Magma V2.19-8 Wed Aug 21 2013 00:07:07 on localhost [Seed = 3802434565] Type ? for help. Type -D to quit. Loading file "K13n2271__sl2_c0.magma" ==TRIANGULATION=BEGINS== % Triangulation K13n2271 geometric_solution 11.58064615 oriented_manifold CS_known -0.0000000000000004 1 0 torus 0.000000000000 0.000000000000 13 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 6 0 0 -6 0 -1 0 1 0 -6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.067317576487 1.422554194762 0 5 7 6 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 0 0 0 -6 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.291728353022 0.764014310205 6 0 9 8 1302 0132 0132 0132 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 1 -1 0 0 0 0 0 0 6 0 -6 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.352846392874 0.659480128960 4 10 9 0 0213 0132 2103 0132 0 0 0 0 0 0 0 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 0 0 0 -7 0 7 0 6 0 0 -6 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.392459676459 0.471277109823 3 7 0 6 0213 3012 0132 2310 0 0 0 0 0 0 0 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 0 -1 1 -6 0 6 0 7 0 0 -7 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.421792265344 0.403293722324 6 1 8 11 3120 0132 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 0.587270819648 0.393197557891 4 2 1 5 3201 2031 0132 3120 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 7 0 -6 -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 0.716519785668 0.714648299633 4 12 11 1 1230 0132 2103 0132 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 7 -7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.795818513811 1.503161861284 5 12 2 11 2310 2310 0132 0213 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 1 -1 0 0 0 -6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.762572311582 0.686713765009 3 12 10 2 2103 2031 1302 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 -1 1 -7 0 7 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 0.046114185279 0.925298864258 9 3 11 12 2031 0132 3012 3012 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 1 0 0 -1 0 0 0 0 -7 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.117954077611 1.235374698847 7 10 5 8 2103 1230 0132 0213 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 7 -7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.837679303018 0.549523631662 9 7 10 8 1302 0132 1230 3201 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 -7 1 6 -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 0.925167276536 0.932956904057 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_1001_1'], 'c_1001_10' : negation(d['c_0011_11']), 'c_1001_12' : d['c_1001_1'], 'c_1001_5' : negation(d['c_0101_8']), 'c_1001_4' : d['c_0011_12'], 'c_1001_7' : d['c_0011_11'], 'c_1001_6' : negation(d['c_0101_8']), 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : negation(d['c_0011_11']), 'c_1001_3' : d['c_0011_9'], 'c_1001_2' : d['c_0011_12'], 'c_1001_9' : negation(d['c_0011_8']), 'c_1001_8' : negation(d['c_0011_11']), 'c_1010_12' : d['c_0011_11'], 'c_1010_11' : d['c_0101_10'], 'c_1010_10' : d['c_0011_9'], 's_3_11' : 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_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_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' : 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_1100_8' : d['c_0101_10'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_0011_8']), 'c_1100_4' : d['c_0011_6'], 'c_1100_7' : negation(d['c_0101_5']), 'c_1100_6' : negation(d['c_0101_5']), 'c_1100_1' : negation(d['c_0101_5']), 'c_1100_0' : d['c_0011_6'], 'c_1100_3' : d['c_0011_6'], 'c_1100_2' : d['c_0101_10'], 's_0_10' : d['1'], 'c_1100_11' : negation(d['c_0011_8']), 'c_1100_10' : negation(d['c_1001_1']), 's_0_11' : d['1'], 'c_1010_7' : d['c_1001_1'], 'c_1010_6' : negation(d['c_0011_0']), 'c_1010_5' : d['c_1001_1'], 'c_1010_4' : negation(d['c_0101_11']), 'c_1010_3' : negation(d['c_0011_11']), 'c_1010_2' : negation(d['c_0011_11']), 'c_1010_1' : negation(d['c_0101_8']), 'c_1010_0' : d['c_0011_12'], 'c_1010_9' : d['c_0011_12'], 'c_1010_8' : negation(d['c_0011_8']), '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'], 'c_1100_12' : negation(d['c_0011_8']), '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_8'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_10']), 'c_0011_7' : negation(d['c_0011_12']), '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' : negation(d['c_0011_10']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_5'], 'c_0110_10' : negation(d['c_0011_8']), 'c_0110_12' : d['c_0011_8'], 'c_0101_12' : negation(d['c_0011_9']), 'c_0110_0' : negation(d['c_0011_10']), 'c_0101_7' : d['c_0101_11'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : negation(d['c_0011_10']), 'c_0101_3' : negation(d['c_0011_10']), 'c_0101_2' : negation(d['c_0011_6']), 'c_0101_1' : negation(d['c_0011_10']), 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0011_10']), 'c_0101_8' : d['c_0101_8'], 'c_0011_10' : d['c_0011_10'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : negation(d['c_0011_6']), 'c_0110_8' : negation(d['c_0101_5']), 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : d['c_0101_10'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_8'], 'c_0110_5' : d['c_0101_11'], 'c_0110_4' : negation(d['c_0101_0']), 'c_0110_7' : negation(d['c_0011_10']), 'c_0110_6' : d['c_0101_11']})} 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_12, c_0011_6, c_0011_8, c_0011_9, c_0101_0, c_0101_10, c_0101_11, c_0101_5, c_0101_8, c_1001_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 6 Groebner basis: [ t + 63/125*c_1001_1^5 - 4/125*c_1001_1^4 - 97/250*c_1001_1^3 + 89/50*c_1001_1^2 + 128/25*c_1001_1 + 307/250, c_0011_0 - 1, c_0011_10 + 4/25*c_1001_1^5 + 3/25*c_1001_1^4 - 8/25*c_1001_1^3 + 2/5*c_1001_1^2 + 12/5*c_1001_1 + 28/25, c_0011_11 + 8/25*c_1001_1^5 - 4/25*c_1001_1^4 - 6/25*c_1001_1^3 + 7/5*c_1001_1^2 + 3*c_1001_1 - 9/25, c_0011_12 + 7/25*c_1001_1^5 - 1/25*c_1001_1^4 - 14/25*c_1001_1^3 + 6/5*c_1001_1^2 + 11/5*c_1001_1 - 1/25, c_0011_6 - 1/25*c_1001_1^5 - 2/25*c_1001_1^4 - 3/25*c_1001_1^3 - 2/5*c_1001_1^2 - 6/5*c_1001_1 - 12/25, c_0011_8 - 1, c_0011_9 + 4/25*c_1001_1^5 - 2/25*c_1001_1^4 - 3/25*c_1001_1^3 + 6/5*c_1001_1^2 + c_1001_1 - 17/25, c_0101_0 + 1/5*c_1001_1^5 + 1/5*c_1001_1^4 - 1/5*c_1001_1^3 + 4/5*c_1001_1^2 + 13/5*c_1001_1 + 8/5, c_0101_10 + 8/25*c_1001_1^5 - 4/25*c_1001_1^4 - 6/25*c_1001_1^3 + 7/5*c_1001_1^2 + 2*c_1001_1 - 9/25, c_0101_11 - 8/25*c_1001_1^5 + 4/25*c_1001_1^4 + 6/25*c_1001_1^3 - 7/5*c_1001_1^2 - 2*c_1001_1 + 9/25, c_0101_5 + 12/25*c_1001_1^5 + 4/25*c_1001_1^4 - 19/25*c_1001_1^3 + 2*c_1001_1^2 + 29/5*c_1001_1 + 39/25, c_0101_8 - 9/25*c_1001_1^5 - 3/25*c_1001_1^4 + 8/25*c_1001_1^3 - c_1001_1^2 - 18/5*c_1001_1 - 48/25, c_1001_1^6 - c_1001_1^4 + 4*c_1001_1^3 + 10*c_1001_1^2 + 2*c_1001_1 + 1 ], 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_12, c_0011_6, c_0011_8, c_0011_9, c_0101_0, c_0101_10, c_0101_11, c_0101_5, c_0101_8, c_1001_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 12 Groebner basis: [ t + 472728514/1116612065*c_1001_1^11 - 72392469/110555650*c_1001_1^10 - 21396727539/5583060325*c_1001_1^9 + 21035881242/5583060325*c_1001_1^8 + 183604056339/11166120650*c_1001_1^7 + 10048491093/5583060325*c_1001_1^6 - 313120351549/11166120650*c_1001_1^5 - 474879846377/11166120650*c_1001_1^4 - 66629375603/5583060325*c_1001_1^3 + 59394668811/1116612065*c_1001_1^2 + 680402316289/11166120650*c_1001_1 + 188986956939/11166120650, c_0011_0 - 1, c_0011_10 - 33022/63905*c_1001_1^11 + 4572/12781*c_1001_1^10 + 70590/12781*c_1001_1^9 - 65067/63905*c_1001_1^8 - 1611776/63905*c_1001_1^7 - 1063473/63905*c_1001_1^6 + 2395428/63905*c_1001_1^5 + 4943229/63905*c_1001_1^4 + 2968796/63905*c_1001_1^3 - 4111333/63905*c_1001_1^2 - 7879672/63905*c_1001_1 - 3636054/63905, c_0011_11 - 7565326/11950235*c_1001_1^11 + 5548847/11950235*c_1001_1^10 + 81131264/11950235*c_1001_1^9 - 17263668/11950235*c_1001_1^8 - 74786226/2390047*c_1001_1^7 - 238542472/11950235*c_1001_1^6 + 52415176/1086385*c_1001_1^5 + 1158137113/11950235*c_1001_1^4 + 665845306/11950235*c_1001_1^3 - 1001555514/11950235*c_1001_1^2 - 1887902323/11950235*c_1001_1 - 888551119/11950235, c_0011_12 + 3229472/11950235*c_1001_1^11 - 3174638/11950235*c_1001_1^10 - 31319631/11950235*c_1001_1^9 + 2591071/2390047*c_1001_1^8 + 135605499/11950235*c_1001_1^7 + 14753213/2390047*c_1001_1^6 - 17345986/1086385*c_1001_1^5 - 382915188/11950235*c_1001_1^4 - 219972458/11950235*c_1001_1^3 + 313874648/11950235*c_1001_1^2 + 107599297/2390047*c_1001_1 + 220679307/11950235, c_0011_6 - 9015/2390047*c_1001_1^11 + 547637/2390047*c_1001_1^10 - 1411836/2390047*c_1001_1^9 - 4296180/2390047*c_1001_1^8 + 10034085/2390047*c_1001_1^7 + 18785433/2390047*c_1001_1^6 - 1627386/217277*c_1001_1^5 - 49767944/2390047*c_1001_1^4 - 40751444/2390047*c_1001_1^3 + 30929697/2390047*c_1001_1^2 + 111761864/2390047*c_1001_1 + 73763060/2390047, c_0011_8 - 564636/2390047*c_1001_1^11 + 4137649/11950235*c_1001_1^10 + 24816708/11950235*c_1001_1^9 - 21329969/11950235*c_1001_1^8 - 104571294/11950235*c_1001_1^7 - 27981336/11950235*c_1001_1^6 + 15005614/1086385*c_1001_1^5 + 284506632/11950235*c_1001_1^4 + 104181466/11950235*c_1001_1^3 - 58671661/2390047*c_1001_1^2 - 383702624/11950235*c_1001_1 - 122925114/11950235, c_0011_9 - 7436162/11950235*c_1001_1^11 + 9781034/11950235*c_1001_1^10 + 68842228/11950235*c_1001_1^9 - 50070516/11950235*c_1001_1^8 - 59171865/2390047*c_1001_1^7 - 95439199/11950235*c_1001_1^6 + 42021797/1086385*c_1001_1^5 + 810894626/11950235*c_1001_1^4 + 347132592/11950235*c_1001_1^3 - 829455603/11950235*c_1001_1^2 - 1153589786/11950235*c_1001_1 - 404966698/11950235, c_0101_0 - 211164/702955*c_1001_1^11 + 25852/140591*c_1001_1^10 + 455469/140591*c_1001_1^9 - 270029/702955*c_1001_1^8 - 10436517/702955*c_1001_1^7 - 7272736/702955*c_1001_1^6 + 1385631/63905*c_1001_1^5 + 31675823/702955*c_1001_1^4 + 20062552/702955*c_1001_1^3 - 24982516/702955*c_1001_1^2 - 50739444/702955*c_1001_1 - 23582728/702955, c_0101_10 - 13443477/11950235*c_1001_1^11 + 2479816/2390047*c_1001_1^10 + 27742888/2390047*c_1001_1^9 - 51269107/11950235*c_1001_1^8 - 628771371/11950235*c_1001_1^7 - 339690518/11950235*c_1001_1^6 + 89509258/1086385*c_1001_1^5 + 1888545084/11950235*c_1001_1^4 + 999150731/11950235*c_1001_1^3 - 1732478013/11950235*c_1001_1^2 - 3013184452/11950235*c_1001_1 - 1345978839/11950235, c_0101_11 - 13644/63905*c_1001_1^11 - 595/12781*c_1001_1^10 + 34876/12781*c_1001_1^9 + 70771/63905*c_1001_1^8 - 847902/63905*c_1001_1^7 - 850106/63905*c_1001_1^6 + 1206246/63905*c_1001_1^5 + 2927963/63905*c_1001_1^4 + 2161242/63905*c_1001_1^3 - 1973871/63905*c_1001_1^2 - 5123084/63905*c_1001_1 - 2814993/63905, c_0101_5 + 11464482/11950235*c_1001_1^11 - 14406904/11950235*c_1001_1^10 - 109026828/11950235*c_1001_1^9 + 70371746/11950235*c_1001_1^8 + 96205651/2390047*c_1001_1^7 + 185394529/11950235*c_1001_1^6 - 70829147/1086385*c_1001_1^5 - 1397971436/11950235*c_1001_1^4 - 605400332/11950235*c_1001_1^3 + 1413887553/11950235*c_1001_1^2 + 2122358586/11950235*c_1001_1 + 850718768/11950235, c_0101_8 + 3515401/2390047*c_1001_1^11 - 22936718/11950235*c_1001_1^10 - 166266411/11950235*c_1001_1^9 + 117671728/11950235*c_1001_1^8 + 729317638/11950235*c_1001_1^7 + 240588737/11950235*c_1001_1^6 - 108250408/1086385*c_1001_1^5 - 2062545424/11950235*c_1001_1^4 - 852963477/11950235*c_1001_1^3 + 433068133/2390047*c_1001_1^2 + 3124676968/11950235*c_1001_1 + 1192708718/11950235, c_1001_1^12 - 11*c_1001_1^10 - 6*c_1001_1^9 + 49*c_1001_1^8 + 70*c_1001_1^7 - 45*c_1001_1^6 - 208*c_1001_1^5 - 211*c_1001_1^4 + 50*c_1001_1^3 + 341*c_1001_1^2 + 318*c_1001_1 + 101 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 5.180 Total time: 5.379 seconds, Total memory usage: 137.75MB