Magma V2.19-8 Tue Aug 20 2013 16:16:11 on localhost [Seed = 3953817391] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v0453 geometric_solution 4.49351520 oriented_manifold CS_known -0.0000000000000005 1 0 torus 0.000000000000 0.000000000000 7 0 0 1 1 1230 3012 0132 3201 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.352914220874 0.188685526696 2 0 3 0 0132 2310 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 0.443447110369 0.989489503580 1 4 3 3 0132 0132 3012 1230 0 0 0 0 0 -1 1 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 1 -1 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 1.537571675944 1.457340648742 2 2 4 1 3012 1230 3201 0132 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 1 0 -1 0 0 1 0 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.537571675944 1.457340648742 3 2 5 5 2310 0132 3201 0132 0 0 0 0 0 1 0 -1 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 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.186690031793 0.435209583247 4 6 4 6 2310 0132 0132 2310 0 0 0 0 0 -1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.042841696400 2.131777251457 5 5 6 6 3201 0132 2031 1302 0 0 0 0 0 1 0 -1 0 0 1 -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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.362753976010 0.094812157549 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 's_3_1' : d['1'], 's_3_3' : negation(d['1']), 's_3_2' : negation(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' : 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_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' : negation(d['1']), 's_0_3' : negation(d['1']), 's_0_0' : d['1'], 's_0_1' : negation(d['1']), 'c_1100_6' : d['c_0011_3'], 'c_1100_5' : negation(d['c_0011_5']), 'c_1100_4' : negation(d['c_0011_5']), 's_3_6' : d['1'], 'c_1100_1' : negation(d['c_0011_1']), 'c_1100_0' : negation(d['c_0011_1']), 'c_1100_3' : negation(d['c_0011_1']), 'c_1100_2' : d['c_0011_3'], 'c_0101_6' : d['c_0011_3'], 'c_0101_5' : negation(d['c_0101_3']), 'c_0101_4' : d['c_0011_3'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0101_0'], 'c_0101_1' : d['c_0011_3'], 'c_0101_0' : d['c_0101_0'], 'c_0011_5' : d['c_0011_5'], 'c_0011_4' : d['c_0011_1'], 'c_0011_6' : negation(d['c_0011_5']), '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' : negation(d['c_0011_3']), 'c_1001_4' : d['c_0101_3'], 'c_1001_6' : negation(d['c_0110_6']), 'c_1001_1' : d['c_0101_0'], 'c_1001_0' : negation(d['c_0011_0']), 'c_1001_3' : negation(d['c_0011_3']), 'c_1001_2' : negation(d['c_0011_3']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0011_0'], 'c_0110_3' : d['c_0011_3'], 'c_0110_2' : d['c_0011_3'], 'c_0110_5' : negation(d['c_0011_3']), 'c_0110_4' : negation(d['c_0101_3']), 'c_0110_6' : d['c_0110_6'], 'c_1010_6' : negation(d['c_0011_3']), 'c_1010_5' : negation(d['c_0110_6']), 'c_1010_4' : negation(d['c_0011_3']), 'c_1010_3' : d['c_0101_0'], 'c_1010_2' : d['c_0101_3'], '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_0011_5, c_0101_0, c_0101_3, c_0110_6 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 6 Groebner basis: [ t + 53/5*c_0110_6^5 + 2178/25*c_0110_6^3 + 6042/25*c_0110_6, c_0011_0 - 1, c_0011_1 + 1/25*c_0110_6^4 + 14/25*c_0110_6^2 + 1/5, c_0011_3 + 2/25*c_0110_6^4 + 3/25*c_0110_6^2 - 3/5, c_0011_5 - 1/5*c_0110_6^4 - 4/5*c_0110_6^2, c_0101_0 - 3/25*c_0110_6^5 - 17/25*c_0110_6^3 - 8/5*c_0110_6, c_0101_3 - 1/25*c_0110_6^5 - 14/25*c_0110_6^3 - 6/5*c_0110_6, c_0110_6^6 + 8*c_0110_6^4 + 21*c_0110_6^2 - 5 ], Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_1, c_0011_3, c_0011_5, c_0101_0, c_0101_3, c_0110_6 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 10 Groebner basis: [ t + 170805/22976*c_0110_6^9 + 43925/718*c_0110_6^7 + 1517843/22976*c_0110_6^5 - 3071835/11488*c_0110_6^3 + 5933751/22976*c_0110_6, c_0011_0 - 1, c_0011_1 + 49/718*c_0110_6^8 + 212/359*c_0110_6^6 + 255/359*c_0110_6^4 - 2181/718*c_0110_6^2 + 345/359, c_0011_3 - 14/359*c_0110_6^8 - 191/718*c_0110_6^6 - 35/718*c_0110_6^4 + 1195/718*c_0110_6^2 - 351/359, c_0011_5 + 27/718*c_0110_6^8 + 197/718*c_0110_6^6 + 303/718*c_0110_6^4 - 121/359*c_0110_6^2 - 59/359, c_0101_0 - 1/359*c_0110_6^9 + 6/359*c_0110_6^7 + 177/718*c_0110_6^5 + 111/718*c_0110_6^3 - 1281/718*c_0110_6, c_0101_3 - 12/359*c_0110_6^9 - 215/718*c_0110_6^7 - 389/718*c_0110_6^5 + 255/718*c_0110_6^3 - 506/359*c_0110_6, c_0110_6^10 + 8*c_0110_6^8 + 7*c_0110_6^6 - 38*c_0110_6^4 + 43*c_0110_6^2 - 8 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.010 Total time: 0.220 seconds, Total memory usage: 32.09MB