Magma V2.19-8 Tue Aug 20 2013 16:08:56 on localhost [Seed = 4300472] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation m169 geometric_solution 3.85733613 oriented_manifold CS_known 0.0000000000000003 1 0 torus 0.000000000000 0.000000000000 5 1 0 1 0 0132 1302 2310 2031 0 0 0 0 0 -1 0 1 -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 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.090780278536 0.797251454520 0 0 3 2 0132 3201 0132 0132 0 0 0 0 0 0 0 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 -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 0.763870792513 0.958716209903 4 3 1 3 0132 2031 0132 1302 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 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 0.743206738979 0.449739426553 2 4 2 1 1302 2310 2031 0132 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 1 -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 0.743206738979 0.449739426553 2 4 4 3 0132 3201 2310 3201 0 0 0 0 0 0 0 0 0 0 1 -1 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 -1 1 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.527725397632 0.325164436847 ==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_4' : d['1'], 's_3_0' : negation(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_1_4' : d['1'], 's_1_3' : d['1'], 's_1_2' : d['1'], 's_1_1' : d['1'], 's_1_0' : negation(d['1']), 's_0_4' : d['1'], 's_0_2' : d['1'], 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_1100_4' : negation(d['c_0011_2']), 'c_1100_1' : negation(d['c_0011_2']), 'c_1100_0' : negation(d['c_0011_0']), 'c_1100_3' : negation(d['c_0011_2']), 'c_1100_2' : negation(d['c_0011_2']), 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : negation(d['c_0011_2']), 'c_0101_2' : d['c_0101_0'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0011_4' : negation(d['c_0011_2']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_2'], 'c_0011_2' : d['c_0011_2'], 'c_1001_4' : negation(d['c_0101_4']), 'c_1001_1' : negation(d['c_0101_0']), 'c_1001_0' : d['c_0101_1'], 'c_1001_3' : negation(d['c_0101_4']), 'c_1001_2' : negation(d['c_0101_1']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_1'], 'c_0110_2' : d['c_0101_4'], 'c_0110_4' : d['c_0101_0'], 'c_1010_4' : d['c_0101_4'], 'c_1010_3' : negation(d['c_0101_0']), 'c_1010_2' : d['c_0011_2'], 'c_1010_1' : negation(d['c_0101_1']), 'c_1010_0' : d['c_0011_0']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 6 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_2, c_0101_0, c_0101_1, c_0101_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 10 Groebner basis: [ t - 6116980577/1188982168*c_0101_4^9 + 41798333091/1188982168*c_0101_4^8 + 66287795141/1188982168*c_0101_4^7 - 283401676511/1188982168*c_0101_4^6 + 421444628089/1188982168*c_0101_4^5 + 20202980291/108089288*c_0101_4^4 - 514199306385/594491084*c_0101_4^3 - 354844114923/1188982168*c_0101_4^2 + 339059911059/1188982168*c_0101_4 + 128761928577/1188982168, c_0011_0 - 1, c_0011_2 + 90070251/148622771*c_0101_4^9 - 583241782/148622771*c_0101_4^8 - 1163013746/148622771*c_0101_4^7 + 3608793983/148622771*c_0101_4^6 - 5142960008/148622771*c_0101_4^5 - 378846599/13511161*c_0101_4^4 + 12098862412/148622771*c_0101_4^3 + 9082242146/148622771*c_0101_4^2 + 1241023741/148622771*c_0101_4 - 163399977/148622771, c_0101_0 - 95044747/148622771*c_0101_4^9 + 631072164/148622771*c_0101_4^8 + 1117512786/148622771*c_0101_4^7 - 3951035342/148622771*c_0101_4^6 + 6140802070/148622771*c_0101_4^5 + 285789257/13511161*c_0101_4^4 - 12848605216/148622771*c_0101_4^3 - 7430023927/148622771*c_0101_4^2 - 733863508/148622771*c_0101_4 + 63179627/148622771, c_0101_1 - 48626834/148622771*c_0101_4^9 + 318264115/148622771*c_0101_4^8 + 600236018/148622771*c_0101_4^7 - 1951900418/148622771*c_0101_4^6 + 2962528853/148622771*c_0101_4^5 + 164617722/13511161*c_0101_4^4 - 6172279243/148622771*c_0101_4^3 - 4494898791/148622771*c_0101_4^2 - 1032184881/148622771*c_0101_4 + 32184886/148622771, c_0101_4^10 - 6*c_0101_4^9 - 16*c_0101_4^8 + 34*c_0101_4^7 - 38*c_0101_4^6 - 74*c_0101_4^5 + 113*c_0101_4^4 + 165*c_0101_4^3 + 60*c_0101_4^2 + 4*c_0101_4 - 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.010 Total time: 0.210 seconds, Total memory usage: 32.09MB