Magma V2.19-8 Tue Aug 20 2013 23:42:21 on localhost [Seed = 2985809127] Type ? for help. Type -D to quit. Loading file "K12n838__sl2_c0.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n838 geometric_solution 11.10242556 oriented_manifold CS_known 0.0000000000000003 1 0 torus 0.000000000000 0.000000000000 12 1 2 3 4 0132 0132 0132 0132 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 -1 0 1 -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 0.500000000000 0.866025403784 0 5 7 6 0132 0132 0132 0132 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 -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 0 0 0 0 0.500000000000 0.288675134595 8 0 10 9 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 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 0.726280827069 0.626639449348 6 11 10 0 0132 0132 0321 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 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.866025403784 9 5 0 11 1302 1023 0132 1302 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 -1 0 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 4 1 7 10 1023 0132 1302 3120 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 0 -1 -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 0.905826095683 0.839042616530 3 9 1 8 0132 3012 0132 3012 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 1.500000000000 0.866025403784 5 10 11 1 2031 3120 3201 0132 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 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 0 0 0 0 0 0 0.905826095683 0.839042616530 2 9 6 11 0132 1302 1230 2103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.905826095683 0.839042616530 6 4 2 8 1230 2031 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 0.905826095683 0.839042616530 5 7 3 2 3120 3120 0321 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 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.210702307584 0.681010778356 7 3 4 8 2310 0132 2031 2103 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 1 -1 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 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_0110_6' : negation(d['c_0101_10']), 'c_1001_11' : negation(d['c_0110_4']), 'c_1001_10' : d['c_0101_11'], 'c_1001_5' : negation(d['c_0011_9']), 'c_1001_4' : negation(d['c_0011_7']), 'c_1001_7' : negation(d['c_0101_11']), 'c_1001_6' : negation(d['c_0011_9']), 'c_1001_1' : negation(d['c_0011_10']), 'c_1001_0' : negation(d['c_0110_4']), 'c_1001_3' : d['c_1001_3'], 'c_1001_2' : negation(d['c_0011_7']), 'c_1001_9' : negation(d['c_0110_4']), 'c_1001_8' : d['c_0011_11'], 'c_1010_11' : d['c_1001_3'], 'c_1010_10' : negation(d['c_0011_7']), 's_0_10' : d['1'], 's_3_10' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0101_11'], 'c_0101_10' : d['c_0101_10'], '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_2_7' : 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' : d['1'], 's_0_7' : 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_0011_11' : d['c_0011_11'], 'c_0011_10' : d['c_0011_10'], 'c_1100_5' : negation(d['c_0101_10']), 'c_1100_4' : d['c_0101_11'], 'c_1100_7' : negation(d['c_0011_11']), 'c_1100_6' : negation(d['c_0011_11']), 'c_1100_1' : negation(d['c_0011_11']), 'c_1100_0' : d['c_0101_11'], 'c_1100_3' : d['c_0101_11'], 'c_1100_2' : d['c_1001_3'], 's_3_11' : d['1'], 'c_1100_11' : negation(d['c_0101_2']), 'c_1100_10' : d['c_1001_3'], 's_0_11' : d['1'], 'c_1010_7' : negation(d['c_0011_10']), 'c_1010_6' : negation(d['c_0101_8']), 'c_1010_5' : negation(d['c_0011_10']), 'c_1010_4' : d['c_0101_2'], 'c_1010_3' : negation(d['c_0110_4']), 'c_1010_2' : negation(d['c_0110_4']), 'c_1010_1' : negation(d['c_0011_9']), 'c_1010_0' : negation(d['c_0011_7']), 'c_1010_9' : d['c_0011_0'], 'c_1010_8' : negation(d['c_1001_3']), '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' : d['1'], 's_1_7' : 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_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : d['c_0011_9'], 'c_0011_8' : d['c_0011_0'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : d['c_0011_0'], 'c_0011_7' : d['c_0011_7'], 'c_0011_6' : d['c_0011_11'], 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : negation(d['c_0011_11']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_10'], 'c_0110_10' : d['c_0101_2'], 'c_0110_0' : negation(d['c_0011_9']), 'c_0101_7' : negation(d['c_0101_10']), 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : negation(d['c_0011_7']), 'c_0101_4' : negation(d['c_0011_9']), 'c_0101_3' : negation(d['c_0101_10']), 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : negation(d['c_0011_9']), 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_8'], 'c_0101_8' : d['c_0101_8'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0011_11'], 'c_0110_8' : d['c_0101_2'], 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : d['c_1001_3'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_8'], 'c_0110_5' : d['c_0101_2'], 'c_0110_4' : d['c_0110_4'], 'c_0110_7' : negation(d['c_0011_9']), 'c_1100_8' : negation(d['c_0101_10'])})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 13 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_7, c_0011_9, c_0101_0, c_0101_10, c_0101_11, c_0101_2, c_0101_8, c_0110_4, c_1001_3 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 2 Groebner basis: [ t - 1/720, c_0011_0 - 1, c_0011_10 - c_1001_3 + 2, c_0011_11 + c_1001_3 - 1, c_0011_7 + c_1001_3 - 1, c_0011_9 + c_1001_3, c_0101_0 + 2, c_0101_10 + 1, c_0101_11 - 2, c_0101_2 - 2, c_0101_8 - c_1001_3 - 1, c_0110_4 - 2, c_1001_3^2 - c_1001_3 + 3 ], Ideal of Polynomial ring of rank 13 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_7, c_0011_9, c_0101_0, c_0101_10, c_0101_11, c_0101_2, c_0101_8, c_0110_4, c_1001_3 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 4 Groebner basis: [ t - 9/2*c_1001_3^3 + 3*c_1001_3^2 + 21*c_1001_3 - 5/2, c_0011_0 - 1, c_0011_10 + 3/2*c_1001_3^3 - c_1001_3^2 - 1/2, c_0011_11 - c_1001_3, c_0011_7 - c_1001_3, c_0011_9 + c_1001_3, c_0101_0 + 3/2*c_1001_3^3 - c_1001_3^2 - c_1001_3 + 1/2, c_0101_10 + 1, c_0101_11 + 3/2*c_1001_3^3 + 1/2*c_1001_3^2 - 1/2*c_1001_3, c_0101_2 - 3/2*c_1001_3^3 + c_1001_3^2 + c_1001_3 - 1/2, c_0101_8 - 3/2*c_1001_3^3 + c_1001_3^2 + 1/2, c_0110_4 + 3/2*c_1001_3^3 + 1/2*c_1001_3^2 - 1/2*c_1001_3, c_1001_3^4 - 2/3*c_1001_3^3 - 1/3*c_1001_3^2 + 1/3 ], Ideal of Polynomial ring of rank 13 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_7, c_0011_9, c_0101_0, c_0101_10, c_0101_11, c_0101_2, c_0101_8, c_0110_4, c_1001_3 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 6 Groebner basis: [ t - 3*c_0110_4*c_1001_3^2 - 5/2*c_0110_4*c_1001_3 - 9/2*c_0110_4 - 412/117*c_1001_3^2 - 392/117*c_1001_3 - 1303/234, c_0011_0 - 1, c_0011_10 + c_0110_4*c_1001_3^2 + 2*c_0110_4 + c_1001_3^2 + c_1001_3 + 1, c_0011_11 - c_1001_3, c_0011_7 - c_0110_4*c_1001_3^2 - c_0110_4*c_1001_3 - c_0110_4 - c_1001_3^2 - 2, c_0011_9 + c_0110_4*c_1001_3^2 + c_0110_4*c_1001_3 + c_0110_4 + c_1001_3^2 + 2, c_0101_0 - c_0110_4*c_1001_3^2 - 2*c_0110_4 - 2*c_1001_3^2 - c_1001_3 - 2, c_0101_10 + c_0110_4*c_1001_3^2 + c_0110_4*c_1001_3 + 2*c_0110_4 + 2*c_1001_3^2 + c_1001_3 + 2, c_0101_11 + 2*c_0110_4*c_1001_3^2 + c_0110_4*c_1001_3 + 2*c_0110_4 + c_1001_3^2 + 2*c_1001_3 + 2, c_0101_2 + c_0110_4*c_1001_3^2 + 2*c_0110_4 + 2*c_1001_3^2 + c_1001_3 + 2, c_0101_8 + c_0110_4*c_1001_3^2 + c_0110_4*c_1001_3 + c_0110_4 + c_1001_3 + 1, c_0110_4^2 + c_0110_4*c_1001_3^2 + 2*c_0110_4 + 2*c_1001_3^2 + c_1001_3, c_1001_3^3 + c_1001_3 - 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 1.280 Total time: 1.490 seconds, Total memory usage: 64.12MB