Magma V2.19-8 Fri Sep 13 2013 01:03:52 on localhost [Seed = 2431671903] Type ? for help. Type -D to quit. Loading file "m202__sl3_c2.magma" ==TRIANGULATION=BEGINS== % Triangulation m202 geometric_solution 4.05976643 oriented_manifold CS_known 0.0000000000000002 2 0 torus 0.000000000000 0.000000000000 torus 0.000000000000 0.000000000000 4 1 1 2 1 0132 1230 0132 2031 0 0 1 0 0 1 0 -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 1 -1 0 -1 0 1 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 0.500000000000 0.866025403784 0 0 0 3 0132 1302 3012 0132 0 0 0 1 0 0 0 0 1 0 -1 0 0 1 0 -1 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 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 0.500000000000 0.866025403784 3 3 3 0 0213 0321 2310 0132 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 -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 0.500000000000 0.866025403784 2 2 1 2 0213 3201 0132 0321 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 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.866025403784 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1020_2' : d['c_1002_0'], 'c_1020_3' : d['c_1002_0'], 'c_1020_0' : d['c_0012_1'], 'c_1020_1' : d['c_0021_3'] * d['u'] ** 1, 'c_0201_0' : d['c_0021_2'], 'c_0201_1' : d['c_0012_0'], 'c_0201_2' : d['c_0021_3'] * d['u'] ** 1, 'c_0201_3' : d['c_0021_2'], 'c_2100_0' : d['c_0021_3'], 'c_2100_1' : d['c_1002_0'], 'c_2100_2' : d['c_0021_3'], 'c_2100_3' : d['c_1002_0'] * d['u'] ** 2, 'c_2010_2' : d['c_1002_2'], 'c_2010_3' : d['c_1002_2'], 'c_2010_0' : d['c_0012_0'], 'c_2010_1' : d['c_0012_3'] * d['u'] ** 2, 'c_0102_0' : d['c_0012_2'], 'c_0102_1' : d['c_0012_1'], 'c_0102_2' : d['c_0012_3'] * d['u'] ** 2, 'c_0102_3' : d['c_0012_2'], 'c_1101_0' : d['c_1101_0'], 'c_1101_1' : d['c_1011_0'], 'c_1101_2' : d['c_1011_3'], 'c_1101_3' : d['c_1101_3'], 'c_1200_2' : d['c_0012_3'], 'c_1200_3' : d['c_1002_2'] * d['u'] ** 1, 'c_1200_0' : d['c_0012_3'], 'c_1200_1' : d['c_1002_2'], 'c_1110_2' : d['c_1101_0'], 'c_1110_3' : negation(d['c_1011_2']) * d['u'] ** 2, 'c_1110_0' : negation(d['c_1011_1']) * d['u'] ** 2, 'c_1110_1' : d['c_1101_3'] * d['u'] ** 1, 'c_0120_0' : d['c_0012_1'] * d['u'] ** 2, 'c_0120_1' : d['c_0012_2'] * d['u'] ** 1, 'c_0120_2' : d['c_0012_2'], 'c_0120_3' : d['c_0021_2'] * d['u'] ** 2, 'c_2001_0' : d['c_1002_2'], 'c_2001_1' : d['c_0012_0'], 'c_2001_2' : d['c_1002_0'], 'c_2001_3' : d['c_0012_3'] * d['u'] ** 2, 'c_0012_2' : d['c_0012_2'], 'c_0012_3' : d['c_0012_3'], 'c_0012_0' : d['c_0012_0'], 'c_0012_1' : d['c_0012_1'], 'c_0111_0' : d['c_0111_0'], 'c_0111_1' : negation(d['c_0111_0']) * d['u'] ** 1, 'c_0111_2' : d['c_0111_2'], 'c_0111_3' : negation(d['c_0111_2']) * d['u'] ** 1, 'c_0210_2' : d['c_0021_2'], 'c_0210_3' : d['c_0012_2'] * d['u'] ** 1, 'c_0210_0' : d['c_0012_0'] * d['u'] ** 1, 'c_0210_1' : d['c_0021_2'] * d['u'] ** 2, 'c_1002_2' : d['c_1002_2'], 'c_1002_3' : d['c_0021_3'] * d['u'] ** 1, 'c_1002_0' : d['c_1002_0'], 'c_1002_1' : d['c_0012_1'], 'c_1011_2' : d['c_1011_2'], 'c_1011_3' : d['c_1011_3'], 'c_1011_0' : d['c_1011_0'], 'c_1011_1' : d['c_1011_1'], 'c_0021_0' : d['c_0012_1'], 'c_0021_1' : d['c_0012_0'], 'c_0021_2' : d['c_0021_2'], 'c_0021_3' : d['c_0021_3']}), 'non_trivial_generalized_obstruction_class' : True} PY=EVAL=SECTION=ENDS=HERE PRIMARY_DECOMPOSITION_TIME: 40.460 PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 18 over Rational Field Order: Lexicographical Variables: t, c_0012_0, c_0012_1, c_0012_2, c_0012_3, c_0021_2, c_0021_3, c_0111_0, c_0111_2, c_1002_0, c_1002_2, c_1011_0, c_1011_1, c_1011_2, c_1011_3, c_1101_0, c_1101_3, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 4 Groebner basis: [ t + 20/9*c_1101_3*u + 1/9*c_1101_3 + 34/9*u + 47/9, c_0012_0 - 1, c_0012_1 - 1, c_0012_2 - 1, c_0012_3 - 1, c_0021_2 + c_1101_3 + 1, c_0021_3 - c_1101_3*u - c_1101_3 - u - 1, c_0111_0 - 1, c_0111_2 - u - 1, c_1002_0 + c_1101_3*u + u, c_1002_2 - 1, c_1011_0 - u - 1, c_1011_1 - 1, c_1011_2 + u + 1, c_1011_3 + 1, c_1101_0 - c_1101_3*u - 2*u - 1, c_1101_3^2 - 2*c_1101_3*u + c_1101_3 - 3*u, u^2 + u + 1 ], Ideal of Polynomial ring of rank 18 over Rational Field Order: Lexicographical Variables: t, c_0012_0, c_0012_1, c_0012_2, c_0012_3, c_0021_2, c_0021_3, c_0111_0, c_0111_2, c_1002_0, c_1002_2, c_1011_0, c_1011_1, c_1011_2, c_1011_3, c_1101_0, c_1101_3, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 4 Groebner basis: [ t - 121/9*c_1101_3*u - 449/9*c_1101_3 + 370/9*u + 1121/9, c_0012_0 - 1, c_0012_1 - 1, c_0012_2 - 1, c_0012_3 - u, c_0021_2 - c_1101_3*u - c_1101_3 + u, c_0021_3 - c_1101_3*u - c_1101_3 + u, c_0111_0 - 1, c_0111_2 + c_1101_3*u + c_1101_3 - u, c_1002_0 - c_1101_3*u - c_1101_3 + u, c_1002_2 + u + 1, c_1011_0 + 1, c_1011_1 + u + 1, c_1011_2 - c_1101_3*u - c_1101_3 + u, c_1011_3 - c_1101_3 + u + 1, c_1101_0 + c_1101_3*u + c_1101_3 - u + 1, c_1101_3^2 - c_1101_3*u - 3*c_1101_3 + 2*u + 1, u^2 + u + 1 ], Ideal of Polynomial ring of rank 18 over Rational Field Order: Lexicographical Variables: t, c_0012_0, c_0012_1, c_0012_2, c_0012_3, c_0021_2, c_0021_3, c_0111_0, c_0111_2, c_1002_0, c_1002_2, c_1011_0, c_1011_1, c_1011_2, c_1011_3, c_1101_0, c_1101_3, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t - 198100747121357/314573778*c_1101_3^3*u - 2625188558879833/1258295112*c_1101_3^3 - 4420337821326853/524289630*c_1101_3^2*u + 1079701828242191/419431704*c_1101_3^2 - 8212110371026856/786434445*c_1101_3*u - 151899104314342361/6291475560*c_1101_3 + 68459997956622707/6291475560*u - 4212623738660231/6291475560, c_0012_0 - 1, c_0012_1 - 1, c_0012_2 - 1, c_0012_3 - 156315/472333*c_1101_3^3*u + 11915/472333*c_1101_3^3 + 960736/472333*c_1101_3^2*u + 1036977/472333*c_1101_3^2 - 1029350/472333*c_1101_3*u + 146011/472333*c_1101_3 - 328219/472333*u - 106485/472333, c_0021_2 - 1070/472333*c_1101_3^3*u + 143460/472333*c_1101_3^3 + 779989/472333*c_1101_3^2*u + 91267/472333*c_1101_3^2 + 471708/472333*c_1101_3*u + 2017272/472333*c_1101_3 - 645123/472333*u + 172549/472333, c_0021_3 + 68305/472333*c_1101_3^3*u + 112110/472333*c_1101_3^3 + 366064/472333*c_1101_3^2*u - 385503/472333*c_1101_3^2 + 2376/472333*c_1101_3*u + 405388/472333*c_1101_3 - 102633/472333*u - 294722/472333, c_0111_0 - 1, c_0111_2 - 142660/1416999*c_1101_3^3*u - 119360/1416999*c_1101_3^3 + 261401/1416999*c_1101_3^2*u + 850030/1416999*c_1101_3^2 - 1103039/1416999*c_1101_3*u - 1221859/1416999*c_1101_3 + 13504/472333*u - 141930/472333, c_1002_0 + 43535/472333*c_1101_3^3*u + 100325/472333*c_1101_3^3 + 381090/472333*c_1101_3^2*u - 113489/472333*c_1101_3^2 + 844287/472333*c_1101_3*u + 921602/472333*c_1101_3 - 151818/472333*u + 194731/472333, c_1002_2 - 44205/472333*c_1101_3^3*u + 55720/472333*c_1101_3^3 + 575233/472333*c_1101_3^2*u + 285410/472333*c_1101_3^2 - 623962/472333*c_1101_3*u + 549023/472333*c_1101_3 - 150608/472333*u - 298574/472333, c_1011_0 - 43805/472333*c_1101_3^3*u + 68305/472333*c_1101_3^3 + 751567/472333*c_1101_3^2*u + 366064/472333*c_1101_3^2 - 403012/472333*c_1101_3*u + 474709/472333*c_1101_3 - 280244/472333*u - 102633/472333, c_1011_1 - 43805/472333*c_1101_3^3*u + 68305/472333*c_1101_3^3 + 751567/472333*c_1101_3^2*u + 366064/472333*c_1101_3^2 - 403012/472333*c_1101_3*u + 474709/472333*c_1101_3 + 192089/472333*u - 102633/472333, c_1011_2 - 119360/1416999*c_1101_3^3*u + 23300/1416999*c_1101_3^3 + 850030/1416999*c_1101_3^2*u + 588629/1416999*c_1101_3^2 - 1221859/1416999*c_1101_3*u + 1298179/1416999*c_1101_3 - 141930/472333*u - 155434/472333, c_1011_3 + 325475/1416999*c_1101_3^3*u + 350785/1416999*c_1101_3^3 + 777164/1416999*c_1101_3^2*u - 1503176/1416999*c_1101_3^2 + 1891837/1416999*c_1101_3*u + 2529041/1416999*c_1101_3 - 90339/472333*u + 56653/472333, c_1101_0 - 87340/472333*c_1101_3^3*u - 32020/472333*c_1101_3^3 + 370477/472333*c_1101_3^2*u + 479553/472333*c_1101_3^2 - 1247299/472333*c_1101_3*u - 446893/472333*c_1101_3 - 128426/472333*u - 297364/472333, c_1101_3^4 + 27/5*c_1101_3^3*u + 2/5*c_1101_3^3 + 13/5*c_1101_3^2*u + 66/5*c_1101_3^2 - 44/5*c_1101_3*u - 2*c_1101_3 - 3/5*u - 6/5, u^2 + u + 1 ], Ideal of Polynomial ring of rank 18 over Rational Field Order: Lexicographical Variables: t, c_0012_0, c_0012_1, c_0012_2, c_0012_3, c_0021_2, c_0021_3, c_0111_0, c_0111_2, c_1002_0, c_1002_2, c_1011_0, c_1011_1, c_1011_2, c_1011_3, c_1101_0, c_1101_3, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t + 10816715/123432*c_1101_3^3*u + 4932523/154290*c_1101_3^3 + 104857973/231435*c_1101_3^2*u + 218834221/925740*c_1101_3^2 - 10733765/46287*c_1101_3*u + 1934812139/1851480*c_1101_3 - 319008125/370296*u - 370827419/462870, c_0012_0 - 1, c_0012_1 - 1, c_0012_2 - 1, c_0012_3 + 46/139*c_1101_3^3*u + 32/139*c_1101_3^3 + 272/139*c_1101_3^2*u + 159/139*c_1101_3^2 - 42/139*c_1101_3*u + 140/139*c_1101_3 - 22/139*u + 27/139, c_0021_2 - 10/139*c_1101_3^3*u - 13/139*c_1101_3^3 - 41/139*c_1101_3^2*u - 95/139*c_1101_3^2 + 130/139*c_1101_3*u - 109/139*c_1101_3 + 174/139*u + 115/139, c_0021_3 + 35/139*c_1101_3^3*u - 24/139*c_1101_3^3 + 213/139*c_1101_3^2*u - 154/139*c_1101_3^2 + 379/139*c_1101_3*u + 312/139*c_1101_3 + 225/139*u + 223/139, c_0111_0 - 1, c_0111_2 - 94/417*c_1101_3^3*u - 11/417*c_1101_3^3 - 580/417*c_1101_3^2*u - 59/417*c_1101_3^2 - 446/417*c_1101_3*u - 1108/417*c_1101_3 + 17/139*u - 103/139, c_1002_0 + c_1101_3*u + c_1101_3 + 1, c_1002_2 - 14/139*c_1101_3^3*u - 46/139*c_1101_3^3 - 113/139*c_1101_3^2*u - 272/139*c_1101_3^2 + 321/139*c_1101_3*u + 181/139*c_1101_3 + 49/139*u + 22/139, c_1011_0 + 59/139*c_1101_3^3*u + 35/139*c_1101_3^3 + 367/139*c_1101_3^2*u + 213/139*c_1101_3^2 + 67/139*c_1101_3*u + 518/139*c_1101_3 - 137/139*u + 225/139, c_1011_1 + 59/139*c_1101_3^3*u + 35/139*c_1101_3^3 + 367/139*c_1101_3^2*u + 213/139*c_1101_3^2 + 67/139*c_1101_3*u + 518/139*c_1101_3 + 2/139*u + 225/139, c_1011_2 - 44/417*c_1101_3^3*u - 85/417*c_1101_3^3 - 236/417*c_1101_3^2*u - 418/417*c_1101_3^2 + 572/417*c_1101_3*u + 271/417*c_1101_3 + 5/139*u - 63/139, c_1011_3 + 11/417*c_1101_3^3*u - 83/417*c_1101_3^3 + 59/417*c_1101_3^2*u - 521/417*c_1101_3^2 + 691/417*c_1101_3*u + 245/417*c_1101_3 + 103/139*u + 120/139, c_1101_0 + 59/139*c_1101_3^3*u + 35/139*c_1101_3^3 + 367/139*c_1101_3^2*u + 213/139*c_1101_3^2 - 72/139*c_1101_3*u + 379/139*c_1101_3 - 137/139*u + 86/139, c_1101_3^4 - c_1101_3^3*u + 5*c_1101_3^3 - 17*c_1101_3^2*u - 11*c_1101_3^2 - c_1101_3*u - 11*c_1101_3 + 3*u - 3, u^2 + u + 1 ], Ideal of Polynomial ring of rank 18 over Rational Field Order: Lexicographical Variables: t, c_0012_0, c_0012_1, c_0012_2, c_0012_3, c_0021_2, c_0021_3, c_0111_0, c_0111_2, c_1002_0, c_1002_2, c_1011_0, c_1011_1, c_1011_2, c_1011_3, c_1101_0, c_1101_3, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t - 201541628/1665*c_1101_3^3*u - 562744/1665*c_1101_3^3 - 49997531/555*c_1101_3^2*u - 30945785/111*c_1101_3^2 + 121011629/555*c_1101_3*u + 79645432/555*c_1101_3 - 73392443/1665*u + 3228391/333, c_0012_0 - 1, c_0012_1 - 1, c_0012_2 - 1, c_0012_3 - 176/3*c_1101_3^3*u - 4*c_1101_3^3 - 31*c_1101_3^2*u - 380/3*c_1101_3^2 + 301/3*c_1101_3*u + 230/3*c_1101_3 - 23*u + 1, c_0021_2 + 56/3*c_1101_3^3*u + 172/3*c_1101_3^3 - 349/3*c_1101_3^2*u - 134/3*c_1101_3^2 + 31*c_1101_3*u - 57*c_1101_3 + 12*u + 22, c_0021_3 + 112/3*c_1101_3^3*u + 16*c_1101_3^3 - 4*c_1101_3^2*u + 184/3*c_1101_3^2 - 134/3*c_1101_3*u - 139/3*c_1101_3 + 11*u + 2, c_0111_0 - 1, c_0111_2 + 4*c_1101_3^3*u - 16/3*c_1101_3^3 + 35/3*c_1101_3^2*u + 13*c_1101_3^2 - 8*c_1101_3*u - 3*c_1101_3 + u, c_1002_0 + 60*c_1101_3^3*u + 56/3*c_1101_3^3 + 19/3*c_1101_3^2*u + 337/3*c_1101_3^2 - 259/3*c_1101_3*u - 227/3*c_1101_3 + 19*u, c_1002_2 - 68/3*c_1101_3^3*u - 8/3*c_1101_3^3 - 31/3*c_1101_3^2*u - 51*c_1101_3^2 + 137/3*c_1101_3*u + 100/3*c_1101_3 - 10*u + 3, c_1011_0 + 64/3*c_1101_3^3*u + 112/3*c_1101_3^3 - 196/3*c_1101_3^2*u - 4*c_1101_3^2 + 5/3*c_1101_3*u - 131/3*c_1101_3 + 8*u + 11, c_1011_1 + 64/3*c_1101_3^3*u + 112/3*c_1101_3^3 - 196/3*c_1101_3^2*u - 4*c_1101_3^2 + 5/3*c_1101_3*u - 131/3*c_1101_3 + 9*u + 11, c_1011_2 + 32*c_1101_3^3*u + 20/3*c_1101_3^3 + 9*c_1101_3^2*u + 188/3*c_1101_3^2 - 146/3*c_1101_3*u - 121/3*c_1101_3 + 11*u, c_1011_3 - 32*c_1101_3^3*u - 20/3*c_1101_3^3 - 9*c_1101_3^2*u - 188/3*c_1101_3^2 + 143/3*c_1101_3*u + 121/3*c_1101_3 - 11*u, c_1101_0 - 116/3*c_1101_3^3*u + 56/3*c_1101_3^3 - 215/3*c_1101_3^2*u - 349/3*c_1101_3^2 + 88*c_1101_3*u + 32*c_1101_3 - 11*u + 11, c_1101_3^4 - 405/148*c_1101_3^3*u - 79/37*c_1101_3^3 + 325/148*c_1101_3^2*u - 105/148*c_1101_3^2 + 25/148*c_1101_3*u + 97/74*c_1101_3 - 15/74*u - 33/148, u^2 + u + 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE FREE=VARIABLES=IN=COMPONENTS=BEGINS=HERE [ [ ], [ ], [ ], [ ], [ ] ] FREE=VARIABLES=IN=COMPONENTS=ENDS=HERE CPUTIME: 40.460 Total time: 40.670 seconds, Total memory usage: 96.75MB