Magma V2.19-8 Tue Aug 20 2013 16:17:49 on localhost [Seed = 2732801600] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v2060 geometric_solution 5.58292224 oriented_manifold CS_known -0.0000000000000004 1 0 torus 0.000000000000 0.000000000000 7 1 0 0 2 0132 3201 2310 0132 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 0 0 0 0 -1 1 0 0 0 1 -1 1 -1 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.844364021196 0.912402554394 0 3 5 4 0132 0132 0132 0132 0 0 0 0 0 -1 0 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 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 -0.144463103460 0.658767049548 4 6 0 5 3012 0132 0132 3012 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 -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 0.224134240649 0.804414837184 5 1 3 3 1230 0132 2031 1302 0 0 0 0 0 1 -1 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 0.693462458610 1.242158115541 6 5 1 2 3012 2031 0132 1230 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 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 -0.431917511069 0.299886615072 4 3 2 1 1302 3012 1230 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 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.271835920780 1.679813376252 6 2 6 4 2031 0132 1302 1230 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.376670076967 0.726734123119 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 's_3_1' : negation(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_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_1_6' : d['1'], 's_1_5' : negation(d['1']), 's_1_4' : negation(d['1']), 's_1_3' : negation(d['1']), 's_1_2' : d['1'], 's_1_1' : negation(d['1']), 's_1_0' : negation(d['1']), 's_0_6' : d['1'], 's_0_4' : d['1'], 's_0_5' : negation(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_6' : d['c_0011_2'], 'c_1100_5' : d['c_0110_2'], 'c_1100_4' : d['c_0110_2'], 's_3_6' : d['1'], 'c_1100_1' : d['c_0110_2'], 'c_1100_0' : d['c_0011_0'], 'c_1100_3' : d['c_0101_3'], 'c_1100_2' : d['c_0011_0'], 'c_0101_6' : d['c_0011_2'], 'c_0101_5' : negation(d['c_0011_4']), 'c_0101_4' : d['c_0101_0'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0011_5'], 'c_0101_1' : d['c_0011_5'], 'c_0101_0' : d['c_0101_0'], 'c_0011_5' : d['c_0011_5'], 'c_0011_4' : d['c_0011_4'], 'c_0011_6' : negation(d['c_0011_2']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_0'], 'c_0011_2' : d['c_0011_2'], 'c_1001_5' : negation(d['c_0011_0']), 'c_1001_4' : negation(d['c_0011_5']), 'c_1001_6' : d['c_0011_4'], 'c_1001_1' : negation(d['c_0101_3']), 'c_1001_0' : negation(d['c_0101_0']), 'c_1001_3' : negation(d['c_0011_5']), 'c_1001_2' : d['c_0101_0'], 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0011_5'], 'c_0110_3' : d['c_0011_5'], 'c_0110_2' : d['c_0110_2'], 'c_0110_5' : d['c_0011_5'], 'c_0110_4' : d['c_0011_2'], 'c_0110_6' : d['c_0011_4'], 'c_1010_6' : d['c_0101_0'], 'c_1010_5' : negation(d['c_0101_3']), 'c_1010_4' : d['c_0011_5'], 'c_1010_3' : negation(d['c_0101_3']), 'c_1010_2' : d['c_0011_4'], 'c_1010_1' : negation(d['c_0011_5']), 'c_1010_0' : 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_2, c_0011_4, c_0011_5, c_0101_0, c_0101_3, c_0110_2 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 23 Groebner basis: [ t - 440876552844834895204214767113451645654515024830259/111013651981283\ 44794314248000786110818954138428096*c_0110_2^22 - 3575118272741194827152866388044671425968107298117067/11101365198128\ 344794314248000786110818954138428096*c_0110_2^21 - 2495900037789554776770014007857460444600453041914949/27753412995320\ 86198578562000196527704738534607024*c_0110_2^20 + 48187777805646833288576019023598837338305135147448/1734588312207553\ 87411160125012282981546158412939*c_0110_2^19 + 65954705756196954947070303501915560282883041671384331/5550682599064\ 172397157124000393055409477069214048*c_0110_2^18 + 596736765164048901992943456465632184788966940503130971/111013651981\ 28344794314248000786110818954138428096*c_0110_2^17 + 842954995213236043878451927070971764273859348347535883/555068259906\ 4172397157124000393055409477069214048*c_0110_2^16 + 3544486526804953329360804577102090338210068696814181407/11101365198\ 128344794314248000786110818954138428096*c_0110_2^15 + 2891227089357037302978504701711782962193304370003873883/55506825990\ 64172397157124000393055409477069214048*c_0110_2^14 + 7160207259355693183665928329801691243924484674865825023/11101365198\ 128344794314248000786110818954138428096*c_0110_2^13 + 6084261088083961937609419325265194869858837784730916505/11101365198\ 128344794314248000786110818954138428096*c_0110_2^12 + 484023325771368138362577311420713461891146323637868201/277534129953\ 2086198578562000196527704738534607024*c_0110_2^11 - 951837620344743384141234458256771956931111510658296159/277534129953\ 2086198578562000196527704738534607024*c_0110_2^10 - 8262174814850860014870809023288174560026418444021845991/11101365198\ 128344794314248000786110818954138428096*c_0110_2^9 - 213077068585143285600235801938536418591102229678013259/252303754502\ 916927143505636381502518612594055184*c_0110_2^8 - 7356300600580392998014571130714256569296633315270340727/11101365198\ 128344794314248000786110818954138428096*c_0110_2^7 - 4145994057517455247307869639466676420013403839915084187/11101365198\ 128344794314248000786110818954138428096*c_0110_2^6 - 1602937901453712442596072803147179281019881871685378745/11101365198\ 128344794314248000786110818954138428096*c_0110_2^5 - 175346069235090535093132059336809445377100106394794767/555068259906\ 4172397157124000393055409477069214048*c_0110_2^4 + 2072708309205014664709771683662438292228271161170553/55506825990641\ 72397157124000393055409477069214048*c_0110_2^3 + 6945542317920097623157412748431468355822889230452869/27753412995320\ 86198578562000196527704738534607024*c_0110_2^2 + 7372208254945433103718651842131895784912811307536179/11101365198128\ 344794314248000786110818954138428096*c_0110_2 + 490651616023444234928947041104445420424471378021105/111013651981283\ 44794314248000786110818954138428096, c_0011_0 - 1, c_0011_2 - 3050855394543299683135366638531830531749983680887/2775341299\ 532086198578562000196527704738534607024*c_0110_2^22 - 24192112944234236643609521369004299658357838159677/2775341299532086\ 198578562000196527704738534607024*c_0110_2^21 - 32262124605897671425903798369191849843890008370273/1387670649766043\ 099289281000098263852369267303512*c_0110_2^20 + 17191317499665159326579498990302859641359063537385/1387670649766043\ 099289281000098263852369267303512*c_0110_2^19 + 56838293229096778459454837623976756795217675636984/1734588312207553\ 87411160125012282981546158412939*c_0110_2^18 + 3960294344222779386939561557062091488814442102752749/27753412995320\ 86198578562000196527704738534607024*c_0110_2^17 + 5449318514515344658660763185655892099577965816469063/13876706497660\ 43099289281000098263852369267303512*c_0110_2^16 + 22361035716778594824580437246125534336418335935151613/2775341299532\ 086198578562000196527704738534607024*c_0110_2^15 + 8870239299971548961690078732662203128686522637836615/69383532488302\ 1549644640500049131926184633651756*c_0110_2^14 + 42197183719837866263081997738780594591324104675942257/2775341299532\ 086198578562000196527704738534607024*c_0110_2^13 + 33100621659469856870639259291126139374521151863674713/2775341299532\ 086198578562000196527704738534607024*c_0110_2^12 + 1485739849204306025353467576962364299963247879669251/69383532488302\ 1549644640500049131926184633651756*c_0110_2^11 - 3548597001729421185281334445532601614031192992160671/34691766244151\ 0774822320250024565963092316825878*c_0110_2^10 - 51947053572700154612459204465491048073380561740320699/2775341299532\ 086198578562000196527704738534607024*c_0110_2^9 - 2466694457381840409207057807069238461608665435439281/12615187725145\ 8463571752818190751259306297027592*c_0110_2^8 - 39229873008176693337555606647213519179615223913109619/2775341299532\ 086198578562000196527704738534607024*c_0110_2^7 - 19781770844510444454600200582085599414820567380622079/2775341299532\ 086198578562000196527704738534607024*c_0110_2^6 - 6261374760624044393701887018985347868463204992975587/27753412995320\ 86198578562000196527704738534607024*c_0110_2^5 - 40748346017789217087540238052848990381465771123333/1734588312207553\ 87411160125012282981546158412939*c_0110_2^4 + 45974552265556900459981332900573783355508634600913/3469176624415107\ 74822320250024565963092316825878*c_0110_2^3 + 85438598598972859750779777752220132307666644075311/1387670649766043\ 099289281000098263852369267303512*c_0110_2^2 + 17187447607710054932177289072901221234758023461677/2775341299532086\ 198578562000196527704738534607024*c_0110_2 - 4159582248193059870747173368607903476893851799707/27753412995320861\ 98578562000196527704738534607024, c_0011_4 + 784735459962583460113903485797046416808205915321/69383532488\ 3021549644640500049131926184633651756*c_0110_2^22 + 3349693047166830998218494108264186333311093917767/34691766244151077\ 4822320250024565963092316825878*c_0110_2^21 + 20194204805126213835014310909401417612231252474547/6938353248830215\ 49644640500049131926184633651756*c_0110_2^20 - 54326291832646827390614992706938116559351714247/6938353248830215496\ 44640500049131926184633651756*c_0110_2^19 - 241990972193316571544712584533215560884234933020091/693835324883021\ 549644640500049131926184633651756*c_0110_2^18 - 577989928725495467331784909997445245639905634858683/346917662441510\ 774822320250024565963092316825878*c_0110_2^17 - 842720923837680550369176802153898386654139364039107/173458831220755\ 387411160125012282981546158412939*c_0110_2^16 - 3631360367259290012527310939832242064739439287202085/34691766244151\ 0774822320250024565963092316825878*c_0110_2^15 - 12148046204617622595299278578990659652802134749167763/6938353248830\ 21549644640500049131926184633651756*c_0110_2^14 - 3881142304215828893110942183760548722753368549102997/17345883122075\ 5387411160125012282981546158412939*c_0110_2^13 - 13884140728443344289611083728497922264061999613853829/6938353248830\ 21549644640500049131926184633651756*c_0110_2^12 - 1377553247891781002232757845928653641640754355921993/17345883122075\ 5387411160125012282981546158412939*c_0110_2^11 + 3460970235780612903781494942841459279374585199955115/34691766244151\ 0774822320250024565963092316825878*c_0110_2^10 + 17262169085764733449699623156986096338746516039577921/6938353248830\ 21549644640500049131926184633651756*c_0110_2^9 + 1873236843983325305614623575285518545276253867556153/63075938625729\ 231785876409095375629653148513796*c_0110_2^8 + 16842405454548111056552174751078502159619863668333671/6938353248830\ 21549644640500049131926184633651756*c_0110_2^7 + 9901464100378507352621083530934867488136294248933303/69383532488302\ 1549644640500049131926184633651756*c_0110_2^6 + 2029179158250243150440458581102951047996735225705243/34691766244151\ 0774822320250024565963092316825878*c_0110_2^5 + 990931697968432830440139139853199286968301446484597/693835324883021\ 549644640500049131926184633651756*c_0110_2^4 + 36323304930209805870094667941838565732279492178287/6938353248830215\ 49644640500049131926184633651756*c_0110_2^3 - 64503211458249940640810286536275983647764645374771/6938353248830215\ 49644640500049131926184633651756*c_0110_2^2 - 5124872781203257384668398673230200848770243469657/17345883122075538\ 7411160125012282981546158412939*c_0110_2 - 977736168247391992310619908000373765862938062479/693835324883021549\ 644640500049131926184633651756, c_0011_5 - 3929286066854356654409136229542311619090091339/9520896396336\ 487816736061750245378060852605856*c_0110_2^22 - 27994823129368429768091466871166461655481851325/9520896396336487816\ 736061750245378060852605856*c_0110_2^21 - 1842915396133309840799845693719690914342995133/29752801238551524427\ 3001929695168064401643933*c_0110_2^20 + 26169915392188790499932893127114468188395503201/2380224099084121954\ 184015437561344515213151464*c_0110_2^19 + 561272267422375683932322198280884130566819286049/476044819816824390\ 8368030875122689030426302928*c_0110_2^18 + 4181903561875339425940475126914052144535272930379/95208963963364878\ 16736061750245378060852605856*c_0110_2^17 + 636546972028207756343631550238003250938418713883/595056024771030488\ 546003859390336128803287866*c_0110_2^16 + 18455884795152584597124576359291007174513908970117/9520896396336487\ 816736061750245378060852605856*c_0110_2^15 + 12449278340324069837792528673261473384763065581775/4760448198168243\ 908368030875122689030426302928*c_0110_2^14 + 22085267859624754685133041216432830382161147309515/9520896396336487\ 816736061750245378060852605856*c_0110_2^13 + 5459827348152975217988870559177122523607562159023/95208963963364878\ 16736061750245378060852605856*c_0110_2^12 - 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