Magma V2.19-8 Tue Aug 20 2013 18:03:17 on localhost [Seed = 273786265] Type ? for help. Type -D to quit. Loading file "8_18__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation 8_18 geometric_solution 12.35090621 oriented_manifold CS_known 0.0000000000000000 1 0 torus 0.000000000000 0.000000000000 13 1 2 3 1 0132 0132 0132 2031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 0 1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.207106781187 0.978318343479 0 0 5 4 0132 1302 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 -1 1 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.792893218813 0.978318343479 6 0 8 7 0132 0132 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.207106781187 0.978318343479 6 9 10 0 2031 0132 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 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 0 0 0 0.671572875254 0.740938508395 8 10 1 10 2310 1230 0132 2031 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 0 0 0 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 0.500000000000 0.616929442872 11 12 9 1 0132 0132 2031 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 -1 1 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 0.292893218813 1.383551069666 2 8 3 11 0132 3120 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 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.414213562373 0.810465452374 11 9 2 8 1023 0213 0132 3120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.707106781187 0.573085617291 7 6 4 2 3120 3120 3201 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 -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 0.292893218813 0.573085617291 12 3 7 5 0213 0132 0213 1302 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.585786437627 0.810465452374 12 4 4 3 3012 1302 3012 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 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 0.207106781187 0.978318343479 5 7 12 6 0132 1023 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 1 -1 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 0.146446609407 0.691775534833 9 5 11 10 0213 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 1 -1 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 -0.207106781187 0.978318343479 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : negation(d['c_0011_3']), 'c_1001_10' : negation(d['c_0011_4']), 'c_1001_12' : d['c_0101_1'], 'c_1001_5' : d['c_0011_10'], 'c_1001_4' : d['c_1001_4'], 'c_1001_7' : d['c_1001_0'], 'c_1001_6' : d['c_0101_0'], 'c_1001_1' : d['c_0101_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_1001_3'], 'c_1001_2' : negation(d['c_0011_0']), 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : negation(d['c_0101_0']), 'c_1010_12' : d['c_0011_10'], 'c_1010_11' : d['c_0101_2'], 'c_1010_10' : d['c_1001_3'], 's_0_10' : d['1'], 's_3_10' : d['1'], 's_0_12' : d['1'], 's_3_12' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0101_1'], 'c_0101_10' : d['c_0011_10'], 's_2_0' : d['1'], 's_2_1' : d['1'], 's_2_2' : negation(d['1']), 's_2_3' : d['1'], 's_2_4' : d['1'], 's_2_5' : d['1'], 's_2_6' : d['1'], 's_2_7' : d['1'], 's_2_12' : d['1'], 's_2_10' : d['1'], 's_2_11' : d['1'], 's_0_8' : d['1'], 's_0_9' : d['1'], 's_0_6' : negation(d['1']), 's_0_7' : d['1'], 's_0_4' : d['1'], 's_0_5' : d['1'], 's_0_2' : negation(d['1']), 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_1100_9' : negation(d['c_0011_8']), 'c_1100_8' : negation(d['c_0011_4']), 'c_0011_12' : d['c_0011_11'], 'c_1100_5' : negation(d['c_1001_3']), 'c_1100_4' : negation(d['c_1001_3']), 'c_1100_7' : negation(d['c_0011_4']), 'c_1100_6' : d['c_0101_3'], 'c_1100_1' : negation(d['c_1001_3']), 'c_1100_0' : negation(d['c_1001_4']), 'c_1100_3' : negation(d['c_1001_4']), 'c_1100_2' : negation(d['c_0011_4']), 's_3_11' : d['1'], 'c_1100_11' : negation(d['c_0101_3']), 'c_1100_10' : negation(d['c_1001_4']), 's_0_11' : d['1'], 'c_1010_7' : negation(d['c_0011_8']), 'c_1010_6' : negation(d['c_0011_8']), 'c_1010_5' : d['c_0101_1'], 'c_1010_4' : d['c_0011_10'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_1001_4'], 'c_1010_0' : negation(d['c_0011_0']), 'c_1010_9' : d['c_1001_3'], 'c_1010_8' : negation(d['c_0011_0']), 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : d['1'], 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : d['1'], 's_3_7' : d['1'], 's_3_6' : d['1'], 's_3_9' : d['1'], 's_3_8' : negation(d['1']), 'c_1100_12' : d['c_0101_3'], 's_1_7' : d['1'], 's_1_6' : negation(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_1_9' : d['1'], 's_1_8' : negation(d['1']), 'c_0011_9' : negation(d['c_0011_3']), 'c_0011_8' : d['c_0011_8'], 'c_0011_5' : negation(d['c_0011_11']), 'c_0011_4' : d['c_0011_4'], 'c_0011_7' : d['c_0011_11'], 'c_0110_6' : d['c_0101_2'], 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_3'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : negation(d['c_0011_8']), 'c_0110_10' : d['c_0101_3'], 'c_0110_12' : d['c_0011_10'], 'c_0101_12' : negation(d['c_0011_3']), 'c_0011_6' : d['c_0011_0'], 'c_0011_11' : d['c_0011_11'], 'c_0101_7' : negation(d['c_0011_3']), 'c_0101_6' : negation(d['c_0011_3']), 'c_0101_5' : negation(d['c_0011_8']), 'c_0101_4' : d['c_0101_0'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0011_11'], 'c_0101_8' : d['c_0011_4'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : negation(d['c_0011_10']), 'c_0110_8' : d['c_0101_2'], 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : negation(d['c_0011_3']), 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : negation(d['c_0011_4']), 'c_0110_7' : d['c_0101_2'], 'c_0011_10' : d['c_0011_10']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_3, c_0011_4, c_0011_8, c_0101_0, c_0101_1, c_0101_2, c_0101_3, c_1001_0, c_1001_3, c_1001_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 4 Groebner basis: [ t + 40149/30478*c_1001_4^3 - 125577/30478*c_1001_4^2 + 168759/30478*c_1001_4 + 1422/311, c_0011_0 - 1, c_0011_10 - 30/2177*c_1001_4^3 + 555/2177*c_1001_4^2 + 114/2177*c_1001_4 - 4/311, c_0011_11 + 183/2177*c_1001_4^3 - 120/2177*c_1001_4^2 - 260/2177*c_1001_4 + 211/311, c_0011_3 + 6/2177*c_1001_4^3 - 111/2177*c_1001_4^2 + 848/2177*c_1001_4 + 63/311, c_0011_4 - 171/2177*c_1001_4^3 - 102/2177*c_1001_4^2 - 221/2177*c_1001_4 - 85/311, c_0011_8 + 24/2177*c_1001_4^3 - 444/2177*c_1001_4^2 - 962/2177*c_1001_4 + 252/311, c_0101_0 + 24/2177*c_1001_4^3 - 444/2177*c_1001_4^2 - 962/2177*c_1001_4 - 59/311, c_0101_1 + 183/2177*c_1001_4^3 - 120/2177*c_1001_4^2 - 260/2177*c_1001_4 + 211/311, c_0101_2 + 171/2177*c_1001_4^3 + 102/2177*c_1001_4^2 + 221/2177*c_1001_4 + 85/311, c_0101_3 + 195/2177*c_1001_4^3 - 342/2177*c_1001_4^2 - 741/2177*c_1001_4 - 285/311, c_1001_0 + 219/2177*c_1001_4^3 - 786/2177*c_1001_4^2 + 474/2177*c_1001_4 - 33/311, c_1001_3 + 6/2177*c_1001_4^3 - 111/2177*c_1001_4^2 + 848/2177*c_1001_4 - 248/311, c_1001_4^4 - c_1001_4^3 - c_1001_4^2 + 7*c_1001_4 + 49/3 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_3, c_0011_4, c_0011_8, c_0101_0, c_0101_1, c_0101_2, c_0101_3, c_1001_0, c_1001_3, c_1001_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 4 Groebner basis: [ t - 11654/189*c_1001_4^3 + 6995/63*c_1001_4^2 - 28733/63*c_1001_4 - 13648/27, c_0011_0 - 1, c_0011_10 - 1/9*c_1001_4^3 - 2/3*c_1001_4 - 2/9, c_0011_11 + 2/9*c_1001_4^3 - 1/3*c_1001_4^2 + c_1001_4 + 19/9, c_0011_3 - 1/9*c_1001_4^3 - 2/3*c_1001_4 - 2/9, c_0011_4 - 2/9*c_1001_4^3 + 2/3*c_1001_4^2 - 5/3*c_1001_4 - 16/9, c_0011_8 - 1/9*c_1001_4^3 + 1/3*c_1001_4^2 - 4/3*c_1001_4 - 8/9, c_0101_0 + 1/3*c_1001_4^3 - 2/3*c_1001_4^2 + 4/3*c_1001_4 + 2, c_0101_1 + 2/9*c_1001_4^3 - 1/3*c_1001_4^2 + 2*c_1001_4 + 19/9, c_0101_2 - 2/9*c_1001_4^3 + 1/3*c_1001_4^2 - 2*c_1001_4 - 19/9, c_0101_3 - 1/3*c_1001_4^2 - 1/3*c_1001_4 - 1/3, c_1001_0 + 4/9*c_1001_4^3 - 2/3*c_1001_4^2 + 3*c_1001_4 + 38/9, c_1001_3 - 1/9*c_1001_4^3 - 2/3*c_1001_4 - 11/9, c_1001_4^4 - c_1001_4^3 + 6*c_1001_4^2 + 14*c_1001_4 + 7 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_3, c_0011_4, c_0011_8, c_0101_0, c_0101_1, c_0101_2, c_0101_3, c_1001_0, c_1001_3, c_1001_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 4 Groebner basis: [ t + 26/63*c_1001_4^3 + 41/21*c_1001_4^2 + 5/21*c_1001_4 - 53/9, c_0011_0 - 1, c_0011_10 - 1, c_0011_11 - 2/3*c_1001_4^2 - 5/3*c_1001_4 + 4/3, c_0011_3 + 1/3*c_1001_4^3 + 2/3*c_1001_4^2 - 1/3*c_1001_4 + 4/3, c_0011_4 - 1/3*c_1001_4^3 - 1/3*c_1001_4^2 + 5/3*c_1001_4 - 1, c_0011_8 + 1/3*c_1001_4^3 + c_1001_4^2 + 2/3, c_0101_0 - 1/3*c_1001_4^3 - 2/3*c_1001_4^2 + 1/3*c_1001_4 - 1/3, c_0101_1 - 1/3*c_1001_4^3 - 1/3*c_1001_4^2 + 5/3*c_1001_4 - 1, c_0101_2 + 2/3*c_1001_4^2 + 5/3*c_1001_4 - 4/3, c_0101_3 + 1/3*c_1001_4^3 + c_1001_4^2 - 1/3, c_1001_0 - 1/3*c_1001_4^3 - c_1001_4^2 + 1/3, c_1001_3 + 1/3*c_1001_4^3 + 2/3*c_1001_4^2 - 1/3*c_1001_4 + 1/3, c_1001_4^4 + 5*c_1001_4^3 + 3*c_1001_4^2 - 7*c_1001_4 + 7 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_3, c_0011_4, c_0011_8, c_0101_0, c_0101_1, c_0101_2, c_0101_3, c_1001_0, c_1001_3, c_1001_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 4 Groebner basis: [ t - 2593/28*c_1001_4^3 + 831/7*c_1001_4^2 + 3838/7*c_1001_4 - 3611/4, c_0011_0 - 1, c_0011_10 - 1, c_0011_11 + 1/2*c_1001_4^3 - 3*c_1001_4 + 5/2, c_0011_3 - 1, c_0011_4 + 1/2*c_1001_4^3 - 3*c_1001_4 + 5/2, c_0011_8 - 1/2*c_1001_4^3 + 2*c_1001_4 - 1/2, c_0101_0 - 1/2*c_1001_4^3 + 2*c_1001_4 - 3/2, c_0101_1 + 1/2*c_1001_4^3 - 3*c_1001_4 + 5/2, c_0101_2 - 1/2*c_1001_4^3 + 3*c_1001_4 - 5/2, c_0101_3 + 1/2*c_1001_4^2 + 1/2*c_1001_4 - 3/2, c_1001_0 - 1/2*c_1001_4^2 - 1/2*c_1001_4 + 3/2, c_1001_3 + 1/2*c_1001_4^3 - 2*c_1001_4 + 3/2, c_1001_4^4 - 2*c_1001_4^3 - 5*c_1001_4^2 + 14*c_1001_4 - 7 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_3, c_0011_4, c_0011_8, c_0101_0, c_0101_1, c_0101_2, c_0101_3, c_1001_0, c_1001_3, c_1001_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 4 Groebner basis: [ t - 10/21*c_1001_4^3 + 110/21*c_1001_4^2 - 319/21*c_1001_4 + 41/3, c_0011_0 - 1, c_0011_10 + 1/5*c_1001_4^3 + 1/5*c_1001_4 + 2/5, c_0011_11 - 3/5*c_1001_4^3 + c_1001_4^2 - 3/5*c_1001_4 + 9/5, c_0011_3 - 1, c_0011_4 - 3/5*c_1001_4^3 + c_1001_4^2 - 3/5*c_1001_4 + 9/5, c_0011_8 + 2/5*c_1001_4^3 - c_1001_4^2 + 2/5*c_1001_4 - 6/5, c_0101_0 - 1/5*c_1001_4^3 - 1/5*c_1001_4 + 3/5, c_0101_1 + 4/5*c_1001_4^3 - 2*c_1001_4^2 + 9/5*c_1001_4 - 12/5, c_0101_2 + 3/5*c_1001_4^3 - c_1001_4^2 + 8/5*c_1001_4 - 9/5, c_0101_3 + 6/5*c_1001_4^3 - 2*c_1001_4^2 + 11/5*c_1001_4 - 18/5, c_1001_0 + 1/5*c_1001_4^3 - c_1001_4^2 + 6/5*c_1001_4 - 3/5, c_1001_3 + 4/5*c_1001_4^3 - 2*c_1001_4^2 + 14/5*c_1001_4 - 17/5, c_1001_4^4 - 4*c_1001_4^3 + 6*c_1001_4^2 - 7*c_1001_4 + 7 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 3.250 Total time: 3.459 seconds, Total memory usage: 88.25MB