Magma V2.19-8 Tue Aug 20 2013 16:19:02 on localhost [Seed = 627357774] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v3181 geometric_solution 6.32807460 oriented_manifold CS_known 0.0000000000000001 1 0 torus 0.000000000000 0.000000000000 7 1 2 0 0 0132 0132 1230 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 0 1 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 0.283300191521 0.780036327177 0 3 5 4 0132 0132 0132 0132 0 0 0 0 0 1 0 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.137391057806 1.035179093465 3 0 4 5 0132 0132 0132 2310 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 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.137391057806 1.035179093465 2 1 6 6 0132 0132 0132 2310 0 0 0 0 0 -1 1 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 1 -1 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 -0.635083921544 0.904273959600 4 4 1 2 1230 3012 0132 0132 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 -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 0.898332190393 1.213883237901 2 5 5 1 3201 3201 2310 0132 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.256121829056 0.735971396003 3 6 6 3 3201 1230 3012 0132 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 0 -1 1 0 0 0 0 0 1 0 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.009009938840 0.727466192130 ==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_6'], 'c_1100_5' : d['c_0011_5'], 'c_1100_4' : d['c_0011_5'], 's_3_6' : d['1'], 'c_1100_1' : d['c_0011_5'], 'c_1100_0' : d['c_0101_1'], 'c_1100_3' : d['c_0011_6'], 'c_1100_2' : d['c_0011_5'], 'c_0101_6' : negation(d['c_0011_4']), 'c_0101_5' : negation(d['c_0101_3']), 'c_0101_4' : d['c_0101_0'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0011_4'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0011_5' : d['c_0011_5'], 'c_0011_4' : d['c_0011_4'], 'c_0011_6' : d['c_0011_6'], 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_0'], 'c_0011_2' : negation(d['c_0011_0']), 'c_1001_5' : d['c_0101_3'], 'c_1001_4' : negation(d['c_0011_4']), 'c_1001_6' : negation(d['c_0011_6']), 'c_1001_1' : negation(d['c_0101_3']), 'c_1001_0' : negation(d['c_0101_1']), 'c_1001_3' : negation(d['c_0011_4']), 'c_1001_2' : negation(d['c_0101_0']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0011_4'], 'c_0110_2' : d['c_0101_3'], 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : d['c_0011_4'], 'c_0110_6' : d['c_0101_3'], 'c_1010_6' : negation(d['c_0011_4']), 'c_1010_5' : negation(d['c_0101_3']), 'c_1010_4' : negation(d['c_0101_0']), 'c_1010_3' : negation(d['c_0101_3']), 'c_1010_2' : negation(d['c_0101_1']), 'c_1010_1' : negation(d['c_0011_4']), '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_4, c_0011_5, c_0011_6, c_0101_0, c_0101_1, c_0101_3 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 5 Groebner basis: [ t + 10*c_0101_3^4 - 23*c_0101_3^3 - 46*c_0101_3^2 + 9*c_0101_3 + 10, c_0011_0 - 1, c_0011_4 + c_0101_3^4 - 3*c_0101_3^3 - 3*c_0101_3^2 + 3*c_0101_3 + 1, c_0011_5 - 1, c_0011_6 - c_0101_3^4 + 2*c_0101_3^3 + 6*c_0101_3^2 - c_0101_3 - 3, c_0101_0 - 2*c_0101_3^4 + 5*c_0101_3^3 + 8*c_0101_3^2 - 3*c_0101_3 - 3, c_0101_1 + c_0101_3^4 - 3*c_0101_3^3 - 3*c_0101_3^2 + 3*c_0101_3 + 1, c_0101_3^5 - 3*c_0101_3^4 - 3*c_0101_3^3 + 4*c_0101_3^2 + c_0101_3 - 1 ], Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_4, c_0011_5, c_0011_6, c_0101_0, c_0101_1, c_0101_3 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 5 Groebner basis: [ t - 10*c_0101_3^4 + 23*c_0101_3^3 + 46*c_0101_3^2 - 9*c_0101_3 - 10, c_0011_0 - 1, c_0011_4 - c_0101_3^4 + 3*c_0101_3^3 + 3*c_0101_3^2 - 3*c_0101_3 - 1, c_0011_5 + 1, c_0011_6 - c_0101_3^4 + 2*c_0101_3^3 + 6*c_0101_3^2 - c_0101_3 - 3, c_0101_0 + 2*c_0101_3^4 - 5*c_0101_3^3 - 8*c_0101_3^2 + 3*c_0101_3 + 3, c_0101_1 + c_0101_3^4 - 3*c_0101_3^3 - 3*c_0101_3^2 + 3*c_0101_3 + 1, c_0101_3^5 - 3*c_0101_3^4 - 3*c_0101_3^3 + 4*c_0101_3^2 + c_0101_3 - 1 ], Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_4, c_0011_5, c_0011_6, c_0101_0, c_0101_1, c_0101_3 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 18 Groebner basis: [ t - 78037640/147777*c_0101_0*c_0101_3^8 - 1258703900/147777*c_0101_0*c_0101_3^7 + 1781710894/49259*c_0101_0*c_0101_3^6 + 11669013626/147777*c_0101_0*c_0101_3^5 + 13158885385/147777*c_0101_0*c_0101_3^4 + 8127390977/147777*c_0101_0*c_0101_3^3 + 5698759105/147777*c_0101_0*c_0101_3^2 + 1476192229/147777*c_0101_0*c_0101_3 + 488048518/147777*c_0101_0, c_0011_0 - 1, c_0011_4 + 116852/7037*c_0101_0*c_0101_3^8 + 17260582/49259*c_0101_0*c_0101_3^7 + 29963461/49259*c_0101_0*c_0101_3^6 + 30105029/49259*c_0101_0*c_0101_3^5 + 17848770/49259*c_0101_0*c_0101_3^4 + 1619421/7037*c_0101_0*c_0101_3^3 + 2506061/49259*c_0101_0*c_0101_3^2 + 835168/49259*c_0101_0*c_0101_3 - 99093/49259*c_0101_0, c_0011_5 - 220072/49259*c_0101_0*c_0101_3^8 - 4616072/49259*c_0101_0*c_0101_3^7 - 7485372/49259*c_0101_0*c_0101_3^6 - 7330215/49259*c_0101_0*c_0101_3^5 - 612980/7037*c_0101_0*c_0101_3^4 - 2846077/49259*c_0101_0*c_0101_3^3 - 423475/49259*c_0101_0*c_0101_3^2 - 80806/49259*c_0101_0*c_0101_3 + 10326/7037*c_0101_0, c_0011_6 + 2824/1589*c_0101_3^8 + 8216/227*c_0101_3^7 + 8484/227*c_0101_3^6 + 23855/1589*c_0101_3^5 - 26014/1589*c_0101_3^4 - 19896/1589*c_0101_3^3 - 4067/227*c_0101_3^2 - 8644/1589*c_0101_3 - 4374/1589, c_0101_0^2 - 138776/49259*c_0101_3^8 - 3146200/49259*c_0101_3^7 - 9696968/49259*c_0101_3^6 - 13474191/49259*c_0101_3^5 - 1694563/7037*c_0101_3^4 - 7636661/49259*c_0101_3^3 - 4077840/49259*c_0101_3^2 - 1193747/49259*c_0101_3 - 45457/7037, c_0101_1 + 27932/49259*c_0101_3^8 + 690014/49259*c_0101_3^7 + 3152789/49259*c_0101_3^6 + 696125/7037*c_0101_3^5 + 4892625/49259*c_0101_3^4 + 3329327/49259*c_0101_3^3 + 2067147/49259*c_0101_3^2 + 615336/49259*c_0101_3 + 190612/49259, c_0101_3^9 + 43/2*c_0101_3^8 + 181/4*c_0101_3^7 + 56*c_0101_3^6 + 45*c_0101_3^5 + 63/2*c_0101_3^4 + 57/4*c_0101_3^3 + 23/4*c_0101_3^2 + 5/4*c_0101_3 + 1/4 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.020 Total time: 0.230 seconds, Total memory usage: 32.09MB