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Gröbner basis compution in Maple
ideal := [f0,f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12,f13,f14,f15,f16,f17,f18,f19,f20,f21];
with(Groebner);
infolevel[GroebnerBasis] := 5;
vars := [a1,b1,b2,a2,a3,b3,b4,a4,a5,a6,b5,b6,a7,a8,a9,a10];
mybasis = Basis(ideal, tdeg);
-> MGb
domain: rat_int_cof
F4 algorithm
1: prime=1292765389
deg pairs taken matrix found
3 71 1 7 x 39 10.0 per row, 0.0 MB 1 new, 0 zero 0.008 sec
3 72 2 11 x 60 12.1 per row, 0.0 MB 1 new, 1 zero 0.001 sec
4 78 11 93 x 277 9.9 per row, 0.0 MB 6 new, 5 zero 0.002 sec
3 77 5 34 x 111 11.3 per row, 0.0 MB 1 new, 4 zero 0.001 sec
3 76 3 28 x 104 12.4 per row, 0.0 MB 0 new, 3 zero 0.001 sec
4 73 10 103 x 274 10.3 per row, 0.0 MB 2 new, 8 zero 0.001 sec
4 74 3 44 x 128 11.3 per row, 0.0 MB 0 new, 3 zero 0.001 sec
5 71 31 299 x 779 13.2 per row, 0.0 MB 14 new, 17 zero 0.004 sec
4 100 20 124 x 358 13.9 per row, 0.0 MB 6 new, 14 zero 0.001 sec
3 96 4 15 x 41 6.0 per row, 0.0 MB 0 new, 4 zero 0.000 sec
5 92 43 737 x 2038 19.3 per row, 0.1 MB 13 new, 30 zero 0.006 sec
4 136 2 106 x 642 20.2 per row, 0.0 MB 1 new, 1 zero 0.001 sec
5 139 35 1303 x 3318 23.2 per row, 0.2 MB 3 new, 32 zero 0.008 sec
6 124 99 4359 x 11221 23.7 per row, 0.8 MB 43 new, 56 zero 0.030 sec
5 362 7 211 x 949 19.6 per row, 0.0 MB 5 new, 2 zero 0.002 sec
6 359 166 6178 x 15251 39.5 per row, 1.9 MB 57 new, 109 zero 0.031 sec
5 629 10 439 x 2167 44.0 per row, 0.1 MB 5 new, 5 zero 0.003 sec
6 647 109 5579 x 16100 61.2 per row, 2.6 MB 58 new, 51 zero 0.034 sec
6 941 92 5680 x 16099 73.9 per row, 3.2 MB 54 new, 38 zero 0.029 sec
6 1305 37 5255 x 15943 85.2 per row, 3.4 MB 21 new, 16 zero 0.025 sec
7 1480 1336 36282 x 69393 143.4 per row, 39.8 MB 514 new, 822 zero 0.555 sec
6 4569 12 415 x 4216 254.0 per row, 0.8 MB 10 new, 2 zero 0.021 sec
7 4560 1096 38615 x 73176 261.1 per row, 77.1 MB 514 new, 582 zero 0.854 sec
6 8389 33 3124 x 12305 137.5 per row, 3.3 MB 17 new, 16 zero 0.072 sec
5 8359 6 134 x 1093 65.6 per row, 0.1 MB 2 new, 4 zero 0.030 sec
6 8372 29 3072 x 12167 133.3 per row, 3.1 MB 16 new, 13 zero 0.055 sec
7 8427 581 37406 x 71347 300.0 per row, 85.8 MB 302 new, 279 zero 0.671 sec
6 10518 15 2119 x 8782 188.0 per row, 3.0 MB 7 new, 8 zero 0.063 sec
5 10503 4 117 x 362 14.0 per row, 0.0 MB 1 new, 3 zero 0.039 sec
6 10493 32 3013 x 10012 178.1 per row, 4.1 MB 17 new, 15 zero 0.080 sec
7 10575 497 37675 x 72392 335.6 per row, 96.6 MB 257 new, 240 zero 0.760 sec
7 12496 276 38305 x 73462 366.7 per row, 107.3 MB 182 new, 94 zero 0.678 sec
7 13842 236 34899 x 68998 416.3 per row, 111.0 MB 159 new, 77 zero 0.841 sec
7 15175 90 32873 x 65968 430.9 per row, 108.2 MB 64 new, 26 zero 0.502 sec
7 15786 15 25207 x 54254 451.5 per row, 86.9 MB 11 new, 4 zero 0.231 sec
7 15850 15 31595 x 64249 438.5 per row, 105.8 MB 11 new, 4 zero 0.240 sec
8 15965 15671 175110 x 242751 1069.8 per row, 1429.9 MB 4582 new, 11106 zero 51.359 sec
7 34997 957 46722 x 82936 926.7 per row, 330.5 MB 573 new, 384 zero 3.596 sec
7 37740 892 44773 x 79444 991.1 per row, 338.7 MB 488 new, 404 zero 3.061 sec
7 40721 400 41222 x 75872 1075.1 per row, 338.3 MB 197 new, 203 zero 1.924 sec
7 41922 153 37712 x 70594 1056.5 per row, 304.1 MB 79 new, 74 zero 1.446 sec
7 42471 15 25537 x 54120 985.6 per row, 192.1 MB 7 new, 8 zero 0.776 sec
8 42542 38167 233640 x 274275 2558.2 per row, 4561.0 MB 10372 new, 27837 zero 282.695 sec
7 79781 4342 73633 x 107703 1842.3 per row, 1035.2 MB 2369 new, 1973 zero 28.462 sec
7 85100 13930 91830 x 115798 2349.0 per row, 1646.1 MB 6796 new, 7134 zero 92.611 sec
7 91133 53135 140361 x 116937 2899.4 per row, 3105.4 MB 7363 new, 45772 zero 79.431 sec
6 70231 21133 50325 x 40210 1773.8 per row, 681.2 MB 1234 new, 19899 zero 6.477 sec
6 53489 7185 34604 x 36435 1277.3 per row, 337.4 MB 484 new, 6701 zero 3.106 sec
6 49413 2352 29256 x 35654 1153.0 per row, 257.5 MB 165 new, 2187 zero 1.985 sec
6 48541 447 25143 x 32920 1118.0 per row, 214.6 MB 45 new, 402 zero 1.564 sec
6 48531 90 19368 x 26751 1123.1 per row, 166.0 MB 6 new, 84 zero 1.225 sec
6 48434 60 17946 x 25059 1092.8 per row, 149.7 MB 4 new, 56 zero 1.202 sec
6 48325 60 17935 x 25044 1092.0 per row, 149.5 MB 4 new, 56 zero 1.197 sec
6 48271 60 17920 x 25025 1091.6 per row, 149.3 MB 4 new, 56 zero 1.180 sec
6 48235 60 17905 x 25006 1091.7 per row, 149.2 MB 4 new, 56 zero 1.185 sec
6 48205 60 17888 x 24985 1092.0 per row, 149.1 MB 4 new, 56 zero 1.213 sec
6 48160 60 17883 x 24974 1092.0 per row, 149.1 MB 4 new, 56 zero 1.195 sec
6 48114 60 17872 x 24957 1091.4 per row, 148.9 MB 4 new, 56 zero 1.195 sec
6 48058 30 17830 x 24941 1089.3 per row, 148.2 MB 2 new, 28 zero 1.182 sec
6 48047 30 17809 x 24916 1089.0 per row, 148.0 MB 2 new, 28 zero 1.176 sec
6 47978 30 17795 x 24900 1089.0 per row, 147.9 MB 2 new, 28 zero 1.200 sec
6 47962 30 17717 x 24816 1091.5 per row, 147.6 MB 2 new, 28 zero 1.177 sec
6 47912 30 17701 x 24798 1092.4 per row, 147.6 MB 2 new, 28 zero 1.168 sec
6 47844 30 17700 x 24795 1091.8 per row, 147.5 MB 2 new, 28 zero 1.187 sec
6 47811 30 17698 x 24791 1091.6 per row, 147.5 MB 2 new, 28 zero 1.163 sec
6 47794 30 17696 x 24787 1091.2 per row, 147.4 MB 2 new, 28 zero 1.162 sec
6 47773 30 17690 x 24779 1091.1 per row, 147.3 MB 2 new, 28 zero 1.181 sec
6 47753 13 21660 x 29425 1118.9 per row, 185.0 MB 1 new, 12 zero 1.169 sec
7 47753 40981 146744 x 119267 1524.6 per row, 1707.4 MB 135 new, 41522 zero 4.626 sec
6 8368 58 24634 x 32886 1105.6 per row, 207.9 MB 11 new, 47 zero 1.323 sec
7 8449 768 95968 x 108549 918.4 per row, 672.8 MB 34 new, 734 zero 2.131 sec
7 8075 208 92825 x 105447 912.8 per row, 646.8 MB 21 new, 187 zero 1.993 sec
6 8099 30 23411 x 31497 1115.1 per row, 199.3 MB 10 new, 20 zero 1.197 sec
6 8183 60 23228 x 31202 1122.8 per row, 199.1 MB 8 new, 52 zero 1.173 sec
6 8197 90 22336 x 29937 1120.8 per row, 191.1 MB 8 new, 82 zero 1.174 sec
6 8195 45 22908 x 30751 1111.6 per row, 194.4 MB 3 new, 42 zero 1.153 sec
7 8192 383 91513 x 103774 916.7 per row, 640.4 MB 4 new, 379 zero 1.790 sec
7 7865 14 83509 x 95567 903.3 per row, 575.8 MB 0 new, 14 zero 1.566 sec
8 7851 7809 296558 x 309026 1179.4 per row, 2669.5 MB 25 new, 7949 zero 7.711 sec
8 335 108 277369 x 296994 731.4 per row, 1548.9 MB 9 new, 99 zero 2.788 sec
8 337 26 279112 x 298790 730.6 per row, 1556.9 MB 1 new, 25 zero 2.322 sec
9 324 324 744493 x 774524 587.3 per row, 3338.9 MB 5 new, 319 zero 7.390 sec
10 67 67 1778748 x 1824279 476.2 per row, 6469.7 MB 2 new, 65 zero 14.632 sec
11 28 28 3989352 x 4056954 392.9 per row, 11972.6 MB 2 new, 26 zero 31.947 sec
12 26 26 8378513 x 8476622 327.8 per row, 20989.0 MB 0 new, 26 zero 71.621 sec
reduce: 64093 x 79880 953.3 per row, 466.4 MB
memory used=79.0MB, alloc=112.5MB, time=17737.22
memory used=98.6MB, alloc=388.5MB, time=17737.55
select: 46.198 sec 6%
symbol: 130.891 sec 17%
matrix: 426.800 sec 57% 37460 good, 82.7% zero
update: 138.377 sec 18% 215560 pair, 99.9% elim
gbasis: 751.289 sec 7% 5401 polynomials
memory used=248.6MB, alloc=324.8MB, time=17739.42
0% use 5278 of 5401, 17739.491 sec
2: prime=994186751
deg pairs taken matrix found
3 71 1 7 x 39 10.0 per row, 0.0 MB 1 new, 0 zero 0.006 sec
3 72 2 11 x 60 12.1 per row, 0.0 MB 1 new, 1 zero 0.000 sec
4 78 11 93 x 277 9.9 per row, 0.0 MB 6 new, 5 zero 0.002 sec
3 77 5 34 x 111 11.3 per row, 0.0 MB 1 new, 4 zero 0.001 sec
3 76 3 28 x 104 12.4 per row, 0.0 MB 0 new, 3 zero 0.001 sec
4 73 10 103 x 274 10.3 per row, 0.0 MB 2 new, 8 zero 0.001 sec
4 74 3 44 x 128 11.3 per row, 0.0 MB 0 new, 3 zero 0.001 sec
5 71 31 299 x 779 13.2 per row, 0.0 MB 14 new, 17 zero 0.008 sec
4 100 20 124 x 358 13.9 per row, 0.0 MB 6 new, 14 zero 0.001 sec
3 96 4 15 x 41 6.0 per row, 0.0 MB 0 new, 4 zero 0.005 sec
5 92 43 737 x 2038 19.3 per row, 0.1 MB 13 new, 30 zero 0.005 sec
4 136 2 106 x 642 20.2 per row, 0.0 MB 1 new, 1 zero 0.001 sec
5 139 35 1303 x 3318 23.2 per row, 0.2 MB 3 new, 32 zero 0.007 sec
6 124 99 4359 x 11221 23.7 per row, 0.8 MB 43 new, 56 zero 0.030 sec
5 362 7 211 x 949 19.6 per row, 0.0 MB 5 new, 2 zero 0.002 sec
6 359 166 6178 x 15251 39.5 per row, 1.9 MB 57 new, 109 zero 0.030 sec
5 629 10 439 x 2167 44.0 per row, 0.1 MB 5 new, 5 zero 0.003 sec
6 647 109 5579 x 16100 61.2 per row, 2.6 MB 58 new, 51 zero 0.036 sec
6 941 92 5680 x 16099 73.9 per row, 3.2 MB 54 new, 38 zero 0.029 sec
6 1305 37 5255 x 15943 85.2 per row, 3.4 MB 21 new, 16 zero 0.023 sec
7 1480 1336 36282 x 69393 143.4 per row, 39.8 MB 514 new, 822 zero 0.577 sec
6 4572 12 415 x 4216 254.0 per row, 0.8 MB 10 new, 2 zero 0.025 sec
7 4563 1097 38616 x 73176 261.3 per row, 77.1 MB 514 new, 583 zero 0.844 sec
6 8391 33 3124 x 12305 137.5 per row, 3.3 MB 17 new, 16 zero 0.057 sec
5 8361 6 134 x 1093 65.6 per row, 0.1 MB 2 new, 4 zero 0.028 sec
6 8374 29 3072 x 12167 133.3 per row, 3.1 MB 16 new, 13 zero 0.057 sec
7 8429 581 37406 x 71347 300.0 per row, 85.8 MB 302 new, 279 zero 0.771 sec
6 10520 15 2119 x 8782 188.0 per row, 3.0 MB 7 new, 8 zero 0.053 sec
5 10505 4 117 x 362 14.0 per row, 0.0 MB 1 new, 3 zero 0.035 sec
6 10495 32 3013 x 10012 178.1 per row, 4.1 MB 17 new, 15 zero 0.062 sec
7 10577 497 37675 x 72392 335.6 per row, 96.6 MB 257 new, 240 zero 0.806 sec
7 12498 276 38305 x 73462 366.7 per row, 107.3 MB 182 new, 94 zero 0.686 sec
7 13844 236 34899 x 68998 416.3 per row, 111.0 MB 159 new, 77 zero 0.715 sec
7 15177 90 32873 x 65968 430.9 per row, 108.2 MB 64 new, 26 zero 0.467 sec
7 15788 15 25207 x 54254 451.5 per row, 86.9 MB 11 new, 4 zero 0.200 sec
7 15852 15 31595 x 64249 438.5 per row, 105.8 MB 11 new, 4 zero 0.229 sec
8 15967 15673 175112 x 242751 1069.9 per row, 1430.1 MB 4582 new, 11108 zero 54.645 sec
7 34997 957 46722 x 82936 926.7 per row, 330.5 MB 573 new, 384 zero 3.168 sec
7 37740 892 44773 x 79444 991.1 per row, 338.7 MB 488 new, 404 zero 2.945 sec
7 40721 400 41222 x 75872 1075.1 per row, 338.3 MB 197 new, 203 zero 1.846 sec
7 41922 153 37712 x 70594 1056.5 per row, 304.1 MB 79 new, 74 zero 1.313 sec
7 42471 15 25537 x 54120 985.6 per row, 192.1 MB 7 new, 8 zero 0.723 sec
8 42542 38167 233640 x 274275 2558.2 per row, 4561.0 MB 10372 new, 27837 zero 283.704 sec
7 79781 4342 73633 x 107703 1842.3 per row, 1035.2 MB 2369 new, 1973 zero 28.412 sec
7 85100 13930 91830 x 115798 2349.0 per row, 1646.1 MB 6796 new, 7134 zero 95.180 sec
7 91133 53135 140361 x 116937 2899.4 per row, 3105.4 MB 7363 new, 45772 zero 77.544 sec
6 70231 21133 50325 x 40210 1773.8 per row, 681.2 MB 1234 new, 19899 zero 5.635 sec
6 53489 7185 34604 x 36435 1277.3 per row, 337.4 MB 484 new, 6701 zero 2.877 sec
6 49413 2352 29256 x 35654 1153.0 per row, 257.5 MB 165 new, 2187 zero 1.774 sec
6 48541 447 25143 x 32920 1118.0 per row, 214.6 MB 45 new, 402 zero 1.364 sec
6 48531 90 19368 x 26751 1123.1 per row, 166.0 MB 6 new, 84 zero 1.123 sec
6 48434 60 17946 x 25059 1092.8 per row, 149.7 MB 4 new, 56 zero 1.093 sec
6 48325 60 17935 x 25044 1092.0 per row, 149.5 MB 4 new, 56 zero 1.098 sec
6 48271 60 17920 x 25025 1091.6 per row, 149.3 MB 4 new, 56 zero 1.085 sec
6 48235 60 17905 x 25006 1091.7 per row, 149.2 MB 4 new, 56 zero 1.095 sec
6 48205 60 17888 x 24985 1092.0 per row, 149.1 MB 4 new, 56 zero 1.089 sec
6 48160 60 17883 x 24974 1092.0 per row, 149.1 MB 4 new, 56 zero 1.084 sec
6 48114 60 17872 x 24957 1091.4 per row, 148.9 MB 4 new, 56 zero 1.086 sec
6 48058 30 17830 x 24941 1089.3 per row, 148.2 MB 2 new, 28 zero 1.080 sec
6 48047 30 17809 x 24916 1089.0 per row, 148.0 MB 2 new, 28 zero 1.075 sec
6 47978 30 17795 x 24900 1089.0 per row, 147.9 MB 2 new, 28 zero 1.076 sec
6 47962 30 17717 x 24816 1091.5 per row, 147.6 MB 2 new, 28 zero 1.075 sec
6 47912 30 17701 x 24798 1092.4 per row, 147.6 MB 2 new, 28 zero 1.073 sec
6 47844 30 17700 x 24795 1091.8 per row, 147.5 MB 2 new, 28 zero 1.075 sec
6 47811 30 17698 x 24791 1091.6 per row, 147.5 MB 2 new, 28 zero 1.077 sec
6 47794 30 17696 x 24787 1091.2 per row, 147.4 MB 2 new, 28 zero 1.090 sec
6 47773 30 17690 x 24779 1091.1 per row, 147.3 MB 2 new, 28 zero 1.072 sec
6 47753 13 21660 x 29425 1118.9 per row, 185.0 MB 1 new, 12 zero 1.086 sec
7 47753 40981 146744 x 119267 1524.6 per row, 1707.4 MB 135 new, 41522 zero 4.392 sec
6 8368 58 24634 x 32886 1105.6 per row, 207.9 MB 11 new, 47 zero 1.176 sec
7 8449 768 95968 x 108549 918.4 per row, 672.8 MB 34 new, 734 zero 1.943 sec
7 8075 208 92825 x 105447 912.8 per row, 646.8 MB 21 new, 187 zero 1.834 sec
6 8099 30 23411 x 31497 1115.1 per row, 199.3 MB 10 new, 20 zero 1.108 sec
6 8183 60 23228 x 31202 1122.8 per row, 199.1 MB 8 new, 52 zero 1.084 sec
6 8197 90 22336 x 29937 1120.8 per row, 191.1 MB 8 new, 82 zero 1.076 sec
6 8195 45 22908 x 30751 1111.6 per row, 194.4 MB 3 new, 42 zero 1.065 sec
7 8192 383 91513 x 103774 916.7 per row, 640.4 MB 4 new, 379 zero 1.681 sec
7 7865 14 83509 x 95567 903.3 per row, 575.8 MB 0 new, 14 zero 1.449 sec
8 7851 7809 296558 x 309026 1179.4 per row, 2669.5 MB 25 new, 7949 zero 7.246 sec
8 335 108 277369 x 296994 731.4 per row, 1548.9 MB 9 new, 99 zero 2.892 sec
8 337 26 279112 x 298790 730.6 per row, 1556.9 MB 1 new, 25 zero 2.491 sec
9 324 324 744493 x 774524 587.3 per row, 3338.9 MB 5 new, 319 zero 7.555 sec
10 67 67 1778748 x 1824279 476.2 per row, 6469.7 MB 2 new, 65 zero 14.713 sec
11 28 28 3989352 x 4056954 392.9 per row, 11972.6 MB 2 new, 26 zero 31.663 sec
12 26 26 8378513 x 8476622 327.8 per row, 20989.0 MB 0 new, 26 zero 72.256 sec
reduce: 64093 x 79880 953.3 per row, 466.4 MB
memory used=420.8MB, alloc=389.5MB, time=35658.14
memory used=420.9MB, alloc=645.5MB, time=35658.30
select: 42.802 sec 6%
symbol: 128.954 sec 17%
matrix: 434.077 sec 58% 37460 good, 82.7% zero
update: 136.257 sec 18% 215563 pair, 99.9% elim
gbasis: 751.342 sec 7% 5401 polynomials
memory used=676.2MB, alloc=581.8MB, time=35659.95
... 40 more computations with different primes follow, all exactly the same otherwise ...
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