Magma V2.19-8 Tue Aug 20 2013 23:49:55 on localhost [Seed = 1999707573] Type ? for help. Type -D to quit. Loading file "K11n86__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K11n86 geometric_solution 11.71947558 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 0 1 -1 0 0 -1 1 1 -1 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.091646108346 1.122312312215 0 5 7 6 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 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 0.373060846892 0.427267386135 4 0 8 5 0213 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 0 0 0 0 0 0 0 -1 1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.473750142688 0.378019487375 9 10 11 0 0132 0132 0132 0132 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 1 -1 0 0 -1 1 -1 2 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.728340919976 0.615461078606 2 8 0 6 0213 0132 0132 0213 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 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 0.619161431967 0.566339632949 9 1 2 12 3120 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 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 0.953182297808 0.668179742446 9 10 1 4 2103 0213 0132 0213 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 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 0.253988044750 1.076436903954 9 12 10 1 1023 0132 2103 0132 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 1 0 0 -1 1 1 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.780236029766 1.550656195496 11 4 10 2 2031 0132 2031 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 -1 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.841292478350 0.755702507900 3 7 6 5 0132 1023 2103 3120 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 1 -1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.506866947859 0.407766542284 7 3 6 8 2103 0132 0213 1302 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 -1 0 1 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.734837190868 0.567852543774 12 12 8 3 0132 1302 1302 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 0 1 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.428744609417 0.756194555397 11 7 5 11 0132 0132 0132 2031 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 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 0.636026464114 0.841934723383 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_0110_6' : d['c_0101_5'], 'c_1001_11' : d['c_0011_4'], 'c_1001_10' : d['c_1001_0'], 'c_1001_12' : d['c_1001_1'], 'c_1001_5' : d['c_1001_0'], 'c_1001_4' : d['c_1001_2'], 'c_1001_7' : d['c_0011_10'], 'c_1001_6' : d['c_1001_0'], 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_1001_3'], 'c_1001_2' : d['c_1001_2'], 'c_1001_9' : d['c_0011_6'], 'c_1001_8' : negation(d['c_0110_10']), 'c_1010_12' : d['c_0011_10'], 'c_1010_11' : d['c_1001_3'], 'c_1010_10' : d['c_1001_3'], 's_3_11' : d['1'], 's_0_11' : d['1'], 's_0_12' : d['1'], 's_3_12' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0011_4'], 'c_0101_10' : d['c_0011_6'], 's_2_0' : negation(d['1']), 's_2_1' : negation(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' : negation(d['1']), 's_0_6' : d['1'], 's_0_7' : negation(d['1']), 's_0_4' : d['1'], 's_0_5' : d['1'], 's_0_2' : d['1'], 's_0_3' : negation(d['1']), 's_0_0' : negation(d['1']), 's_0_1' : negation(d['1']), 'c_0011_11' : d['c_0011_10'], 'c_0011_10' : d['c_0011_10'], 'c_0011_12' : negation(d['c_0011_10']), 'c_1100_5' : negation(d['c_1001_3']), 'c_1100_4' : d['c_0101_8'], 'c_1100_7' : negation(d['c_0110_10']), 'c_1100_6' : negation(d['c_0110_10']), 'c_1100_1' : negation(d['c_0110_10']), 'c_1100_0' : d['c_0101_8'], 'c_1100_3' : d['c_0101_8'], 'c_1100_2' : negation(d['c_1001_3']), 's_0_10' : d['1'], 'c_1100_9' : negation(d['c_0101_5']), 'c_1100_11' : d['c_0101_8'], 'c_1100_10' : d['c_0101_8'], 's_3_10' : d['1'], 'c_1010_7' : d['c_1001_1'], 'c_1010_6' : d['c_0101_8'], 'c_1010_5' : d['c_1001_1'], 'c_1010_4' : negation(d['c_0110_10']), 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_1001_0'], 'c_1010_0' : d['c_1001_2'], 'c_1010_9' : negation(d['c_0011_0']), 'c_1010_8' : d['c_1001_2'], 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : negation(d['1']), 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : d['1'], 's_3_7' : negation(d['1']), 's_3_6' : d['1'], 's_3_9' : d['1'], 's_3_8' : d['1'], 'c_1100_12' : negation(d['c_1001_3']), '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' : negation(d['1']), 's_1_8' : d['1'], 'c_0011_9' : d['c_0011_10'], 'c_0011_8' : negation(d['c_0011_4']), 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : d['c_0011_4'], 'c_0011_7' : d['c_0011_10'], '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_10']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_12'], 'c_0110_10' : d['c_0110_10'], 'c_0110_12' : d['c_0011_4'], 'c_0101_12' : d['c_0101_12'], 'c_0101_7' : d['c_0011_6'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : negation(d['c_0011_0']), 'c_0101_3' : d['c_0101_12'], 'c_0101_2' : d['c_0011_4'], 'c_0101_1' : negation(d['c_0011_0']), 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_0'], 'c_0101_8' : d['c_0101_8'], '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' : d['c_0011_4'], 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : negation(d['c_0011_0']), 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_5'], 'c_0110_5' : d['c_0101_12'], 'c_0110_4' : negation(d['c_0101_5']), 'c_0110_7' : negation(d['c_0011_0']), 'c_1100_8' : negation(d['c_1001_3'])})} 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_4, c_0011_6, c_0101_0, c_0101_12, c_0101_5, c_0101_8, c_0110_10, c_1001_0, c_1001_1, c_1001_2, c_1001_3 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 10 Groebner basis: [ t - 228838771/251537*c_1001_3^9 - 137712132/251537*c_1001_3^8 + 294226370/251537*c_1001_3^7 + 802445271/251537*c_1001_3^6 + 2535570789/503074*c_1001_3^5 + 1209967047/503074*c_1001_3^4 + 164829746/251537*c_1001_3^3 - 624773759/503074*c_1001_3^2 - 3878709011/503074*c_1001_3 - 713487831/503074, c_0011_0 - 1, c_0011_10 + 2077/5277*c_1001_3^9 + 618/1759*c_1001_3^8 - 3178/5277*c_1001_3^7 - 2941/1759*c_1001_3^6 - 13048/5277*c_1001_3^5 - 5107/5277*c_1001_3^4 + 1745/5277*c_1001_3^3 + 7220/5277*c_1001_3^2 + 21208/5277*c_1001_3 + 8578/5277, c_0011_4 - 2077/5277*c_1001_3^9 - 618/1759*c_1001_3^8 + 3178/5277*c_1001_3^7 + 2941/1759*c_1001_3^6 + 13048/5277*c_1001_3^5 + 5107/5277*c_1001_3^4 - 1745/5277*c_1001_3^3 - 7220/5277*c_1001_3^2 - 21208/5277*c_1001_3 - 8578/5277, c_0011_6 - 4004/5277*c_1001_3^9 - 1210/1759*c_1001_3^8 + 4691/5277*c_1001_3^7 + 4893/1759*c_1001_3^6 + 26048/5277*c_1001_3^5 + 17297/5277*c_1001_3^4 + 8219/5277*c_1001_3^3 - 3235/5277*c_1001_3^2 - 34835/5277*c_1001_3 - 12446/5277, c_0101_0 + 964/1759*c_1001_3^9 + 642/1759*c_1001_3^8 - 850/1759*c_1001_3^7 - 3448/1759*c_1001_3^6 - 6078/1759*c_1001_3^5 - 3943/1759*c_1001_3^4 - 1724/1759*c_1001_3^3 + 1299/1759*c_1001_3^2 + 8545/1759*c_1001_3 + 3181/1759, c_0101_12 + 653/5277*c_1001_3^9 + 207/1759*c_1001_3^8 - 740/5277*c_1001_3^7 - 635/1759*c_1001_3^6 - 4712/5277*c_1001_3^5 - 2129/5277*c_1001_3^4 - 1832/5277*c_1001_3^3 - 3815/5277*c_1001_3^2 - 2494/5277*c_1001_3 - 2011/5277, c_0101_5 - 398/5277*c_1001_3^9 + 189/1759*c_1001_3^8 + 548/5277*c_1001_3^7 + 185/1759*c_1001_3^6 - 1702/5277*c_1001_3^5 - 3244/5277*c_1001_3^4 + 1157/5277*c_1001_3^3 + 4394/5277*c_1001_3^2 + 4300/5277*c_1001_3 + 4741/5277, c_0101_8 + 653/5277*c_1001_3^9 + 207/1759*c_1001_3^8 - 740/5277*c_1001_3^7 - 635/1759*c_1001_3^6 - 4712/5277*c_1001_3^5 - 2129/5277*c_1001_3^4 - 1832/5277*c_1001_3^3 - 3815/5277*c_1001_3^2 + 2783/5277*c_1001_3 - 2011/5277, c_0110_10 + 878/5277*c_1001_3^9 + 246/1759*c_1001_3^8 - 599/5277*c_1001_3^7 - 1239/1759*c_1001_3^6 - 4784/5277*c_1001_3^5 - 4697/5277*c_1001_3^4 - 2738/5277*c_1001_3^3 - 200/5277*c_1001_3^2 + 962/5277*c_1001_3 - 223/5277, c_1001_0 - 910/5277*c_1001_3^9 - 275/1759*c_1001_3^8 + 1306/5277*c_1001_3^7 + 1192/1759*c_1001_3^6 + 5920/5277*c_1001_3^5 + 4171/5277*c_1001_3^4 - 1730/5277*c_1001_3^3 - 2894/5277*c_1001_3^2 - 11515/5277*c_1001_3 - 5707/5277, c_1001_1 - 653/5277*c_1001_3^9 - 207/1759*c_1001_3^8 + 740/5277*c_1001_3^7 + 635/1759*c_1001_3^6 + 4712/5277*c_1001_3^5 + 2129/5277*c_1001_3^4 + 1832/5277*c_1001_3^3 + 3815/5277*c_1001_3^2 - 2783/5277*c_1001_3 + 2011/5277, c_1001_2 + 910/5277*c_1001_3^9 + 275/1759*c_1001_3^8 - 1306/5277*c_1001_3^7 - 1192/1759*c_1001_3^6 - 5920/5277*c_1001_3^5 - 4171/5277*c_1001_3^4 + 1730/5277*c_1001_3^3 + 2894/5277*c_1001_3^2 + 11515/5277*c_1001_3 + 5707/5277, c_1001_3^10 + c_1001_3^9 - c_1001_3^8 - 4*c_1001_3^7 - 7*c_1001_3^6 - 5*c_1001_3^5 - 2*c_1001_3^4 + c_1001_3^3 + 9*c_1001_3^2 + 5*c_1001_3 + 1 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_4, c_0011_6, c_0101_0, c_0101_12, c_0101_5, c_0101_8, c_0110_10, c_1001_0, c_1001_1, c_1001_2, c_1001_3 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 14 Groebner basis: [ t + 1138501/308396*c_1001_2*c_1001_3^6 + 68817/154198*c_1001_2*c_1001_3^5 - 6296461/308396*c_1001_2*c_1001_3^4 + 235806/77099*c_1001_2*c_1001_3^3 + 4281724/77099*c_1001_2*c_1001_3^2 - 430879/7172*c_1001_2*c_1001_3 + 1836710/77099*c_1001_2 + 3322831/925188*c_1001_3^6 + 1464992/231297*c_1001_3^5 - 919745/84108*c_1001_3^4 - 2848309/154198*c_1001_3^3 + 1953172/77099*c_1001_3^2 - 75899/7172*c_1001_3 - 739085/462594, c_0011_0 - 1, c_0011_10 + 1/3*c_1001_2*c_1001_3^6 - 1/3*c_1001_2*c_1001_3^5 - 7/3*c_1001_2*c_1001_3^4 + 2*c_1001_2*c_1001_3^3 + 7*c_1001_2*c_1001_3^2 - 9*c_1001_2*c_1001_3 + 11/3*c_1001_2 + 4/3*c_1001_3^6 + 5/3*c_1001_3^5 - 16/3*c_1001_3^4 - 5*c_1001_3^3 + 13*c_1001_3^2 - 8*c_1001_3 + 2/3, c_0011_4 + 1/3*c_1001_2*c_1001_3^6 - 1/3*c_1001_2*c_1001_3^5 - 7/3*c_1001_2*c_1001_3^4 + 2*c_1001_2*c_1001_3^3 + 7*c_1001_2*c_1001_3^2 - 9*c_1001_2*c_1001_3 + 11/3*c_1001_2 + 7/6*c_1001_3^6 + 1/3*c_1001_3^5 - 37/6*c_1001_3^4 + 16*c_1001_3^2 - 35/2*c_1001_3 + 22/3, c_0011_6 + 3/2*c_1001_2*c_1001_3^6 + c_1001_2*c_1001_3^5 - 15/2*c_1001_2*c_1001_3^4 - 3*c_1001_2*c_1001_3^3 + 18*c_1001_2*c_1001_3^2 - 33/2*c_1001_2*c_1001_3 + 5*c_1001_2 + c_1001_3^5 + c_1001_3^4 - 5*c_1001_3^3 - 4*c_1001_3^2 + 11*c_1001_3 - 7, c_0101_0 + 1/6*c_1001_3^6 + 4/3*c_1001_3^5 + 5/6*c_1001_3^4 - 5*c_1001_3^3 - 3*c_1001_3^2 + 19/2*c_1001_3 - 20/3, c_0101_12 - 7/6*c_1001_3^6 - 1/3*c_1001_3^5 + 37/6*c_1001_3^4 - 16*c_1001_3^2 + 35/2*c_1001_3 - 19/3, c_0101_5 + 3/2*c_1001_2*c_1001_3^6 + c_1001_2*c_1001_3^5 - 15/2*c_1001_2*c_1001_3^4 - 3*c_1001_2*c_1001_3^3 + 18*c_1001_2*c_1001_3^2 - 33/2*c_1001_2*c_1001_3 + 5*c_1001_2 + 1/2*c_1001_3^6 + c_1001_3^5 - 3/2*c_1001_3^4 - 4*c_1001_3^3 + 2*c_1001_3^2 + 1/2*c_1001_3 - 1, c_0101_8 - 1/6*c_1001_2*c_1001_3^6 - 4/3*c_1001_2*c_1001_3^5 - 5/6*c_1001_2*c_1001_3^4 + 5*c_1001_2*c_1001_3^3 + 3*c_1001_2*c_1001_3^2 - 19/2*c_1001_2*c_1001_3 + 17/3*c_1001_2 + 1/6*c_1001_3^6 - 2/3*c_1001_3^5 - 13/6*c_1001_3^4 + 2*c_1001_3^3 + 6*c_1001_3^2 - 15/2*c_1001_3 + 10/3, c_0110_10 - c_1001_2*c_1001_3^6 - c_1001_2*c_1001_3^5 + 4*c_1001_2*c_1001_3^4 + 2*c_1001_2*c_1001_3^3 - 10*c_1001_2*c_1001_3^2 + 11*c_1001_2*c_1001_3 - 4*c_1001_2 - 1/6*c_1001_3^6 - 1/3*c_1001_3^5 + 1/6*c_1001_3^4 - c_1001_3^2 + 3/2*c_1001_3 - 1/3, c_1001_0 - c_1001_2 + 1/6*c_1001_3^6 - 2/3*c_1001_3^5 - 13/6*c_1001_3^4 + 2*c_1001_3^3 + 6*c_1001_3^2 - 15/2*c_1001_3 + 10/3, c_1001_1 - 1/6*c_1001_2*c_1001_3^6 - 4/3*c_1001_2*c_1001_3^5 - 5/6*c_1001_2*c_1001_3^4 + 5*c_1001_2*c_1001_3^3 + 3*c_1001_2*c_1001_3^2 - 19/2*c_1001_2*c_1001_3 + 17/3*c_1001_2 + 3/2*c_1001_3^6 + c_1001_3^5 - 15/2*c_1001_3^4 - 3*c_1001_3^3 + 18*c_1001_3^2 - 33/2*c_1001_3 + 5, c_1001_2^2 - 1/6*c_1001_2*c_1001_3^6 + 2/3*c_1001_2*c_1001_3^5 + 13/6*c_1001_2*c_1001_3^4 - 2*c_1001_2*c_1001_3^3 - 6*c_1001_2*c_1001_3^2 + 15/2*c_1001_2*c_1001_3 - 10/3*c_1001_2 + 5/6*c_1001_3^6 - 1/3*c_1001_3^5 - 29/6*c_1001_3^4 + 3*c_1001_3^3 + 13*c_1001_3^2 - 39/2*c_1001_3 + 26/3, c_1001_3^7 - 5*c_1001_3^5 + 2*c_1001_3^4 + 12*c_1001_3^3 - 21*c_1001_3^2 + 14*c_1001_3 - 4 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 3.930 Total time: 4.139 seconds, Total memory usage: 122.59MB