-
Notifications
You must be signed in to change notification settings - Fork 0
/
final_equations.pkl
13806 lines (13806 loc) · 85.7 KB
/
final_equations.pkl
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
(lp0
csympy.core.add
Add
p1
(csympy.core.mul
Mul
p2
(csympy.core.numbers
Rational
p3
(I1
I4
tp4
Rp5
(dp6
bcsympy.core.power
Pow
p7
(csympy.core.numbers
Pi
p8
(tRp9
(dp10
bcsympy.core.numbers
Integer
p11
(I2
tp12
Rp13
(dp14
btp15
Rp16
(dp17
bg7
(csympy.core.symbol
Symbol
p18
(S'Re'
p19
tp20
Rp21
(dp22
S'_assumptions'
p23
ccopy_reg
_reconstructor
p24
(csympy.core.assumptions
StdFactKB
p25
c__builtin__
dict
p26
(dp27
S'real'
p28
NsS'even'
p29
NsS'irrational'
p30
NsS'antihermitian'
p31
NsS'extended_nonpositive'
p32
NsS'algebraic'
p33
NsS'hermitian'
p34
NsS'infinite'
p35
NsS'integer'
p36
NsS'imaginary'
p37
NsS'nonzero'
p38
NsS'extended_real'
p39
NsS'commutative'
p40
I01
sS'zero'
p41
NsS'positive'
p42
NsS'negative'
p43
NsS'extended_negative'
p44
NsS'complex'
p45
NsS'rational'
p46
NsS'extended_positive'
p47
NsS'finite'
p48
NsS'extended_nonnegative'
p49
Nstp50
Rp51
(dp52
S'rules'
p53
g24
(csympy.core.facts
FactRules
p54
c__builtin__
object
p55
Ntp56
Rp57
(dp58
S'beta_rules'
p59
(lp60
(c__builtin__
set
p61
((lp62
(S'algebraic'
p63
I00
tp64
a(S'complex'
p65
I01
tp66
atp67
Rp68
(S'transcendental'
p69
I01
tp70
tp71
a(g61
((lp72
(g29
I00
tp73
a(S'integer'
p74
I01
tp75
atp76
Rp77
(S'odd'
p78
I01
tp79
tp80
a(g61
((lp81
(S'integer'
p82
I01
tp83
a(S'odd'
p84
I00
tp85
atp86
Rp87
(S'even'
p88
I01
tp89
tp90
a(g61
((lp91
(g35
I00
tp92
a(S'real'
p93
I00
tp94
atp95
Rp96
(S'extended_real'
p97
I00
tp98
tp99
a(g61
((lp100
(g97
I01
tp101
a(g93
I00
tp102
atp103
Rp104
(g35
I01
tp105
tp106
a(g61
((lp107
(g97
I01
tp108
a(g35
I00
tp109
atp110
Rp111
(g93
I01
tp112
tp113
a(g61
((lp114
(S'extended_real'
p115
I01
tp116
a(S'finite'
p117
I01
tp118
atp119
Rp120
(S'real'
p121
I01
tp122
tp123
a(g61
((lp124
(S'zero'
p125
I00
tp126
a(S'extended_negative'
p127
I00
tp128
a(g47
I00
tp129
atp130
Rp131
(S'extended_real'
p132
I00
tp133
tp134
a(g61
((lp135
(g125
I00
tp136
a(g132
I01
tp137
a(g47
I00
tp138
atp139
Rp140
(g127
I01
tp141
tp142
a(g61
((lp143
(g47
I00
tp144
a(g132
I01
tp145
a(g127
I00
tp146
atp147
Rp148
(g125
I01
tp149
tp150
a(g61
((lp151
(g125
I00
tp152
a(g132
I01
tp153
a(g127
I00
tp154
atp155
Rp156
(g47
I01
tp157
tp158
a(g61
((lp159
(S'extended_nonzero'
p160
I01
tp161
a(S'extended_nonpositive'
p162
I01
tp163
atp164
Rp165
(S'extended_negative'
p166
I01
tp167
tp168
a(g61
((lp169
(S'extended_nonzero'
p170
I01
tp171
a(g49
I01
tp172
atp173
Rp174
(S'extended_positive'
p175
I01
tp176
tp177
a(g61
((lp178
(S'extended_positive'
p179
I00
tp180
a(S'extended_real'
p181
I01
tp182
atp183
Rp184
(S'extended_nonpositive'
p185
I01
tp186
tp187
a(g61
((lp188
(S'extended_real'
p189
I01
tp190
a(S'extended_negative'
p191
I00
tp192
atp193
Rp194
(S'extended_nonnegative'
p195
I01
tp196
tp197
a(g61
((lp198
(S'zero'
p199
I00
tp200
a(S'positive'
p201
I00
tp202
a(S'negative'
p203
I00
tp204
atp205
Rp206
(S'real'
p207
I00
tp208
tp209
a(g61
((lp210
(g207
I01
tp211
a(g199
I00
tp212
a(g201
I00
tp213
atp214
Rp215
(g203
I01
tp216
tp217
a(g61
((lp218
(g207
I01
tp219
a(g201
I00
tp220
a(g203
I00
tp221
atp222
Rp223
(g199
I01
tp224
tp225
a(g61
((lp226
(g207
I01
tp227
a(g199
I00
tp228
a(g203
I00
tp229
atp230
Rp231
(g201
I01
tp232
tp233
a(g61
((lp234
(S'nonzero'
p235
I01
tp236
a(S'nonpositive'
p237
I01
tp238
atp239
Rp240
(g43
I01
tp241
tp242
a(g61
((lp243
(S'nonzero'
p244
I01
tp245
a(S'nonnegative'
p246
I01
tp247
atp248
Rp249
(S'positive'
p250
I01
tp251
tp252
a(g61
((lp253
(S'real'
p254
I01
tp255
a(S'positive'
p256
I00
tp257
atp258
Rp259
(S'nonpositive'
p260
I01
tp261
tp262
a(g61
((lp263
(S'real'
p264
I01
tp265
a(S'negative'
p266
I00
tp267
atp268
Rp269
(S'nonnegative'
p270
I01
tp271
tp272
a(g61
((lp273
(S'finite'
p274
I01
tp275
a(S'extended_positive'
p276
I01
tp277
atp278
Rp279
(g42
I01
tp280
tp281
a(g61
((lp282
(g44
I01
tp283
a(S'finite'
p284
I01
tp285
atp286
Rp287
(S'negative'
p288
I01
tp289
tp290
a(g61
((lp291
(S'finite'
p292
I01
tp293
a(g32
I01
tp294
atp295
Rp296
(S'nonpositive'
p297
I01
tp298
tp299
a(g61
((lp300
(S'finite'
p301
I01
tp302
a(S'extended_nonnegative'
p303
I01
tp304
atp305
Rp306
(S'nonnegative'
p307
I01
tp308
tp309
a(g61
((lp310
(S'finite'
p311
I01
tp312
a(S'extended_nonzero'
p313
I01
tp314
atp315
Rp316
(g38
I01
tp317
tp318
a(g61
((lp319
(S'extended_nonnegative'
p320
I01
tp321
a(S'extended_nonpositive'
p322
I01
tp323
atp324
Rp325
(S'zero'
p326
I01
tp327
tp328
a(g61
((lp329
(S'nonpositive'
p330
I01
tp331
a(S'nonnegative'
p332
I01
tp333
atp334
Rp335
(g41
I01
tp336
tp337
a(g61
((lp338
(S'even'
p339
I01
tp340
a(S'prime'
p341
I00
tp342
a(S'positive'
p343
I01
tp344
atp345
Rp346
(S'composite'
p347
I01
tp348
tp349
a(g61
((lp350
(g339
I01
tp351
a(g347
I00
tp352
a(g343
I01
tp353
atp354
Rp355
(g341
I01
tp356
tp357
a(g61
((lp358
(g347
I00
tp359
a(g341
I00
tp360
a(g343
I01
tp361
atp362
Rp363
(g339
I00
tp364
tp365
a(g61
((lp366
(g339
I01
tp367
a(g347
I00
tp368
a(g341
I00
tp369
atp370
Rp371
(g343
I00
tp372
tp373
a(g61
((lp374
(S'real'
p375
I01
tp376
a(g46
I00
tp377
atp378
Rp379
(g30
I01
tp380
tp381
a(g61
((lp382
(S'integer'
p383
I00
tp384
a(S'extended_real'
p385
I01
tp386
atp387
Rp388
(S'noninteger'
p389
I01
tp390
tp391
a(g61
((lp392
(S'zero'
p393
I00
tp394
a(S'extended_real'
p395
I01
tp396
atp397
Rp398
(S'extended_nonzero'
p399
I01
tp400
tp401
asS'defined_facts'
p402
g61
((lp403
g330
ag34
ag84
ag29
aS'commutative'
p404
ag42
ag389
ag43
ag44
ag45
ag46
ag48
ag49
ag28
ag38
ag30
ag31
aS'composite'
p405
ag32
ag313
ag35
ag36
ag37
ag341
ag39
ag33
ag41
ag246
ag47
ag69
atp406
Rp407
sS'full_implications'
p408
ccollections
defaultdict
p409
(g61
tp410
Rp411
(g29
I01
tp412
g61
((lp413
(S'real'
p414
I01
tp415
a(S'infinite'
p416
I00
tp417
a(S'imaginary'
p418
I00
tp419
a(g39
I01
tp420
a(g33
I01
tp421
a(g389
I00
tp422
a(S'finite'
p423
I01
tp424
a(g82
I01
tp425
a(g30
I00
tp426
a(g78
I00
tp427
a(g404
I01
tp428
a(g46
I01
tp429
a(S'complex'
p430
I01
tp431
a(g69
I00
tp432
a(g34
I01
tp433
atp434
Rp435
s(g34
I00
tp436
g61
((lp437
(S'zero'
p438
I00
tp439
a(S'positive'
p440
I00
tp441
a(S'prime'
p442
I00
tp443
a(g330
I00
tp444
a(g405
I00
tp445
a(g307
I00
tp446
a(S'nonzero'
p447
I00
tp448
a(g36
I00
tp449
a(g414
I00
tp450
a(g88
I00
tp451
a(g30
I00
tp452
a(g78
I00
tp453
a(g46
I00
tp454
a(g43
I00
tp455
atp456
Rp457
s(S'real'
p458
I00
tp459
g61
((lp460
(g199
I00
tp461
a(g201
I00
tp462
a(g447
I00
tp463
a(g260
I00
tp464
a(g405
I00
tp465
a(g270
I00
tp466
a(g36
I00
tp467
a(g442
I00
tp468
a(g88
I00
tp469
a(g30
I00
tp470
a(g78
I00
tp471
a(S'rational'
p472
I00
tp473
a(g203
I00
tp474
atp475
Rp476
s(g320
I01
tp477
g61
((lp478
(g418
I00
tp479
a(g189
I01
tp480
a(g191
I00
tp481
a(g43
I00
tp482
a(g404
I01
tp483
atp484
Rp485
s(g43
I01
tp486
g61
((lp487
(g207
I01
tp488
a(g235
I01
tp489
a(g440
I00
tp490
a(g442
I00
tp491
a(g416
I00
tp492
a(g237
I01
tp493
a(g39
I01
tp494
a(g47
I00
tp495
a(g405
I00
tp496