Magma V2.19-8 Tue Aug 20 2013 16:18:07 on localhost [Seed = 3953817390] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v2341 geometric_solution 5.72395667 oriented_manifold CS_known -0.0000000000000003 1 0 torus 0.000000000000 0.000000000000 7 0 0 1 2 1230 3012 0132 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 1 0 -1 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 0.480687474601 0.776251324031 3 4 2 0 0132 0132 2031 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 0 0 0 0 1 -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 0.487852160091 0.583868205849 4 3 0 1 2310 3201 0132 1302 0 0 0 0 0 -1 1 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 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 0.487852160091 0.583868205849 1 5 2 5 0132 0132 2310 1023 0 0 0 0 0 0 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.901951440060 1.190542756133 6 1 2 6 0132 0132 3201 3201 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0.790994507233 0.584939632217 5 3 5 3 2031 0132 1302 1023 0 0 0 0 0 0 0 0 0 0 1 -1 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.474414685678 0.194729412056 4 4 6 6 0132 2310 1230 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.638008244395 0.473649594126 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 's_3_1' : d['1'], 's_3_3' : d['1'], 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : d['1'], 's_3_0' : 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' : d['1'], 's_2_5' : d['1'], 's_2_6' : 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_0_6' : 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_6' : d['c_0101_4'], 'c_1100_5' : negation(d['c_0011_1']), 'c_1100_4' : negation(d['c_0011_1']), 's_3_6' : d['1'], 'c_1100_1' : d['c_0101_1'], 'c_1100_0' : d['c_0101_1'], 'c_1100_3' : d['c_0011_1'], 'c_1100_2' : d['c_0101_1'], 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : negation(d['c_0011_1']), 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : d['c_0101_0'], 'c_0101_2' : d['c_0011_0'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0011_5' : d['c_0011_1'], 'c_0011_4' : negation(d['c_0011_1']), 'c_0011_6' : d['c_0011_1'], 'c_0011_1' : d['c_0011_1'], 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : negation(d['c_0011_1']), 'c_0011_2' : d['c_0011_1'], 'c_1001_5' : d['c_0110_5'], 'c_1001_4' : negation(d['c_0011_0']), 'c_1001_6' : negation(d['c_0101_4']), 'c_1001_1' : d['c_0101_4'], 'c_1001_0' : negation(d['c_0011_0']), 'c_1001_3' : d['c_0101_1'], 'c_1001_2' : negation(d['c_0101_0']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0011_0'], 'c_0110_3' : d['c_0101_1'], 'c_0110_2' : negation(d['c_0101_4']), 'c_0110_5' : d['c_0110_5'], 'c_0110_4' : d['c_0101_6'], 'c_0110_6' : d['c_0101_4'], 'c_1010_6' : negation(d['c_0101_6']), 'c_1010_5' : d['c_0101_1'], 'c_1010_4' : d['c_0101_4'], 'c_1010_3' : d['c_0110_5'], 'c_1010_2' : negation(d['c_0101_1']), 'c_1010_1' : negation(d['c_0011_0']), 'c_1010_0' : negation(d['c_0101_0'])})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_1, c_0101_0, c_0101_1, c_0101_4, c_0101_6, c_0110_5 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 28 Groebner basis: [ t + 21649762090056871901497341344908/117951610617805613032405216027*c_0\ 110_5^27 - 38383805173266439827541417857777/11795161061780561303240\ 5216027*c_0110_5^26 - 154632707430959070504069015807944/11795161061\ 7805613032405216027*c_0110_5^25 + 255740801032270484819467163566257\ /117951610617805613032405216027*c_0110_5^24 - 496847314416719750565493885676328/117951610617805613032405216027*c_\ 0110_5^23 - 811453244201533650465609093085939/117951610617805613032\ 405216027*c_0110_5^22 + 1927410700642664334638971103555755/11795161\ 0617805613032405216027*c_0110_5^21 + 830278454383884186478373485628737/16850230088257944718915030861*c_0\ 110_5^20 + 3915715539473029347405647119184730/117951610617805613032\ 405216027*c_0110_5^19 - 3623279345471330904517934071976782/16850230\ 088257944718915030861*c_0110_5^18 - 17577043614594012591826688421787541/117951610617805613032405216027*\ c_0110_5^17 + 54005550876519602731064690626606799/11795161061780561\ 3032405216027*c_0110_5^16 + 29512279134722071711513649611958200/117\ 951610617805613032405216027*c_0110_5^15 - 64056495725778681358488324697075275/117951610617805613032405216027*\ c_0110_5^14 - 45377259717260728886586053279577417/11795161061780561\ 3032405216027*c_0110_5^13 + 46956318157527727947429476961350207/117\ 951610617805613032405216027*c_0110_5^12 + 59749031635939220289099834924603325/117951610617805613032405216027*\ c_0110_5^11 - 22347080453858203349224958961085201/11795161061780561\ 3032405216027*c_0110_5^10 - 51912352054271399363064325440423204/117\ 951610617805613032405216027*c_0110_5^9 + 5460455458664550575942418867025821/117951610617805613032405216027*c\ _0110_5^8 + 27761696078115941247900642902618671/1179516106178056130\ 32405216027*c_0110_5^7 + 947057933404106084702628361144356/11795161\ 0617805613032405216027*c_0110_5^6 - 8749414839501880119442586486665992/117951610617805613032405216027*c\ _0110_5^5 - 1115317194185633690491560283511518/11795161061780561303\ 2405216027*c_0110_5^4 + 1479126590225421935881604992625383/11795161\ 0617805613032405216027*c_0110_5^3 + 287763386737915455900125210583870/117951610617805613032405216027*c_\ 0110_5^2 - 103924710205508287322734854839773/1179516106178056130324\ 05216027*c_0110_5 - 25279939588995136531709505209457/11795161061780\ 5613032405216027, c_0011_0 - 1, c_0011_1 - 191860151517065398833843959755/16850230088257944718915030861\ *c_0110_5^27 + 236829429602544260103133289079/168502300882579447189\ 15030861*c_0110_5^26 + 1569701812832601020697871471736/168502300882\ 57944718915030861*c_0110_5^25 - 1587241213390328952295688699480/168\ 50230088257944718915030861*c_0110_5^24 + 3128957766217749059475308166093/16850230088257944718915030861*c_011\ 0_5^23 + 9939009428407239013609748322806/16850230088257944718915030\ 861*c_0110_5^22 - 13957583760549942335640127911524/1685023008825794\ 4718915030861*c_0110_5^21 - 60436819212916719434233844328856/168502\ 30088257944718915030861*c_0110_5^20 - 60272713503868358554335655974834/16850230088257944718915030861*c_01\ 10_5^19 + 207944790766453576721689756065877/16850230088257944718915\ 030861*c_0110_5^18 + 272524101782812646273336663884582/168502300882\ 57944718915030861*c_0110_5^17 - 418133431862572217783454389951527/1\ 6850230088257944718915030861*c_0110_5^16 - 498819398184062813122522880537995/16850230088257944718915030861*c_0\ 110_5^15 + 480592269905688893719458523350466/1685023008825794471891\ 5030861*c_0110_5^14 + 665115330010313823996223379455871/16850230088\ 257944718915030861*c_0110_5^13 - 266799028208313707117308199032261/\ 16850230088257944718915030861*c_0110_5^12 - 718059470632687218086125062398449/16850230088257944718915030861*c_0\ 110_5^11 - 13522117752169302183048338519462/16850230088257944718915\ 030861*c_0110_5^10 + 560264420894587510257206182576215/168502300882\ 57944718915030861*c_0110_5^9 + 127867928238527201272248705625517/16\ 850230088257944718915030861*c_0110_5^8 - 282902096919879643097622719249376/16850230088257944718915030861*c_0\ 110_5^7 - 92285076396150111917540272165858/168502300882579447189150\ 30861*c_0110_5^6 + 83751816751851127746704071424056/168502300882579\ 44718915030861*c_0110_5^5 + 31401721819052691517276748828976/168502\ 30088257944718915030861*c_0110_5^4 - 12778792578947144105099408113196/16850230088257944718915030861*c_01\ 10_5^3 - 5060212404256642062768620496888/16850230088257944718915030\ 861*c_0110_5^2 + 762321365192290560924795054494/1685023008825794471\ 8915030861*c_0110_5 + 293664124568637484393234878643/16850230088257\ 944718915030861, c_0101_0 - 438120606650167690919031650460/16850230088257944718915030861\ *c_0110_5^27 + 631640366960012534034024516406/168502300882579447189\ 15030861*c_0110_5^26 + 3390243136632581741387821462768/168502300882\ 57944718915030861*c_0110_5^25 - 4173440803962105512715043813737/168\ 50230088257944718915030861*c_0110_5^24 + 8351558791971393757934895519517/16850230088257944718915030861*c_011\ 0_5^23 + 20016276432380658506249389421710/1685023008825794471891503\ 0861*c_0110_5^22 - 33905716648333956691917009942266/168502300882579\ 44718915030861*c_0110_5^21 - 130135240268000814619085502840912/1685\ 0230088257944718915030861*c_0110_5^20 - 116482700633331388466807663473108/16850230088257944718915030861*c_0\ 110_5^19 + 485816913084448394202013394263902/1685023008825794471891\ 5030861*c_0110_5^18 + 518235987940412647251042861431667/16850230088\ 257944718915030861*c_0110_5^17 - 987671597166551138958951465610161/\ 16850230088257944718915030861*c_0110_5^16 - 932781541844975776287949266181703/16850230088257944718915030861*c_0\ 110_5^15 + 1141662509536311517745763871441672/168502300882579447189\ 15030861*c_0110_5^14 + 1292148301372644540680201480648197/168502300\ 88257944718915030861*c_0110_5^13 - 710793936143454368322027340539960/16850230088257944718915030861*c_0\ 110_5^12 - 1465448581388919124644146410447458/168502300882579447189\ 15030861*c_0110_5^11 + 129194189723974194942799480890977/1685023008\ 8257944718915030861*c_0110_5^10 + 117539527918268982452398951583728\ 7/16850230088257944718915030861*c_0110_5^9 + 154966970575298039011640307526110/16850230088257944718915030861*c_0\ 110_5^8 - 602683290014150690898306996466212/16850230088257944718915\ 030861*c_0110_5^7 - 144633768504455845675298238993626/1685023008825\ 7944718915030861*c_0110_5^6 + 181603655400566050968925811449878/168\ 50230088257944718915030861*c_0110_5^5 + 54947015929071416773973080769701/16850230088257944718915030861*c_01\ 10_5^4 - 28734045614230983573474670671823/1685023008825794471891503\ 0861*c_0110_5^3 - 9909545702530314946977596829051/16850230088257944\ 718915030861*c_0110_5^2 + 1865054216041813192365743668077/168502300\ 88257944718915030861*c_0110_5 + 680309311200952428594380986914/1685\ 0230088257944718915030861, c_0101_1 - 286433146712841331881724793509/16850230088257944718915030861\ *c_0110_5^27 + 397340192232477024998025984557/168502300882579447189\ 15030861*c_0110_5^26 + 2278858066996094084397614654725/168502300882\ 57944718915030861*c_0110_5^25 - 2674629595500474660052106372063/168\ 50230088257944718915030861*c_0110_5^24 + 5036487306304049414082819862819/16850230088257944718915030861*c_011\ 0_5^23 + 13795461742585170034221258961149/1685023008825794471891503\ 0861*c_0110_5^22 - 22425710738181962936816798180835/168502300882579\ 44718915030861*c_0110_5^21 - 87683690723255401061699087418282/16850\ 230088257944718915030861*c_0110_5^20 - 77865354909180767465395684024622/16850230088257944718915030861*c_01\ 10_5^19 + 324128884196502438355619557708118/16850230088257944718915\ 030861*c_0110_5^18 + 365484529121220509087650012892025/168502300882\ 57944718915030861*c_0110_5^17 - 669151183898386250576571267013589/1\ 6850230088257944718915030861*c_0110_5^16 - 678547261715206083302052148620335/16850230088257944718915030861*c_0\ 110_5^15 + 792241037726235630800390879403639/1685023008825794471891\ 5030861*c_0110_5^14 + 940095640352081226825765381393188/16850230088\ 257944718915030861*c_0110_5^13 - 502047745802812609568462269451241/\ 16850230088257944718915030861*c_0110_5^12 - 1062699306081183015480029874322822/16850230088257944718915030861*c_\ 0110_5^11 + 82709103713040662387418538730738/1685023008825794471891\ 5030861*c_0110_5^10 + 864199561978815002511579205060622/16850230088\ 257944718915030861*c_0110_5^9 + 129944845462276158902553572477465/1\ 6850230088257944718915030861*c_0110_5^8 - 456745685267345697465704570014471/16850230088257944718915030861*c_0\ 110_5^7 - 119831441007567955164930032191761/16850230088257944718915\ 030861*c_0110_5^6 + 144037368322410852640036465742903/1685023008825\ 7944718915030861*c_0110_5^5 + 46654540858471072489837740457606/1685\ 0230088257944718915030861*c_0110_5^4 - 23973187673118667317727897359001/16850230088257944718915030861*c_01\ 10_5^3 - 8599780913398585151303169886546/16850230088257944718915030\ 861*c_0110_5^2 + 1602323300440388461289986351015/168502300882579447\ 18915030861*c_0110_5 + 592155804711451449870112842211/1685023008825\ 7944718915030861, c_0101_4 + 28752850056154691936743354249/16850230088257944718915030861*\ c_0110_5^27 - 105038694599138420133879056082/1685023008825794471891\ 5030861*c_0110_5^26 - 141757064744883966814390034573/16850230088257\ 944718915030861*c_0110_5^25 + 771998153867639302808105220158/168502\ 30088257944718915030861*c_0110_5^24 - 1055214658458796068928583778499/16850230088257944718915030861*c_011\ 0_5^23 - 136635564719602955046029203120/168502300882579447189150308\ 61*c_0110_5^22 + 5259995236246207315782985730109/168502300882579447\ 18915030861*c_0110_5^21 + 4336562853885392476552855227151/168502300\ 88257944718915030861*c_0110_5^20 - 11725846536883296574303782543485/16850230088257944718915030861*c_01\ 10_5^19 - 52591691263777703989968946510329/168502300882579447189150\ 30861*c_0110_5^18 + 30792451804855928669768780459708/16850230088257\ 944718915030861*c_0110_5^17 + 149099347809371815417828060885565/168\ 50230088257944718915030861*c_0110_5^16 - 59763382759443603750209242769430/16850230088257944718915030861*c_01\ 10_5^15 - 224116627713422802626231996080862/16850230088257944718915\ 030861*c_0110_5^14 + 42432888269557486156088756812032/1685023008825\ 7944718915030861*c_0110_5^13 + 243141850041852796107847062620625/16\ 850230088257944718915030861*c_0110_5^12 + 38419791988790688707239376607140/16850230088257944718915030861*c_01\ 10_5^11 - 211693806862072683408785649446161/16850230088257944718915\ 030861*c_0110_5^10 - 98475662926743514687960370902014/1685023008825\ 7944718915030861*c_0110_5^9 + 136691775720036025163709701359796/168\ 50230088257944718915030861*c_0110_5^8 + 84810066118980879921825156384615/16850230088257944718915030861*c_01\ 10_5^7 - 56861803702529694627989613766193/1685023008825794471891503\ 0861*c_0110_5^6 - 38877062035475313915853516743248/1685023008825794\ 4718915030861*c_0110_5^5 + 12639114947488518981828173833564/1685023\ 0088257944718915030861*c_0110_5^4 + 9143082521320710494527976221448/16850230088257944718915030861*c_011\ 0_5^3 - 1063574460544758009033390269758/168502300882579447189150308\ 61*c_0110_5^2 - 844707264962525524276074276789/16850230088257944718\ 915030861*c_0110_5 - 9636057606253654184008577413/16850230088257944\ 718915030861, c_0101_6 + 184498186675269268645944370091/16850230088257944718915030861\ *c_0110_5^27 - 349051001175674182639964001512/168502300882579447189\ 15030861*c_0110_5^26 - 1276156396395117975221147817814/168502300882\ 57944718915030861*c_0110_5^25 + 2346992086498244262050726363007/168\ 50230088257944718915030861*c_0110_5^24 - 4546815318331916108746235326852/16850230088257944718915030861*c_011\ 0_5^23 - 6469250892980113838868841993387/16850230088257944718915030\ 861*c_0110_5^22 + 17394496878244860593775651294428/1685023008825794\ 4718915030861*c_0110_5^21 + 46976400332917739385725961929025/168502\ 30088257944718915030861*c_0110_5^20 + 27412777685790339184537385183160/16850230088257944718915030861*c_01\ 10_5^19 - 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