Magma V2.19-8 Tue Sep 10 2013 02:42:12 on localhost [Seed = 3267243929] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation m003 geometric_solution 2.02988321 oriented_manifold CS_known -0.0000000000000000 1 0 torus 0.000000000000 0.000000000000 2 1 1 1 1 0132 2103 0321 1023 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 -1 1 0 1 0 0 -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 0 0 0 0 0132 2103 0321 1023 0 0 0 0 0 0 0 0 0 0 1 -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 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 0.500000000000 0.866025403784 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1020_0' : d['c_0102_0'], 'c_1020_1' : d['c_0102_1'], 'c_0201_0' : d['c_0102_1'], 'c_0201_1' : d['c_0102_0'], 'c_2100_0' : d['c_0012_1'] * d['u'] ** 2, 'c_2100_1' : d['c_0012_0'] * d['u'] ** 1, 'c_2010_0' : d['c_0102_1'], 'c_2010_1' : d['c_0102_0'], 'c_0102_0' : d['c_0102_0'], 'c_0102_1' : d['c_0102_1'], 'c_1101_0' : d['c_1101_0'], 'c_1101_1' : negation(d['c_1101_0']) * d['u'] ** 2, 'c_1200_0' : d['c_0012_0'] * d['u'] ** 1, 'c_1200_1' : d['c_0012_1'] * d['u'] ** 2, 'c_1110_0' : d['c_1110_0'], 'c_1110_1' : negation(d['c_1110_0']) * d['u'] ** 2, 'c_0120_0' : d['c_0102_1'] * d['u'] ** 2, 'c_0120_1' : d['c_0102_0'] * d['u'] ** 1, 'c_2001_0' : d['c_0012_0'], 'c_2001_1' : d['c_0012_1'], '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_0210_0' : d['c_0102_0'] * d['u'] ** 1, 'c_0210_1' : d['c_0102_1'] * d['u'] ** 2, 'c_1002_0' : d['c_0012_1'], 'c_1002_1' : d['c_0012_0'], 'c_1011_0' : d['c_1011_0'], 'c_1011_1' : negation(d['c_1011_0']), 'c_0021_0' : d['c_0012_1'], 'c_0021_1' : d['c_0012_0']}), 'non_trivial_generalized_obstruction_class' : True} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 10 over Rational Field Order: Lexicographical Variables: t, c_0012_0, c_0012_1, c_0102_0, c_0102_1, c_0111_0, c_1011_0, c_1101_0, c_1110_0, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 2 Groebner basis: [ t - u, c_0012_0 - 1, c_0012_1 + u + 1, c_0102_0 - u, c_0102_1 - u, c_0111_0 - 1, c_1011_0 - u - 1, c_1101_0 - u, c_1110_0 + u, u^2 + u + 1 ], Ideal of Polynomial ring of rank 10 over Rational Field Order: Lexicographical Variables: t, c_0012_0, c_0012_1, c_0102_0, c_0102_1, c_0111_0, c_1011_0, c_1101_0, c_1110_0, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t + 3*c_1110_0^3*u + 3*c_1110_0^3 + 3*c_1110_0^2*u + 4*c_1110_0*u + 7*c_1110_0 + 2, c_0012_0 - 1, c_0012_1 + c_1110_0*u, c_0102_0 + 1/3*c_1110_0^2*u - 1/3*c_1110_0^2 + 1/3*c_1110_0*u - 1/3*c_1110_0 + 1/3*u - 1/3, c_0102_1 + 1/3*c_1110_0^3*u + 2/3*c_1110_0^3 + 2/3*c_1110_0^2*u + 1/3*c_1110_0^2 - 1/3*c_1110_0*u + 1/3*c_1110_0 + 1/3*u + 2/3, c_0111_0 - 1, c_1011_0 + 2/3*c_1110_0^2*u + 1/3*c_1110_0^2 + 2/3*c_1110_0*u + 1/3*c_1110_0 + 2/3*u + 1/3, c_1101_0 + 1/3*c_1110_0^3*u + 2/3*c_1110_0^3 + 2/3*c_1110_0^2*u + 1/3*c_1110_0^2 - 1/3*c_1110_0*u + 1/3*c_1110_0 + 1/3*u + 2/3, c_1110_0^4 + c_1110_0^3*u + c_1110_0^3 - c_1110_0^2*u + c_1110_0^2 - c_1110_0*u + u, u^2 + u + 1 ], Ideal of Polynomial ring of rank 10 over Rational Field Order: Lexicographical Variables: t, c_0012_0, c_0012_1, c_0102_0, c_0102_1, c_0111_0, c_1011_0, c_1101_0, c_1110_0, u Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t + c_1110_0^3 - c_1110_0^2 + 2*c_1110_0*u - 1, c_0012_0 - 1, c_0012_1 + c_1110_0^3*u + c_1110_0^3 - c_1110_0^2*u - c_1110_0^2 - c_1110_0*u - 2*c_1110_0 + u, c_0102_0 - 1/3*c_1110_0^3*u - 2/3*c_1110_0^3 + 2/3*c_1110_0^2*u + 1/3*c_1110_0^2 - 1/3*c_1110_0*u + 4/3*c_1110_0 - u, c_0102_1 + 2/3*c_1110_0^3*u + 1/3*c_1110_0^3 - 2/3*c_1110_0^2*u - 1/3*c_1110_0^2 - 5/3*c_1110_0*u - 4/3*c_1110_0 + 2/3*u - 2/3, c_0111_0 - 1, c_1011_0 - 2/3*c_1110_0^2*u - 1/3*c_1110_0^2 + 1/3*c_1110_0*u - 1/3*c_1110_0 + 1/3*u + 2/3, c_1101_0 - 1/3*c_1110_0^3*u - 2/3*c_1110_0^3 + 1/3*c_1110_0^2*u + 2/3*c_1110_0^2 + 1/3*c_1110_0*u + 2/3*c_1110_0 - 1/3*u - 2/3, c_1110_0^4 - c_1110_0^3 + c_1110_0^2*u - c_1110_0^2 + c_1110_0*u + c_1110_0 + u, u^2 + u + 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE Total time: 0.360 seconds, Total memory usage: 32.09MB