Magma V2.19-8 Tue Aug 20 2013 23:53:45 on localhost [Seed = 1999707384] Type ? for help. Type -D to quit. Loading file "K12n419__sl2_c0.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n419 geometric_solution 11.86452221 oriented_manifold CS_known 0.0000000000000002 1 0 torus 0.000000000000 0.000000000000 13 1 2 3 4 0132 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.595234276563 0.525034821412 0 5 7 6 0132 0132 0132 0132 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.911594920654 0.970099078646 8 0 10 9 0132 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 0 1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.359709602979 0.395045644895 5 11 9 0 0132 0132 3012 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 1 -1 0 0 0 11 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.372381193264 0.722564241519 7 12 0 11 0132 0132 0132 3012 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.292527510137 0.487205089378 3 1 12 10 0132 0132 3201 1230 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -10 0 10 1 0 0 -1 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.371503776179 1.281377140384 12 9 1 10 3201 2031 0132 3201 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.346087450994 0.971219426813 4 8 9 1 0132 0321 2031 0132 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -11 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.797350025788 0.651744006645 2 11 12 7 0132 1023 3120 0321 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -11 0 11 1 0 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.789460969166 0.538807046023 6 3 2 7 1302 1230 0132 1302 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 11 0 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.043765329264 1.541393646356 5 6 11 2 3012 2310 0132 0132 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -10 0 11 -1 1 0 0 -1 0 10 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.652803578498 0.980930747698 8 3 4 10 1023 0132 1230 0132 0 0 0 0 0 0 0 0 -1 0 0 1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 -11 1 -11 0 10 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.022669085103 1.369210326344 5 4 8 6 2310 0132 3120 2310 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.320309612666 0.668976706159 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_1001_0'], 'c_1001_10' : negation(d['c_0011_9']), 'c_1001_12' : negation(d['c_0101_11']), 'c_1001_5' : negation(d['c_0101_12']), 'c_1001_4' : negation(d['c_0110_6']), 'c_1001_7' : negation(d['c_0101_12']), 'c_1001_6' : negation(d['c_0101_12']), 'c_1001_1' : d['c_0101_10'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : negation(d['c_0011_9']), 'c_1001_2' : negation(d['c_0110_6']), 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : d['c_0101_11'], 'c_1010_12' : negation(d['c_0110_6']), 'c_1010_11' : negation(d['c_0011_9']), 'c_1010_10' : negation(d['c_0110_6']), 's_0_10' : d['1'], 's_3_10' : d['1'], 's_0_12' : d['1'], 's_3_12' : d['1'], 's_2_8' : d['1'], 'c_0101_12' : d['c_0101_12'], 'c_0101_11' : d['c_0101_11'], 'c_0101_10' : d['c_0101_10'], 's_2_0' : d['1'], 's_2_1' : d['1'], 's_2_2' : d['1'], 's_2_3' : d['1'], 's_2_4' : d['1'], 's_2_5' : d['1'], 's_2_6' : d['1'], 's_2_7' : d['1'], 's_2_12' : d['1'], 's_2_10' : d['1'], 's_2_11' : d['1'], 's_0_8' : d['1'], 's_0_9' : d['1'], 's_0_6' : d['1'], 's_0_7' : d['1'], 's_0_4' : d['1'], 's_0_5' : d['1'], 's_0_2' : d['1'], 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_0011_11' : d['c_0011_0'], 'c_1100_8' : negation(d['c_0101_12']), 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_0011_12']), 'c_1100_4' : negation(d['c_1001_0']), 'c_1100_7' : negation(d['c_0011_10']), 'c_1100_6' : negation(d['c_0011_10']), 'c_1100_1' : negation(d['c_0011_10']), 'c_1100_0' : negation(d['c_1001_0']), 'c_1100_3' : negation(d['c_1001_0']), 'c_1100_2' : d['c_0101_7'], 's_3_11' : d['1'], 'c_1100_11' : d['c_0101_7'], 'c_1100_10' : d['c_0101_7'], 's_0_11' : d['1'], 'c_1010_7' : d['c_0101_10'], 'c_1010_6' : d['c_0011_9'], 'c_1010_5' : d['c_0101_10'], 'c_1010_4' : negation(d['c_0101_11']), 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : negation(d['c_0101_12']), 'c_1010_0' : negation(d['c_0110_6']), 'c_1010_9' : d['c_0011_10'], 'c_1010_8' : d['c_0101_10'], 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : d['1'], 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : d['1'], 's_3_7' : d['1'], 's_3_6' : d['1'], 's_3_9' : d['1'], 's_3_8' : d['1'], 'c_1100_12' : d['c_0011_6'], 's_1_7' : d['1'], 's_1_6' : d['1'], 's_1_5' : d['1'], 's_1_4' : d['1'], 's_1_3' : d['1'], 's_1_2' : d['1'], 's_1_1' : d['1'], 's_1_0' : d['1'], 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : d['c_0011_9'], 'c_0011_8' : d['c_0011_0'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_12']), 'c_0011_7' : d['c_0011_12'], 'c_0011_6' : d['c_0011_6'], 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : negation(d['c_0011_0']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_10'], 'c_0110_10' : negation(d['c_0011_12']), 'c_0110_12' : negation(d['c_0101_0']), 'c_0110_0' : d['c_0101_1'], 'c_0101_7' : d['c_0101_7'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0011_10'], 'c_0101_2' : negation(d['c_0011_12']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0011_6']), 'c_0101_8' : negation(d['c_0011_6']), 'c_0011_10' : d['c_0011_10'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_12'], 'c_0110_8' : negation(d['c_0011_12']), 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : d['c_0101_7'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : negation(d['c_0011_6']), 'c_0110_5' : d['c_0011_10'], 'c_0110_4' : d['c_0101_7'], 'c_0110_7' : d['c_0101_1'], 'c_0110_6' : d['c_0110_6'], 's_2_9' : d['1']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_12, c_0011_6, c_0011_9, c_0101_0, c_0101_1, c_0101_10, c_0101_11, c_0101_12, c_0101_7, c_0110_6, c_1001_0 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t + 42187/30814*c_1001_0^7 - 48925/8804*c_1001_0^6 + 116205/30814*c_1001_0^5 + 260457/61628*c_1001_0^4 + 194447/30814*c_1001_0^3 - 207575/61628*c_1001_0^2 + 225237/15407*c_1001_0 + 294603/30814, c_0011_0 - 1, c_0011_10 + 381/2201*c_1001_0^7 - 3137/4402*c_1001_0^6 + 1163/2201*c_1001_0^5 + 2685/4402*c_1001_0^4 + 98/2201*c_1001_0^3 + 3679/4402*c_1001_0^2 + 4644/2201*c_1001_0 + 3527/2201, c_0011_12 + 19/62*c_1001_0^7 - 89/62*c_1001_0^6 + 113/62*c_1001_0^5 - 23/62*c_1001_0^4 + 45/62*c_1001_0^3 + 17/62*c_1001_0^2 + 128/31*c_1001_0 + 15/31, c_0011_6 - 199/4402*c_1001_0^7 + 955/4402*c_1001_0^6 - 619/4402*c_1001_0^5 - 2027/4402*c_1001_0^4 + 1653/4402*c_1001_0^3 - 1033/4402*c_1001_0^2 + 87/2201*c_1001_0 - 69/2201, c_0011_9 - 293/4402*c_1001_0^7 + 1937/4402*c_1001_0^6 - 4141/4402*c_1001_0^5 + 2789/4402*c_1001_0^4 - 1017/4402*c_1001_0^3 + 2505/4402*c_1001_0^2 - 1907/2201*c_1001_0 + 374/2201, c_0101_0 - 190/2201*c_1001_0^7 + 580/2201*c_1001_0^6 + 327/2201*c_1001_0^5 - 1692/2201*c_1001_0^4 - 667/2201*c_1001_0^3 - 201/2201*c_1001_0^2 - 3893/2201*c_1001_0 - 4578/2201, c_0101_1 - 1241/4402*c_1001_0^7 + 6221/4402*c_1001_0^6 - 9877/4402*c_1001_0^5 + 5653/4402*c_1001_0^4 - 4623/4402*c_1001_0^3 - 27/4402*c_1001_0^2 - 7078/2201*c_1001_0 - 1293/2201, c_0101_10 - 101/2201*c_1001_0^7 + 540/2201*c_1001_0^6 - 834/2201*c_1001_0^5 + 398/2201*c_1001_0^4 - 621/2201*c_1001_0^3 + 1179/2201*c_1001_0^2 - 1803/2201*c_1001_0 + 671/2201, c_0101_11 - 428/2201*c_1001_0^7 + 4119/4402*c_1001_0^6 - 2924/2201*c_1001_0^5 + 2131/4402*c_1001_0^4 - 1433/2201*c_1001_0^3 - 141/4402*c_1001_0^2 - 4437/2201*c_1001_0 - 883/2201, c_0101_12 + 708/2201*c_1001_0^7 - 3088/2201*c_1001_0^6 + 3253/2201*c_1001_0^5 + 675/2201*c_1001_0^4 + 910/2201*c_1001_0^3 + 888/2201*c_1001_0^2 + 9479/2201*c_1001_0 + 5081/2201, c_0101_7 - 765/4402*c_1001_0^7 + 1631/2201*c_1001_0^6 - 3375/4402*c_1001_0^5 + 69/2201*c_1001_0^4 - 3091/4402*c_1001_0^3 - 144/2201*c_1001_0^2 - 6534/2201*c_1001_0 - 2787/2201, c_0110_6 - 482/2201*c_1001_0^7 + 4217/4402*c_1001_0^6 - 1997/2201*c_1001_0^5 - 1889/4402*c_1001_0^4 - 719/2201*c_1001_0^3 - 1321/4402*c_1001_0^2 - 6447/2201*c_1001_0 - 2856/2201, c_1001_0^8 - 4*c_1001_0^7 + 3*c_1001_0^6 + 2*c_1001_0^5 + 3*c_1001_0^4 + 2*c_1001_0^3 + 14*c_1001_0^2 + 12*c_1001_0 + 4 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_12, c_0011_6, c_0011_9, c_0101_0, c_0101_1, c_0101_10, c_0101_11, c_0101_12, c_0101_7, c_0110_6, c_1001_0 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 12 Groebner basis: [ t - 4566092023/193747617*c_1001_0^11 - 3995800030/193747617*c_1001_0^10 - 2882070008/21527513*c_1001_0^9 + 49924608488/64582539*c_1001_0^8 + 4762351709/193747617*c_1001_0^7 - 413401111195/193747617*c_1001_0^6 + 302681769533/193747617*c_1001_0^5 + 1005125421/3075359*c_1001_0^4 - 81765507851/193747617*c_1001_0^3 + 976559936/64582539*c_1001_0^2 + 24250073462/193747617*c_1001_0 + 5798418002/193747617, c_0011_0 - 1, c_0011_10 - 15450/161861*c_1001_0^11 - 169990/485583*c_1001_0^10 - 411997/485583*c_1001_0^9 + 699806/485583*c_1001_0^8 + 575549/69369*c_1001_0^7 - 467081/69369*c_1001_0^6 - 7011812/485583*c_1001_0^5 + 295889/23123*c_1001_0^4 - 418676/485583*c_1001_0^3 + 1551184/485583*c_1001_0^2 - 886070/485583*c_1001_0 + 63334/161861, c_0011_12 - 3440006/3399081*c_1001_0^11 - 2944709/3399081*c_1001_0^10 - 20657600/3399081*c_1001_0^9 + 112393033/3399081*c_1001_0^8 - 5407462/3399081*c_1001_0^7 - 272409706/3399081*c_1001_0^6 + 75096281/1133027*c_1001_0^5 - 7766314/485583*c_1001_0^4 + 36305900/3399081*c_1001_0^3 - 11526397/3399081*c_1001_0^2 + 3117599/1133027*c_1001_0 + 2032102/1133027, c_0011_6 - 23957/59633*c_1001_0^11 - 18170/59633*c_1001_0^10 - 390755/178899*c_1001_0^9 + 2453071/178899*c_1001_0^8 - 64454/178899*c_1001_0^7 - 6521381/178899*c_1001_0^6 + 4632350/178899*c_1001_0^5 + 72581/25557*c_1001_0^4 + 10354/59633*c_1001_0^3 - 426037/178899*c_1001_0^2 + 240062/178899*c_1001_0 + 123764/178899, c_0011_9 - 146868/1133027*c_1001_0^11 - 276680/3399081*c_1001_0^10 - 2775190/3399081*c_1001_0^9 + 14594864/3399081*c_1001_0^8 - 5369620/3399081*c_1001_0^7 - 9545161/1133027*c_1001_0^6 + 45022099/3399081*c_1001_0^5 - 4349845/485583*c_1001_0^4 - 1154572/3399081*c_1001_0^3 + 7101310/3399081*c_1001_0^2 + 2836735/3399081*c_1001_0 + 1303994/3399081, c_0101_0 - 1087573/3399081*c_1001_0^11 - 145504/3399081*c_1001_0^10 - 5615234/3399081*c_1001_0^9 + 40903138/3399081*c_1001_0^8 - 8317583/1133027*c_1001_0^7 - 29636863/1133027*c_1001_0^6 + 124318618/3399081*c_1001_0^5 - 8728927/485583*c_1001_0^4 + 26531791/3399081*c_1001_0^3 - 10068610/3399081*c_1001_0^2 + 9589525/3399081*c_1001_0 - 1094813/3399081, c_0101_1 - 3062317/3399081*c_1001_0^11 - 3272132/3399081*c_1001_0^10 - 18748418/3399081*c_1001_0^9 + 96228679/3399081*c_1001_0^8 + 5761268/1133027*c_1001_0^7 - 251166787/3399081*c_1001_0^6 + 149524969/3399081*c_1001_0^5 + 2141035/485583*c_1001_0^4 + 9354284/3399081*c_1001_0^3 - 6578917/3399081*c_1001_0^2 + 4984684/3399081*c_1001_0 + 2268256/1133027, c_0101_10 + 1106654/1133027*c_1001_0^11 + 850092/1133027*c_1001_0^10 + 19512284/3399081*c_1001_0^9 - 110740747/3399081*c_1001_0^8 + 12967610/3399081*c_1001_0^7 + 265119119/3399081*c_1001_0^6 - 232217897/3399081*c_1001_0^5 + 9508438/485583*c_1001_0^4 - 16066492/1133027*c_1001_0^3 + 11865052/3399081*c_1001_0^2 - 8624564/3399081*c_1001_0 - 1668440/3399081, c_0101_11 + 1530250/3399081*c_1001_0^11 + 1542265/3399081*c_1001_0^10 + 9103889/3399081*c_1001_0^9 - 48774613/3399081*c_1001_0^8 - 2158168/1133027*c_1001_0^7 + 44026214/1133027*c_1001_0^6 - 81218089/3399081*c_1001_0^5 - 2914169/485583*c_1001_0^4 + 2353199/3399081*c_1001_0^3 + 7707250/3399081*c_1001_0^2 - 869416/3399081*c_1001_0 - 2141701/3399081, c_0101_12 + 2025547/3399081*c_1001_0^11 + 1524701/3399081*c_1001_0^10 + 11416730/3399081*c_1001_0^9 - 67942099/3399081*c_1001_0^8 + 2212096/1133027*c_1001_0^7 + 178487173/3399081*c_1001_0^6 - 149342311/3399081*c_1001_0^5 - 184759/485583*c_1001_0^4 + 11466838/3399081*c_1001_0^3 + 6740029/3399081*c_1001_0^2 - 5093128/3399081*c_1001_0 - 1860569/1133027, c_0101_7 + 332254/1133027*c_1001_0^11 + 205320/1133027*c_1001_0^10 + 5638453/3399081*c_1001_0^9 - 33875663/3399081*c_1001_0^8 + 9099142/3399081*c_1001_0^7 + 85537870/3399081*c_1001_0^6 - 88554904/3399081*c_1001_0^5 + 1392983/485583*c_1001_0^4 + 1471965/1133027*c_1001_0^3 + 12460895/3399081*c_1001_0^2 - 2345428/3399081*c_1001_0 - 3223585/3399081, c_0110_6 - 92917/485583*c_1001_0^11 - 93028/485583*c_1001_0^10 - 648665/485583*c_1001_0^9 + 400600/69369*c_1001_0^8 - 112576/161861*c_1001_0^7 - 1826238/161861*c_1001_0^6 + 6822868/485583*c_1001_0^5 - 742984/69369*c_1001_0^4 + 1520059/485583*c_1001_0^3 + 414149/485583*c_1001_0^2 + 550519/485583*c_1001_0 + 234394/485583, c_1001_0^12 + c_1001_0^11 + 6*c_1001_0^10 - 32*c_1001_0^9 - 4*c_1001_0^8 + 83*c_1001_0^7 - 52*c_1001_0^6 - 4*c_1001_0^5 - 5*c_1001_0^4 + 6*c_1001_0^3 - 3*c_1001_0^2 - 3*c_1001_0 - 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 3.340 Total time: 3.549 seconds, Total memory usage: 123.03MB