Magma V2.19-8 Tue Aug 20 2013 16:17:54 on localhost [Seed = 2176851265] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v2133 geometric_solution 5.62013761 oriented_manifold CS_known 0.0000000000000001 1 0 torus 0.000000000000 0.000000000000 7 0 0 1 1 1230 3012 0132 2310 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.681803023402 0.556761161042 0 2 3 0 3201 0132 0132 0132 0 0 0 0 0 0 1 -1 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 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 0.654818038625 0.588242211358 4 1 3 5 0132 0132 1302 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 -1 0 1 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 0.484684370543 0.496911507480 2 5 4 1 2031 1023 1023 0132 0 0 0 0 0 1 0 -1 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 -1 0 1 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 0.484684370543 0.496911507480 2 6 3 6 0132 0132 1023 1023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.319113780472 1.237016470631 3 5 2 5 1023 2310 0132 3201 0 0 0 0 0 0 0 0 -1 0 0 1 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 1 0 0 -1 -1 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.782824686162 0.803706440005 6 4 6 4 2031 0132 1302 1023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0.462108890998 0.243988025297 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 's_3_1' : d['1'], 's_3_3' : d['1'], 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : d['1'], 's_3_0' : d['1'], '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_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_0_6' : 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_1100_6' : d['c_0011_1'], 'c_1100_5' : negation(d['c_0011_3']), 'c_1100_4' : negation(d['c_0011_1']), 's_3_6' : d['1'], 'c_1100_1' : d['c_0011_1'], 'c_1100_0' : d['c_0011_1'], 'c_1100_3' : d['c_0011_1'], 'c_1100_2' : negation(d['c_0011_3']), 'c_0101_6' : d['c_0011_1'], 'c_0101_5' : d['c_0101_4'], 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : negation(d['c_0011_3']), 'c_0101_2' : negation(d['c_0011_3']), 'c_0101_1' : negation(d['c_0011_0']), 'c_0101_0' : d['c_0101_0'], 'c_0011_5' : d['c_0011_3'], 'c_0011_4' : d['c_0011_1'], 'c_0011_6' : negation(d['c_0011_1']), 'c_0011_1' : d['c_0011_1'], 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_3'], 'c_0011_2' : negation(d['c_0011_1']), 'c_1001_5' : d['c_0110_5'], 'c_1001_4' : negation(d['c_0011_3']), 'c_1001_6' : d['c_0110_6'], 'c_1001_1' : d['c_0110_5'], 'c_1001_0' : negation(d['c_0011_0']), 'c_1001_3' : d['c_0101_4'], 'c_1001_2' : negation(d['c_0011_0']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0011_0'], 'c_0110_3' : negation(d['c_0011_0']), 'c_0110_2' : d['c_0101_4'], 'c_0110_5' : d['c_0110_5'], 'c_0110_4' : negation(d['c_0011_3']), 'c_0110_6' : d['c_0110_6'], 'c_1010_6' : negation(d['c_0011_3']), 'c_1010_5' : negation(d['c_0110_5']), 'c_1010_4' : d['c_0110_6'], 'c_1010_3' : d['c_0110_5'], 'c_1010_2' : d['c_0110_5'], 'c_1010_1' : negation(d['c_0011_0']), 'c_1010_0' : negation(d['c_0101_0'])})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_1, c_0011_3, c_0101_0, c_0101_4, c_0110_5, c_0110_6 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 5 Groebner basis: [ t + 183/7*c_0110_6^4 + 688/7*c_0110_6^3 + 1299/7*c_0110_6^2 + 1338/7*c_0110_6 + 781/7, c_0011_0 - 1, c_0011_1 + c_0110_6^4 + 3*c_0110_6^3 + 4*c_0110_6^2 + 3*c_0110_6 + 1, c_0011_3 - c_0110_6^3 - 2*c_0110_6^2 - 2*c_0110_6, c_0101_0 + c_0110_6^3 + 3*c_0110_6^2 + 4*c_0110_6 + 2, c_0101_4 + c_0110_6^2 + 2*c_0110_6, c_0110_5 + c_0110_6^3 + 2*c_0110_6^2 + 2*c_0110_6 + 1, c_0110_6^5 + 4*c_0110_6^4 + 8*c_0110_6^3 + 9*c_0110_6^2 + 6*c_0110_6 + 1 ], Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_1, c_0011_3, c_0101_0, c_0101_4, c_0110_5, c_0110_6 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 6 Groebner basis: [ t + 31/13*c_0110_5^5 - 6*c_0110_5^4 - 196/13*c_0110_5^3 + 317/13*c_0110_5^2 - 75/13*c_0110_5 - 274/13, c_0011_0 - 1, c_0011_1 + 6/13*c_0110_5^5 - 2*c_0110_5^4 + 17/13*c_0110_5^3 + 6/13*c_0110_5^2 - 25/13*c_0110_5 + 4/13, c_0011_3 - 5/13*c_0110_5^5 + 2*c_0110_5^4 - 25/13*c_0110_5^3 - 18/13*c_0110_5^2 + 23/13*c_0110_5 + 1/13, c_0101_0 + 2/13*c_0110_5^5 - c_0110_5^4 + 23/13*c_0110_5^3 + 2/13*c_0110_5^2 - 30/13*c_0110_5 + 10/13, c_0101_4 + 4/13*c_0110_5^5 - c_0110_5^4 - 6/13*c_0110_5^3 + 4/13*c_0110_5^2 + 5/13*c_0110_5 + 7/13, c_0110_5^6 - 5*c_0110_5^5 + 5*c_0110_5^4 + 2*c_0110_5^3 - 7*c_0110_5^2 + 2*c_0110_5 + 1, c_0110_6 - 1 ], Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_1, c_0011_3, c_0101_0, c_0101_4, c_0110_5, c_0110_6 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t + 139*c_0110_6^7 - 442*c_0110_6^6 - 1598*c_0110_6^5 + 1577*c_0110_6^4 + 3269*c_0110_6^3 - 633*c_0110_6^2 - 1922*c_0110_6 - 486, c_0011_0 - 1, c_0011_1 - 14*c_0110_6^7 + 46*c_0110_6^6 + 155*c_0110_6^5 - 171*c_0110_6^4 - 302*c_0110_6^3 + 77*c_0110_6^2 + 175*c_0110_6 + 44, c_0011_3 - 5*c_0110_6^7 + 16*c_0110_6^6 + 57*c_0110_6^5 - 57*c_0110_6^4 - 116*c_0110_6^3 + 20*c_0110_6^2 + 70*c_0110_6 + 20, c_0101_0 - 25*c_0110_6^7 + 84*c_0110_6^6 + 270*c_0110_6^5 - 323*c_0110_6^4 - 511*c_0110_6^3 + 161*c_0110_6^2 + 294*c_0110_6 + 69, c_0101_4 + 21*c_0110_6^7 - 72*c_0110_6^6 - 221*c_0110_6^5 + 283*c_0110_6^4 + 403*c_0110_6^3 - 148*c_0110_6^2 - 230*c_0110_6 - 51, c_0110_5 + c_0110_6^7 - 3*c_0110_6^6 - 12*c_0110_6^5 + 9*c_0110_6^4 + 25*c_0110_6^3 + c_0110_6^2 - 15*c_0110_6 - 6, c_0110_6^8 - 3*c_0110_6^7 - 12*c_0110_6^6 + 9*c_0110_6^5 + 25*c_0110_6^4 + c_0110_6^3 - 14*c_0110_6^2 - 7*c_0110_6 - 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.030 Total time: 0.230 seconds, Total memory usage: 32.09MB