Magma V2.19-8 Wed Aug 21 2013 00:43:56 on localhost [Seed = 3220809736] Type ? for help. Type -D to quit. Loading file "K14n6025__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K14n6025 geometric_solution 11.67141734 oriented_manifold CS_known -0.0000000000000004 1 0 torus 0.000000000000 0.000000000000 13 1 2 3 1 0132 0132 0132 2031 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 1 0 -1 -13 0 14 -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 0.529250220806 1.153723230842 0 0 5 4 0132 1302 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 1 -1 0 13 0 0 -13 0 1 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.671514538466 0.716072082858 3 0 6 5 2103 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 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 1.303184800707 0.743051538788 7 8 2 0 0132 0132 2103 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 14 0 0 -14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.343029076932 1.432144165717 9 5 1 10 0132 1023 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 13 -13 0 -1 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.264625110403 0.576861615421 4 11 2 1 1023 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 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.470749779194 1.153723230842 12 8 10 2 0132 0321 0132 0132 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 -14 13 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.403784169857 0.502938926654 3 10 9 12 0132 1023 0132 0132 0 0 0 0 0 -1 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 0 13 -13 0 -14 0 0 14 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.958252580453 0.934327113626 9 3 11 6 2103 0132 0132 0321 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 13 0 0 -13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.086687916548 0.614533799605 4 11 8 7 0132 1023 2103 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 -13 13 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 0.277454730424 0.808502032144 7 11 4 6 1023 0213 0132 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 -13 0 13 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 0.769779537334 1.086181472448 9 5 10 8 1023 0132 0213 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.539440361360 1.377448911894 6 12 7 12 0132 1302 0132 2031 0 0 0 0 0 1 0 -1 0 0 1 -1 0 1 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -14 0 14 0 0 -14 14 0 -14 0 14 14 -14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.531991034609 0.477134513141 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_0110_6' : d['c_0101_12'], 'c_1001_11' : d['c_0101_1'], 'c_1001_10' : d['c_0101_1'], 'c_1001_12' : d['c_0101_6'], 'c_1001_5' : d['c_1001_0'], 'c_1001_4' : d['c_0101_5'], 'c_1001_7' : d['c_0101_10'], 'c_1001_6' : d['c_1001_6'], 'c_1001_1' : d['c_0101_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : negation(d['c_0011_0']), 'c_1001_2' : negation(d['c_0011_0']), 'c_1001_9' : d['c_0011_10'], 'c_1001_8' : d['c_1001_0'], 'c_1010_12' : d['c_0011_12'], 'c_1010_11' : d['c_1001_0'], 'c_1010_10' : d['c_1001_6'], 's_0_10' : 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_0011_10'], 'c_0101_10' : d['c_0101_10'], 's_2_0' : negation(d['1']), 's_2_1' : d['1'], 's_2_2' : negation(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_1100_9' : negation(d['c_0011_12']), 'c_1100_8' : d['c_1001_6'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : d['c_1100_1'], 'c_1100_4' : d['c_1100_1'], 'c_1100_7' : negation(d['c_0011_12']), 'c_1100_6' : d['c_1100_1'], 'c_1100_1' : d['c_1100_1'], 'c_1100_0' : negation(d['c_0101_5']), 'c_1100_3' : negation(d['c_0101_5']), 'c_1100_2' : d['c_1100_1'], 's_3_11' : d['1'], 'c_1100_11' : d['c_1001_6'], 'c_1100_10' : d['c_1100_1'], 's_0_11' : d['1'], 'c_1010_7' : d['c_0101_6'], 'c_1010_6' : negation(d['c_0011_0']), 'c_1010_5' : d['c_0101_1'], 'c_1010_4' : d['c_0101_1'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_0101_5'], 'c_1010_0' : negation(d['c_0011_0']), 'c_1010_9' : d['c_0101_10'], 'c_1010_8' : negation(d['c_0011_0']), 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : negation(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' : negation(d['1']), 's_3_9' : d['1'], 's_3_8' : negation(d['1']), 'c_1100_12' : negation(d['c_0011_12']), 's_1_7' : d['1'], 's_1_6' : negation(d['1']), 's_1_5' : d['1'], 's_1_4' : d['1'], 's_1_3' : negation(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' : negation(d['1']), 'c_0011_9' : d['c_0011_11'], 'c_0011_8' : d['c_0011_10'], 'c_0011_5' : negation(d['c_0011_11']), 'c_0011_4' : negation(d['c_0011_11']), 'c_0011_7' : d['c_0011_10'], 'c_0011_6' : negation(d['c_0011_12']), '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_10'], 'c_0110_10' : d['c_0101_6'], 'c_0110_12' : d['c_0101_6'], 'c_0101_12' : d['c_0101_12'], 'c_0011_11' : d['c_0011_11'], 'c_0101_7' : d['c_0101_0'], 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : d['c_0101_0'], 'c_0101_3' : d['c_0101_12'], 'c_0101_2' : d['c_0101_12'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_10'], 'c_0101_8' : d['c_0101_10'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_0'], 'c_0110_8' : d['c_0011_12'], '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_5'], 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : d['c_0101_12'], 'c_0011_10' : d['c_0011_10']})} 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_0101_0, c_0101_1, c_0101_10, c_0101_12, c_0101_5, c_0101_6, c_1001_0, c_1001_6, c_1100_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 10 Groebner basis: [ t - 130885421/3555328*c_1100_1^9 - 35104031/3555328*c_1100_1^8 - 532959513/3555328*c_1100_1^7 + 16977073/507904*c_1100_1^6 - 753460545/3555328*c_1100_1^5 + 583154259/3555328*c_1100_1^4 - 118181267/1777664*c_1100_1^3 + 852541945/3555328*c_1100_1^2 + 22461989/222208*c_1100_1 + 488667383/3555328, c_0011_0 - 1, c_0011_10 - c_1100_1^2 - 1, c_0011_11 - c_1100_1^8 - 3*c_1100_1^6 + 2*c_1100_1^5 - 3*c_1100_1^4 + 4*c_1100_1^3 + 3*c_1100_1, c_0011_12 + 1/4*c_1100_1^9 - 1/4*c_1100_1^8 + 5/4*c_1100_1^7 - 7/4*c_1100_1^6 + 13/4*c_1100_1^5 - 15/4*c_1100_1^4 + 9/2*c_1100_1^3 - 13/4*c_1100_1^2 + 2*c_1100_1 - 3/4, c_0101_0 + c_1100_1^9 + 3*c_1100_1^7 - 2*c_1100_1^6 + 3*c_1100_1^5 - 4*c_1100_1^4 - 3*c_1100_1^2 - 2*c_1100_1, c_0101_1 - 1, c_0101_10 - c_1100_1^2 - 1, c_0101_12 + c_1100_1^8 + 3*c_1100_1^6 - 2*c_1100_1^5 + 3*c_1100_1^4 - 4*c_1100_1^3 - 3*c_1100_1, c_0101_5 + c_1100_1^9 + 3*c_1100_1^7 - 2*c_1100_1^6 + 3*c_1100_1^5 - 4*c_1100_1^4 - 3*c_1100_1^2 - c_1100_1, c_0101_6 + 1/4*c_1100_1^9 - 1/4*c_1100_1^8 + 5/4*c_1100_1^7 - 7/4*c_1100_1^6 + 9/4*c_1100_1^5 - 15/4*c_1100_1^4 + 5/2*c_1100_1^3 - 13/4*c_1100_1^2 + c_1100_1 - 3/4, c_1001_0 - c_1100_1, c_1001_6 + 1/8*c_1100_1^9 - 1/8*c_1100_1^8 + 5/8*c_1100_1^7 - 7/8*c_1100_1^6 + 13/8*c_1100_1^5 - 19/8*c_1100_1^4 + 7/4*c_1100_1^3 - 21/8*c_1100_1^2 + 1/2*c_1100_1 - 7/8, c_1100_1^10 + 4*c_1100_1^8 - 2*c_1100_1^7 + 6*c_1100_1^6 - 6*c_1100_1^5 + 3*c_1100_1^4 - 7*c_1100_1^3 - c_1100_1^2 - 3*c_1100_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_0101_0, c_0101_1, c_0101_10, c_0101_12, c_0101_5, c_0101_6, c_1001_0, c_1001_6, c_1100_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 16 Groebner basis: [ t - 93219907623113350341/40899128216916049*c_1100_1^15 + 1058550712650923212923/81798256433832098*c_1100_1^14 - 2825968488794890537367/81798256433832098*c_1100_1^13 + 656705297694941623742/40899128216916049*c_1100_1^12 + 3584704199069558524778/40899128216916049*c_1100_1^11 - 13177246179149598955249/81798256433832098*c_1100_1^10 - 3380541175797063147900/40899128216916049*c_1100_1^9 + 34891317314058456138141/81798256433832098*c_1100_1^8 - 22200581299824663330068/40899128216916049*c_1100_1^7 + 27405094997527189294758/40899128216916049*c_1100_1^6 - 41250778655502795916739/40899128216916049*c_1100_1^5 + 36625429763611923370864/40899128216916049*c_1100_1^4 - 58352688685697348489989/81798256433832098*c_1100_1^3 + 9837870752665241045985/40899128216916049*c_1100_1^2 - 2831600148002307376660/40899128216916049*c_1100_1 + 204099782888458838148/40899128216916049, c_0011_0 - 1, c_0011_10 - 1009352379572310/517710483758431*c_1100_1^15 + 11702922346048653/1035420967516862*c_1100_1^14 - 15989824752259362/517710483758431*c_1100_1^13 + 8968797366270865/517710483758431*c_1100_1^12 + 37895395419088394/517710483758431*c_1100_1^11 - 151980917670915455/1035420967516862*c_1100_1^10 - 55601490821040417/1035420967516862*c_1100_1^9 + 192974640015001353/517710483758431*c_1100_1^8 - 263500926470935827/517710483758431*c_1100_1^7 + 326620059216541730/517710483758431*c_1100_1^6 - 482588331886873182/517710483758431*c_1100_1^5 + 900833155592073297/1035420967516862*c_1100_1^4 - 364896965252278015/517710483758431*c_1100_1^3 + 290579134518939467/1035420967516862*c_1100_1^2 - 42945076516451645/517710483758431*c_1100_1 + 10948448806338457/1035420967516862, c_0011_11 + 2842475060722875/1035420967516862*c_1100_1^15 - 16468664625708667/1035420967516862*c_1100_1^14 + 44946661742786477/1035420967516862*c_1100_1^13 - 12480298789814476/517710483758431*c_1100_1^12 - 107155240953472839/1035420967516862*c_1100_1^11 + 213681824837312977/1035420967516862*c_1100_1^10 + 40076063071948028/517710483758431*c_1100_1^9 - 544692558237553583/1035420967516862*c_1100_1^8 + 738421632540733119/1035420967516862*c_1100_1^7 - 912345144854767287/1035420967516862*c_1100_1^6 + 675932537479240678/517710483758431*c_1100_1^5 - 629292367709906738/517710483758431*c_1100_1^4 + 1013878139867624127/1035420967516862*c_1100_1^3 - 199139140028343160/517710483758431*c_1100_1^2 + 116114734045225217/1035420967516862*c_1100_1 - 13499452048110377/1035420967516862, c_0011_12 - 70173994929747/60907115736286*c_1100_1^15 + 399729126556343/60907115736286*c_1100_1^14 - 535859894278798/30453557868143*c_1100_1^13 + 518699545288799/60907115736286*c_1100_1^12 + 2675484585177801/60907115736286*c_1100_1^11 - 2498936833515544/30453557868143*c_1100_1^10 - 1210161825356775/30453557868143*c_1100_1^9 + 13101116933188785/60907115736286*c_1100_1^8 - 16966560661932993/60907115736286*c_1100_1^7 + 21144167753435897/60907115736286*c_1100_1^6 - 15836131247274398/30453557868143*c_1100_1^5 + 14187331595254715/30453557868143*c_1100_1^4 - 11454812285532734/30453557868143*c_1100_1^3 + 8233289057390757/60907115736286*c_1100_1^2 - 1233344998121908/30453557868143*c_1100_1 + 315088214387087/60907115736286, c_0101_0 - 5478984195599749/1035420967516862*c_1100_1^15 + 15918089562213720/517710483758431*c_1100_1^14 - 43553923926804884/517710483758431*c_1100_1^13 + 24602497285313486/517710483758431*c_1100_1^12 + 206730477039073443/1035420967516862*c_1100_1^11 - 415876061073644711/1035420967516862*c_1100_1^10 - 75047467256161113/517710483758431*c_1100_1^9 + 528729359286306864/517710483758431*c_1100_1^8 - 719457695156992180/517710483758431*c_1100_1^7 + 884672594018399501/517710483758431*c_1100_1^6 - 2618848656820859003/1035420967516862*c_1100_1^5 + 1226125684631303067/517710483758431*c_1100_1^4 - 1967870169263220059/1035420967516862*c_1100_1^3 + 387552389105672646/517710483758431*c_1100_1^2 - 218511012038312409/1035420967516862*c_1100_1 + 13237484835086825/517710483758431, c_0101_1 - 2842475060722875/1035420967516862*c_1100_1^15 + 16468664625708667/1035420967516862*c_1100_1^14 - 44946661742786477/1035420967516862*c_1100_1^13 + 12480298789814476/517710483758431*c_1100_1^12 + 107155240953472839/1035420967516862*c_1100_1^11 - 213681824837312977/1035420967516862*c_1100_1^10 - 40076063071948028/517710483758431*c_1100_1^9 + 544692558237553583/1035420967516862*c_1100_1^8 - 738421632540733119/1035420967516862*c_1100_1^7 + 912345144854767287/1035420967516862*c_1100_1^6 - 675932537479240678/517710483758431*c_1100_1^5 + 629292367709906738/517710483758431*c_1100_1^4 - 1013878139867624127/1035420967516862*c_1100_1^3 + 199139140028343160/517710483758431*c_1100_1^2 - 116114734045225217/1035420967516862*c_1100_1 + 14534873015627239/1035420967516862, c_0101_10 - 1009352379572310/517710483758431*c_1100_1^15 + 11702922346048653/1035420967516862*c_1100_1^14 - 15989824752259362/517710483758431*c_1100_1^13 + 8968797366270865/517710483758431*c_1100_1^12 + 37895395419088394/517710483758431*c_1100_1^11 - 151980917670915455/1035420967516862*c_1100_1^10 - 55601490821040417/1035420967516862*c_1100_1^9 + 192974640015001353/517710483758431*c_1100_1^8 - 263500926470935827/517710483758431*c_1100_1^7 + 326620059216541730/517710483758431*c_1100_1^6 - 482588331886873182/517710483758431*c_1100_1^5 + 900833155592073297/1035420967516862*c_1100_1^4 - 364896965252278015/517710483758431*c_1100_1^3 + 290579134518939467/1035420967516862*c_1100_1^2 - 42945076516451645/517710483758431*c_1100_1 + 10948448806338457/1035420967516862, c_0101_12 - 2842475060722875/1035420967516862*c_1100_1^15 + 16468664625708667/1035420967516862*c_1100_1^14 - 44946661742786477/1035420967516862*c_1100_1^13 + 12480298789814476/517710483758431*c_1100_1^12 + 107155240953472839/1035420967516862*c_1100_1^11 - 213681824837312977/1035420967516862*c_1100_1^10 - 40076063071948028/517710483758431*c_1100_1^9 + 544692558237553583/1035420967516862*c_1100_1^8 - 738421632540733119/1035420967516862*c_1100_1^7 + 912345144854767287/1035420967516862*c_1100_1^6 - 675932537479240678/517710483758431*c_1100_1^5 + 629292367709906738/517710483758431*c_1100_1^4 - 1013878139867624127/1035420967516862*c_1100_1^3 + 199139140028343160/517710483758431*c_1100_1^2 - 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