-
Notifications
You must be signed in to change notification settings - Fork 0
/
ver 4.0 20210220 macOS.py
884 lines (800 loc) · 33.8 KB
/
ver 4.0 20210220 macOS.py
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
import tkinter as tk
import tkinter.messagebox
import tkinter.filedialog
import sympy
import datetime
import yagmail
from tkinter import *
from sympy import *
from PIL import Image, ImageTk
a, b, c = sympy.symbols('a, b, c')
s, t, d = sympy.symbols('s, t, d')
as_prove, as_cs, as_sc, as_pqr, as_ast = False, False, False, False, False
ast, _same_, check = False, False, True
OS, ver, time0 = 'Windows', '4.0', datetime.datetime.now()
def info():
str0 = '\n 基于Python 3开发的 三元轮换对称不等式运算程序\n\n' \
' ----------------- Author ------------------\n' \
' Nova cx0222 Jinan, Shandong\n' \
' 2913026224@qq.com, 1929842479@qq.com\n\n' \
' ------------- Current Version -------------\n' \
' ver 4.0 [20210220] Jinan, Shandong\n' \
' 该程序装载的最新算法版本为 Sigma_Core_2+ 等\n\n' \
' ------------- Historic Version ------------\n' \
' ver 3.5 [20210219] Jinan, Shandong\n' \
' ver 3.4 [20210206] Jinan, Shandong\n' \
' ver 3.3 [20210131] Jinan, Shandong\n' \
' ver 3.2 [20210130] Jinan, Shandong\n' \
' ver 3.1 [20210128] Jinan, Shandong\n' \
' ver 3.0 [20210116] Jinan, Shandong\n\n' \
' ver 2.7 [20210115] Jinan, Shandong\n' \
' ver 2.6 [20210114] Jinan, Shandong\n' \
' ver 2.5 [20210113] Jinan, Shandong\n' \
' ver 2.4 [20210111] Jinan, Shandong\n' \
' ver 2.3 [20210110] Jinan, Shandong\n' \
' ver 2.2 [20210105] Jinan, Shandong\n' \
' ver 2.1 [20210104] Jinan, Shandong\n\n' \
' ver 1.6 [20201229] Jinan, Shandong\n' \
' ver 1.5 [20201225] Jinan, Shandong\n' \
' ver 1.4 [20201223] Jinan, Shandong\n' \
' ver 1.3 [20201222] Jinan, Shandong\n' \
' ver 1.2 [20201221] Jinan, Shandong\n' \
' ver 1.1 [20201221] Jinan, Shandong\n\n' \
' ver 0.1 [20201218] Changping, Beijing\n\n' \
' ------ Recommended Version for Python -----\n' \
' Python 3.7.x or later with sympy\n\n'
return str0
file8_0 = 'result.txt'
time1 = time0.strftime('%Y/%m/%d %H:%M:%S')
with open(file8_0, 'a') as file0:
file0.write('Sigma 4.0 已启动！时间：')
file0.write('{0}\n'.format(time1))
file0.write('{0}\n'.format(info()))
def ex_0(expr):
expr0 = [i for i in expr]
expr1 = ''
for i in range(0, expr0.__len__()):
if expr0[i] == 'a':
expr0[i] = 'b'
continue
if expr0[i] == 'b':
expr0[i] = 'c'
continue
if expr0[i] == 'c':
expr0[i] = 'a'
continue
for i in range(0, expr0.__len__()):
expr1 += expr0[i]
expr1 = str(expr1)
return expr1
def ex_1(expr):
expr0 = [i for i in expr]
expr1 = ''
for i in range(0, expr0.__len__()):
if expr0[i] == 'a':
expr0[i] = 'c'
continue
if expr0[i] == 'b':
expr0[i] = 'a'
continue
if expr0[i] == 'c':
expr0[i] = 'b'
continue
for i in range(0, expr0.__len__()):
expr1 += expr0[i]
expr1 = str(expr1)
return expr1
def sigma(expr):
expr0 = ex_0(expr) + ' + ' + ex_1(expr) + ' + ' + expr
expr0 = str(expr0)
return expr0
def pi(expr):
expr0 = '(' + ex_0(expr) + ') * (' + ex_1(expr) + ') * (' + expr + ')'
expr0 = str(expr0)
return expr0
# noinspection PyGlobalUndefined
def judge0(expr):
global jud1, same0, sym0
expr0 = sympy.simplify(numer(cancel(expr)))
jud0, jud1 = 1, 1
try:
Poly(expr0, a, b, c)
except sympy.polys.polyerrors.PolynomialError:
jud0 = 0
except NameError:
jud1 = 0
if jud0 == 1:
deg0 = Poly(expr0, a, b, c).total_degree()
expr1 = list(sympy.Poly(expr0, a, b, c).as_dict().keys())
len0 = expr1.__len__()
same0 = 1
for i in range(0, len0):
if sum(expr1[i]) != deg0:
same0 = 0
break
cyc0 = 0
if expr0.subs({(a, b, c): (b, c, a)}) == expr0:
if expr0.subs({(a, b, c): (c, a, b)}) == expr0:
cyc0 = 1
if cyc0 == 1:
sym0 = 0
if expr0.subs({(a, b, c): (a, c, b)}) == expr0:
if expr0.subs({(a, b, c): (c, b, a)}) == expr0:
if expr0.subs({(a, b, c): (b, a, c)}) == expr0:
sym0 = 1
return [jud0, jud1, same0, cyc0, sym0]
def judge1(expr):
expr1 = sympy.simplify(numer(cancel(sigma(expr))))
deg0 = Poly(expr1, a, b, c).total_degree()
return deg0
def normal0(expr):
expr0 = sympy.simplify(numer(cancel(sigma(expr))))
return expr0
def normal1(expr):
expr0 = sympy.simplify(numer(cancel(expr)))
return expr0
def cs3_0(expr):
if as_cs:
out0 = '\n[整理] ' + str(normal0(expr))
expr0 = str(numer(cancel(sigma(expr))))
expr2 = numer(cancel(sigma(expr)))
else:
out0 = '\n[整理] ' + str(normal1(expr))
expr0 = str(numer(cancel(expr)))
expr2 = numer(cancel(expr))
s_bc, s_ca, s_ab = (b - c) ** 2, (c - a) ** 2, (a - b) ** 2
deg0 = judge1(expr0)
fnum = dict1(deg0).__len__()
varlistf = sympy.symbols('v:{}:a'.format(fnum))
s_a, s_b, s_c = 0, 0, 0
for i in range(0, fnum):
s_a += varlistf[i] * dict1(deg0)[i]
s_b += varlistf[i] * sympy.simplify(ex_0('{0}'.format(dict1(deg0)[i])))
s_c += varlistf[i] * sympy.simplify(ex_1('{0}'.format(dict1(deg0)[i])))
ineq = s_a * s_bc + s_b * s_ca + s_c * s_ab
ineq0 = expand(s_a * s_bc + s_b * s_ca + s_c * s_ab)
func0 = sympy.poly(ineq0 - expr2, a, b, c)
equlist0 = []
for i in range(0, dict0(deg0).__len__()):
equlist0.append(func0.coeff_monomial(dict0(deg0)[i]))
ans = solve(equlist0, varlistf)
result0 = ineq.subs(ans)
result2_a, result2_b, result2_c = s_a.subs(ans), s_b.subs(ans), s_c.subs(ans)
result0 = str(result0)
varlistf0 = [str(varlistf[i]) for i in range(0, fnum)]
varlistf1, i = [], 0
result2 = s_a.subs(ans)
for j in range(0, fnum):
if varlistf0[j] in result0:
varlistf1.append(varlistf0[j])
fnum0 = varlistf1.__len__()
if fnum0 == 0:
out0 += '\n[结果] ' + 'Σ (' + str(result2) + ') * (b - c) ** 2'
else:
out0 += '\n[通式] ' + 'Σ (' + str(result2) + ') * (b - c) ** 2'
varlistf2 = [[] for _ in range(0, fnum0)]
for k in range(0, fnum0):
varlistf2[k] = sympy.symbols(varlistf1[k])
varlistf3 = [varlistf2[i] for i in range(0, fnum0)]
out0 += '\n[参数] ' + str(varlistf2)
if judge1(expr0) == 4:
add_a = sympy.poly(result2_a, a, b, c)
equlist_4_1 = [add_a.coeff_monomial(c ** 2) - add_a.coeff_monomial(a ** 2)]
equlist_4_2 = [add_a.coeff_monomial(a ** 2) - add_a.coeff_monomial(b ** 2)]
add0_4 = solve(equlist_4_1 + equlist_4_2, varlistf3)
result2 = numer(factor(add_a.subs(add0_4)))
out0 += '\n[默认] ' + 'Σ (' + str(result2) + ') * (b - c) ** 2'
if judge1(expr0) >= 5:
add_a = sympy.poly(result2_a, a, b, c)
add0_5 = {varlistf2[i]: 0 for i in range(0, fnum0)}
result2 = numer(factor(add_a.subs(add0_5)))
out0 += '\n[默认] ' + 'Σ (' + str(result2) + ') * (b - c) ** 2'
return [out0, str(result2)]
def sc3_0(expr):
if as_sc:
out0 = '\n[整理] ' + str(normal0(expr))
expr0 = str(numer(cancel(sigma(expr))))
expr2 = numer(cancel(sigma(expr)))
else:
out0 = '\n[整理] ' + str(normal1(expr))
expr0 = str(numer(cancel(expr)))
expr2 = numer(cancel(expr))
s_bc, s_ca, s_ab = (a - b) * (a - c), (b - c) * (b - a), (c - a) * (c - b)
deg0 = judge1(expr0)
fnum = dict1(deg0).__len__()
varlistf = sympy.symbols('v:{}:a'.format(fnum))
s_a, s_b, s_c = 0, 0, 0
for i in range(0, fnum):
s_a += varlistf[i] * dict1(deg0)[i]
s_b += varlistf[i] * sympy.simplify(ex_0('{0}'.format(dict1(deg0)[i])))
s_c += varlistf[i] * sympy.simplify(ex_1('{0}'.format(dict1(deg0)[i])))
ineq = s_a * s_bc + s_b * s_ca + s_c * s_ab
ineq0 = expand(s_a * s_bc + s_b * s_ca + s_c * s_ab)
func0 = sympy.poly(ineq0 - expr2, a, b, c)
equlist0 = []
for i in range(0, dict0(deg0).__len__()):
equlist0.append(func0.coeff_monomial(dict0(deg0)[i]))
ans = solve(equlist0, varlistf)
result0 = ineq.subs(ans)
result2_a, result2_b, result2_c = s_a.subs(ans), s_b.subs(ans), s_c.subs(ans)
result0 = str(result0)
varlistf0 = [str(varlistf[i]) for i in range(0, fnum)]
varlistf1, i = [], 0
result2 = s_a.subs(ans)
for j in range(0, fnum):
if varlistf0[j] in result0:
varlistf1.append(varlistf0[j])
fnum0 = varlistf1.__len__()
if fnum0 == 0:
out0 += '\n[结果] ' + 'Σ (' + str(result2) + ') * (a - b) * (a - c)'
else:
out0 += '\n[通式] ' + 'Σ (' + str(result2) + ') * (a - b) * (a - c)'
varlistf2 = [[] for _ in range(0, fnum0)]
for k in range(0, fnum0):
varlistf2[k] = sympy.symbols(varlistf1[k])
varlistf3 = [varlistf2[i] for i in range(0, fnum0)]
out0 += '\n[参数] ' + str(varlistf2)
if judge1(expr0) == 4:
add_a = sympy.poly(result2_a, a, b, c)
equlist_4_1 = [add_a.coeff_monomial(c ** 2) - add_a.coeff_monomial(a ** 2)]
equlist_4_2 = [add_a.coeff_monomial(a ** 2) - add_a.coeff_monomial(b ** 2)]
add0_4 = solve(equlist_4_1 + equlist_4_2, varlistf3)
result2 = numer(factor(add_a.subs(add0_4)))
out0 += '\n[默认] ' + 'Σ (' + str(result2) + ') * (a - b) * (a - c)'
if judge1(expr0) >= 5:
add_a = sympy.poly(result2_a, a, b, c)
add0_5 = {varlistf2[i]: 1 for i in range(0, fnum0)}
result2 = numer(factor(add_a.subs(add0_5)))
out0 += '\n[默认] ' + 'Σ (' + str(result2) + ') * (a - b) * (a - c)'
return out0
def pqr2_6(expr):
if _same_:
result2_6_1 = pqr2_6_1(expr)
return result2_6_1
else:
result2_6_2 = pqr2_6_2(expr)
return result2_6_2
def pqr2_6_1(expr):
if as_pqr:
ineq0 = numer(cancel(sigma(expr)))
else:
ineq0 = numer(cancel(expr))
a, b, c = sympy.symbols('a, b, c')
p, q, r = sympy.symbols('p, q, r')
list1, list2, equlist0 = [], dict0(judge1(expr)), []
list0 = dict2(judge1(expr))[-1]
fnum0, fnum1, result0, resultpqr = list0.__len__(), list2.__len__(), 0, 0
varlistf = sympy.symbols('c:{}:a'.format(fnum0))
for i in range(0, fnum0):
list1.append(list0[i].subs({p: (a + b + c), q: a * b + b * c + c * a, r: a * b * c}))
result0 += list1[i] * varlistf[i]
resultpqr += list0[i] * varlistf[i]
result1 = sympy.poly(sympy.simplify(result0) - ineq0, a, b, c)
for i in range(0, fnum1):
equlist0.append(result1.coeff_monomial(list2[i]))
ans = solve(equlist0, varlistf)
result2 = factor(resultpqr.subs(ans))
return result2
def pqr2_6_2(expr):
if as_pqr:
ineq0 = numer(cancel(sigma(expr)))
else:
ineq0 = numer(cancel(expr))
a, b, c = sympy.symbols('a, b, c')
deg0 = judge1(expr)
poly0 = sympy.poly(ineq0, a, b, c)
polydict0 = poly0.as_dict()
all0 = list(zip(list(polydict0.keys()), list(polydict0.values())))
length0 = all0.__len__()
listcy = [[] for _ in range(0, deg0 + 1)]
listcy0 = [0 * a for _ in range(0, deg0 + 1)]
for cy in range(1, deg0 + 1):
for len in range(0, length0):
if sum(all0[len][0]) == cy:
listcy[cy].append(
(a ** all0[len][0][0] * b ** all0[len][0][1] * c ** all0[len][0][2]) * all0[len][1])
count0 = listcy[cy].__len__()
for i in range(0, count0):
listcy0[cy] += listcy[cy][i]
listcy0[cy] = sympy.simplify(listcy0[cy])
for len in range(0, length0):
if sum(all0[len][0]) == 0:
listcy0[0] = all0[len][1]
result3 = listcy0[0]
for i in range(1, deg0 + 1):
if as_pqr:
result3 += pqr2_6_1(str(listcy0[i])) / 3
else:
result3 += pqr2_6_1(str(listcy0[i]))
return result3
def ast3_0(expr):
if as_ast:
exprast = str(normal0(str(expr)))
else:
exprast = str(normal1(str(expr)))
expr0, expr1 = [i for i in exprast], ''
for i in range(0, expr0.__len__()):
if expr0[i] == 'b':
expr0[i] = '(a+s)'
continue
if expr0[i] == 'c':
if ast:
expr0[i] = '(a+t)'
continue
else:
expr0[i] = '(a+s+t)'
for i in range(0, expr0.__len__()):
expr1 += expr0[i]
expr1 = sympy.poly(sympy.simplify(expand(expr1)), a)
deg0 = expr1.total_degree()
expr2, expr3 = '', []
for n in range(0, deg0):
expr_temp = factor(expr1.coeff_monomial(a ** (deg0 - n)))
expr2 += str(expr_temp * a ** (deg0 - n)) + ' + '
expr3.append(expr_temp)
constant0 = str(factor(expr1.coeff_monomial(a ** 0)))
expr2 += constant0
expr3.append(constant0)
return [expr2, expr3]
def dict0(jud0):
termlist0 = []
for i in range(0, jud0 + 1):
for j in range(0, jud0 + 1):
for k in range(0, jud0 + 1):
if i + j + k == jud0:
termlist0.append(a ** i * b ** j * c ** k)
return termlist0
def dict1(jud1):
termlist1 = []
for i in range(0, jud1 - 1):
for j in range(0, jud1 - 1):
for k in range(0, jud1 - 1):
if i + j + k == jud1 - 2:
termlist1.append(a ** i * b ** j * c ** k)
return termlist1
def dict2(deg0):
pqrdict = [[] for _ in range(0, deg0 + 1)]
p, q, r = sympy.symbols('p, q, r')
for d in range(0, deg0 + 1):
for p0 in range(0, d + 1):
for q0 in range(0, d + 1):
for r0 in range(0, d + 1):
if p0 + 2 * q0 + 3 * r0 == d:
pqrdict[d].append(p ** p0 * q ** q0 * r ** r0)
return pqrdict
def _get_(func):
exp0 = entry0.get()
out0 = '\n[输入] ' + str(exp0)
if func == 1:
listcs = cs3_0(exp0)
out0 += listcs[0]
outcut = listcs[1]
window3 = tk.Toplevel()
window3.title('三元轮换对称不等式运算程序 ver 4.0 SOS分拆结果')
window3.geometry('800x400')
window3.resizable(True, False)
result3 = tk.Text(window3, width=400, height=28, borderwidth=1)
result3.pack()
result3.insert(END, out0)
if judge1(entry0.get()) != 3:
cs = tk.Button(window3, text='进一步运算', command=lambda: _further_(outcut))
cs.pack()
window3.mainloop()
if func == 2:
window4 = tk.Toplevel()
out0 += sc3_0(exp0)
window4.title('三元轮换对称不等式运算程序 ver 4.0 Schur分拆结果')
scroll = tkinter.Scrollbar()
title4 = tk.Text(window4, width=800, height=500)
scroll.pack(side=tkinter.RIGHT, fill=tkinter.Y)
title4.pack(side=tkinter.LEFT, fill=tkinter.Y)
scroll.config(command=title4.yview)
title4.config(yscrollcommand=scroll.set)
window4.geometry('800x500')
window4.resizable(True, True)
title4.insert(tkinter.INSERT, out0)
window4.mainloop()
def _catch_(func):
exp0 = entry0.get()
out0 = '\n[输入] {0}'.format(str(exp0))
window5 = tk.Toplevel()
if func == 1:
if as_pqr:
out0 += '\n[整理] ' + str(normal0(exp0))
else:
out0 += '\n[整理] ' + str(normal1(exp0))
out0 += '\n[换元] (a + b + c, a*b + b*c + c*a, a*b*c) ⬅ (p, q, r)'
out0 += '\n[结果] ' + str(pqr2_6(exp0))
window5.title('三元轮换对称不等式运算程序 ver 4.0 pqr分拆结果')
if func == 2:
if as_ast:
out0 += '\n[整理] ' + str(normal0(exp0))
else:
out0 += '\n[整理] ' + str(normal1(exp0))
if ast:
out0 += '\n[换元] (a, a + s, a + t) ⬅ (a, b, c)'
else:
out0 += '\n[换元] (a, a + s, a + s + t) ⬅ (a, b, c)'
listast = ast3_0(exp0)
out0 += '\n[结果] ' + listast[0]
window5.title('三元轮换对称不等式运算程序 ver 4.0 差分代换结果')
cs = tk.Button(window5, text='机器证明', command=lambda: _more_(listast[1]))
cs.pack()
title = tk.Text(window5, width=800, height=500)
title.pack(side=tkinter.LEFT, fill=tkinter.Y)
window5.geometry('800x500')
window5.resizable(True, True)
title.insert(tkinter.INSERT, out0)
file8_0 = 'result.txt'
with open(file8_0, 'a') as file0:
file0.write('{0}\n'.format(out0))
window5.mainloop()
def _zero_(deg0):
a, b, c, co = sympy.symbols('a, b, c, co')
if deg0 == 4:
expr_a = 2 * a ** 2 + a * b + a * c + 2 * b * c
return expr_a
def _further_(out):
window7 = tk.Toplevel()
scroll_7 = Scrollbar(window7)
scroll_7.pack(side=RIGHT, fill=Y)
window7.geometry('800x520')
window7.resizable(True, True)
window7.title('三元轮换对称不等式运算程序 ver 4.0 进一步运算')
title7_0_0 = tk.Label(window7, text='初步结果：')
title7_0_1 = tk.Label(window7, text='Sa = ' + out)
title7_0_2 = tk.Label(window7, text='Sb = ' + ex_0(out))
title7_0_3 = tk.Label(window7, text='Sc = ' + ex_0(ex_0(out)))
title7_0_0.pack(), title7_0_1.pack(), title7_0_2.pack(), title7_0_3.pack()
deg0 = judge1(entry0.get())
if deg0 == 4:
title7_1_0 = tk.Label(window7, text='请配置零因式：')
title7_1_1 = tk.Label(window7, text='Ta = ' + str(_zero_(deg0)))
title7_1_0.pack(), title7_1_1.pack()
entry7_4_1, entry7_4_0 = tk.Entry(window7, width=8), tk.Entry(window7, width=8)
input7_4_1 = tk.Label(window7, text='请输入零因式所乘系数：')
input7_4_0 = tk.Label(window7, text='请输入原式所乘系数：')
input7_4_1.pack(), entry7_4_1.pack(), input7_4_0.pack(), entry7_4_0.pack()
def add_4():
k1, k0 = entry7_4_1.get(), entry7_4_0.get()
out7_4 = sympy.simplify(_zero_(deg0)) * int(k1) + sympy.simplify(out) * int(k0)
out_4 = '[调整] ' + 'Σ (' + str(out7_4) + ') * (b - c) ** 2'
title7_5 = tk.Text(window7, height=10)
title7_5.pack()
title7_5.insert(tkinter.INSERT, out_4)
return out_4
button7_6 = tk.Button(window7, text='确定', command=add_4)
button7_6.pack()
window7.mainloop()
def _more_(list0):
num0 = list0.__len__()
window8 = tk.Toplevel()
window8.geometry('1000x520')
window8.resizable(True, True)
window8.title('三元轮换对称不等式运算程序 ver 4.0 进一步运算')
scroll_8 = Scrollbar(window8)
scroll_8.pack(side=RIGHT, fill=Y)
title8_0 = tk.Label(window8, text='初步结果：')
title8_0.pack()
file8_0 = 'result.txt'
with open(file8_0, 'a') as file0:
file0.write('初步结果：\n')
for i in range(0, num0):
text8 = Text(window8, width=100, height=2, bd=0)
text8.pack()
text8.insert(END, list0[i])
with open(file8_0, 'a') as file0:
file0.write('{0}\n'.format(list0[i]))
def auto_prove_0(n, l_0):
l_1, l_2, l_3, result1, result2, result3 = [], [], [], [], [], []
for i in range(0, n):
result1.append(factor_list(l_0[i])[1])
len1 = result1[i].__len__()
for j in range(0, len1):
if result1[i][j][1] % 2 == 1:
l_1.append(result1[i][j][0])
len2 = l_1.__len__()
for k in range(0, len2):
l_2.append(Poly(l_1[k], s, t))
result2.append(list(l_2[k].as_dict().values()))
len3 = result2[k].__len__()
for m_0 in range(0, len3):
if result2[k][m_0] < 0:
l_3.append(result2[k][m_0])
if l_3.__len__() != 0:
if result3.__len__() != 0:
temp = 0
for m_1 in range(0, result3.__len__()):
if l_1[k] != result3[m_1]:
temp += 1
if temp == result3.__len__():
result3.append(l_1[k])
else:
result3.append(l_1[k])
l_3 = []
return result3
def poly_cut(poly0):
poly_0 = Poly(poly0, s, t)
poly_1 = list(poly_0.as_dict().keys())
poly_mono = [poly_1[i] for i in range(0, poly_1.__len__())]
poly_coeff = list(poly_0.as_dict().values())
max0 = poly_mono[-1][0]
coeff0 = poly_coeff[-1]
poly_2 = factor(sympy.simplify(poly0) - sympy.simplify(coeff0 * sympy.simplify(s - t) ** max0))
return poly_2
result4 = auto_prove_0(num0, list0)
while True:
if result4.__len__() != 0:
title8_1 = tk.Label(window8, text='进一步结果：')
title8_1.pack()
with open(file8_0, 'a') as file0:
file0.write('进一步结果:\n')
for i in range(0, result4.__len__()):
text8 = Text(window8, width=100, height=2, bd=0)
text8.pack()
text8.insert(END, result4[i])
with open(file8_0, 'a') as file0:
file0.write('{0}\n'.format(result4[i]))
title8_2 = tk.Label(window8, text='只需要证明上述多项式非负！')
title8_2.pack()
with open(file8_0, 'a') as file0:
file0.write('只需要证明上述多项式非负！\n')
result5 = [poly_cut(result4[i]) for i in range(0, result4.__len__())]
result4 = auto_prove_0(result5.__len__(), result5)
else:
title8_3 = tk.Label(window8, text='显然！证毕！')
title8_3.pack()
with open(file8_0, 'a') as file0:
file0.write('显然！证毕！\n')
break
window8.mainloop()
def _core_2_():
expr = entry0.get()
if as_prove:
exprast = str(normal0(str(expr)))
else:
exprast = str(normal1(str(expr)))
expr0, expr1 = [i for i in exprast], ''
for i in range(0, expr0.__len__()):
if expr0[i] == 'b':
expr0[i] = '(a+s)'
continue
if expr0[i] == 'c':
expr0[i] = '(a+t)'
continue
for i in range(0, expr0.__len__()):
expr1 += expr0[i]
expr1 = sympy.poly(sympy.simplify(expand(expr1)), a)
deg0 = expr1.total_degree()
list0 = []
for n in range(0, deg0):
list0.append(expr1.coeff_monomial(a ** (deg0 - n)))
list0.append(expr1.coeff_monomial(a ** 0))
len0 = list0.__len__()
def _core_(coefflist):
global TypeError
error = 0
errortype = ''
for i in range(0, len0):
current0 = coefflist[i]
s_gt_t = sympy.simplify(expand(current0.subs({s: (t + 1)}), t))
if not s_gt_t.is_Add:
s_gt_t_list = [s_gt_t]
else:
try:
list(((sympy.Poly(s_gt_t, t)).as_dict()).values())
except TypeError:
error += 1
errortype += 'TypeError'
break
else:
s_gt_t_list = list(((sympy.Poly(s_gt_t, t)).as_dict()).values())
len1 = s_gt_t_list.__len__()
for j in range(0, len1):
if s_gt_t_list[j] < 0:
error += 1
break
if error != 0:
break
s_lt_t = sympy.simplify(expand(current0.subs({t: (s + 1)}), s))
if not s_lt_t.is_Add:
s_lt_t_list = [s_lt_t]
else:
try:
list(((sympy.Poly(s_lt_t, s)).as_dict()).values())
except TypeError:
error += 1
errortype += 'TypeError'
break
else:
s_lt_t_list = list(((sympy.Poly(s_lt_t, s)).as_dict()).values())
len2 = s_lt_t_list.__len__()
for j in range(0, len2):
if s_lt_t_list[j] < 0:
error += 1
break
if error != 0:
break
if error != 0:
print('Error!')
tkinter.messagebox.showinfo(title='检查到有错误发生！',
message='该不等式不成立，或者本软件未能达成您的请求。\n'
'请您检查键入的不等式，或重新输入一个三元轮换齐次轮换对称的有理不等式。\n'
'注意：变量为a, b, c；并且保证定义域为正实数集。')
report0 = tkinter.messagebox.askokcancel(title='是否发送一份错误报告？',
message='仅为改进我们的产品，一份错误报告在您的许可下可能将被发送。\n'
'错误报告仅存贮您的基本操作信息，与您的任何隐私信息均无关。')
if report0:
yag = yagmail.SMTP('gdsb7770002@163.com', 'QMMYHEMPBVPHYAII', 'smtp.163.com')
yag.send(['2913026224@qq.com', '1929842479@qq.com'], '错误报告',
['错误个数：{0}\n'.format(error),
'键入信息：{0}\n'.format([expr, as_prove, as_cs, as_sc, as_pqr, as_ast, ast, _same_, check]),
'启动时间：{0}\n'.format(time0.strftime('%Y/%m/%d %H:%M:%S')),
'版本信息：{0} based on {1}\n'.format(ver, OS)])
else:
print('OK!')
tkinter.messagebox.showinfo(title='Success！',
message='原不等式成立！其中，a, b, c > 0.')
_core_(list0)
def _pre_(n):
if n == 3:
str0 = '轮换对称'
else:
str0 = '全对称'
if as_prove:
expr0 = sigma(entry0.get())
else:
expr0 = entry0.get()
if judge0(expr0)[0] * judge0(expr0)[1] * judge0(expr0)[2] * judge0(expr0)[3] == 1:
_core_2_()
else:
tkinter.messagebox.showinfo(title='检查到有错误发生！',
message='该版本的此软件不能达成您的请求。\n'
'请您检查键入的不等式，或重新输入一个三元轮换齐次{0}有理不等式。\n'
'注意：变量为a, b, c；并且保证定义域为正实数集。'.format(str0))
def _true_(func):
global as_prove, as_cs, as_sc, as_pqr, as_ast, ast, _same_, check
if func == 0:
as_prove = not as_prove
if func == 1:
as_cs = not as_cs
if func == 2:
as_sc = not as_sc
if func == 3:
as_pqr = not as_pqr
if func == 4:
as_ast = not as_ast
if func == 5:
ast = not ast
if func == 6:
_same_ = not _same_
if func == 7:
check = not check
def _exit_():
file_8 = 'result.txt'
time2 = time0.strftime('%Y/%m/%d %H:%M:%S')
with open(file_8, 'a') as file_8_0:
file_8_0.write('Sigma 4.0 正常关闭！时间：')
file_8_0.write('{0}\n\n\n'.format(time2))
window0.quit()
window0.destroy()
exit()
def _all_():
window1 = tk.Toplevel()
window1.geometry('800x660')
window1.resizable(True, True)
title2 = tk.Label(window1, text=info())
title2.pack()
window1.mainloop()
def _about_():
window2 = tk.Toplevel()
window2.geometry('800x400')
window2.resizable(True, True)
bg0 = ImageTk.PhotoImage(Image.open('ver4_0.gif'))
canvas0 = tk.Canvas(window2, width=800, height=400, bg='white')
canvas0.create_image(400, 200, image=bg0)
canvas0.pack()
window2.mainloop()
def _report_():
window9 = tk.Toplevel()
window9.title('三元轮换对称不等式运算程序 ver 4.0 [20210220] 反馈系统')
window9.geometry('800x600')
window9.resizable(True, True)
bg0 = ImageTk.PhotoImage(Image.open('ver4_0_1.gif'))
canvas0 = tk.Canvas(window9, width=800, height=400, bg='white')
canvas0.create_image(400, 200, image=bg0)
title9_1 = tk.Label(window9,
text='请输入您遇到的问题，开发商将认真考虑您的意见与建议！',
font=('Arial', 18))
entry1 = tk.Entry(window9, width=80)
title2 = tk.Label(window9,
text='如果您愿意，请您留下您的联系方式，开发商将会与您联系。',
font=('Arial', 18))
entry2 = tk.Entry(window9, width=80)
title3 = tk.Label(window9,
text='感谢您的反馈！',
font=('Arial', 18))
report1 = tk.Button(window9, text='发送至官方邮箱', command=lambda: _sent_(entry1.get(), entry2.get()))
canvas0.pack(), title9_1.pack(), entry1.pack(), title2.pack(), entry2.pack(), title3.pack(), report1.pack()
window9.mainloop()
def _sent_(str0, str1):
report2 = tkinter.messagebox.askokcancel(title='请问您确定发送吗？',
message='它仅存贮您的基本操作信息以及您的反馈意见、建议，与您的其他任何信息均无关。')
if report2:
yag = yagmail.SMTP('gdsb7770002@163.com', 'QMMYHEMPBVPHYAII', 'smtp.163.com')
yag.send(['2913026224@qq.com', '1929842479@qq.com'], '反馈',
['意见建议：{0}\n'.format(str0),
'联系方式：{0}\n'.format(str1),
'配置信息：{0}\n'.format([as_prove, as_cs, as_sc, as_pqr, as_ast, ast, _same_, check]),
'启动时间：{0}\n'.format(time0.strftime('%Y/%m/%d %H:%M:%S')),
'版本信息：{0} based on {1}\n'.format(ver, OS)])
tkinter.messagebox.showinfo(title='请问您确定提交吗？',
message='您已发出。')
else:
tkinter.messagebox.showinfo(title='请问您确定发送吗？',
message='您已取消发送。')
window0 = Tk()
window0.title('三元轮换对称不等式运算程序 ver 4.0 [20210220]')
window0.geometry('800x500')
window0.resizable(True, True)
canvas1 = tk.Canvas(window0, highlightthickness=0, width=800, height=500, bg='white')
canvas1.pack(fill=BOTH, expand=YES)
title0 = tk.Label(canvas1,
text='\n基于Python 3开发的 三元轮换对称不等式运算程序（发行版）'
'\n ver 4.0 [20210220] cx0222 Jinan, Shandong',
font=('Arial', 18))
title0.place(relheight=0.15, relwidth=0.8, relx=0.1, rely=0)
title1 = tk.Label(canvas1,
text='请输入不等式，并以a, b, c作为不等式的变量',
font=('Arial', 13))
title1.place(relheight=0.15, relwidth=0.8, relx=0.1, rely=0.27)
menu0 = tk.Menu(window0)
window0.config(menu=menu0)
menu_operate = tk.Menu(menu0, tearoff=False)
menu_operate.add_command(label='SOS分拆', command=lambda: _get_(1))
menu_operate.add_command(label='Schur分拆', command=lambda: _get_(2))
menu_operate.add_command(label='pqr分拆', command=lambda: _catch_(1))
menu0.add_cascade(label='配方与分拆', menu=menu_operate)
menu_2 = tk.Menu(menu0, tearoff=False)
menu_2.add_command(label='差分代换', command=lambda: _catch_(2))
menu_2.add_separator()
menu_2.add_command(label='预先检测并机器证明', command=lambda: _pre_(3))
menu0.add_cascade(label='代换与证明', menu=menu_2)
menu_1 = tk.Menu(menu0, tearoff=False)
menu_1.add_command(label='关于Sigma 4.0', command=_about_)
menu_1.add_command(label='发行说明及开发信息', command=_all_)
menu_1.add_command(label='反馈给开发者', command=_report_)
menu_1.add_separator()
menu_1.add_command(label='退出Sigma 4.0', command=_exit_)
menu0.add_cascade(label='说明与反馈', menu=menu_1)
about0 = tk.Button(canvas1, text='关 于', command=_about_)
about0.place(relheight=0.07, relwidth=0.15, relx=0.3, rely=0.15)
report0 = tk.Button(canvas1, text='反 馈', command=_report_)
report0.place(relheight=0.07, relwidth=0.15, relx=0.55, rely=0.15)
entry0 = tk.Entry(canvas1)
entry0.place(relheight=0.07, relwidth=0.80, relx=0.1, rely=0.24)
cs0 = tk.Button(canvas1, text='SOS分拆', command=lambda: _get_(1))
cs0.place(relheight=0.07, relwidth=0.15, relx=0.3, rely=0.38)
sc0 = tk.Button(canvas1, text='Schur分拆', command=lambda: _get_(2))
sc0.place(relheight=0.07, relwidth=0.15, relx=0.3, rely=0.48)
pqr0 = tk.Button(canvas1, text='pqr分拆', command=lambda: _catch_(1))
pqr0.place(relheight=0.07, relwidth=0.15, relx=0.3, rely=0.58)
ast0 = tk.Button(canvas1, text='差分代换', command=lambda: _catch_(2))
ast0.place(relheight=0.07, relwidth=0.15, relx=0.3, rely=0.68)
prove0 = tk.Button(canvas1, text='机器证明', command=lambda: _pre_(3))
prove0.place(relheight=0.07, relwidth=0.15, relx=0.3, rely=0.78)
note0 = tk.Button(canvas1, text='说 明', command=_all_)
note0.place(relheight=0.07, relwidth=0.15, relx=0.3, rely=0.88)
exit0 = tk.Button(canvas1, text='退 出', command=_exit_)
exit0.place(relheight=0.07, relwidth=0.15, relx=0.55, rely=0.88)
cs1 = tk.Checkbutton(canvas1, text='自动求和', command=lambda: _true_(1))
sc1 = tk.Checkbutton(canvas1, text='自动求和', command=lambda: _true_(2))
pqr1 = tk.Checkbutton(canvas1, text='自动求和', command=lambda: _true_(3))
pqr2 = tk.Checkbutton(canvas1, text='是否为齐次不等式', command=lambda: _true_(6))
ast1 = tk.Checkbutton(canvas1, text='自动求和', command=lambda: _true_(4))
ast2 = tk.Checkbutton(canvas1, text='(a, a + s, a + s + t)', command=lambda: _true_(5))
prove1 = tk.Checkbutton(canvas1, text='自动求和', command=lambda: _true_(0))
cs1.pack(), sc1.pack()
pqr1.pack(), pqr2.pack(), ast1.pack(), ast2.pack()
prove1.pack()
window0.mainloop()