/
out_g43_multicolor_contradiction.txt
109 lines (109 loc) · 8.72 KB
/
out_g43_multicolor_contradiction.txt
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+ ./Singular/Singular/Singular -q --no-rc -e 2>&1 < "g43_multicolor_contradiction.s"
STDIN 1> // try to find a solution to n=4 c=3 with a non-zero multi-color edge weight
STDIN 2. // without loss of generality, choose w0101 to be non-zero
STDIN 3. // and again without loss of generality, let it equal 1
STDIN 4. // (by scaling all w01xx weights by 1/w0101 and all w23xx weights by w0101)
STDIN 5. //
STDIN 6. // this leads to a contradiction
STDIN 7. // (the ideal is {1}, so a solution would have to satisfy constraint 1 == 0)
STDIN 8. // so there are no n=4 c=3 solutions with a non-zero multi-color edge weight
STDIN 9. ring R = QQ[
STDIN 10. w0100, w0101, w0102, w0110, w0111, w0112, w0120, w0121, w0122,
STDIN 11. w0200, w0201, w0202, w0210, w0211, w0212, w0220, w0221, w0222,
STDIN 12. w0300, w0301, w0302, w0310, w0311, w0312, w0320, w0321, w0322,
STDIN 13. w1200, w1201, w1202, w1210, w1211, w1212, w1220, w1221, w1222,
STDIN 14. w1300, w1301, w1302, w1310, w1311, w1312, w1320, w1321, w1322,
STDIN 15. w2300, w2301, w2302, w2310, w2311, w2312, w2320, w2321, w2322];
STDIN 16> ideal I =
STDIN 17. w0101 - 1,
STDIN 18. w0100*w2300 + w0200*w1300 + w0300*w1200 - 1,
STDIN 19. w0100*w2301 + w0200*w1301 + w0301*w1200,
STDIN 20. w0100*w2302 + w0200*w1302 + w0302*w1200,
STDIN 21. w0100*w2310 + w0201*w1300 + w0300*w1201,
STDIN 22. w0100*w2311 + w0201*w1301 + w0301*w1201,
STDIN 23. w0100*w2312 + w0201*w1302 + w0302*w1201,
STDIN 24. w0100*w2320 + w0202*w1300 + w0300*w1202,
STDIN 25. w0100*w2321 + w0202*w1301 + w0301*w1202,
STDIN 26. w0100*w2322 + w0202*w1302 + w0302*w1202,
STDIN 27. w0101*w2300 + w0200*w1310 + w0300*w1210,
STDIN 28. w0101*w2301 + w0200*w1311 + w0301*w1210,
STDIN 29. w0101*w2302 + w0200*w1312 + w0302*w1210,
STDIN 30. w0101*w2310 + w0201*w1310 + w0300*w1211,
STDIN 31. w0101*w2311 + w0201*w1311 + w0301*w1211,
STDIN 32. w0101*w2312 + w0201*w1312 + w0302*w1211,
STDIN 33. w0101*w2320 + w0202*w1310 + w0300*w1212,
STDIN 34. w0101*w2321 + w0202*w1311 + w0301*w1212,
STDIN 35. w0101*w2322 + w0202*w1312 + w0302*w1212,
STDIN 36. w0102*w2300 + w0200*w1320 + w0300*w1220,
STDIN 37. w0102*w2301 + w0200*w1321 + w0301*w1220,
STDIN 38. w0102*w2302 + w0200*w1322 + w0302*w1220,
STDIN 39. w0102*w2310 + w0201*w1320 + w0300*w1221,
STDIN 40. w0102*w2311 + w0201*w1321 + w0301*w1221,
STDIN 41. w0102*w2312 + w0201*w1322 + w0302*w1221,
STDIN 42. w0102*w2320 + w0202*w1320 + w0300*w1222,
STDIN 43. w0102*w2321 + w0202*w1321 + w0301*w1222,
STDIN 44. w0102*w2322 + w0202*w1322 + w0302*w1222,
STDIN 45. w0110*w2300 + w0210*w1300 + w0310*w1200,
STDIN 46. w0110*w2301 + w0210*w1301 + w0311*w1200,
STDIN 47. w0110*w2302 + w0210*w1302 + w0312*w1200,
STDIN 48. w0110*w2310 + w0211*w1300 + w0310*w1201,
STDIN 49. w0110*w2311 + w0211*w1301 + w0311*w1201,
STDIN 50. w0110*w2312 + w0211*w1302 + w0312*w1201,
STDIN 51. w0110*w2320 + w0212*w1300 + w0310*w1202,
STDIN 52. w0110*w2321 + w0212*w1301 + w0311*w1202,
STDIN 53. w0110*w2322 + w0212*w1302 + w0312*w1202,
STDIN 54. w0111*w2300 + w0210*w1310 + w0310*w1210,
STDIN 55. w0111*w2301 + w0210*w1311 + w0311*w1210,
STDIN 56. w0111*w2302 + w0210*w1312 + w0312*w1210,
STDIN 57. w0111*w2310 + w0211*w1310 + w0310*w1211,
STDIN 58. w0111*w2311 + w0211*w1311 + w0311*w1211 - 1,
STDIN 59. w0111*w2312 + w0211*w1312 + w0312*w1211,
STDIN 60. w0111*w2320 + w0212*w1310 + w0310*w1212,
STDIN 61. w0111*w2321 + w0212*w1311 + w0311*w1212,
STDIN 62. w0111*w2322 + w0212*w1312 + w0312*w1212,
STDIN 63. w0112*w2300 + w0210*w1320 + w0310*w1220,
STDIN 64. w0112*w2301 + w0210*w1321 + w0311*w1220,
STDIN 65. w0112*w2302 + w0210*w1322 + w0312*w1220,
STDIN 66. w0112*w2310 + w0211*w1320 + w0310*w1221,
STDIN 67. w0112*w2311 + w0211*w1321 + w0311*w1221,
STDIN 68. w0112*w2312 + w0211*w1322 + w0312*w1221,
STDIN 69. w0112*w2320 + w0212*w1320 + w0310*w1222,
STDIN 70. w0112*w2321 + w0212*w1321 + w0311*w1222,
STDIN 71. w0112*w2322 + w0212*w1322 + w0312*w1222,
STDIN 72. w0120*w2300 + w0220*w1300 + w0320*w1200,
STDIN 73. w0120*w2301 + w0220*w1301 + w0321*w1200,
STDIN 74. w0120*w2302 + w0220*w1302 + w0322*w1200,
STDIN 75. w0120*w2310 + w0221*w1300 + w0320*w1201,
STDIN 76. w0120*w2311 + w0221*w1301 + w0321*w1201,
STDIN 77. w0120*w2312 + w0221*w1302 + w0322*w1201,
STDIN 78. w0120*w2320 + w0222*w1300 + w0320*w1202,
STDIN 79. w0120*w2321 + w0222*w1301 + w0321*w1202,
STDIN 80. w0120*w2322 + w0222*w1302 + w0322*w1202,
STDIN 81. w0121*w2300 + w0220*w1310 + w0320*w1210,
STDIN 82. w0121*w2301 + w0220*w1311 + w0321*w1210,
STDIN 83. w0121*w2302 + w0220*w1312 + w0322*w1210,
STDIN 84. w0121*w2310 + w0221*w1310 + w0320*w1211,
STDIN 85. w0121*w2311 + w0221*w1311 + w0321*w1211,
STDIN 86. w0121*w2312 + w0221*w1312 + w0322*w1211,
STDIN 87. w0121*w2320 + w0222*w1310 + w0320*w1212,
STDIN 88. w0121*w2321 + w0222*w1311 + w0321*w1212,
STDIN 89. w0121*w2322 + w0222*w1312 + w0322*w1212,
STDIN 90. w0122*w2300 + w0220*w1320 + w0320*w1220,
STDIN 91. w0122*w2301 + w0220*w1321 + w0321*w1220,
STDIN 92. w0122*w2302 + w0220*w1322 + w0322*w1220,
STDIN 93. w0122*w2310 + w0221*w1320 + w0320*w1221,
STDIN 94. w0122*w2311 + w0221*w1321 + w0321*w1221,
STDIN 95. w0122*w2312 + w0221*w1322 + w0322*w1221,
STDIN 96. w0122*w2320 + w0222*w1320 + w0320*w1222,
STDIN 97. w0122*w2321 + w0222*w1321 + w0321*w1222,
STDIN 98. w0122*w2322 + w0222*w1322 + w0322*w1222 - 1;
STDIN 99> option(redSB);
STDIN 100> option(prot);
STDIN 101> ideal I2 = slimgb(I);
2M[81:0,81](648)3M[100:547,100](2061)3M[100:448,100](3833)3M[100:348,100](5768)3M[100:248,100](7465)3M[100:148,100](9490)3M[100:48,100](11436)3M[48:0,48](12558)4M[100:11132,100](16143)4M[100:11032,74](19655)4M[100:10932,78](24730)4M[100:10832,bb97](28400)4M[100:10732,bb100](32116)4M[100:10632,100](36030)4M[100:10532,22](36949)4M[100:10432,22](38348)4M[100:10332,100](43891)4M[100:10232,bbbbb100](49037)4M[100:10132,71](52215)4M[100:10032,bbbbbbbbbbbbbbb72](54411)4M[100:9932,bbbb100](57770)4M[100:9832,bbbbbbbbbbbbbbb100](61902)4M[100:9732,bbbbbb88](65942)4M[100:9632,6](66245)4M[100:9532,6](66405)4M[100:9432,36](67965)4M[100:9332,b100](74004)4M[100:9232,bbb100](79575)4M[100:9132,b100](84289)4M[100:9032,57](86796)4M[100:8932,44](88945)4M[100:8832,bbbbbbbbbb64](91533)4M[100:8732,bbbbbbbbbb49](93150)4M[100:8632,bbbbbbbbbbbbbbbbbbbbbbbbb94](96225)4M[100:8532,bbbbb100](99934)4M[100:8521,98](105142)3M[28:0,28](107171)3M[11:0,11](108309)4M[100:9267,eeee75](113447)3M[36:0,36](116110)4M[100:9972,74](120597)3M[56:0,e56](124737)3M[2:0,2](124986)3M[100:11,100](130912)3M[42:0,eeeeeeeeeeeeeeeeee29](133708)4M[100:14023,eb84](139775)4M[100:13945,eee100](145617)3M[9:0,9](147411)4M[100:14149,eeeeeeeeeeeeeeeeeeeeee65](151605)3M[17:0,16](153480)4M[100:14021,bbbeeeeeeeeee70](156296)3M[15:0,bbb12](156902)4M[100:13825,ebbbbbbbeeb82](160271)3M[11:0,11](160380)3M[1:0,1](160430)4M[100:13734,eeebbbeeebeeeeeeeeeeeeee81](164584)3M[13:0,13](165861)4M[100:13883,eeeeeeeeeee87](174111)3M[22:0,bbb22](175972)3M[16:0,16](176771)3M[75:0,75](181159)3M[17:0,eee14](182294)4M[100:16275,eeeeeee75](185901)3M[10:0,10](186898)4M[100:16065,eeeeeeeeeeeeeeee78](190897)3M[7:0,7](191383)4M[100:15812,beeeeeeeeeeeeeeebbbeeeeeeebb73](193651)3M[4:0,bbb1](193719)4M[100:15765,eebbbeeeee88](197649)3M[1:0,1](197612)4M[100:15842,100](199635)4M[100:15605,eeeeeeeeee76](203248)4M[100:15442,eeeeeeeeeeeeeeeeeeeee36](205285)4M[100:15112,eeeeeeeeeeeeeeeeeeeeeeeeeee66](209257)3M[40:0,beee37](211173)3M[27:0,eeeeee20](212567)2M[6:0,6](213034)3M[34:0,25](214831)3M[7:0,7](215401)4M[100:17542,eeeeeeeeeeeeeeeeeb75](219558)3M[23:0,23](221470)3M[1:0,1](221518)3M[8:0,8](221923)4M[100:16617,eeeeeeeeeeb78](225294)3M[42:0,eee38](227293)2M[6:0,6](227935)3M[3:0,3](228024)4M[100:17101,79](230390)4M[100:16418,100](236188)3M[49:0,bb49](239559)4M[100:17643,eeeeeeeeeee87](245692)3M[22:0,22](247784)4M[100:16752,92](255312)3M[91:0,bbbbbbe90](263660)4M[100:19378,bbeebeebbbbbbbbbb74](270635)3M[56:0,55](276015)4M[100:20827,eebbbbbeebeeeee73](280104)3M[8:0,8](280745)4M[100:20340,beeeeeeeee84](289750)3M[19:0,bbebbb17](290694)2M[1:0,1](290753)3M[16:0,bbb13](292213)3M[7:0,7](293211)2M[4:0,4](293476)3M[33:0,bb28](296769)4M[100:21800,eeeeeeeebbbbbbbbeeeeebe73](304551)3M[42:0,40](306899)3M[1:0,1](306841)3M[5:0,5](307349)4M[100:23233,eeeeeeeeeeeeeebbbbbeeeeeeeebbbb42](312057)3M[30:0,eeeeeee28](314203)4M[100:25235,bb96](318310)3M[20:0,19](320047)3M[1:0,1](320051)4M[100:22081,eeeebbbbbbbbeeebbbbbb52](321368)3M[23:0,23](323359)3M[1:0,1](323469)4M[100:10930,eeeeeeeeeeeebbebeebbbbbbe62](315739)3M[38:0,37](316885)3M[16:0,16](319212)2M[12:0,12](320100)3M[15:0,11](320812)2M[2:0,1](320188)
NF:7831 product criterion:14010406, ext_product criterion:392310
[65535:14]s
(S:0)
STDIN 102> I2;
I2[1]=1
max memory(KB):98008 time(sec):5.21 = 0:05.21