Magma V2.19-8 Tue Aug 20 2013 17:56:29 on localhost [Seed = 1124267898] Type ? for help. Type -D to quit. Loading file "8_16__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation 8_16 geometric_solution 10.57902192 oriented_manifold CS_known 0.0000000000000002 1 0 torus 0.000000000000 0.000000000000 11 1 2 2 3 0132 0132 1302 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 -4 0 0 4 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.930410942910 0.768971613932 0 4 5 4 0132 0132 0132 1230 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 4 0 0 -4 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.476356444714 0.727680747949 0 0 7 6 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 -1 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 0.361412132298 0.527783929248 8 5 0 9 0132 3201 0132 0132 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 -1 1 0 0 -4 4 -1 0 0 1 5 -5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.737919433670 0.954333571422 1 1 9 10 3012 0132 3201 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 4 0 0 -4 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.651523358786 0.905388790221 7 6 3 1 1230 0321 2310 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 0 0 0 -5 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.886016174014 1.123165194804 10 10 2 5 3012 0132 0132 0321 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 0 -4 4 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.651523358786 0.905388790221 8 5 9 2 3012 3012 3012 0132 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 0 -1 1 0 0 0 0 -5 5 0 0 -5 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.267582384248 0.974367752578 3 10 9 7 0132 2031 0132 1230 0 0 0 0 0 0 0 0 0 0 1 -1 1 0 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 -5 5 -5 0 0 5 1 4 -5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.022301946517 0.686389881967 4 7 3 8 2310 1230 0132 0132 0 0 0 0 0 0 0 0 0 0 1 -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 0 -1 1 -1 0 -4 5 0 -5 0 5 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.022301946517 0.686389881967 8 6 4 6 1302 0132 0132 1230 0 0 0 0 0 0 0 0 1 0 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 0 0 -4 0 0 4 -1 1 0 0 0 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.476356444714 0.727680747949 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_10' : d['c_1001_1'], 'c_1001_5' : d['c_1001_5'], 'c_1001_4' : d['c_0101_4'], 'c_1001_7' : negation(d['c_0011_5']), 'c_1001_6' : d['c_0101_6'], 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_0101_6'], 'c_1001_3' : negation(d['c_0101_5']), 'c_1001_2' : negation(d['c_0101_5']), 'c_1001_9' : negation(d['c_1001_5']), 'c_1001_8' : d['c_0011_10'], 'c_1010_10' : d['c_0101_6'], 's_0_10' : d['1'], 's_3_10' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_10' : d['c_0011_3'], '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_0_8' : d['1'], 's_0_9' : d['1'], 's_0_6' : d['1'], 's_0_7' : d['1'], 's_0_4' : negation(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_9' : d['c_0101_2'], 'c_0011_10' : d['c_0011_10'], 'c_1100_5' : d['c_0011_3'], 'c_1100_4' : negation(d['c_0011_5']), 'c_1100_7' : d['c_1001_5'], 'c_1100_6' : d['c_1001_5'], 'c_1100_1' : d['c_0011_3'], 'c_1100_0' : d['c_0101_2'], 'c_1100_3' : d['c_0101_2'], 'c_1100_2' : d['c_1001_5'], 'c_1100_10' : negation(d['c_0011_5']), 'c_1010_7' : negation(d['c_0101_5']), 'c_1010_6' : d['c_1001_1'], 'c_1010_5' : d['c_1001_1'], 'c_1010_4' : d['c_1001_1'], 'c_1010_3' : negation(d['c_1001_5']), 'c_1010_2' : d['c_0101_6'], 'c_1010_1' : d['c_0101_4'], 'c_1010_0' : negation(d['c_0101_5']), 'c_1010_9' : d['c_0011_10'], 'c_1010_8' : d['c_0011_10'], 'c_1100_8' : d['c_0101_2'], 's_3_1' : negation(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' : negation(d['1']), 's_1_3' : d['1'], 's_1_2' : d['1'], 's_1_1' : negation(d['1']), 's_1_0' : d['1'], 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : d['c_0011_5'], 'c_0011_8' : negation(d['c_0011_3']), 'c_0011_5' : d['c_0011_5'], 'c_0011_4' : d['c_0011_0'], 'c_0011_7' : d['c_0011_7'], 'c_0011_6' : negation(d['c_0011_10']), '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_10' : negation(d['c_0011_10']), 'c_0101_7' : d['c_0011_10'], 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : d['c_0011_7'], 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0011_7'], 'c_0101_0' : d['c_0011_0'], 'c_0101_9' : negation(d['c_0101_4']), 'c_0101_8' : negation(d['c_0101_4']), 's_1_10' : d['1'], 'c_0110_9' : negation(d['c_0101_4']), 'c_0110_8' : d['c_0011_7'], 'c_0110_1' : d['c_0011_0'], 'c_0110_0' : d['c_0011_7'], 'c_0110_3' : negation(d['c_0101_4']), 'c_0110_2' : d['c_0101_6'], 'c_0110_5' : d['c_0011_7'], 'c_0110_4' : d['c_0011_3'], 'c_0110_7' : d['c_0101_2'], 'c_0110_6' : negation(d['c_0011_5'])})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 12 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_3, c_0011_5, c_0011_7, c_0101_2, c_0101_4, c_0101_5, c_0101_6, c_1001_1, c_1001_5 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 5 Groebner basis: [ t + 9/4*c_1001_5^4 + 55/8*c_1001_5^3 + 59/8*c_1001_5^2 + 15/4*c_1001_5 + 17/8, c_0011_0 - 1, c_0011_10 - c_1001_5^3 - c_1001_5^2 + c_1001_5 + 1, c_0011_3 - c_1001_5^2 + 1, c_0011_5 + c_1001_5^2 - 1, c_0011_7 - c_1001_5, c_0101_2 - c_1001_5^4 - 2*c_1001_5^3 - c_1001_5^2 + c_1001_5 + 1, c_0101_4 - c_1001_5^3 - c_1001_5^2 + c_1001_5 + 1, c_0101_5 + c_1001_5^4 + 2*c_1001_5^3 + c_1001_5^2 - 1, c_0101_6 - 1, c_1001_1 + c_1001_5^4 + c_1001_5^3 - 2*c_1001_5^2 - c_1001_5 + 1, c_1001_5^5 + 2*c_1001_5^4 - 2*c_1001_5^2 - c_1001_5 - 1 ], Ideal of Polynomial ring of rank 12 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_3, c_0011_5, c_0011_7, c_0101_2, c_0101_4, c_0101_5, c_0101_6, c_1001_1, c_1001_5 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 12 Groebner basis: [ t + 4227808987326/114389194255*c_1001_5^11 - 30888082488594/114389194255*c_1001_5^10 + 10528022095436/16341313465*c_1001_5^9 - 16590359605537/114389194255*c_1001_5^8 - 42808516420764/114389194255*c_1001_5^7 - 12228185409377/3268262693*c_1001_5^6 + 1538699874329801/114389194255*c_1001_5^5 - 2066219575121619/114389194255*c_1001_5^4 + 28427761932625/3268262693*c_1001_5^3 + 521283904773493/114389194255*c_1001_5^2 - 824836080761886/114389194255*c_1001_5 + 283547177311221/114389194255, c_0011_0 - 1, c_0011_10 - 16757031472/81706567325*c_1001_5^11 + 115414724918/81706567325*c_1001_5^10 - 259808377479/81706567325*c_1001_5^9 + 68865942134/81706567325*c_1001_5^8 - 53633843787/81706567325*c_1001_5^7 + 344557448934/16341313465*c_1001_5^6 - 5368312190762/81706567325*c_1001_5^5 + 7637956170153/81706567325*c_1001_5^4 - 1196388414502/16341313465*c_1001_5^3 + 2549419804664/81706567325*c_1001_5^2 - 511837734158/81706567325*c_1001_5 + 34700708098/81706567325, c_0011_3 - 20315585896/81706567325*c_1001_5^11 + 136328704524/81706567325*c_1001_5^10 - 281237653447/81706567325*c_1001_5^9 - 20610993238/81706567325*c_1001_5^8 + 7709179359/81706567325*c_1001_5^7 + 434653084052/16341313465*c_1001_5^6 - 6018911469191/81706567325*c_1001_5^5 + 7275530857029/81706567325*c_1001_5^4 - 825808311121/16341313465*c_1001_5^3 + 768319048602/81706567325*c_1001_5^2 + 89916362706/81706567325*c_1001_5 + 28535584989/81706567325, c_0011_5 - 43349091217/81706567325*c_1001_5^11 + 308520755098/81706567325*c_1001_5^10 - 722797305094/81706567325*c_1001_5^9 + 212689072974/81706567325*c_1001_5^8 + 64667515143/81706567325*c_1001_5^7 + 904373146094/16341313465*c_1001_5^6 - 14935094431282/81706567325*c_1001_5^5 + 21002938529583/81706567325*c_1001_5^4 - 2949035169057/16341313465*c_1001_5^3 + 4053106992929/81706567325*c_1001_5^2 + 181400797812/81706567325*c_1001_5 + 38712665928/81706567325, c_0011_7 + 36091214681/81706567325*c_1001_5^11 - 256996784364/81706567325*c_1001_5^10 + 596592173817/81706567325*c_1001_5^9 - 149776861557/81706567325*c_1001_5^8 - 74652554674/81706567325*c_1001_5^7 - 769713871772/16341313465*c_1001_5^6 + 12324925758976/81706567325*c_1001_5^5 - 17021566854319/81706567325*c_1001_5^4 + 2328987447971/16341313465*c_1001_5^3 - 3181262459397/81706567325*c_1001_5^2 - 35082252891/81706567325*c_1001_5 - 113986041529/81706567325, c_0101_2 + 4353888696/16341313465*c_1001_5^11 - 30817810699/16341313465*c_1001_5^10 + 72748154462/16341313465*c_1001_5^9 - 27743452602/16341313465*c_1001_5^8 + 11451611211/16341313465*c_1001_5^7 - 90079504985/3268262693*c_1001_5^6 + 1475810116021/16341313465*c_1001_5^5 - 2204094042514/16341313465*c_1001_5^4 + 361946483906/3268262693*c_1001_5^3 - 783814398797/16341313465*c_1001_5^2 + 137016956874/16341313465*c_1001_5 + 2196173736/16341313465, c_0101_4 - 16624146826/81706567325*c_1001_5^11 + 120490172044/81706567325*c_1001_5^10 - 286242478832/81706567325*c_1001_5^9 + 81056462222/81706567325*c_1001_5^8 + 67100032829/81706567325*c_1001_5^7 + 357281226342/16341313465*c_1001_5^6 - 5892901157021/81706567325*c_1001_5^5 + 8178369625974/81706567325*c_1001_5^4 - 1088493732196/16341313465*c_1001_5^3 + 1161221254912/81706567325*c_1001_5^2 + 260746952411/81706567325*c_1001_5 + 51499627859/81706567325, c_0101_5 + 2710036383/81706567325*c_1001_5^11 - 21091887402/81706567325*c_1001_5^10 + 50541317506/81706567325*c_1001_5^9 + 145542799/81706567325*c_1001_5^8 - 61186365632/81706567325*c_1001_5^7 - 67875196496/16341313465*c_1001_5^6 + 1063712411193/81706567325*c_1001_5^5 - 1205241058192/81706567325*c_1001_5^4 + 44105301273/16341313465*c_1001_5^3 + 529378600179/81706567325*c_1001_5^2 - 367879601963/81706567325*c_1001_5 - 27785705572/81706567325, c_0101_6 - 339312111/81706567325*c_1001_5^11 + 12417242509/81706567325*c_1001_5^10 - 69780223602/81706567325*c_1001_5^9 + 122457222267/81706567325*c_1001_5^8 + 37788521994/81706567325*c_1001_5^7 + 11404961742/16341313465*c_1001_5^6 - 1167604791406/81706567325*c_1001_5^5 + 2818549110589/81706567325*c_1001_5^4 - 611280070281/16341313465*c_1001_5^3 + 1533780114332/81706567325*c_1001_5^2 - 195508925129/81706567325*c_1001_5 - 4056105126/81706567325, c_1001_1 + 551699791/3268262693*c_1001_5^11 - 3962034080/3268262693*c_1001_5^10 + 9600426462/3268262693*c_1001_5^9 - 3979686392/3268262693*c_1001_5^8 - 385277373/3268262693*c_1001_5^7 - 54949829289/3268262693*c_1001_5^6 + 197205112568/3268262693*c_1001_5^5 - 292729761464/3268262693*c_1001_5^4 + 216180472352/3268262693*c_1001_5^3 - 57202406569/3268262693*c_1001_5^2 - 8835158383/3268262693*c_1001_5 - 1061770173/3268262693, c_1001_5^12 - 8*c_1001_5^11 + 23*c_1001_5^10 - 20*c_1001_5^9 + 4*c_1001_5^8 - 104*c_1001_5^7 + 436*c_1001_5^6 - 793*c_1001_5^5 + 791*c_1001_5^4 - 432*c_1001_5^3 + 107*c_1001_5^2 - 5*c_1001_5 + 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.220 Total time: 0.420 seconds, Total memory usage: 32.09MB