Magma V2.19-8 Wed Aug 21 2013 00:00:35 on localhost [Seed = 1208885575] Type ? for help. Type -D to quit. Loading file "K13n1541__sl2_c0.magma" ==TRIANGULATION=BEGINS== % Triangulation K13n1541 geometric_solution 11.26148367 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 1 0 -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 4 -1 -3 1 0 0 -1 4 0 0 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.905782785447 1.018041385695 0 5 7 6 0132 0132 0132 0132 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 -4 4 0 -1 0 1 0 0 0 0 0 -4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.476410386158 0.438825408656 8 0 5 9 0132 0132 0321 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 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.452604648544 0.868918603924 6 10 4 0 0132 0132 2103 0132 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 -1 1 0 0 0 0 -1 1 0 0 -3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.566323122293 0.250319108292 3 9 0 10 2103 0132 0132 0132 0 0 0 0 0 -1 1 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 -3 3 0 0 0 1 -1 1 0 0 -1 0 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.637397177468 1.128381953296 8 1 2 11 1023 0132 0321 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 4 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.252792585936 0.738679430145 3 8 1 11 0132 0321 0132 1230 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 3 0 0 -3 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.025321237543 1.576941956454 12 10 9 1 0132 2310 2103 0132 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 0 4 -4 1 0 0 -1 0 4 0 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.656533888408 0.707126613408 2 5 12 6 0132 1023 0132 0321 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.122698371498 0.966191648399 7 4 2 11 2103 0132 0132 0213 0 0 0 0 0 1 0 -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 3 0 -3 0 0 0 0 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.558095819702 0.657883515254 12 3 4 7 1302 0132 0132 3201 0 0 0 0 0 0 0 0 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 3 0 1 -4 3 -3 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.575659876504 0.602144153809 6 12 5 9 3012 0213 0132 0213 0 0 0 0 0 -1 0 1 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 -3 0 3 0 0 0 0 0 0 0 0 3 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.816192903575 0.711239485717 7 10 11 8 0132 2031 0213 0132 0 0 0 0 0 -1 1 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 -3 3 0 -1 0 0 1 0 0 0 0 0 -3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.779203125310 0.482374600300 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_0110_6' : d['c_0011_11'], 'c_1001_11' : negation(d['c_0110_10']), 'c_1001_10' : d['c_1001_0'], 'c_1001_12' : negation(d['c_0110_10']), 'c_1001_5' : d['c_1001_5'], 'c_1001_4' : d['c_1001_2'], 'c_1001_7' : negation(d['c_0011_4']), 'c_1001_6' : d['c_1001_5'], 'c_1001_1' : negation(d['c_0110_10']), 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_0011_4'], 'c_1001_2' : d['c_1001_2'], 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : d['c_0011_10'], 'c_1010_12' : d['c_0011_10'], 'c_1010_11' : d['c_1001_5'], 'c_1010_10' : d['c_0011_4'], 's_0_10' : d['1'], 's_0_11' : 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' : negation(d['c_0011_12']), '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_1100_9' : d['c_1001_5'], 'c_1100_8' : d['c_1001_5'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : d['c_1001_2'], 'c_1100_4' : d['c_0011_12'], 'c_1100_7' : d['c_0110_11'], 'c_1100_6' : d['c_0110_11'], 'c_1100_1' : d['c_0110_11'], 'c_1100_0' : d['c_0011_12'], 'c_1100_3' : d['c_0011_12'], 'c_1100_2' : d['c_1001_5'], 's_3_11' : d['1'], 'c_1100_11' : d['c_1001_2'], 'c_1100_10' : d['c_0011_12'], 's_3_10' : d['1'], 'c_1010_7' : negation(d['c_0110_10']), 'c_1010_6' : d['c_0101_11'], 'c_1010_5' : negation(d['c_0110_10']), 'c_1010_4' : d['c_1001_0'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_1001_5'], 'c_1010_0' : d['c_1001_2'], 'c_1010_9' : d['c_1001_2'], 'c_1010_8' : d['c_0101_11'], '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' : d['c_1001_5'], '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' : negation(d['c_0011_4']), 'c_0011_8' : d['c_0011_0'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : d['c_0011_4'], 'c_0011_7' : negation(d['c_0011_12']), 'c_0011_6' : d['c_0011_10'], '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_0110_11'], 'c_0110_10' : d['c_0110_10'], 'c_0110_12' : d['c_0101_7'], 'c_0101_12' : d['c_0011_11'], 'c_0110_0' : d['c_0011_11'], 'c_0101_7' : d['c_0101_7'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0011_10'], 'c_0101_4' : d['c_0011_11'], 'c_0101_3' : d['c_0011_11'], 'c_0101_2' : negation(d['c_0011_10']), 'c_0101_1' : d['c_0011_11'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_7'], 'c_0101_8' : d['c_0101_7'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : negation(d['c_0110_11']), 'c_0110_8' : negation(d['c_0011_10']), 'c_0110_1' : d['c_0101_0'], 'c_0011_11' : d['c_0011_11'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_7'], 'c_0110_5' : d['c_0101_11'], 'c_0110_4' : negation(d['c_0011_12']), 'c_0110_7' : d['c_0011_11'], '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_0011_4, c_0101_0, c_0101_11, c_0101_7, c_0110_10, c_0110_11, c_1001_0, c_1001_2, c_1001_5 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 16 Groebner basis: [ t + 1929879398615334701393693089/188680380298714392363205*c_1001_5^15 + 431188062988659416581180878/188680380298714392363205*c_1001_5^14 - 1666724105192020848283232653/26954340042673484623315*c_1001_5^13 + 6407715288944400706946409596/188680380298714392363205*c_1001_5^12 + 5192939005941094305787600173/188680380298714392363205*c_1001_5^11 - 4798338694925147571998143759/188680380298714392363205*c_1001_5^10 + 3382876303509453742653091613/188680380298714392363205*c_1001_5^9 + 4245349248911625690771810974/188680380298714392363205*c_1001_5^8 + 8374023718393870811227192252/188680380298714392363205*c_1001_5^7 + 570361583538138499246640/26896704247856648947*c_1001_5^6 + 932853873006533868854882241/188680380298714392363205*c_1001_5^5 - 5601459188283744772280855/37736076059742878472641*c_1001_5^4 + 117758109995753886731239677/188680380298714392363205*c_1001_5^3 + 445383952933580807311911384/188680380298714392363205*c_1001_5^2 + 9965265662298923844880323/8203494795596277928835*c_1001_5 + 81770827770557280628001061/188680380298714392363205, c_0011_0 - 1, c_0011_10 + 15714135851018608212/548912331588911203*c_1001_5^15 - 6812768214924629541/548912331588911203*c_1001_5^14 - 89211592206931359832/548912331588911203*c_1001_5^13 + 113879454990799056307/548912331588911203*c_1001_5^12 - 41214332873358192229/548912331588911203*c_1001_5^11 - 24889030855675903247/548912331588911203*c_1001_5^10 + 65392439191674363144/548912331588911203*c_1001_5^9 - 8668994282076472468/548912331588911203*c_1001_5^8 + 63159544021634638010/548912331588911203*c_1001_5^7 + 4139574001649822663/548912331588911203*c_1001_5^6 + 15974103694459730792/548912331588911203*c_1001_5^5 - 1344958101559479676/548912331588911203*c_1001_5^4 + 3233389326039287655/548912331588911203*c_1001_5^3 + 1849580868875511378/548912331588911203*c_1001_5^2 + 384002914564191605/548912331588911203*c_1001_5 + 402574942061912779/548912331588911203, c_0011_11 - 1911642312989386644/548912331588911203*c_1001_5^15 - 8327904865917034937/548912331588911203*c_1001_5^14 + 16945425370999554002/548912331588911203*c_1001_5^13 + 37870436021631340352/548912331588911203*c_1001_5^12 - 73324992239436627783/548912331588911203*c_1001_5^11 + 38082723262103349880/548912331588911203*c_1001_5^10 + 3912122357582003400/548912331588911203*c_1001_5^9 - 37001097431884945075/548912331588911203*c_1001_5^8 + 1128391017648975609/548912331588911203*c_1001_5^7 - 35505395456870200132/548912331588911203*c_1001_5^6 + 6104221863157876662/548912331588911203*c_1001_5^5 - 7740433964281112441/548912331588911203*c_1001_5^4 + 4290996525101655174/548912331588911203*c_1001_5^3 - 3509334696714425771/548912331588911203*c_1001_5^2 - 316268269102599888/548912331588911203*c_1001_5 - 304874148025458371/548912331588911203, c_0011_12 - 25244665058665639109/548912331588911203*c_1001_5^15 - 6248184999427100766/548912331588911203*c_1001_5^14 + 156134845213546680380/548912331588911203*c_1001_5^13 - 85334500813212465999/548912331588911203*c_1001_5^12 - 88817977155137535005/548912331588911203*c_1001_5^11 + 109168764169170217229/548912331588911203*c_1001_5^10 - 80728785465584532881/548912331588911203*c_1001_5^9 - 58281064244863834453/548912331588911203*c_1001_5^8 - 81794850128532101109/548912331588911203*c_1001_5^7 - 71525911574921755253/548912331588911203*c_1001_5^6 - 2542892445025357646/548912331588911203*c_1001_5^5 - 8130289118873776449/548912331588911203*c_1001_5^4 + 5153975708381233803/548912331588911203*c_1001_5^3 - 7857719995172684979/548912331588911203*c_1001_5^2 - 2099256775611891728/548912331588911203*c_1001_5 - 1587083923038001706/548912331588911203, c_0011_4 + 31056428986038180057/548912331588911203*c_1001_5^15 + 420556630666227979/548912331588911203*c_1001_5^14 - 192204471795891693652/548912331588911203*c_1001_5^13 + 146791075094986933343/548912331588911203*c_1001_5^12 + 78322108820664388536/548912331588911203*c_1001_5^11 - 135116688199815773922/548912331588911203*c_1001_5^10 + 97031005816765963478/548912331588911203*c_1001_5^9 + 67625197225229866579/548912331588911203*c_1001_5^8 + 89334242839358045965/548912331588911203*c_1001_5^7 + 51059653529393115913/548912331588911203*c_1001_5^6 - 2846865544942604321/548912331588911203*c_1001_5^5 + 22600257329484093/548912331588911203*c_1001_5^4 + 917517131818256596/548912331588911203*c_1001_5^3 + 7431701898841393680/548912331588911203*c_1001_5^2 + 2804982657311465982/548912331588911203*c_1001_5 + 364173734574621440/548912331588911203, c_0101_0 - 94855464947725721412/548912331588911203*c_1001_5^15 - 110617635168471194849/548912331588911203*c_1001_5^14 + 598120300748175927643/548912331588911203*c_1001_5^13 + 205857442261946896236/548912331588911203*c_1001_5^12 - 814513186213314213044/548912331588911203*c_1001_5^11 + 322159686457750263511/548912331588911203*c_1001_5^10 - 5834477431585307015/548912331588911203*c_1001_5^9 - 485764166658322970205/548912331588911203*c_1001_5^8 - 454695126155576661013/548912331588911203*c_1001_5^7 - 543039874665461734170/548912331588911203*c_1001_5^6 - 92245946101599633292/548912331588911203*c_1001_5^5 - 63928999171951868187/548912331588911203*c_1001_5^4 + 34488296137307581621/548912331588911203*c_1001_5^3 - 42700402336773519091/548912331588911203*c_1001_5^2 - 21679507749363386424/548912331588911203*c_1001_5 - 12945141759932605706/548912331588911203, c_0101_11 - 166206929244999243913/548912331588911203*c_1001_5^15 - 118622267429391570525/548912331588911203*c_1001_5^14 + 1025458749157786624307/548912331588911203*c_1001_5^13 - 80001529279779622520/548912331588911203*c_1001_5^12 - 944329132085090310802/548912331588911203*c_1001_5^11 + 501435364734185981375/548912331588911203*c_1001_5^10 - 170651065330303735770/548912331588911203*c_1001_5^9 - 620537746680408044815/548912331588911203*c_1001_5^8 - 742102733723291418443/548912331588911203*c_1001_5^7 - 671240681085040228504/548912331588911203*c_1001_5^6 - 143995232082513868655/548912331588911203*c_1001_5^5 - 59235398824986785379/548912331588911203*c_1001_5^4 + 34063315989033834004/548912331588911203*c_1001_5^3 - 56034864404972682014/548912331588911203*c_1001_5^2 - 29902948504247894880/548912331588911203*c_1001_5 - 15909592496135021065/548912331588911203, c_0101_7 - 108028505688516602476/548912331588911203*c_1001_5^15 + 85948643215945639574/548912331588911203*c_1001_5^14 + 616189956543801665559/548912331588911203*c_1001_5^13 - 1005714542782443859914/548912331588911203*c_1001_5^12 + 438225227428262292382/548912331588911203*c_1001_5^11 + 173144269098995000297/548912331588911203*c_1001_5^10 - 434125452886484908178/548912331588911203*c_1001_5^9 + 81577591862576128412/548912331588911203*c_1001_5^8 - 366758371338210424596/548912331588911203*c_1001_5^7 + 179066669267819386266/548912331588911203*c_1001_5^6 - 68186633911938294025/548912331588911203*c_1001_5^5 + 80308240304341580064/548912331588911203*c_1001_5^4 - 45594558861859602682/548912331588911203*c_1001_5^3 + 3217765298463867847/548912331588911203*c_1001_5^2 - 4530248465010800759/548912331588911203*c_1001_5 + 4726154248914077874/548912331588911203, c_0110_10 - 205572883396297594235/548912331588911203*c_1001_5^15 - 16404446772015756093/548912331588911203*c_1001_5^14 + 1226360277910618677796/548912331588911203*c_1001_5^13 - 859954965628351333806/548912331588911203*c_1001_5^12 - 317658421046896310168/548912331588911203*c_1001_5^11 + 482294060450127832919/548912331588911203*c_1001_5^10 - 460017529305943577287/548912331588911203*c_1001_5^9 - 377144434570800655962/548912331588911203*c_1001_5^8 - 835138655875644760596/548912331588911203*c_1001_5^7 - 336472503805734189800/548912331588911203*c_1001_5^6 - 164203264520294677288/548912331588911203*c_1001_5^5 + 22953688346748727573/548912331588911203*c_1001_5^4 - 16254964607457586725/548912331588911203*c_1001_5^3 - 39088157891961930998/548912331588911203*c_1001_5^2 - 26230058990541867886/548912331588911203*c_1001_5 - 7727084801632851148/548912331588911203, c_0110_11 + 13802493538029221568/548912331588911203*c_1001_5^15 - 15140673080841664478/548912331588911203*c_1001_5^14 - 72266166835931805830/548912331588911203*c_1001_5^13 + 151749891012430396659/548912331588911203*c_1001_5^12 - 114539325112794820012/548912331588911203*c_1001_5^11 + 13193692406427446633/548912331588911203*c_1001_5^10 + 69304561549256366544/548912331588911203*c_1001_5^9 - 45670091713961417543/548912331588911203*c_1001_5^8 + 64287935039283613619/548912331588911203*c_1001_5^7 - 31365821455220377469/548912331588911203*c_1001_5^6 + 22078325557617607454/548912331588911203*c_1001_5^5 - 9085392065840592117/548912331588911203*c_1001_5^4 + 7524385851140942829/548912331588911203*c_1001_5^3 - 1659753827838914393/548912331588911203*c_1001_5^2 + 67734645461591717/548912331588911203*c_1001_5 + 97700794036454408/548912331588911203, c_1001_0 + 22685993567026851519/548912331588911203*c_1001_5^15 - 34113107647950735401/548912331588911203*c_1001_5^14 - 122311638507200236368/548912331588911203*c_1001_5^13 + 305150034773285919285/548912331588911203*c_1001_5^12 - 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