Magma V2.19-8 Tue Aug 20 2013 23:38:34 on localhost [Seed = 1982861893] Type ? for help. Type -D to quit. Loading file "K11n63__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K11n63 geometric_solution 9.89996175 oriented_manifold CS_known -0.0000000000000003 1 0 torus 0.000000000000 0.000000000000 11 1 2 3 4 0132 0132 0132 0132 0 0 0 0 0 0 0 0 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 -1 0 1 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 0.621208193763 0.621057948234 0 1 1 4 0132 3201 2310 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.742479231582 0.647022683133 5 0 7 6 0132 0132 0132 0132 0 0 0 0 0 0 1 -1 0 0 0 0 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 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 0.771675172077 1.688856224998 8 5 7 0 0132 0132 0213 0132 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 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 0.703271508874 0.288470546319 1 8 0 8 3012 0213 0132 0321 0 0 0 0 0 0 0 0 0 0 -1 1 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 -1 1 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 0.715787076404 1.173587299736 2 3 9 10 0132 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 -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 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 0.616084088403 0.884278159073 10 9 2 7 0132 0132 0132 3120 0 0 0 0 0 0 1 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.942510717443 0.724767366638 6 3 10 2 3120 0213 0213 0132 0 0 0 0 0 0 1 -1 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 -1 1 -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 0.217952195881 0.313236554421 3 4 4 9 0132 0321 0213 1302 0 0 0 0 0 0 0 0 1 0 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 -1 0 1 -1 0 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 0.621208193763 0.621057948234 10 6 8 5 3120 0132 2031 0132 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -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 -1 0 -1 0 0 1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.521286119894 0.428197126259 6 7 5 9 0132 0213 0132 3120 0 0 0 0 0 -1 0 1 0 0 0 0 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 0 -1 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 0.639176793430 0.609806794800 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_10' : d['c_1001_10'], 'c_1001_5' : d['c_1001_0'], 'c_1001_4' : d['c_1001_2'], 'c_1001_7' : d['c_1001_10'], 'c_1001_6' : d['c_1001_0'], 'c_1001_1' : negation(d['c_0101_1']), 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_1001_10'], 'c_1001_2' : d['c_1001_2'], 'c_1001_9' : negation(d['c_0011_7']), 'c_1001_8' : d['c_1001_2'], 'c_1010_10' : negation(d['c_0011_10']), '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_0101_10'], 's_2_0' : negation(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_10' : d['1'], 's_0_8' : negation(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' : negation(d['1']), 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_1100_9' : negation(d['c_0101_9']), 'c_0011_10' : d['c_0011_10'], 'c_1100_5' : negation(d['c_0101_9']), 'c_1100_4' : d['c_1001_2'], 'c_1100_7' : negation(d['c_0011_10']), 'c_1100_6' : negation(d['c_0011_10']), 'c_1100_1' : negation(d['c_0011_0']), 'c_1100_0' : d['c_1001_2'], 'c_1100_3' : d['c_1001_2'], 'c_1100_2' : negation(d['c_0011_10']), 'c_1100_10' : negation(d['c_0101_9']), 'c_1010_7' : d['c_1001_2'], 'c_1010_6' : negation(d['c_0011_7']), 'c_1010_5' : d['c_1001_10'], 'c_1010_4' : d['c_0101_9'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_0101_1'], 'c_1010_0' : d['c_1001_2'], 'c_1010_9' : d['c_1001_0'], 'c_1010_8' : d['c_0101_9'], 'c_1100_8' : d['c_0101_9'], 's_3_1' : d['1'], 's_3_0' : negation(d['1']), 's_3_3' : negation(d['1']), 's_3_2' : 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' : 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' : 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' : negation(d['1']), 'c_0011_9' : d['c_0011_10'], 'c_0011_8' : d['c_0011_0'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : d['c_0011_4'], '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' : negation(d['c_0011_0']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_10' : d['c_0101_5'], 'c_0101_7' : d['c_0011_10'], 'c_0101_6' : d['c_0101_5'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0011_7'], 'c_0101_2' : d['c_0101_10'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0011_4'], 'c_0101_9' : d['c_0101_9'], 'c_0101_8' : d['c_0011_4'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_5'], 'c_0110_8' : d['c_0011_7'], 'c_0110_1' : d['c_0011_4'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0011_4'], 'c_0110_2' : d['c_0101_5'], 'c_0110_5' : d['c_0101_10'], 'c_0110_4' : negation(d['c_0011_0']), 'c_0110_7' : d['c_0101_10'], 'c_0110_6' : d['c_0101_10']})} 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_4, c_0011_7, c_0101_1, c_0101_10, c_0101_5, c_0101_9, c_1001_0, c_1001_10, c_1001_2 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 23 Groebner basis: [ t - 126833051483889906824563175/21648883719436297633932*c_1001_2^22 - 752020814916953668631756741/86595534877745190535728*c_1001_2^21 - 14778946233345809712660635693/707196868168252389375112*c_1001_2^20 - 24136194215682678890224385685/1414393736336504778750224*c_1001_2^19 - 6737266336385732902199363161/530397651126189292031334*c_1001_2^18 + 15488997992802608398137974561/530397651126189292031334*c_1001_2^1\ 7 + 86420134429924552760569247445/1414393736336504778750224*c_1001_\ 2^16 + 40148706980668104313824343621/303084372072108166875048*c_100\ 1_2^15 + 663860157348953290832258264159/4243181209009514336250672*c\ _1001_2^14 + 417147650285754853517367464203/21215906045047571681253\ 36*c_1001_2^13 + 206134154572757674677756887809/1060795302252378584\ 062668*c_1001_2^12 + 31178081244254576169886669175/1767992170420630\ 97343778*c_1001_2^11 + 669589319337983322405966570869/4243181209009\ 514336250672*c_1001_2^10 + 19994290420675588369058425811/1767992170\ 42063097343778*c_1001_2^9 + 46883651701801643773034819797/530397651\ 126189292031334*c_1001_2^8 + 39414668408216420865378179205/70719686\ 8168252389375112*c_1001_2^7 + 23835040475586237561325169435/7071968\ 68168252389375112*c_1001_2^6 + 43282726137260467752510108455/212159\ 0604504757168125336*c_1001_2^5 + 12930196163215392376839375771/1414\ 393736336504778750224*c_1001_2^4 + 19968514111977296212226133265/4243181209009514336250672*c_1001_2^3 + 7584639389474114563438730837/4243181209009514336250672*c_1001_2^2 + 259494331436952833623718713/530397651126189292031334*c_1001_2 + 771665809660114942497100667/4243181209009514336250672, c_0011_0 - 1, c_0011_10 + 497455499747365317354/587072451443657057*c_1001_2^22 + 177809416975848079282/587072451443657057*c_1001_2^21 + 1377031086313525239621/587072451443657057*c_1001_2^20 - 186347040474658630957/587072451443657057*c_1001_2^19 + 798781754940963097022/587072451443657057*c_1001_2^18 - 3288947279282723564929/587072451443657057*c_1001_2^17 - 1616204280640742463831/587072451443657057*c_1001_2^16 - 8089990749630689353551/587072451443657057*c_1001_2^15 - 3374940110789638421296/587072451443657057*c_1001_2^14 - 10039982578909733671107/587072451443657057*c_1001_2^13 - 4074413980068220147714/587072451443657057*c_1001_2^12 - 7432230989334661539309/587072451443657057*c_1001_2^11 - 4005092052129009974056/587072451443657057*c_1001_2^10 - 3360459727481398101693/587072451443657057*c_1001_2^9 - 2831161555015649366316/587072451443657057*c_1001_2^8 - 1032005469225916084517/587072451443657057*c_1001_2^7 - 1151435317622247645739/587072451443657057*c_1001_2^6 - 379267632904326889850/587072451443657057*c_1001_2^5 - 206859131628189028908/587072451443657057*c_1001_2^4 - 132805485539809796499/587072451443657057*c_1001_2^3 - 9543100009121304341/587072451443657057*c_1001_2^2 - 19178218649161462691/587072451443657057*c_1001_2 - 170763955820412907/587072451443657057, c_0011_4 - 41540532813686933005/587072451443657057*c_1001_2^22 - 306380329424901280073/587072451443657057*c_1001_2^21 - 344104409597645097031/587072451443657057*c_1001_2^20 - 894235174794607799274/587072451443657057*c_1001_2^19 - 309061723605009070556/587072451443657057*c_1001_2^18 - 272342539328289571857/587072451443657057*c_1001_2^17 + 1946062487117554103384/587072451443657057*c_1001_2^16 + 2429789620103383651776/587072451443657057*c_1001_2^15 + 5843384412102239452221/587072451443657057*c_1001_2^14 + 4958904759085607437798/587072451443657057*c_1001_2^13 + 7767112740406470377999/587072451443657057*c_1001_2^12 + 5505912241449872906181/587072451443657057*c_1001_2^11 + 6302143556615240333151/587072451443657057*c_1001_2^10 + 4378035222505216199683/587072451443657057*c_1001_2^9 + 3432539051841505528197/587072451443657057*c_1001_2^8 + 2557056822486034875833/587072451443657057*c_1001_2^7 + 1349228411792969720404/587072451443657057*c_1001_2^6 + 989889253101992099804/587072451443657057*c_1001_2^5 + 435199205585610800547/587072451443657057*c_1001_2^4 + 222369009947905792983/587072451443657057*c_1001_2^3 + 106940405041315206874/587072451443657057*c_1001_2^2 + 23256509416941488556/587072451443657057*c_1001_2 + 13210725621522460577/587072451443657057, c_0011_7 - 41540532813686933005/587072451443657057*c_1001_2^22 - 335146879545640475866/587072451443657057*c_1001_2^21 - 344104409597645097031/587072451443657057*c_1001_2^20 - 981121897608269043710/587072451443657057*c_1001_2^19 - 273837376518389647136/587072451443657057*c_1001_2^18 - 353945610078957902780/587072451443657057*c_1001_2^17 + 2155647352282939672733/587072451443657057*c_1001_2^16 + 2434486199714932908232/587072451443657057*c_1001_2^15 + 6349440865246671835355/587072451443657057*c_1001_2^14 + 5022308583841522399954/587072451443657057*c_1001_2^13 + 8463967740270091304658/587072451443657057*c_1001_2^12 + 5617456007224167747011/587072451443657057*c_1001_2^11 + 6888628935607453733094/587072451443657057*c_1001_2^10 + 4561201827355637201467/587072451443657057*c_1001_2^9 + 3730184784723439656096/587072451443657057*c_1001_2^8 + 2755487311073990961099/587072451443657057*c_1001_2^7 + 1439637569315292907182/587072451443657057*c_1001_2^6 + 1109652033196498139432/587072451443657057*c_1001_2^5 + 462791610803462682226/587072451443657057*c_1001_2^4 + 258180429485968873460/587072451443657057*c_1001_2^3 + 121030143875962976242/587072451443657057*c_1001_2^2 + 27366016577047087955/587072451443657057*c_1001_2 + 16733160330184402919/587072451443657057, c_0101_1 + 465837543610286470350/587072451443657057*c_1001_2^22 - 187825057172337982593/587072451443657057*c_1001_2^21 + 1038623104526089398433/587072451443657057*c_1001_2^20 - 1303945597267374310638/587072451443657057*c_1001_2^19 + 504228629254106734578/587072451443657057*c_1001_2^18 - 3848287027621110924773/587072451443657057*c_1001_2^17 + 709887801312152062477/587072451443657057*c_1001_2^16 - 5661886874575931692616/587072451443657057*c_1001_2^15 + 3714610743357289262734/587072451443657057*c_1001_2^14 - 4632965259292318367624/587072451443657057*c_1001_2^13 + 5592339874913270768578/587072451443657057*c_1001_2^12 - 1152355624362716750537/587072451443657057*c_1001_2^11 + 3963631547563284464998/587072451443657057*c_1001_2^10 + 1896080647139078441098/587072451443657057*c_1001_2^9 + 1497277943502125521923/587072451443657057*c_1001_2^8 + 2222187982492815747283/587072451443657057*c_1001_2^7 + 515269623504361764676/587072451443657057*c_1001_2^6 + 953473387142455116611/587072451443657057*c_1001_2^5 + 335496648133952915718/587072451443657057*c_1001_2^4 + 173070804100535410414/587072451443657057*c_1001_2^3 + 140441706624541036414/587072451443657057*c_1001_2^2 + 10268764866202903385/587072451443657057*c_1001_2 + 21041889556927909596/587072451443657057, c_0101_10 - 299464706396322256916/587072451443657057*c_1001_2^22 - 376412004317946771846/587072451443657057*c_1001_2^21 - 1022840553590713391122/587072451443657057*c_1001_2^20 - 738307650686205780700/587072451443657057*c_1001_2^19 - 665189788031150360328/587072451443657057*c_1001_2^18 + 1428337600759554561401/587072451443657057*c_1001_2^17 + 2675129893480013615774/587072451443657057*c_1001_2^16 + 6366919083462852753359/587072451443657057*c_1001_2^15 + 7215232858487724170828/587072451443657057*c_1001_2^14 + 9644923755002090672315/587072451443657057*c_1001_2^13 + 9426269957444003987812/587072451443657057*c_1001_2^12 + 8762481251333197725506/587072451443657057*c_1001_2^11 + 8023982926851520491839/587072451443657057*c_1001_2^10 + 5686129936644490888387/587072451443657057*c_1001_2^9 + 4665962618285617316656/587072451443657057*c_1001_2^8 + 2901023509801156210633/587072451443657057*c_1001_2^7 + 1808235923643246627922/587072451443657057*c_1001_2^6 + 1139739357728968490285/587072451443657057*c_1001_2^5 + 491367770531515725948/587072451443657057*c_1001_2^4 + 278979881847710449271/587072451443657057*c_1001_2^3 + 106739596154436302355/587072451443657057*c_1001_2^2 + 29392443215098160941/587072451443657057*c_1001_2 + 13637809366346185401/587072451443657057, c_0101_5 + 337896885384062111870/587072451443657057*c_1001_2^22 - 44426235981638390173/587072451443657057*c_1001_2^21 + 820060719914076500983/587072451443657057*c_1001_2^20 - 623547578215037945031/587072451443657057*c_1001_2^19 + 448356311434610520809/587072451443657057*c_1001_2^18 - 2523378210933223508934/587072451443657057*c_1001_2^17 - 67184638619643155174/587072451443657057*c_1001_2^16 - 4599710355582588539684/587072451443657057*c_1001_2^15 + 717736637192190382627/587072451443657057*c_1001_2^14 - 4749414301639292996839/587072451443657057*c_1001_2^13 + 1200395505579708948552/587072451443657057*c_1001_2^12 - 2563336661097483712929/587072451443657057*c_1001_2^11 + 431505163407315374770/587072451443657057*c_1001_2^10 - 153278279762700569095/587072451443657057*c_1001_2^9 - 279776677569483989536/587072451443657057*c_1001_2^8 + 605391184123705718805/587072451443657057*c_1001_2^7 - 157006830524241313602/587072451443657057*c_1001_2^6 + 251347931697035328215/587072451443657057*c_1001_2^5 + 70412217817889149998/587072451443657057*c_1001_2^4 + 18931191717773213779/587072451443657057*c_1001_2^3 + 49946026025597304976/587072451443657057*c_1001_2^2 - 2877694731759573727/587072451443657057*c_1001_2 + 7218196500402692941/587072451443657057, c_0101_9 + 536847201692228307538/587072451443657057*c_1001_2^22 - 121193916520386198188/587072451443657057*c_1001_2^21 + 1247741185350112002003/587072451443657057*c_1001_2^20 - 1232341414275739262100/587072451443657057*c_1001_2^19 + 591554277142858398661/587072451443657057*c_1001_2^18 - 4282502672784903962093/587072451443657057*c_1001_2^17 + 215444342403342271729/587072451443657057*c_1001_2^16 - 6935040593013794640580/587072451443657057*c_1001_2^15 + 2669907161550033974425/587072451443657057*c_1001_2^14 - 6257426238225910279191/587072451443657057*c_1001_2^13 + 4373095888627574511875/587072451443657057*c_1001_2^12 - 2461086415451858453317/587072451443657057*c_1001_2^11 + 2946865896864477554127/587072451443657057*c_1001_2^10 + 1151993999774070321836/587072451443657057*c_1001_2^9 + 896671672951322738136/587072451443657057*c_1001_2^8 + 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