Magma V2.19-8 Tue Aug 20 2013 16:16:25 on localhost [Seed = 3768679437] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v0691 geometric_solution 4.65329615 oriented_manifold CS_known 0.0000000000000000 1 0 torus 0.000000000000 0.000000000000 7 0 0 1 1 1230 3012 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.676722467168 0.068809418994 2 0 2 0 0132 2310 1023 0132 0 0 0 0 0 0 -1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.860688449344 0.079907241003 1 3 1 3 0132 0132 1023 1023 0 0 0 0 0 0 1 -1 -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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.781491369623 0.228275465024 4 2 5 2 0132 0132 0132 1023 0 0 0 0 0 0 0 0 -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 0 0 0 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 1.085554110827 0.934117289250 3 6 5 5 0132 0132 0213 2310 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 -1 0 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 0.377011474247 0.738702136808 4 4 6 3 3201 0213 1023 0132 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 -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 0.377011474247 0.738702136808 6 4 5 6 3012 0132 1023 1230 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.451873604747 1.073978292631 ==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_1']), 'c_1100_4' : 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_1'], 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : negation(d['c_0101_3']), 'c_0101_4' : d['c_0011_5'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0101_0'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0011_5' : d['c_0011_5'], 'c_0011_4' : negation(d['c_0011_1']), 'c_0011_6' : d['c_0011_1'], 'c_0011_1' : d['c_0011_1'], 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_1'], 'c_0011_2' : negation(d['c_0011_1']), 'c_1001_5' : d['c_0101_6'], 'c_1001_4' : d['c_0101_6'], 'c_1001_6' : negation(d['c_0101_3']), 'c_1001_1' : d['c_0101_0'], 'c_1001_0' : negation(d['c_0011_0']), 'c_1001_3' : d['c_0011_5'], 'c_1001_2' : d['c_0101_1'], 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0011_0'], 'c_0110_3' : d['c_0011_5'], 'c_0110_2' : d['c_0101_1'], 'c_0110_5' : d['c_0101_3'], 'c_0110_4' : d['c_0101_3'], 'c_0110_6' : d['c_0011_1'], 'c_1010_6' : d['c_0101_6'], 'c_1010_5' : d['c_0011_5'], 'c_1010_4' : negation(d['c_0101_3']), 'c_1010_3' : d['c_0101_1'], 'c_1010_2' : d['c_0011_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_5, c_0101_0, c_0101_1, c_0101_3, c_0101_6 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t - 507*c_0101_6^7 - 2132*c_0101_6^5 + 15349/2*c_0101_6^3 - 4965/2*c_0101_6, c_0011_0 - 1, c_0011_1 + 1/2*c_0101_6^6 + 2*c_0101_6^4 - 17/2*c_0101_6^2 + 2, c_0011_5 + 1/2*c_0101_6^7 + 2*c_0101_6^5 - 17/2*c_0101_6^3 + 2*c_0101_6, c_0101_0 + 2*c_0101_6^7 + 17/2*c_0101_6^5 - 30*c_0101_6^3 + 15/2*c_0101_6, c_0101_1 - 1/2*c_0101_6^6 - 5/2*c_0101_6^4 + 11/2*c_0101_6^2 - 1/2, c_0101_3 - c_0101_6^2, c_0101_6^8 + 4*c_0101_6^6 - 16*c_0101_6^4 + 8*c_0101_6^2 - 1 ], Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_1, c_0011_5, c_0101_0, c_0101_1, c_0101_3, c_0101_6 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 12 Groebner basis: [ t - 1384257/18605*c_0101_6^11 + 30443492/18605*c_0101_6^9 - 40374819/3721*c_0101_6^7 + 405404888/18605*c_0101_6^5 - 370239937/18605*c_0101_6^3 + 102972677/18605*c_0101_6, c_0011_0 - 1, c_0011_1 + 125/3721*c_0101_6^10 - 2650/3721*c_0101_6^8 + 16130/3721*c_0101_6^6 - 23846/3721*c_0101_6^4 + 13929/3721*c_0101_6^2 + 774/3721, c_0011_5 + 56/3721*c_0101_6^11 - 1297/3721*c_0101_6^9 + 9615/3721*c_0101_6^7 - 26096/3721*c_0101_6^5 + 34247/3721*c_0101_6^3 - 14893/3721*c_0101_6, c_0101_0 + 367/3721*c_0101_6^11 - 8122/3721*c_0101_6^9 + 54624/3721*c_0101_6^7 - 114292/3721*c_0101_6^5 + 107306/3721*c_0101_6^3 - 28900/3721*c_0101_6, c_0101_1 - 190/3721*c_0101_6^10 + 4089/3721*c_0101_6^8 - 25762/3721*c_0101_6^6 + 42973/3721*c_0101_6^4 - 28231/3721*c_0101_6^2 + 2891/3721, c_0101_3 + 60/3721*c_0101_6^10 - 1211/3721*c_0101_6^8 + 6498/3721*c_0101_6^6 - 4719/3721*c_0101_6^4 + 3348/3721*c_0101_6^2 + 718/3721, c_0101_6^12 - 22*c_0101_6^10 + 146*c_0101_6^8 - 294*c_0101_6^6 + 270*c_0101_6^4 - 77*c_0101_6^2 + 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.030 Total time: 0.230 seconds, Total memory usage: 32.09MB