Magma V2.19-8 Tue Aug 20 2013 23:38:17 on localhost [Seed = 1225731428] Type ? for help. Type -D to quit. Loading file "K12n462__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n462 geometric_solution 9.75716761 oriented_manifold CS_known -0.0000000000000004 1 0 torus 0.000000000000 0.000000000000 10 1 2 3 4 0132 0132 0132 0132 0 0 0 0 0 0 0 0 -1 0 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 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 0.633091671470 0.814561833060 0 5 7 6 0132 0132 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 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 0.768712538663 0.718697053538 4 0 8 6 3012 0132 0132 1023 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 -1 0 1 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 0.719376789164 1.112125650354 5 8 7 0 3120 0132 3120 0132 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 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 0.410058685834 0.633933134257 9 7 0 2 0132 3120 0132 1230 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 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 1.002246335285 0.969912736635 6 1 8 3 0132 0132 1023 3120 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 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 0.515233233351 0.498611227371 5 9 1 2 0132 0213 0132 1023 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 1 -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 0.601553732167 0.799608199728 9 4 3 1 3120 3120 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 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 0.398446267833 0.799608199728 9 3 5 2 1023 0132 1023 0132 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 -1 1 0 1 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.594834283316 0.765338300944 4 8 6 7 0132 1023 0213 3120 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 1 -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 0.694131934287 0.648968958939 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_5' : d['c_0101_8'], 'c_1001_4' : d['c_1001_2'], 'c_1001_7' : negation(d['c_1001_2']), 'c_1001_6' : d['c_0101_8'], 'c_1001_1' : negation(d['c_0011_3']), 'c_1001_0' : d['c_0101_5'], 'c_1001_3' : d['c_1001_2'], 'c_1001_2' : d['c_1001_2'], 'c_1001_9' : d['c_0101_8'], 'c_1001_8' : d['c_0101_5'], 's_2_8' : d['1'], 's_2_9' : negation(d['1']), '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' : negation(d['1']), 's_2_7' : d['1'], 's_0_8' : d['1'], 's_0_9' : negation(d['1']), 's_0_6' : d['1'], 's_0_7' : d['1'], 's_0_4' : negation(d['1']), 's_0_5' : d['1'], 's_0_2' : d['1'], 's_0_3' : d['1'], 's_0_0' : negation(d['1']), 's_0_1' : negation(d['1']), 'c_1100_9' : negation(d['c_0101_7']), 'c_1100_8' : d['c_0101_3'], 'c_1100_5' : negation(d['c_0101_3']), 'c_1100_4' : negation(d['c_0101_7']), 'c_1100_7' : negation(d['c_0101_3']), 'c_1100_6' : negation(d['c_0101_3']), 'c_1100_1' : negation(d['c_0101_3']), 'c_1100_0' : negation(d['c_0101_7']), 'c_1100_3' : negation(d['c_0101_7']), 'c_1100_2' : d['c_0101_3'], 'c_1010_7' : negation(d['c_0011_3']), 'c_1010_6' : negation(d['c_0101_7']), 'c_1010_5' : negation(d['c_0011_3']), 'c_1010_4' : negation(d['c_0011_7']), 'c_1010_3' : d['c_0101_5'], 'c_1010_2' : d['c_0101_5'], 'c_1010_1' : d['c_0101_8'], 'c_1010_0' : d['c_1001_2'], 'c_1010_9' : negation(d['c_0011_7']), 'c_1010_8' : d['c_1001_2'], 's_3_1' : negation(d['1']), 's_3_0' : negation(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' : negation(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_3']), 'c_0011_8' : negation(d['c_0011_3']), 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : d['c_0011_3'], 'c_0011_7' : d['c_0011_7'], 'c_0011_6' : negation(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_0101_7' : d['c_0101_7'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : negation(d['c_0011_7']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0011_0']), 'c_0101_8' : d['c_0101_8'], 'c_0110_9' : d['c_0101_1'], 'c_0110_8' : negation(d['c_0011_7']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : negation(d['c_0101_7']), 'c_0110_5' : d['c_0101_0'], 'c_0110_4' : negation(d['c_0011_0']), 'c_0110_7' : d['c_0101_1'], 'c_0110_6' : d['c_0101_5']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 11 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_3, c_0011_7, c_0101_0, c_0101_1, c_0101_3, c_0101_5, c_0101_7, c_0101_8, c_1001_2 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 20 Groebner basis: [ t - 1711559629036814351083890919772/20635618412061428025226232711*c_100\ 1_2^19 - 74221390786984482342356583127898/4333479866532899885297508\ 86931*c_1001_2^18 - 455588220821004531023238382620299/2888986577688\ 59992353167257954*c_1001_2^17 - 2419453750947014882134405961191841/\ 866695973306579977059501773862*c_1001_2^16 - 4568535820189801937600401190746420/433347986653289988529750886931*c\ _1001_2^15 - 2089929975765117146201124846941024/1444493288844299961\ 76583628977*c_1001_2^14 - 8888145050168537133806541861170245/288898\ 657768859992353167257954*c_1001_2^13 - 25633879086592171089478701175659419/866695973306579977059501773862*\ c_1001_2^12 - 32322321031968724854515186422210157/86669597330657997\ 7059501773862*c_1001_2^11 - 1255390829751351574526724910260892/6190\ 6855236184284075678698133*c_1001_2^10 - 2570320609122280042247122226215303/288898657768859992353167257954*c\ _1001_2^9 - 125602033344881130604067864864972/433347986653289988529\ 750886931*c_1001_2^8 + 1529314280270417468560793812466285/123813710\ 472368568151357396266*c_1001_2^7 - 292990675564494962346072144523475/144449328884429996176583628977*c_\ 1001_2^6 + 275339000532557917811501877092425/5098211607685764570938\ 2457286*c_1001_2^5 - 257439200032245241401832004940800/254910580384\ 28822854691228643*c_1001_2^4 - 204315119947872834580458859359725/14\ 4449328884429996176583628977*c_1001_2^3 - 918864264793204692950260298522606/144449328884429996176583628977*c_\ 1001_2^2 - 586021028639480857714064235960805/8666959733065799770595\ 01773862*c_1001_2 - 74703128421893564547453661818899/66668921023583\ 075158423213374, c_0011_0 - 1, c_0011_3 - 241734499184931485428558780/173408558084549815338035569*c_10\ 01_2^19 + 124037523843379993476638549/186747677937207493440961382*c\ _1001_2^18 - 55428856099579957995290434173/242771981318369741473249\ 7966*c_1001_2^17 + 40646273006675297537126480515/242771981318369741\ 4732497966*c_1001_2^16 - 149937918839689024591806348199/12138599065\ 91848707366248983*c_1001_2^15 + 371546759061122299797465286445/2427\ 719813183697414732497966*c_1001_2^14 - 749728922253859188497322236243/2427719813183697414732497966*c_1001_\ 2^13 + 736634266524369149277187704784/1213859906591848707366248983*\ c_1001_2^12 - 625760126809880398664260564414/1213859906591848707366\ 248983*c_1001_2^11 + 197958475406366964797528246438/173408558084549\ 815338035569*c_1001_2^10 - 2087557360369002021209988058237/24277198\ 13183697414732497966*c_1001_2^9 + 207938158080499992858267906233/18\ 6747677937207493440961382*c_1001_2^8 - 173267209494844560284436803370/173408558084549815338035569*c_1001_2\ ^7 + 873617618240460688190151535806/1213859906591848707366248983*c_\ 1001_2^6 - 1550197855549438744216038137671/242771981318369741473249\ 7966*c_1001_2^5 + 481334755458538424081651089340/121385990659184870\ 7366248983*c_1001_2^4 - 242622027967283450623134045834/121385990659\ 1848707366248983*c_1001_2^3 + 372287596156850704603817860709/242771\ 9813183697414732497966*c_1001_2^2 - 57085201513240371886418216827/2427719813183697414732497966*c_1001_2 + 57797047419859887518517046793/2427719813183697414732497966, c_0011_7 + 129933688423334878416580603/173408558084549815338035569*c_10\ 01_2^19 + 34370063740522970725348361/26678239705315356205851626*c_1\ 001_2^18 + 4963318658877031260529087325/346817116169099630676071138\ *c_1001_2^17 + 7200943476930298939460101529/34681711616909963067607\ 1138*c_1001_2^16 + 16816525275529855447759294376/173408558084549815\ 338035569*c_1001_2^15 + 36083228929062460974891278429/3468171161690\ 99630676071138*c_1001_2^14 + 102246505235949111858579624763/3468171\ 16169099630676071138*c_1001_2^13 + 32706627551599826362696987264/173408558084549815338035569*c_1001_2^\ 12 + 70697453846466167420064525938/173408558084549815338035569*c_10\ 01_2^11 + 6938981038384131425183117126/173408558084549815338035569*\ c_1001_2^10 + 79203526936612142845985815653/34681711616909963067607\ 1138*c_1001_2^9 - 4912060996731336220013074483/26678239705315356205\ 851626*c_1001_2^8 + 11262428321283284808148290646/17340855808454981\ 5338035569*c_1001_2^7 - 23537269298904917184319944889/1734085580845\ 49815338035569*c_1001_2^6 + 27355614174636976084359559205/346817116\ 169099630676071138*c_1001_2^5 + 671778670446756885890840978/1734085\ 58084549815338035569*c_1001_2^4 + 11409442496481644958415079276/173\ 408558084549815338035569*c_1001_2^3 + 8220043914168877561516263949/346817116169099630676071138*c_1001_2^2 + 5369926022514284543698870079/346817116169099630676071138*c_1001_2 + 1579692446494265173760073857/346817116169099630676071138, c_0101_0 - 1085673090326984119682049977/346817116169099630676071138*c_1\ 001_2^19 - 464217988892496682825239336/93373838968603746720480691*c\ _1001_2^18 - 70305343511435489881576122925/121385990659184870736624\ 8983*c_1001_2^17 - 190052319300125988835864631321/24277198131836974\ 14732497966*c_1001_2^16 - 908232007939108823064985199383/2427719813\ 183697414732497966*c_1001_2^15 - 455012057221571562222462391736/121\ 3859906591848707366248983*c_1001_2^14 - 2583655392808928473977074750949/2427719813183697414732497966*c_1001\ _2^13 - 761906917828499432915311934922/1213859906591848707366248983\ *c_1001_2^12 - 1617104993304532422193496645352/12138599065918487073\ 66248983*c_1001_2^11 - 30981971219734990181646785821/34681711616909\ 9630676071138*c_1001_2^10 - 738952909925339168635074079923/12138599\ 06591848707366248983*c_1001_2^9 + 93299141094233054047957220911/186\ 747677937207493440961382*c_1001_2^8 - 10788464244510095963330472036/173408558084549815338035569*c_1001_2^\ 7 + 600029969813480897571758038719/2427719813183697414732497966*c_1\ 001_2^6 - 320972000591983371614002134573/24277198131836974147324979\ 66*c_1001_2^5 - 162236468285136836547501856819/12138599065918487073\ 66248983*c_1001_2^4 - 319510408759091397181198844157/24277198131836\ 97414732497966*c_1001_2^3 - 142740103657200911612385447950/12138599\ 06591848707366248983*c_1001_2^2 - 32747516438726812401708339017/121\ 3859906591848707366248983*c_1001_2 - 50571162971278467168325916965/2427719813183697414732497966, c_0101_1 - 15860272619631927405642163/346817116169099630676071138*c_100\ 1_2^19 - 152283292383922771993958555/186747677937207493440961382*c_\ 1001_2^18 - 3994382031325912843114979505/24277198131836974147324979\ 66*c_1001_2^17 - 17881099690820083336586469407/12138599065918487073\ 66248983*c_1001_2^16 - 42352552300286695716566471471/24277198131836\ 97414732497966*c_1001_2^15 - 224802682463208783625399590095/2427719\ 813183697414732497966*c_1001_2^14 - 79247469858931731951494446657/1213859906591848707366248983*c_1001_2\ ^13 - 319447597347348066401576227216/1213859906591848707366248983*c\ _1001_2^12 - 73975947873618032861318419276/121385990659184870736624\ 8983*c_1001_2^11 - 126168989728626000720112949401/34681711616909963\ 0676071138*c_1001_2^10 + 318199372216230601679882759587/24277198131\ 83697414732497966*c_1001_2^9 - 25716446123499206712649632895/933738\ 38968603746720480691*c_1001_2^8 + 49901315078585129453496255722/173\ 408558084549815338035569*c_1001_2^7 - 433535011384297062309470864751/2427719813183697414732497966*c_1001_\ 2^6 + 231372664739799860829330759016/1213859906591848707366248983*c\ _1001_2^5 - 173192043618987637816973408919/121385990659184870736624\ 8983*c_1001_2^4 + 115882671987732309380296296443/242771981318369741\ 4732497966*c_1001_2^3 - 177828029451775822459561469861/242771981318\ 3697414732497966*c_1001_2^2 + 8490480930692672897257269311/24277198\ 13183697414732497966*c_1001_2 - 16238848971295651371975314695/12138\ 59906591848707366248983, c_0101_3 + 298954861407992861222855076/173408558084549815338035569*c_10\ 01_2^19 + 625400249533713431215882489/186747677937207493440961382*c\ _1001_2^18 + 78937192620005120611828335307/242771981318369741473249\ 7966*c_1001_2^17 + 131090704563651221840127407777/24277198131836974\ 14732497966*c_1001_2^16 + 260895602258387533935122304781/1213859906\ 591848707366248983*c_1001_2^15 + 663221755395620887655557731799/242\ 7719813183697414732497966*c_1001_2^14 + 1503429898985296755274847225951/2427719813183697414732497966*c_1001\ _2^13 + 640062865698945499470143591941/1213859906591848707366248983\ *c_1001_2^12 + 904251893675288989492027909184/121385990659184870736\ 6248983*c_1001_2^11 + 49335159608143021614991667654/173408558084549\ 815338035569*c_1001_2^10 + 505661004282598182267636820731/242771981\ 3183697414732497966*c_1001_2^9 - 19194734448156876525040213469/1867\ 47677937207493440961382*c_1001_2^8 - 27690679287332717358500744711/173408558084549815338035569*c_1001_2^\ 7 - 23641292507435580369751320607/1213859906591848707366248983*c_10\ 01_2^6 - 83000874015930989383711770001/2427719813183697414732497966\ *c_1001_2^5 + 191856211067400242550998484344/1213859906591848707366\ 248983*c_1001_2^4 + 61024146861050888456996567692/12138599065918487\ 07366248983*c_1001_2^3 + 240482781831574162045595682299/24277198131\ 83697414732497966*c_1001_2^2 + 33215088582746416643598550371/242771\ 9813183697414732497966*c_1001_2 + 38684905673397221414780825033/242\ 7719813183697414732497966, c_0101_5 - 427411483378998852156409893/346817116169099630676071138*c_10\ 01_2^19 - 256188679998279149013706252/93373838968603746720480691*c_\ 1001_2^18 - 28853733007243788094317467658/1213859906591848707366248\ 983*c_1001_2^17 - 108937168996366147782692731437/242771981318369741\ 4732497966*c_1001_2^16 - 392443660107321884514877213635/24277198131\ 83697414732497966*c_1001_2^15 - 283655930456807634219686797235/1213\ 859906591848707366248983*c_1001_2^14 - 1160466329571456473363272231947/2427719813183697414732497966*c_1001\ _2^13 - 578481080456857064235401878723/1213859906591848707366248983\ *c_1001_2^12 - 703609566437361453534694223360/121385990659184870736\ 6248983*c_1001_2^11 - 106803963517435504484330682485/34681711616909\ 9630676071138*c_1001_2^10 - 159221481084564442637878685406/12138599\ 06591848707366248983*c_1001_2^9 + 7640330206956724036685956935/1867\ 47677937207493440961382*c_1001_2^8 + 28845950191907947075608814465/173408558084549815338035569*c_1001_2^\ 7 + 13822164093391466086387712869/2427719813183697414732497966*c_10\ 01_2^6 + 95851750185556908676560932665/2427719813183697414732497966\ *c_1001_2^5 - 164259033669885687459516944955/1213859906591848707366\ 248983*c_1001_2^4 - 111560936307819640421985404291/2427719813183697\ 414732497966*c_1001_2^3 - 100831422994030069493886694904/1213859906\ 591848707366248983*c_1001_2^2 - 17052570353095056140521971816/12138\ 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