Magma V2.19-8 Tue Aug 20 2013 23:52:15 on localhost [Seed = 1478374255] Type ? for help. Type -D to quit. Loading file "K12n245__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n245 geometric_solution 11.80194684 oriented_manifold CS_known 0.0000000000000006 1 0 torus 0.000000000000 0.000000000000 13 1 2 3 4 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 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 0.573154499649 1.329420980418 0 5 7 6 0132 0132 0132 0132 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 -9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.339731713577 0.408729074724 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 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 0.423311763980 0.347557380573 6 5 11 0 0132 3201 0132 0132 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 -1 0 1 0 0 0 0 0 0 0 0 -10 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.711358714256 0.729512153245 12 8 0 9 0132 2310 0132 0213 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 -1 0 10 0 0 -10 1 -1 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.107247259803 0.560218582064 10 1 3 10 2103 0132 2310 3120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.588908963544 1.158567151006 3 11 1 12 0132 3120 0132 0213 0 0 0 0 0 0 0 0 0 0 1 -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 0 -9 9 10 0 0 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.450092826101 0.668259765256 11 8 12 1 0213 3201 3120 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 -1 0 -9 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.847314448381 1.047973433792 2 10 7 4 0132 2103 2310 3201 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.302691506130 1.371822752116 12 11 2 4 1023 0213 0132 0213 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 -10 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.931568445536 0.728857441846 5 8 5 2 3120 2103 2103 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 -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 0.272016274024 0.766616373688 7 6 9 3 0213 3120 0213 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 9 0 0 -9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.093939721947 0.864972982120 4 9 7 6 0132 1023 3120 0213 0 0 0 0 0 0 0 0 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 0 0 0 -10 0 0 10 -1 10 0 -9 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.326940917755 0.924599851940 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_1001_0'], 'c_1001_10' : d['c_0011_0'], 'c_1001_12' : d['c_0101_8'], 'c_1001_5' : negation(d['c_1001_0']), 'c_1001_4' : d['c_1001_2'], 'c_1001_7' : negation(d['c_0101_8']), 'c_1001_6' : negation(d['c_1001_0']), 'c_1001_1' : negation(d['c_0011_10']), 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_0011_3'], 'c_1001_2' : d['c_1001_2'], 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : d['c_0011_10'], 'c_1010_12' : negation(d['c_0101_12']), 'c_1010_11' : d['c_0011_3'], 'c_1010_10' : d['c_1001_2'], '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' : negation(d['1']), 'c_0101_11' : d['c_0011_12'], 'c_0101_10' : negation(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' : negation(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_0011_10' : d['c_0011_10'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : d['c_0011_3'], 'c_1100_4' : d['c_1010_9'], 'c_1100_7' : negation(d['c_0101_12']), 'c_1100_6' : negation(d['c_0101_12']), 'c_1100_1' : negation(d['c_0101_12']), 'c_1100_0' : d['c_1010_9'], 'c_1100_3' : d['c_1010_9'], 'c_1100_2' : negation(d['c_0101_2']), 's_0_10' : d['1'], 'c_1100_9' : negation(d['c_0101_2']), 'c_1100_11' : d['c_1010_9'], 'c_1100_10' : negation(d['c_0101_2']), 's_0_11' : d['1'], 'c_1010_7' : negation(d['c_0011_10']), 'c_1010_6' : negation(d['c_0011_11']), 'c_1010_5' : negation(d['c_0011_10']), 'c_1010_4' : negation(d['c_0101_2']), 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : negation(d['c_1001_0']), 'c_1010_0' : d['c_1001_2'], 'c_1010_9' : d['c_1010_9'], 'c_1010_8' : negation(d['c_1001_2']), 'c_1100_8' : d['c_0011_12'], 's_3_1' : d['1'], 's_3_0' : negation(d['1']), 's_3_3' : d['1'], 's_3_2' : negation(d['1']), 's_3_5' : d['1'], 's_3_4' : negation(d['1']), 's_3_7' : d['1'], 's_3_6' : d['1'], 's_3_9' : negation(d['1']), 's_3_8' : d['1'], 'c_1100_12' : negation(d['c_0011_11']), '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' : negation(d['1']), 's_1_1' : d['1'], 's_1_0' : negation(d['1']), 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : d['c_0011_12'], 'c_0011_8' : d['c_0011_0'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_12']), 'c_0011_7' : d['c_0011_12'], 'c_0011_6' : negation(d['c_0011_3']), '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_11' : negation(d['c_0101_1']), 'c_0110_10' : d['c_0101_2'], 'c_0110_12' : d['c_0101_1'], 'c_0101_12' : d['c_0101_12'], 'c_0101_7' : d['c_0011_11'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : negation(d['c_0011_3']), 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : negation(d['c_0101_1']), 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_8'], 'c_0101_8' : d['c_0101_8'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : negation(d['c_0101_12']), 'c_0110_8' : d['c_0101_2'], 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], '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_0101_12'], 'c_0110_7' : d['c_0101_1'], 'c_0110_6' : negation(d['c_0101_1'])})} 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_3, c_0101_0, c_0101_1, c_0101_12, c_0101_2, c_0101_8, c_1001_0, c_1001_2, c_1010_9 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 10 Groebner basis: [ t - 2255089925941/344187*c_1010_9^9 - 1067735616421/229458*c_1010_9^8 + 4324659532357/229458*c_1010_9^7 + 7041257560972/344187*c_1010_9^6 + 15261052062445/1835664*c_1010_9^5 + 51898410237635/11013984*c_1010_9^4 - 143378226339/611888*c_1010_9^3 - 19427214787231/22027968*c_1010_9^2 + 58975129703033/88111872*c_1010_9 + 4076344362971/176223744, c_0011_0 - 1, c_0011_10 + 52864/1503*c_1010_9^9 + 6080/501*c_1010_9^8 - 54272/501*c_1010_9^7 - 110656/1503*c_1010_9^6 - 5176/501*c_1010_9^5 - 14236/1503*c_1010_9^4 + 1822/167*c_1010_9^3 + 7870/1503*c_1010_9^2 - 13477/3006*c_1010_9 - 311/3006, c_0011_11 + 49600/1503*c_1010_9^9 + 12032/501*c_1010_9^8 - 47408/501*c_1010_9^7 - 159664/1503*c_1010_9^6 - 21592/501*c_1010_9^5 - 30556/1503*c_1010_9^4 + 401/167*c_1010_9^3 + 8323/1503*c_1010_9^2 - 18761/6012*c_1010_9 - 751/6012, c_0011_12 + 49600/1503*c_1010_9^9 + 12032/501*c_1010_9^8 - 47408/501*c_1010_9^7 - 159664/1503*c_1010_9^6 - 21592/501*c_1010_9^5 - 30556/1503*c_1010_9^4 + 401/167*c_1010_9^3 + 8323/1503*c_1010_9^2 - 18761/6012*c_1010_9 - 751/6012, c_0011_3 + 66080/1503*c_1010_9^9 + 15616/501*c_1010_9^8 - 63832/501*c_1010_9^7 - 204452/1503*c_1010_9^6 - 26510/501*c_1010_9^5 - 50861/1503*c_1010_9^4 + 23/167*c_1010_9^3 + 37847/6012*c_1010_9^2 - 7108/1503*c_1010_9 + 1477/6012, c_0101_0 + 11072/501*c_1010_9^9 + 3072/167*c_1010_9^8 - 11024/167*c_1010_9^7 - 39344/501*c_1010_9^6 - 4120/167*c_1010_9^5 - 4760/501*c_1010_9^4 + 865/167*c_1010_9^3 + 2825/501*c_1010_9^2 - 3685/2004*c_1010_9 + 25/2004, c_0101_1 - 9920/1503*c_1010_9^9 + 800/501*c_1010_9^8 + 12688/501*c_1010_9^7 + 5480/1503*c_1010_9^6 - 8908/501*c_1010_9^5 - 12526/1503*c_1010_9^4 - 648/167*c_1010_9^3 - 1364/1503*c_1010_9^2 + 5333/3006*c_1010_9 - 977/3006, c_0101_12 + 64928/1503*c_1010_9^9 + 14416/501*c_1010_9^8 - 62824/501*c_1010_9^7 - 196640/1503*c_1010_9^6 - 25172/501*c_1010_9^5 - 37082/1503*c_1010_9^4 + 2157/334*c_1010_9^3 + 36011/6012*c_1010_9^2 - 41267/12024*c_1010_9 + 3305/12024, c_0101_2 + 66080/1503*c_1010_9^9 + 15616/501*c_1010_9^8 - 63832/501*c_1010_9^7 - 204452/1503*c_1010_9^6 - 26510/501*c_1010_9^5 - 50861/1503*c_1010_9^4 + 23/167*c_1010_9^3 + 37847/6012*c_1010_9^2 - 7108/1503*c_1010_9 + 1477/6012, c_0101_8 + 45280/501*c_1010_9^9 + 9536/167*c_1010_9^8 - 44296/167*c_1010_9^7 - 129868/501*c_1010_9^6 - 15322/167*c_1010_9^5 - 31615/501*c_1010_9^4 + 949/167*c_1010_9^3 + 19393/2004*c_1010_9^2 - 6131/501*c_1010_9 + 2099/2004, c_1001_0 - 52864/1503*c_1010_9^9 - 6080/501*c_1010_9^8 + 54272/501*c_1010_9^7 + 110656/1503*c_1010_9^6 + 5176/501*c_1010_9^5 + 14236/1503*c_1010_9^4 - 1822/167*c_1010_9^3 - 7870/1503*c_1010_9^2 + 13477/3006*c_1010_9 - 2695/3006, c_1001_2 + 52864/1503*c_1010_9^9 + 6080/501*c_1010_9^8 - 54272/501*c_1010_9^7 - 110656/1503*c_1010_9^6 - 5176/501*c_1010_9^5 - 14236/1503*c_1010_9^4 + 1822/167*c_1010_9^3 + 7870/1503*c_1010_9^2 - 13477/3006*c_1010_9 + 2695/3006, c_1010_9^10 + 1/2*c_1010_9^9 - 3*c_1010_9^8 - 5/2*c_1010_9^7 - 11/16*c_1010_9^6 - 17/32*c_1010_9^5 + 5/32*c_1010_9^4 + 7/64*c_1010_9^3 - 33/256*c_1010_9^2 + 11/512*c_1010_9 - 1/512 ], 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_3, c_0101_0, c_0101_1, c_0101_12, c_0101_2, c_0101_8, c_1001_0, c_1001_2, c_1010_9 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 16 Groebner basis: [ t + 3539815653858063127/3639241672811578433*c_1010_9^15 + 20396872265655525/383078070822271414*c_1010_9^14 - 98945699770254211029/7278483345623156866*c_1010_9^13 - 45486156199529358649/3639241672811578433*c_1010_9^12 + 368242919954180308869/3639241672811578433*c_1010_9^11 + 706335759170347831637/7278483345623156866*c_1010_9^10 - 3007176994250581219403/7278483345623156866*c_1010_9^9 - 1928477071263310839153/7278483345623156866*c_1010_9^8 + 5885401033987754626453/7278483345623156866*c_1010_9^7 + 2274464315201245531263/7278483345623156866*c_1010_9^6 - 3011602814395754369379/7278483345623156866*c_1010_9^5 - 1910084610665345578528/3639241672811578433*c_1010_9^4 - 338089734030289181246/3639241672811578433*c_1010_9^3 + 2049073818248908559491/7278483345623156866*c_1010_9^2 + 582623357277218491286/3639241672811578433*c_1010_9 + 138563800268951923680/3639241672811578433, c_0011_0 - 1, c_0011_10 + 4034039271480521/191539035411135707*c_1010_9^15 - 4314464070117632/191539035411135707*c_1010_9^14 - 58747086037964746/191539035411135707*c_1010_9^13 + 8946797821310671/191539035411135707*c_1010_9^12 + 503859228110243531/191539035411135707*c_1010_9^11 - 11790961331963450/191539035411135707*c_1010_9^10 - 2306472922504005543/191539035411135707*c_1010_9^9 + 460831180739659797/191539035411135707*c_1010_9^8 + 4946573801551481163/191539035411135707*c_1010_9^7 - 1605782438657365021/191539035411135707*c_1010_9^6 - 3356337688415891558/191539035411135707*c_1010_9^5 - 608157202574702197/191539035411135707*c_1010_9^4 + 1075549094334952452/191539035411135707*c_1010_9^3 + 855440694731142697/191539035411135707*c_1010_9^2 + 451614892823883584/191539035411135707*c_1010_9 - 198701254636096616/191539035411135707, c_0011_11 + 2422135588034914/191539035411135707*c_1010_9^15 + 1158116625965760/191539035411135707*c_1010_9^14 - 36205979529669168/191539035411135707*c_1010_9^13 - 49367844077504573/191539035411135707*c_1010_9^12 + 263945531042799370/191539035411135707*c_1010_9^11 + 409541768437496584/191539035411135707*c_1010_9^10 - 1059444471193018211/191539035411135707*c_1010_9^9 - 1413261609229494483/191539035411135707*c_1010_9^8 + 2237292424315932949/191539035411135707*c_1010_9^7 + 2314896118216718765/191539035411135707*c_1010_9^6 - 1875529765466886480/191539035411135707*c_1010_9^5 - 2193139545014804965/191539035411135707*c_1010_9^4 + 177896913809593818/191539035411135707*c_1010_9^3 + 693044152148381131/191539035411135707*c_1010_9^2 + 612186660184961393/191539035411135707*c_1010_9 + 208481770926630161/191539035411135707, c_0011_12 + 2422135588034914/191539035411135707*c_1010_9^15 + 1158116625965760/191539035411135707*c_1010_9^14 - 36205979529669168/191539035411135707*c_1010_9^13 - 49367844077504573/191539035411135707*c_1010_9^12 + 263945531042799370/191539035411135707*c_1010_9^11 + 409541768437496584/191539035411135707*c_1010_9^10 - 1059444471193018211/191539035411135707*c_1010_9^9 - 1413261609229494483/191539035411135707*c_1010_9^8 + 2237292424315932949/191539035411135707*c_1010_9^7 + 2314896118216718765/191539035411135707*c_1010_9^6 - 1875529765466886480/191539035411135707*c_1010_9^5 - 2193139545014804965/191539035411135707*c_1010_9^4 + 177896913809593818/191539035411135707*c_1010_9^3 + 693044152148381131/191539035411135707*c_1010_9^2 + 612186660184961393/191539035411135707*c_1010_9 + 208481770926630161/191539035411135707, c_0011_3 + 3410388470163694/191539035411135707*c_1010_9^15 - 527588814313200/191539035411135707*c_1010_9^14 - 47970019336190517/191539035411135707*c_1010_9^13 - 33928559663384307/191539035411135707*c_1010_9^12 + 364914592999727032/191539035411135707*c_1010_9^11 + 263970008399494758/191539035411135707*c_1010_9^10 - 1519576185047203529/191539035411135707*c_1010_9^9 - 556144894783708048/191539035411135707*c_1010_9^8 + 3054017311585130919/191539035411135707*c_1010_9^7 + 48217111392396581/191539035411135707*c_1010_9^6 - 1877749434528015343/191539035411135707*c_1010_9^5 - 462596185784076451/191539035411135707*c_1010_9^4 + 431906165217151480/191539035411135707*c_1010_9^3 + 399110937320499982/191539035411135707*c_1010_9^2 - 11320966429774671/191539035411135707*c_1010_9 - 93725645419819284/191539035411135707, c_0101_0 - 2002051566155446/191539035411135707*c_1010_9^15 - 900546146587689/191539035411135707*c_1010_9^14 + 22933586996087226/191539035411135707*c_1010_9^13 + 29321736342737624/191539035411135707*c_1010_9^12 - 139094971892529599/191539035411135707*c_1010_9^11 - 135152920807773515/191539035411135707*c_1010_9^10 + 461091482336234237/191539035411135707*c_1010_9^9 - 32131461656062627/191539035411135707*c_1010_9^8 - 585790546641399846/191539035411135707*c_1010_9^7 + 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