Magma V2.19-8 Tue Aug 20 2013 23:40:51 on localhost [Seed = 3381636387] Type ? for help. Type -D to quit. Loading file "K12n430__sl2_c0.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n430 geometric_solution 11.40813391 oriented_manifold CS_known -0.0000000000000004 1 0 torus 0.000000000000 0.000000000000 12 1 2 3 4 0132 0132 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 -1 0 0 0 0 -1 -1 0 2 0 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.297851860271 0.626498156729 0 2 4 5 0132 2310 1302 0132 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 2 0 -2 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 0.446832489729 0.919251614754 6 0 7 1 0132 0132 0132 3201 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 0 1 1 0 -1 0 0 2 0 -2 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.606671318669 0.754127519842 7 8 9 0 0213 0132 0132 0132 0 0 0 0 0 0 0 0 1 0 -1 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 1 0 -1 0 0 2 0 -2 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.533206086255 1.702990971267 1 5 0 8 2031 2310 0132 1302 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 1 -1 0 0 0 0 0 0 0 0 0 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.297238281939 0.893155251431 6 10 1 4 3201 0132 0132 3201 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 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.716920964846 0.598994203397 2 11 10 5 0132 0132 1230 2310 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0.962940085323 0.620566928552 3 10 11 2 0213 3201 3201 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 -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 0.624732521577 1.334013279755 9 3 4 11 2031 0132 2031 3012 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 -1 -1 1 0 0 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.845199343010 1.483832990143 11 10 8 3 3201 3012 1302 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 1 0 -2 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 0.496631239410 1.180048513315 9 5 7 6 1230 0132 2310 3012 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.721808969320 0.892008034891 7 6 8 9 2310 0132 1230 2310 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0.762544130418 0.463208410008 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_0110_6' : negation(d['c_0101_0']), 'c_1001_11' : negation(d['c_0110_5']), 'c_1001_10' : d['c_1001_10'], 'c_1001_5' : negation(d['c_0101_6']), 'c_1001_4' : negation(d['c_1001_10']), 'c_1001_7' : negation(d['c_0101_10']), 'c_1001_6' : negation(d['c_0011_7']), 'c_1001_1' : d['c_0110_4'], 'c_1001_0' : negation(d['c_0110_4']), 'c_1001_3' : negation(d['c_0101_10']), 'c_1001_2' : negation(d['c_1001_10']), 'c_1001_9' : negation(d['c_0011_10']), 'c_1001_8' : negation(d['c_0110_4']), 'c_1010_11' : negation(d['c_0011_7']), 'c_1010_10' : negation(d['c_0101_6']), 's_3_11' : d['1'], 's_3_10' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0101_10'], '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_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' : negation(d['c_0011_0']), 'c_1100_8' : d['c_0110_5'], 'c_1100_5' : negation(d['c_0011_4']), 'c_1100_4' : d['c_0101_8'], 'c_1100_7' : d['c_0011_0'], 'c_1100_6' : negation(d['c_0011_10']), 'c_1100_1' : negation(d['c_0011_4']), 'c_1100_0' : d['c_0101_8'], 'c_1100_3' : d['c_0101_8'], 'c_1100_2' : d['c_0011_0'], 's_0_10' : d['1'], 'c_1100_9' : d['c_0101_8'], 'c_1100_11' : negation(d['c_0011_10']), 'c_1100_10' : d['c_0011_7'], 's_0_11' : d['1'], 'c_1010_7' : negation(d['c_1001_10']), 'c_1010_6' : negation(d['c_0110_5']), 'c_1010_5' : d['c_1001_10'], 'c_1010_4' : negation(d['c_0110_5']), 'c_1010_3' : negation(d['c_0110_4']), 'c_1010_2' : negation(d['c_0110_4']), 'c_1010_1' : negation(d['c_0101_6']), 'c_1010_0' : negation(d['c_1001_10']), 'c_1010_9' : negation(d['c_0101_10']), 'c_1010_8' : negation(d['c_0101_10']), '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'], '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_10']), 'c_0011_8' : negation(d['c_0011_3']), 'c_0011_5' : negation(d['c_0011_10']), 'c_0011_4' : d['c_0011_4'], 'c_0011_7' : d['c_0011_7'], 'c_0011_6' : d['c_0011_0'], '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_0011_3']), 'c_0110_10' : negation(d['c_0011_10']), 'c_0101_7' : d['c_0011_3'], 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : negation(d['c_0011_4']), 'c_0101_3' : d['c_0011_7'], 'c_0101_2' : negation(d['c_0101_0']), 'c_0101_1' : negation(d['c_0011_4']), 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0011_3'], 'c_0101_8' : d['c_0101_8'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0011_7'], 'c_0110_8' : negation(d['c_0011_10']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : negation(d['c_0011_4']), 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_6'], 'c_0110_5' : d['c_0110_5'], 'c_0110_4' : d['c_0110_4'], 'c_0110_7' : negation(d['c_0101_0']), 'c_0011_10' : d['c_0011_10']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 13 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_3, c_0011_4, c_0011_7, c_0101_0, c_0101_10, c_0101_6, c_0101_8, c_0110_4, c_0110_5, c_1001_10 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 17 Groebner basis: [ t + 424247466527201231601676991/10038007629039460271512553*c_1001_10^16 + 50417229371666484096627583007/301140228871183808145376590*c_1001_\ 10^15 + 22565885144468911844513730119/60228045774236761629075318*c_\ 1001_10^14 + 21758279846909825485077229399/301140228871183808145376\ 590*c_1001_10^13 - 215854851517876171076892964607/30114022887118380\ 8145376590*c_1001_10^12 - 53602845040584523272387981968/15057011443\ 5591904072688295*c_1001_10^11 + 230513041696539768345561972361/3011\ 40228871183808145376590*c_1001_10^10 - 176584958197025142142687743113/100380076290394602715125530*c_1001_1\ 0^9 - 371380988144762208534195755479/301140228871183808145376590*c_\ 1001_10^8 + 255456051998109345692036647226/150570114435591904072688\ 295*c_1001_10^7 + 324880873251460986269443312918/150570114435591904\ 072688295*c_1001_10^6 - 330664059830419909179759093713/301140228871\ 183808145376590*c_1001_10^5 - 39157930343444145702835266137/1505701\ 14435591904072688295*c_1001_10^4 + 86728881576739094885302867615/60228045774236761629075318*c_1001_10^\ 3 + 194037613680190250758202767029/100380076290394602715125530*c_10\ 01_10^2 + 136810939007650224461150599267/30114022887118380814537659\ 0*c_1001_10 + 3496126432252692787639450927/100380076290394602715125\ 530, c_0011_0 - 1, c_0011_10 - 4022752501009115/7531231065310469*c_1001_10^16 - 1761148568012596/684657369573679*c_1001_10^15 - 48985365408803633/7531231065310469*c_1001_10^14 - 36406957707556162/7531231065310469*c_1001_10^13 + 64320475732425283/7531231065310469*c_1001_10^12 + 91621040802170024/7531231065310469*c_1001_10^11 - 47346052361133236/7531231065310469*c_1001_10^10 + 106580953451535677/7531231065310469*c_1001_10^9 + 264533737783497307/7531231065310469*c_1001_10^8 - 76951925506244219/7531231065310469*c_1001_10^7 - 339264653008683770/7531231065310469*c_1001_10^6 - 6053919674713688/684657369573679*c_1001_10^5 + 117229028433539961/7531231065310469*c_1001_10^4 - 125271966941401752/7531231065310469*c_1001_10^3 - 293994498199736227/7531231065310469*c_1001_10^2 - 195609958816905951/7531231065310469*c_1001_10 - 27531192654886014/7531231065310469, c_0011_3 + 5849302102206298/7531231065310469*c_1001_10^16 + 28290643386008523/7531231065310469*c_1001_10^15 + 6505734605384096/684657369573679*c_1001_10^14 + 53051991098640255/7531231065310469*c_1001_10^13 - 95734981270181929/7531231065310469*c_1001_10^12 - 12471861367170261/684657369573679*c_1001_10^11 + 6705006127821966/684657369573679*c_1001_10^10 - 143023820089247100/7531231065310469*c_1001_10^9 - 35943150071986747/684657369573679*c_1001_10^8 + 103608464210957341/7531231065310469*c_1001_10^7 + 525912170903832343/7531231065310469*c_1001_10^6 + 90104070514254113/7531231065310469*c_1001_10^5 - 216590894921126809/7531231065310469*c_1001_10^4 + 186621544425155156/7531231065310469*c_1001_10^3 + 462249938148533459/7531231065310469*c_1001_10^2 + 276076556527051144/7531231065310469*c_1001_10 + 27660500595097291/7531231065310469, c_0011_4 + 43369750703001/7531231065310469*c_1001_10^16 + 228173802311192/7531231065310469*c_1001_10^15 + 401502807850185/7531231065310469*c_1001_10^14 - 184764987649854/7531231065310469*c_1001_10^13 - 2221361953098952/7531231065310469*c_1001_10^12 - 1139018490169292/7531231065310469*c_1001_10^11 + 4062367474374646/7531231065310469*c_1001_10^10 + 254426019450390/7531231065310469*c_1001_10^9 - 6720748398703485/7531231065310469*c_1001_10^8 + 10510618975716144/7531231065310469*c_1001_10^7 + 7547616575622470/7531231065310469*c_1001_10^6 - 7193606920467063/7531231065310469*c_1001_10^5 - 3367499338242902/7531231065310469*c_1001_10^4 + 2104613618318062/7531231065310469*c_1001_10^3 + 3736573867206651/7531231065310469*c_1001_10^2 - 99335730907933/7531231065310469*c_1001_10 - 5040006581088543/7531231065310469, c_0011_7 + 2709620975318314/7531231065310469*c_1001_10^16 + 13117602931603549/7531231065310469*c_1001_10^15 + 3022866100081271/684657369573679*c_1001_10^14 + 24852128654115716/7531231065310469*c_1001_10^13 - 44040117173476942/7531231065310469*c_1001_10^12 - 5825070400861946/684657369573679*c_1001_10^11 + 3002841935085361/684657369573679*c_1001_10^10 - 65657433878873842/7531231065310469*c_1001_10^9 - 16563919219546609/684657369573679*c_1001_10^8 + 43688011977776093/7531231065310469*c_1001_10^7 + 242303135961037506/7531231065310469*c_1001_10^6 + 46584514154478128/7531231065310469*c_1001_10^5 - 100105518607119607/7531231065310469*c_1001_10^4 + 78245408094080011/7531231065310469*c_1001_10^3 + 215950378242000719/7531231065310469*c_1001_10^2 + 130234738932011183/7531231065310469*c_1001_10 + 11748227077116655/7531231065310469, c_0101_0 - 1870180724725564/7531231065310469*c_1001_10^16 - 791753581380313/684657369573679*c_1001_10^15 - 21379136842741838/7531231065310469*c_1001_10^14 - 13477035976557861/7531231065310469*c_1001_10^13 + 32317227709064110/7531231065310469*c_1001_10^12 + 38134086877024927/7531231065310469*c_1001_10^11 - 26892306968842310/7531231065310469*c_1001_10^10 + 54160202137020072/7531231065310469*c_1001_10^9 + 112719021239036239/7531231065310469*c_1001_10^8 - 54940821809059194/7531231065310469*c_1001_10^7 - 147537192023753398/7531231065310469*c_1001_10^6 - 1096386783713282/684657369573679*c_1001_10^5 + 56344325112389143/7531231065310469*c_1001_10^4 - 60140577079332108/7531231065310469*c_1001_10^3 - 125562564194282898/7531231065310469*c_1001_10^2 - 74210609941739267/7531231065310469*c_1001_10 - 7935245903803935/7531231065310469, c_0101_10 - 2228847635442676/7531231065310469*c_1001_10^16 - 11309810776190257/7531231065310469*c_1001_10^15 - 29899023088622042/7531231065310469*c_1001_10^14 - 27006818498753266/7531231065310469*c_1001_10^13 + 31013782314778992/7531231065310469*c_1001_10^12 + 60897448615828345/7531231065310469*c_1001_10^11 - 13617155298097431/7531231065310469*c_1001_10^10 + 49525717799339274/7531231065310469*c_1001_10^9 + 161524340776030856/7531231065310469*c_1001_10^8 - 1368017831690253/7531231065310469*c_1001_10^7 - 203484895229922574/7531231065310469*c_1001_10^6 - 89902482627638772/7531231065310469*c_1001_10^5 + 64846782578919296/7531231065310469*c_1001_10^4 - 43919460308836322/7531231065310469*c_1001_10^3 - 191875711187253466/7531231065310469*c_1001_10^2 - 153865635324322926/7531231065310469*c_1001_10 - 30223199939407699/7531231065310469, c_0101_6 - 965630292670272/7531231065310469*c_1001_10^16 - 4144842046036452/7531231065310469*c_1001_10^15 - 9614311257698855/7531231065310469*c_1001_10^14 - 351552125656707/684657369573679*c_1001_10^13 + 16997502332427187/7531231065310469*c_1001_10^12 + 12469243918666621/7531231065310469*c_1001_10^11 - 17733807518841825/7531231065310469*c_1001_10^10 + 35955738070936891/7531231065310469*c_1001_10^9 + 45430266150798910/7531231065310469*c_1001_10^8 - 39974139939674087/7531231065310469*c_1001_10^7 - 55607980722270003/7531231065310469*c_1001_10^6 + 12437327367422248/7531231065310469*c_1001_10^5 + 1659063258885109/684657369573679*c_1001_10^4 - 39438011253302262/7531231065310469*c_1001_10^3 - 57120590797100264/7531231065310469*c_1001_10^2 - 27781732796673528/7531231065310469*c_1001_10 + 157291082607785/684657369573679, c_0101_8 + 6544684086941193/7531231065310469*c_1001_10^16 + 2960020516388553/684657369573679*c_1001_10^15 + 83472231475871836/7531231065310469*c_1001_10^14 + 66415626052719470/7531231065310469*c_1001_10^13 - 107739678953223144/7531231065310469*c_1001_10^12 - 170200361324685415/7531231065310469*c_1001_10^11 + 79266332619310027/7531231065310469*c_1001_10^10 - 141523569500422842/7531231065310469*c_1001_10^9 - 486991128833720925/7531231065310469*c_1001_10^8 + 100653910670060955/7531231065310469*c_1001_10^7 + 647356737067485792/7531231065310469*c_1001_10^6 + 10599240813028215/684657369573679*c_1001_10^5 - 265990734254390735/7531231065310469*c_1001_10^4 + 218903956280925697/7531231065310469*c_1001_10^3 + 539920704500675253/7531231065310469*c_1001_10^2 + 330959172233957290/7531231065310469*c_1001_10 + 45975498126911314/7531231065310469, c_0110_4 - 10910101950338842/7531231065310469*c_1001_10^16 - 53548089119371538/7531231065310469*c_1001_10^15 - 136087089628595387/7531231065310469*c_1001_10^14 - 104110901031024883/7531231065310469*c_1001_10^13 + 180609327556392602/7531231065310469*c_1001_10^12 + 268310184117393816/7531231065310469*c_1001_10^11 - 139050421903649076/7531231065310469*c_1001_10^10 + 256528546084175544/7531231065310469*c_1001_10^9 + 782110733382025139/7531231065310469*c_1001_10^8 - 205883614582018735/7531231065310469*c_1001_10^7 - 92872148908188045/684657369573679*c_1001_10^6 - 152810627149802058/7531231065310469*c_1001_10^5 + 403181550339859337/7531231065310469*c_1001_10^4 - 371065141950778557/7531231065310469*c_1001_10^3 - 850157508040458122/7531231065310469*c_1001_10^2 - 518351152249649910/7531231065310469*c_1001_10 - 72012676016292421/7531231065310469, c_0110_5 + 4555274085125341/7531231065310469*c_1001_10^16 + 22069281725539881/7531231065310469*c_1001_10^15 + 55868425400773410/7531231065310469*c_1001_10^14 + 41766538066348276/7531231065310469*c_1001_10^13 - 74089925133577202/7531231065310469*c_1001_10^12 - 106921347731452465/7531231065310469*c_1001_10^11 + 55379554275622925/7531231065310469*c_1001_10^10 - 115365998824656845/7531231065310469*c_1001_10^9 - 307372049262887052/7531231065310469*c_1001_10^8 + 88754651894901799/7531231065310469*c_1001_10^7 + 401370697595031319/7531231065310469*c_1001_10^6 + 70234395428110916/7531231065310469*c_1001_10^5 - 144298276044275967/7531231065310469*c_1001_10^4 + 141977580620486293/7531231065310469*c_1001_10^3 + 342046331180854445/7531231065310469*c_1001_10^2 + 225194535472426292/7531231065310469*c_1001_10 + 29496329097585743/7531231065310469, c_1001_10^17 + 5*c_1001_10^16 + 13*c_1001_10^15 + 11*c_1001_10^14 - 15*c_1001_10^13 - 26*c_1001_10^12 + 9*c_1001_10^11 - 23*c_1001_10^10 - 72*c_1001_10^9 + 9*c_1001_10^8 + 92*c_1001_10^7 + 28*c_1001_10^6 - 32*c_1001_10^5 + 27*c_1001_10^4 + 81*c_1001_10^3 + 59*c_1001_10^2 + 13*c_1001_10 + 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 1.820 Total time: 2.040 seconds, Total memory usage: 32.09MB