
3.834679455119458*^9, {3.8346800786138277`*^9, 3.8346800883758507`*^9}, {
3.8346807964227057`*^9, 3.8346808098541203`*^9}, {3.8346819554592867`*^9,
3.834681997639402*^9}, {3.83468204104747*^9, 3.834682042121311*^9}, {
3.834682080026812*^9, 3.834682096335725*^9}, {3.834682148373375*^9,
3.834682179389247*^9}, {3.8346836477857437`*^9, 3.834683716394456*^9},
3.8346837813418837`*^9, {3.834683819749625*^9, 3.8346839121706142`*^9}, {
3.834684176724844*^9, 3.834684336521636*^9}, {3.8346843743884068`*^9,
3.8346844183662577`*^9}, {3.83468444858576*^9, 3.834684482695051*^9}, {
3.834684520904039*^9, 3.834684522052031*^9}, 3.834687210215148*^9, {
3.834754688121213*^9, 3.834754693608736*^9}, {3.8347549238478413`*^9,
3.834754930863387*^9}, {3.834754963945114*^9, 3.83475497627532*^9}, {
3.834758888073201*^9, 3.834758900759582*^9}, {3.834838329155162*^9,
3.8348383426224747`*^9}, {3.8348384259592247`*^9,
3.8348384353765593`*^9}, {3.834838471724649*^9, 3.834838481012896*^9}, {
3.834838550994288*^9, 3.834838564891837*^9}, {3.8348387518372602`*^9,
3.8348387521640587`*^9}, {3.834838783907261*^9, 3.834838849648807*^9}, {
3.834838971049398*^9, 3.8348391408970823`*^9}, 3.8348415905659447`*^9, {
3.834841686198661*^9, 3.8348416865171623`*^9}, {3.8348427844349546`*^9,
3.8348427853548*^9}, {3.83484281996166*^9, 3.83484284137722*^9}, {
3.834843071097291*^9, 3.834843250876966*^9}, {3.83484330660072*^9,
3.834843329743861*^9}, {3.834843493662513*^9, 3.834843536739396*^9}, {
3.834843572468321*^9, 3.834843600638343*^9}, {3.834843663820249*^9,
3.834843683222616*^9}, {3.834843716478389*^9, 3.834843745047276*^9}, {
3.834843818670876*^9, 3.834843865570857*^9}, {3.834846874712573*^9,
3.83484692612094*^9}, {3.834847079002911*^9, 3.834847090397119*^9}, {
3.834847740886963*^9, 3.834847783754243*^9}, {3.834851810928603*^9,
3.834851834180746*^9}, {3.835093622854772*^9, 3.835093680097352*^9}, {
3.8350937437644253`*^9, 3.835093744183054*^9}, {3.8350937997739477`*^9,
3.83509382086204*^9}, {3.835093858517486*^9, 3.8350938621895647`*^9}, {
3.83509390999479*^9, 3.8350939210267563`*^9}, {3.835093992970145*^9,
3.83509400410506*^9}, {3.8350942687300453`*^9, 3.835094278801458*^9}, {
3.8350943323906927`*^9, 3.835094379188031*^9}, {3.8350958574904222`*^9,
3.835095867584485*^9}, 3.835095912839613*^9, 3.8350959593439217`*^9, {
3.835098587517193*^9, 3.835098620982263*^9}, {3.835098671120639*^9,
3.835098688229958*^9}, {3.8350987555450573`*^9, 3.8350989258651333`*^9}, {
3.835098968104384*^9, 3.835099055820201*^9}, {3.83509908908041*^9,
3.8350991283482733`*^9}, {3.835099158982482*^9, 3.835099159258103*^9}, {
3.835099190714162*^9, 3.8350992212549343`*^9}, {3.835099265696013*^9,
3.835099292129507*^9}, {3.83509939909717*^9, 3.835099437781578*^9}, {
3.835099575517869*^9, 3.835099718283992*^9}, {3.83509980586027*^9,
3.835099865341998*^9}, {3.835099933983185*^9, 3.835099992262561*^9}, {
3.835100048970805*^9, 3.835100059657482*^9}, {3.835100110346006*^9,
3.83510011992062*^9}, {3.8351004108408422`*^9, 3.835100441501831*^9}, {
3.835100573331912*^9, 3.835100573810989*^9}, {3.83510061873977*^9,
3.835100653474009*^9}, {3.83510333474827*^9, 3.835103423487994*^9}, {
3.835104288543331*^9, 3.835104325428842*^9}, {3.835104435634454*^9,
3.835104576198716*^9}, {3.835104706543067*^9, 3.8351047089783897`*^9}, {
3.835104836687978*^9, 3.835104854455573*^9}, {3.835105731535434*^9,
3.8351057619455757`*^9}, {3.835105889400529*^9, 3.835105913021743*^9}, {
3.835106095025276*^9, 3.835106095176293*^9}, {3.8351061503718863`*^9,
3.835106170584442*^9}, {3.835106583275763*^9, 3.835106593871407*^9}, {
3.8351067590140667`*^9, 3.83510676528782*^9}, {3.835106838639739*^9,
3.835106858041757*^9}, {3.835106893221649*^9, 3.835106938511292*^9}, {
3.835107043177187*^9, 3.8351070692905273`*^9}, {3.835107579504311*^9,
3.835107597728971*^9}, {3.835108380556181*^9, 3.835108402106882*^9},
3.835108448766094*^9, 3.835108601165489*^9, {3.835108642518899*^9,
3.835108642781475*^9}, {3.8351086910999937`*^9, 3.835108749626525*^9}, {
3.835109165758304*^9, 3.835109196599436*^9}, {3.835109233270464*^9,
3.83510923674509*^9}, {3.835109956803294*^9, 3.8351100055217047`*^9}, {
3.835110760531966*^9, 3.835110781564266*^9}, {3.835110880453081*^9,
3.8351108809140587`*^9}, {3.835181690033074*^9, 3.8351817149093857`*^9}, {
3.8351883064426947`*^9, 3.8351883200635223`*^9}, {3.8351886846064587`*^9,
3.835188691317367*^9}, {3.835189505669466*^9, 3.8351895098086977`*^9}, {
3.835189971193244*^9, 3.8351899842471523`*^9}, {3.835194517582766*^9,
3.8351945480779963`*^9}, {3.835196629590333*^9, 3.835196634134089*^9}, {
3.835260521002864*^9, 3.835260567080638*^9}, {3.8352606138675117`*^9,
3.835260625252804*^9}, {3.835261488825103*^9, 3.835261507057212*^9}, {
3.835261654938219*^9, 3.835261659187367*^9}, {3.8352617660063953`*^9,
3.835261775668909*^9}, {3.835262616367461*^9, 3.8352626576581697`*^9}, {
3.8352627464927483`*^9, 3.8352627488308153`*^9}, {3.835262960728299*^9,
3.835262993768449*^9}, {3.83526370544869*^9, 3.835263762136791*^9}, {
3.835263917394718*^9, 3.835264015502846*^9}, {3.835264055546052*^9,
3.8352640592799673`*^9}, {3.835264097819086*^9, 3.835264163581009*^9}, {
3.835265135366783*^9, 3.835265157361423*^9}, {3.835266023521789*^9,
3.835266058558518*^9}, {3.83526608918277*^9, 3.835266190427603*^9},
3.83526877023628*^9, {3.8352695026624537`*^9, 3.835269507330784*^9}, {
3.835270052368099*^9, 3.8352701051752377`*^9}, {3.8354509462672*^9,
3.8354509804292727`*^9}, {3.835451138280295*^9, 3.835451144772502*^9}, {
3.83545122439326*^9, 3.835451237047069*^9}, {3.835451354122653*^9,
3.835451443189554*^9}, {3.835451617414214*^9, 3.835451658117518*^9}, {
3.835451867166769*^9, 3.835451873059989*^9}, {3.835453205615014*^9,
3.83545320579185*^9}, {3.835453246513506*^9, 3.835453260763402*^9}, {
3.835453431673143*^9, 3.835453478299961*^9}, {3.8355373585794573`*^9,
3.835537362427245*^9}, {3.8355390754816113`*^9, 3.835539081816844*^9}, {
3.835699043396545*^9, 3.8356990481239862`*^9}, {3.8357002177531567`*^9,
3.8357002183004007`*^9}, {3.835700254164651*^9, 3.83570030750552*^9}, {
3.835700531522623*^9, 3.835700532057989*^9}, {3.8357008811516113`*^9,
3.835700881522698*^9}, {3.835701011448475*^9, 3.835701026167576*^9}, {
3.835703911860652*^9, 3.835704025487904*^9}, {3.835704060698468*^9,
3.835704062046728*^9}, {3.835704097469809*^9, 3.835704117141137*^9},
3.835704428698537*^9, {3.835704623724065*^9, 3.8357046662657137`*^9}, {
3.835704718752914*^9, 3.835704724934573*^9}, {3.835706263597024*^9,
3.8357063310523233`*^9}, {3.835706394246376*^9, 3.8357065247775793`*^9}, {
3.835706590473961*^9, 3.835706605493034*^9}, {3.835712516529233*^9,
3.835712533211677*^9}, {3.835712580363009*^9, 3.835712582016129*^9},
3.8363252010288897`*^9, {3.836405635069483*^9, 3.83640564180516*^9},
3.836405930714267*^9, {3.836406101366102*^9, 3.836406202755967*^9}, {
3.8364078560991993`*^9, 3.836407886610475*^9}, {3.836407944078617*^9,
3.836408035825941*^9}, 3.836929837124928*^9, {3.836929986734062*^9,
3.8369300313402023`*^9}, {3.836938138584982*^9, 3.836938232495059*^9}, {
3.837528730792931*^9, 3.837528734645965*^9}, {3.838823039206539*^9,
3.838823046208743*^9}, {3.838823369280871*^9, 3.83882337443524*^9}, {
3.838993145340375*^9, 3.8389931479290113`*^9}, 3.83899322290683*^9, {
3.8389937352452087`*^9, 3.838993783738987*^9}, {3.838993845905974*^9,
3.838993846198345*^9}, {3.838993897297422*^9, 3.8389939057600718`*^9}, {
3.838993951482025*^9, 3.838993964440493*^9}, {3.8389940331256866`*^9,
3.8389940768992243`*^9}, {3.83899412031678*^9, 3.838994148649638*^9}, {
3.839322354169138*^9, 3.8393224282740726`*^9}, {3.839322491448373*^9,
3.839322550900033*^9}, {3.8393225984306107`*^9, 3.83932259874557*^9}, {
3.839322667246049*^9, 3.839322829850692*^9}, {3.839322861448449*^9,
3.839322903078549*^9}, {3.839322936456164*^9, 3.839322947576742*^9}, {
3.839324559812861*^9, 3.83932457376898*^9}, {3.839324615673635*^9,
3.839324717867072*^9}, {3.839324770581215*^9, 3.839324788650696*^9}, {
3.8393251163643007`*^9, 3.839325147580614*^9}, {3.839325196793051*^9,
3.839325205271834*^9}, {3.839325241154285*^9, 3.8393252654248*^9}, {
3.839325317226729*^9, 3.839325317453261*^9}, {3.8393253574720497`*^9,
3.839325380860662*^9}, {3.839325413896432*^9, 3.839325593632206*^9}, {
3.839325689739354*^9, 3.839325711422963*^9}, {3.8393258523557987`*^9,
3.839325853187461*^9}, {3.839325901771638*^9, 3.839325902114427*^9}, {
3.839326242302635*^9, 3.83932628063347*^9}, {3.839326311579463*^9,
3.839326311747669*^9}, {3.839326484569851*^9, 3.839326496004731*^9}, {
3.839326548461338*^9, 3.839326607126302*^9}, {3.839326641751153*^9,
3.839326710594366*^9}, 3.8417438724829082`*^9, {3.841745098908524*^9,
3.841745134484436*^9}, {3.8417456101195498`*^9, 3.8417456653549223`*^9}, {
3.841745725136282*^9, 3.8417457254918118`*^9}, {3.8417457608215723`*^9,
3.8417458581451607`*^9}, {3.841759097906189*^9, 3.841759123387225*^9}, {
3.841761972888258*^9, 3.84176197551027*^9}, {3.84176201069805*^9,
3.841762083025391*^9}, {3.841762201137285*^9, 3.841762247032434*^9}},
CellLabel->
"In[210]:=",ExpressionUUID->"d17ace15-3282-4e49-a3a4-add9681a8085"],
Cell[BoxData[
TagBox[
RowBox[{"(", "\[NoBreak]", GridBox[{
{
RowBox[{
RowBox[{"-", "wa"}], "-",
RowBox[{"g", " ", "x"}]}],
RowBox[{"g", " ", "x"}], "0", "0", "0", "wa", "1"},
{
FractionBox["g", "x"],
RowBox[{
RowBox[{"-",
FractionBox["g", "x"]}], "-",
FractionBox["wa", "x"]}],
FractionBox["wa", "x"], "0", "0", "0", "1"},
{"0",
RowBox[{"uap", " ", "x"}],
RowBox[{
RowBox[{"-", "g"}], "-",
RowBox[{"uap", " ", "x"}], "-",
RowBox[{"ubp", " ", "x"}]}],
RowBox[{"ubp", " ", "x"}], "0", "g", "1"},
{"0", "0",
FractionBox["wb", "x"],
RowBox[{
RowBox[{"-",
FractionBox["g", "x"]}], "-",
FractionBox["wb", "x"]}],
FractionBox["g", "x"], "0", "1"},
{"0", "0", "0",
RowBox[{"g", " ", "x"}],
RowBox[{
RowBox[{"-", "wb"}], "-",
RowBox[{"g", " ", "x"}]}], "wb", "1"},
{"ua", "0", "g", "0", "ub",
RowBox[{
RowBox[{"-", "g"}], "-", "ua", "-", "ub"}], "1"},
{"0", "0", "0", "0", "0", "0", "1"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}], "\[NoBreak]", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{{3.836938195407806*^9, 3.836938232986184*^9},
3.837528704564706*^9, 3.83882304665547*^9, 3.838823376114694*^9,
3.8389932284644327`*^9, 3.838993786247805*^9, 3.838993851050342*^9,
3.838993913055299*^9, 3.838993965355414*^9, 3.8389940800003347`*^9,
3.838994125620275*^9, {3.83932241205328*^9, 3.839322428974882*^9},
3.83932249362225*^9, {3.839322539095433*^9, 3.839322551405498*^9},
3.839322599393381*^9, {3.83932266787578*^9, 3.839322830165286*^9}, {
3.839322862180274*^9, 3.839322903563691*^9}, 3.839324574570416*^9, {
3.8393246178862667`*^9, 3.8393247183865128`*^9}, {3.839324772329851*^9,
3.839324789056531*^9}, {3.839325129763579*^9, 3.839325148529688*^9}, {
3.839325198227174*^9, 3.8393252056723833`*^9}, {3.8393252416851187`*^9,
3.839325265943548*^9}, {3.839325386644539*^9, 3.839325608581188*^9}, {
3.839325697476049*^9, 3.839325711788529*^9}, 3.839325857477868*^9,
3.839325902516829*^9, {3.839326262573094*^9, 3.8393262810056334`*^9},
3.839326312087734*^9, {3.839326485185902*^9, 3.8393264968998957`*^9}, {
3.839326548906246*^9, 3.839326607593371*^9}, {3.839326642217538*^9,
3.839326710972197*^9}, 3.841745734200685*^9, {3.84174578125191*^9,
3.841745802375101*^9}, {3.8417458354876423`*^9, 3.841745858518124*^9},
3.841762252751617*^9},
CellLabel->
"Out[222]//MatrixForm=",ExpressionUUID->"26241536-6eaf-4666-9bc9-\
09ec22578dae"],
Cell[BoxData[
RowBox[{"g", " ", "wa", " ", "wb", " ", "x", " ",
RowBox[{"(",
RowBox[{
RowBox[{"g", " ",
RowBox[{"(",
RowBox[{"ub", "-", "ubp"}], ")"}], " ",
RowBox[{"(",
RowBox[{"1", "+", "x"}], ")"}]}], "-",
RowBox[{"ubp", " ",
RowBox[{"(",
RowBox[{"wa", "+",
RowBox[{"ua", " ", "x"}]}], ")"}]}], "+",
RowBox[{"ub", " ",
RowBox[{"(",
RowBox[{"wa", "+",
RowBox[{"uap", " ", "x"}]}], ")"}]}]}], ")"}]}]], "Output",
CellChangeTimes->{{3.836938195407806*^9, 3.836938232986184*^9},
3.837528704564706*^9, 3.83882304665547*^9, 3.838823376114694*^9,
3.8389932284644327`*^9, 3.838993786247805*^9, 3.838993851050342*^9,
3.838993913055299*^9, 3.838993965355414*^9, 3.8389940800003347`*^9,
3.838994125620275*^9, {3.83932241205328*^9, 3.839322428974882*^9},
3.83932249362225*^9, {3.839322539095433*^9, 3.839322551405498*^9},
3.839322599393381*^9, {3.83932266787578*^9, 3.839322830165286*^9}, {
3.839322862180274*^9, 3.839322903563691*^9}, 3.839324574570416*^9, {
3.8393246178862667`*^9, 3.8393247183865128`*^9}, {3.839324772329851*^9,
3.839324789056531*^9}, {3.839325129763579*^9, 3.839325148529688*^9}, {
3.839325198227174*^9, 3.8393252056723833`*^9}, {3.8393252416851187`*^9,
3.839325265943548*^9}, {3.839325386644539*^9, 3.839325608581188*^9}, {
3.839325697476049*^9, 3.839325711788529*^9}, 3.839325857477868*^9,
3.839325902516829*^9, {3.839326262573094*^9, 3.8393262810056334`*^9},
3.839326312087734*^9, {3.839326485185902*^9, 3.8393264968998957`*^9}, {
3.839326548906246*^9, 3.839326607593371*^9}, {3.839326642217538*^9,
3.839326710972197*^9}, 3.841745734200685*^9, {3.84174578125191*^9,
3.841745802375101*^9}, {3.8417458354876423`*^9, 3.841745858518124*^9},
3.841762253181815*^9},
CellLabel->
"Out[231]=",ExpressionUUID->"518950f5-e309-4325-88e3-ffd5044cd405"],
Cell[BoxData[
TemplateBox[{
"Solve", "ratnz",
"\"Solve was unable to solve the system with inexact coefficients. The \
answer was obtained by solving a corresponding exact system and numericizing \
the result.\"", 2, 233, 27, 24736184027177411734, "Local"},
"MessageTemplate"]], "Message", "MSG",
CellChangeTimes->{{3.836938195420545*^9, 3.8369382329987297`*^9},
3.837528704578944*^9, 3.838823046580061*^9, 3.838823376448104*^9,
3.83899322837648*^9, 3.8389937863035173`*^9, 3.838993851062438*^9,
3.838993913060375*^9, 3.8389939653600388`*^9, 3.8389940800302267`*^9,
3.838994125625527*^9, {3.839322412080312*^9, 3.839322429006031*^9},
3.839322493653183*^9, {3.83932253912394*^9, 3.839322551438285*^9},
3.83932259942572*^9, {3.839322667910602*^9, 3.839322830201165*^9}, {
3.8393228622173223`*^9, 3.839322903601281*^9}, 3.8393245745887003`*^9, {
3.8393246179143143`*^9, 3.839324718416827*^9}, {3.8393247723752623`*^9,
3.83932478910553*^9}, {3.839325129798134*^9, 3.839325148707127*^9}, {
3.839325198406713*^9, 3.8393252058497257`*^9}, {3.839325241860415*^9,
3.839325266126397*^9}, {3.839325386675208*^9, 3.83932560859309*^9}, {
3.839325697487302*^9, 3.839325711801714*^9}, 3.83932585749072*^9,
3.839325902529505*^9, {3.8393262625938807`*^9, 3.839326281025028*^9},
3.839326312107173*^9, {3.8393264852047977`*^9, 3.839326496919321*^9}, {
3.839326548925709*^9, 3.8393266076083803`*^9}, {3.839326642228965*^9,
3.8393267109857273`*^9}, 3.841745734122957*^9, {3.8417457814354467`*^9,
3.8417458025637417`*^9}, {3.84174583590495*^9, 3.841745858925102*^9},
3.841762253249017*^9},
CellLabel->
"During evaluation of \
In[210]:=",ExpressionUUID->"d57e3f61-d115-4d05-b7b9-e5161a268dc4"],
Cell[BoxData[
RowBox[{"{",
RowBox[{"{",
RowBox[{"ubp", "\[Rule]",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["g", "2"], " ", "ua"}], "+",
RowBox[{"g", " ", "ua", " ", "wa"}], "+",
RowBox[{"2.`", " ", "g", " ", "ub", " ", "wa"}], "+",
RowBox[{"2.`", " ", "ub", " ",
SuperscriptBox["wa", "2"]}], "+",
RowBox[{"g", " ", "ua", " ", "wb"}], "+",
RowBox[{"ua", " ", "wa", " ", "wb"}], "+",
RowBox[{
SuperscriptBox["g", "2"], " ", "ua", " ", "x"}], "+",
RowBox[{
SuperscriptBox["g", "2"], " ", "uap", " ", "x"}], "+",
RowBox[{"g", " ", "ua", " ", "uap", " ", "x"}], "+",
RowBox[{"g", " ", "ua", " ", "wa", " ", "x"}], "+",
RowBox[{"2.`", " ", "g", " ", "ub", " ", "wa", " ", "x"}], "+",
RowBox[{"2.`", " ", "uap", " ", "ub", " ", "wa", " ", "x"}], "+",
RowBox[{"g", " ", "uap", " ", "wb", " ", "x"}], "+",
RowBox[{"ua", " ", "uap", " ", "wb", " ", "x"}], "-",
RowBox[{"1.`", " ",
SuperscriptBox["g", "2"], " ", "ua", " ",
SuperscriptBox["x", "2"]}], "+",
RowBox[{
SuperscriptBox["g", "2"], " ", "uap", " ",
SuperscriptBox["x", "2"]}], "+",
RowBox[{"g", " ", "ua", " ", "uap", " ",
SuperscriptBox["x", "2"]}], "+",
RowBox[{"g", " ", "uap", " ", "ub", " ",
SuperscriptBox["x", "2"]}], "-",
RowBox[{"1.`", " ", "g", " ", "uap", " ", "wa", " ",
SuperscriptBox["x", "2"]}], "-",
RowBox[{"1.`", " ", "g", " ", "ua", " ", "wb", " ",
SuperscriptBox["x", "2"]}], "-",
RowBox[{"1.`", " ", "uap", " ", "wa", " ", "wb", " ",
SuperscriptBox["x", "2"]}], "-",
RowBox[{"1.`", " ",
SuperscriptBox["g", "2"], " ", "ua", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ",
SuperscriptBox["g", "2"], " ", "uap", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ", "g", " ", "ua", " ", "uap", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ", "g", " ", "uap", " ", "wa", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ", "uap", " ", "ub", " ", "wa", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ", "g", " ", "uap", " ", "wb", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ", "ua", " ", "uap", " ", "wb", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ",
SuperscriptBox["g", "2"], " ", "uap", " ",
SuperscriptBox["x", "4"]}], "-",
RowBox[{"1.`", " ", "g", " ", "ua", " ", "uap", " ",
SuperscriptBox["x", "4"]}], "-",
RowBox[{"1.`", " ", "g", " ", "uap", " ", "ub", " ",
SuperscriptBox["x", "4"]}]}], ")"}], "/",
RowBox[{"(",
RowBox[{
RowBox[{"2.`", " ", "g", " ", "wa"}], "+",
RowBox[{"2.`", " ",
SuperscriptBox["wa", "2"]}], "-",
RowBox[{"1.`", " ", "g", " ", "ua", " ", "x"}], "+",
RowBox[{"2.`", " ", "g", " ", "wa", " ", "x"}], "+",
RowBox[{"ua", " ", "wa", " ", "x"}], "+",
RowBox[{"g", " ", "ua", " ",
SuperscriptBox["x", "3"]}]}], ")"}]}]}], "}"}], "}"}]], "Output",
CellChangeTimes->{{3.836938195407806*^9, 3.836938232986184*^9},
3.837528704564706*^9, 3.83882304665547*^9, 3.838823376114694*^9,
3.8389932284644327`*^9, 3.838993786247805*^9, 3.838993851050342*^9,
3.838993913055299*^9, 3.838993965355414*^9, 3.8389940800003347`*^9,
3.838994125620275*^9, {3.83932241205328*^9, 3.839322428974882*^9},
3.83932249362225*^9, {3.839322539095433*^9, 3.839322551405498*^9},
3.839322599393381*^9, {3.83932266787578*^9, 3.839322830165286*^9}, {
3.839322862180274*^9, 3.839322903563691*^9}, 3.839324574570416*^9, {
3.8393246178862667`*^9, 3.8393247183865128`*^9}, {3.839324772329851*^9,
3.839324789056531*^9}, {3.839325129763579*^9, 3.839325148529688*^9}, {
3.839325198227174*^9, 3.8393252056723833`*^9}, {3.8393252416851187`*^9,
3.839325265943548*^9}, {3.839325386644539*^9, 3.839325608581188*^9}, {
3.839325697476049*^9, 3.839325711788529*^9}, 3.839325857477868*^9,
3.839325902516829*^9, {3.839326262573094*^9, 3.8393262810056334`*^9},
3.839326312087734*^9, {3.839326485185902*^9, 3.8393264968998957`*^9}, {
3.839326548906246*^9, 3.839326607593371*^9}, {3.839326642217538*^9,
3.839326710972197*^9}, 3.841745734200685*^9, {3.84174578125191*^9,
3.841745802375101*^9}, {3.8417458354876423`*^9, 3.841745858518124*^9},
3.841762253260363*^9},
CellLabel->
"Out[233]=",ExpressionUUID->"7ae874a2-8878-4d9a-9c90-c5d9b2376d7d"],
Cell[BoxData[
TemplateBox[{
"Part", "partw",
"\"Part \\!\\(\\*RowBox[{\\\"2\\\"}]\\) of \\!\\(\\*RowBox[{\\\"{\\\", \
RowBox[{\\\"{\\\", RowBox[{\\\"ubp\\\", \\\"\[Rule]\\\", \
FractionBox[RowBox[{RowBox[{SuperscriptBox[\\\"g\\\", \\\"2\\\"], \\\" \\\", \
\\\"ua\\\"}], \\\"+\\\", RowBox[{\\\"g\\\", \\\" \\\", \\\"ua\\\", \\\" \\\", \
\\\"wa\\\"}], \\\"+\\\", RowBox[{\\\"2.`\\\", \\\" \\\", \\\"g\\\", \\\" \
\\\", \\\"ub\\\", \\\" \\\", \\\"wa\\\"}], \\\"+\\\", RowBox[{\\\"2.`\\\", \\\
\" \\\", \\\"ub\\\", \\\" \\\", SuperscriptBox[\\\"wa\\\", \\\"2\\\"]}], \
\\\"+\\\", RowBox[{\\\"g\\\", \\\" \\\", \\\"ua\\\", \\\" \\\", \\\"wb\\\"}], \
\\\"+\\\", RowBox[{\\\"ua\\\", \\\" \\\", \\\"wa\\\", \\\" \\\", \
\\\"wb\\\"}], \\\"+\\\", RowBox[{SuperscriptBox[\\\"g\\\", \\\"2\\\"], \\\" \
\\\", \\\"ua\\\", \\\" \\\", \\\"x\\\"}], \\\"+\\\", \
RowBox[{SuperscriptBox[\\\"g\\\", \\\"2\\\"], \\\" \\\", \\\"uap\\\", \\\" \\\
\", \\\"x\\\"}], \\\"+\\\", RowBox[{\\\"g\\\", \\\" \\\", \\\"ua\\\", \\\" \\\
\", \\\"uap\\\", \\\" \\\", \\\"x\\\"}], \\\"+\\\", RowBox[{\\\"g\\\", \\\" \
\\\", \\\"ua\\\", \\\" \\\", \\\"wa\\\", \\\" \\\", \\\"x\\\"}], \\\"+\\\", \
RowBox[{\\\"\[LeftSkeleton]\\\", \\\"21\\\", \\\"\[RightSkeleton]\\\"}]}], \
RowBox[{RowBox[{\\\"2.`\\\", \\\" \\\", \\\"g\\\", \\\" \\\", \\\"wa\\\"}], \
\\\"+\\\", RowBox[{\\\"2.`\\\", \\\" \\\", RowBox[{\\\"Power\\\", \\\"[\\\", \
RowBox[{\\\"\[LeftSkeleton]\\\", \\\"2\\\", \\\"\[RightSkeleton]\\\"}], \\\"]\
\\\"}]}], \\\"-\\\", RowBox[{\\\"1.`\\\", \\\" \\\", \\\"g\\\", \\\" \\\", \\\
\"ua\\\", \\\" \\\", \\\"x\\\"}], \\\"+\\\", RowBox[{\\\"2.`\\\", \\\" \\\", \
\\\"g\\\", \\\" \\\", \\\"wa\\\", \\\" \\\", \\\"x\\\"}], \\\"+\\\", RowBox[{\
\\\"ua\\\", \\\" \\\", \\\"wa\\\", \\\" \\\", \\\"x\\\"}], \\\"+\\\", \
RowBox[{\\\"g\\\", \\\" \\\", \\\"ua\\\", \\\" \\\", RowBox[{\\\"Power\\\", \
\\\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"2\\\", \\\"\[RightSkeleton]\\\
\"}], \\\"]\\\"}]}]}]]}], \\\"}\\\"}], \\\"}\\\"}]\\) does not exist.\"", 2,
234, 28, 24736184027177411734, "Local"},
"MessageTemplate"]], "Message", "MSG",
CellChangeTimes->{{3.836938195420545*^9, 3.8369382329987297`*^9},
3.837528704578944*^9, 3.838823046580061*^9, 3.838823376448104*^9,
3.83899322837648*^9, 3.8389937863035173`*^9, 3.838993851062438*^9,
3.838993913060375*^9, 3.8389939653600388`*^9, 3.8389940800302267`*^9,
3.838994125625527*^9, {3.839322412080312*^9, 3.839322429006031*^9},
3.839322493653183*^9, {3.83932253912394*^9, 3.839322551438285*^9},
3.83932259942572*^9, {3.839322667910602*^9, 3.839322830201165*^9}, {
3.8393228622173223`*^9, 3.839322903601281*^9}, 3.8393245745887003`*^9, {
3.8393246179143143`*^9, 3.839324718416827*^9}, {3.8393247723752623`*^9,
3.83932478910553*^9}, {3.839325129798134*^9, 3.839325148707127*^9}, {
3.839325198406713*^9, 3.8393252058497257`*^9}, {3.839325241860415*^9,
3.839325266126397*^9}, {3.839325386675208*^9, 3.83932560859309*^9}, {
3.839325697487302*^9, 3.839325711801714*^9}, 3.83932585749072*^9,
3.839325902529505*^9, {3.8393262625938807`*^9, 3.839326281025028*^9},
3.839326312107173*^9, {3.8393264852047977`*^9, 3.839326496919321*^9}, {
3.839326548925709*^9, 3.8393266076083803`*^9}, {3.839326642228965*^9,
3.8393267109857273`*^9}, 3.841745734122957*^9, {3.8417457814354467`*^9,
3.8417458025637417`*^9}, {3.84174583590495*^9, 3.841745858925102*^9},
3.841762253263832*^9},
CellLabel->
"During evaluation of \
In[210]:=",ExpressionUUID->"6a1869e3-77ff-4e3f-bf71-55f2d53c2422"],
Cell[BoxData[
TemplateBox[{
"ReplaceAll", "reps",
"\"\\!\\(\\*RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \
RowBox[{\\\"{\\\", RowBox[{\\\"ubp\\\", \\\"\[Rule]\\\", \
FractionBox[RowBox[{RowBox[{\\\"Times\\\", \\\"[\\\", RowBox[{\\\"\
\[LeftSkeleton]\\\", \\\"2\\\", \\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \
\\\"+\\\", RowBox[{\\\"Times\\\", \\\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \
\\\"3\\\", \\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \\\"+\\\", \
RowBox[{\\\"Times\\\", \\\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"4\\\", \
\\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \\\"+\\\", RowBox[{\\\"Times\\\", \\\
\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"3\\\", \
\\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \\\"+\\\", RowBox[{\\\"Times\\\", \\\
\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"3\\\", \
\\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \\\"+\\\", RowBox[{\\\"Times\\\", \\\
\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"3\\\", \
\\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \\\"+\\\", RowBox[{\\\"Times\\\", \\\
\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"3\\\", \
\\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \\\"+\\\", RowBox[{\\\"Times\\\", \\\
\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"3\\\", \
\\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \\\"+\\\", RowBox[{\\\"Times\\\", \\\
\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"4\\\", \
\\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \\\"+\\\", RowBox[{\\\"Times\\\", \\\
\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"4\\\", \
\\\"\[RightSkeleton]\\\"}], \\\"]\\\"}], \\\"+\\\", RowBox[{\\\"\
\[LeftSkeleton]\\\", \\\"21\\\", \\\"\[RightSkeleton]\\\"}]}], \
RowBox[{\\\"Plus\\\", \\\"[\\\", RowBox[{\\\"\[LeftSkeleton]\\\", \\\"6\\\", \
\\\"\[RightSkeleton]\\\"}], \\\"]\\\"}]]}], \\\"}\\\"}], \\\"}\\\"}], \\\"\
\[LeftDoubleBracket]\\\", \\\"2\\\", \\\"\[RightDoubleBracket]\\\"}], \\\"}\\\
\"}]\\) is neither a list of replacement rules nor a valid dispatch table, \
and so cannot be used for replacing.\"", 2, 234, 29, 24736184027177411734,
"Local"},
"MessageTemplate"]], "Message", "MSG",
CellChangeTimes->{{3.836938195420545*^9, 3.8369382329987297`*^9},
3.837528704578944*^9, 3.838823046580061*^9, 3.838823376448104*^9,
3.83899322837648*^9, 3.8389937863035173`*^9, 3.838993851062438*^9,
3.838993913060375*^9, 3.8389939653600388`*^9, 3.8389940800302267`*^9,
3.838994125625527*^9, {3.839322412080312*^9, 3.839322429006031*^9},
3.839322493653183*^9, {3.83932253912394*^9, 3.839322551438285*^9},
3.83932259942572*^9, {3.839322667910602*^9, 3.839322830201165*^9}, {
3.8393228622173223`*^9, 3.839322903601281*^9}, 3.8393245745887003`*^9, {
3.8393246179143143`*^9, 3.839324718416827*^9}, {3.8393247723752623`*^9,
3.83932478910553*^9}, {3.839325129798134*^9, 3.839325148707127*^9}, {
3.839325198406713*^9, 3.8393252058497257`*^9}, {3.839325241860415*^9,
3.839325266126397*^9}, {3.839325386675208*^9, 3.83932560859309*^9}, {
3.839325697487302*^9, 3.839325711801714*^9}, 3.83932585749072*^9,
3.839325902529505*^9, {3.8393262625938807`*^9, 3.839326281025028*^9},
3.839326312107173*^9, {3.8393264852047977`*^9, 3.839326496919321*^9}, {
3.839326548925709*^9, 3.8393266076083803`*^9}, {3.839326642228965*^9,
3.8393267109857273`*^9}, 3.841745734122957*^9, {3.8417457814354467`*^9,
3.8417458025637417`*^9}, {3.84174583590495*^9, 3.841745858925102*^9},
3.841762253323818*^9},
CellLabel->
"During evaluation of \
In[210]:=",ExpressionUUID->"0f6efc47-2375-411f-8b05-37a54a79c6e2"],
Cell[BoxData[
RowBox[{"x", "/.", "\[VeryThinSpace]",
RowBox[{
RowBox[{"{",
RowBox[{"{",
RowBox[{"ubp", "\[Rule]",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["g", "2"], " ", "ua"}], "+",
RowBox[{"g", " ", "ua", " ", "wa"}], "+",
RowBox[{"2.`", " ", "g", " ", "ub", " ", "wa"}], "+",
RowBox[{"2.`", " ", "ub", " ",
SuperscriptBox["wa", "2"]}], "+",
RowBox[{"g", " ", "ua", " ", "wb"}], "+",
RowBox[{"ua", " ", "wa", " ", "wb"}], "+",
RowBox[{
SuperscriptBox["g", "2"], " ", "ua", " ", "x"}], "+",
RowBox[{
SuperscriptBox["g", "2"], " ", "uap", " ", "x"}], "+",
RowBox[{"g", " ", "ua", " ", "uap", " ", "x"}], "+",
RowBox[{"g", " ", "ua", " ", "wa", " ", "x"}], "+",
RowBox[{"2.`", " ", "g", " ", "ub", " ", "wa", " ", "x"}], "+",
RowBox[{"2.`", " ", "uap", " ", "ub", " ", "wa", " ", "x"}], "+",
RowBox[{"g", " ", "uap", " ", "wb", " ", "x"}], "+",
RowBox[{"ua", " ", "uap", " ", "wb", " ", "x"}], "-",
RowBox[{"1.`", " ",
SuperscriptBox["g", "2"], " ", "ua", " ",
SuperscriptBox["x", "2"]}], "+",
RowBox[{
SuperscriptBox["g", "2"], " ", "uap", " ",
SuperscriptBox["x", "2"]}], "+",
RowBox[{"g", " ", "ua", " ", "uap", " ",
SuperscriptBox["x", "2"]}], "+",
RowBox[{"g", " ", "uap", " ", "ub", " ",
SuperscriptBox["x", "2"]}], "-",
RowBox[{"1.`", " ", "g", " ", "uap", " ", "wa", " ",
SuperscriptBox["x", "2"]}], "-",
RowBox[{"1.`", " ", "g", " ", "ua", " ", "wb", " ",
SuperscriptBox["x", "2"]}], "-",
RowBox[{"1.`", " ", "uap", " ", "wa", " ", "wb", " ",
SuperscriptBox["x", "2"]}], "-",
RowBox[{"1.`", " ",
SuperscriptBox["g", "2"], " ", "ua", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ",
SuperscriptBox["g", "2"], " ", "uap", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ", "g", " ", "ua", " ", "uap", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ", "g", " ", "uap", " ", "wa", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ", "uap", " ", "ub", " ", "wa", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ", "g", " ", "uap", " ", "wb", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ", "ua", " ", "uap", " ", "wb", " ",
SuperscriptBox["x", "3"]}], "-",
RowBox[{"1.`", " ",
SuperscriptBox["g", "2"], " ", "uap", " ",
SuperscriptBox["x", "4"]}], "-",
RowBox[{"1.`", " ", "g", " ", "ua", " ", "uap", " ",
SuperscriptBox["x", "4"]}], "-",
RowBox[{"1.`", " ", "g", " ", "uap", " ", "ub", " ",
SuperscriptBox["x", "4"]}]}], ")"}], "/",
RowBox[{"(",
RowBox[{
RowBox[{"2.`", " ", "g", " ", "wa"}], "+",
RowBox[{"2.`", " ",
SuperscriptBox["wa", "2"]}], "-",
RowBox[{"1.`", " ", "g", " ", "ua", " ", "x"}], "+",
RowBox[{"2.`", " ", "g", " ", "wa", " ", "x"}], "+",
RowBox[{"ua", " ", "wa", " ", "x"}], "+",
RowBox[{"g", " ", "ua", " ",
SuperscriptBox["x", "3"]}]}], ")"}]}]}], "}"}], "}"}],
"\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]], "Output",
CellChangeTimes->{{3.836938195407806*^9, 3.836938232986184*^9},
3.837528704564706*^9, 3.83882304665547*^9, 3.838823376114694*^9,
3.8389932284644327`*^9, 3.838993786247805*^9, 3.838993851050342*^9,
3.838993913055299*^9, 3.838993965355414*^9, 3.8389940800003347`*^9,
3.838994125620275*^9, {3.83932241205328*^9, 3.839322428974882*^9},
3.83932249362225*^9, {3.839322539095433*^9, 3.839322551405498*^9},
3.839322599393381*^9, {3.83932266787578*^9, 3.839322830165286*^9}, {
3.839322862180274*^9, 3.839322903563691*^9}, 3.839324574570416*^9, {
3.8393246178862667`*^9, 3.8393247183865128`*^9}, {3.839324772329851*^9,
3.839324789056531*^9}, {3.839325129763579*^9, 3.839325148529688*^9}, {
3.839325198227174*^9, 3.8393252056723833`*^9}, {3.8393252416851187`*^9,
3.839325265943548*^9}, {3.839325386644539*^9, 3.839325608581188*^9}, {
3.839325697476049*^9, 3.839325711788529*^9}, 3.839325857477868*^9,
3.839325902516829*^9, {3.839326262573094*^9, 3.8393262810056334`*^9},