Magma V2.19-8 Tue Aug 20 2013 16:17:46 on localhost [Seed = 3170705503] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v2010 geometric_solution 5.56208712 oriented_manifold CS_known -0.0000000000000003 1 0 torus 0.000000000000 0.000000000000 7 1 2 2 3 0132 0132 1023 0132 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0.112616714676 0.507655880208 0 4 5 3 0132 0132 0132 0321 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 -1 1 -1 0 1 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 0.726601570224 1.124291022701 2 0 0 2 3201 0132 1023 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 -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 1.701596362522 0.781230021051 5 1 0 4 2310 0321 0132 2310 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 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 0.726601570224 1.124291022701 3 1 4 4 3201 0132 2031 1302 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 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 0.441298157487 0.389624759380 6 6 3 1 0132 2310 3201 0132 0 0 0 0 0 -1 0 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 -1 0 1 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 0.482844596241 1.305665568792 5 6 6 5 0132 3201 2310 3201 0 0 0 0 0 -1 1 0 0 0 0 0 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 -1 1 0 0 0 0 0 0 -1 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.695523281368 0.484349202997 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { '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_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' : negation(d['c_0011_5']), 'c_1100_5' : negation(d['c_0011_3']), 'c_1100_4' : d['c_0101_4'], 's_3_6' : d['1'], 'c_1100_1' : negation(d['c_0011_3']), 'c_1100_0' : d['c_0011_0'], 'c_1100_3' : d['c_0011_0'], 'c_1100_2' : negation(d['c_0011_0']), 'c_0101_6' : d['c_0101_1'], 'c_0101_5' : d['c_0101_4'], 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : d['c_0101_1'], 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : negation(d['c_0011_3']), 'c_0011_5' : d['c_0011_5'], 'c_0011_4' : d['c_0011_0'], 'c_0011_6' : negation(d['c_0011_5']), '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_1001_5' : negation(d['c_0101_1']), 'c_1001_4' : negation(d['c_0110_4']), 'c_1001_6' : negation(d['c_0101_1']), 'c_1001_1' : negation(d['c_0101_4']), 'c_1001_0' : d['c_0101_2'], 'c_1001_3' : negation(d['c_0011_3']), 'c_1001_2' : negation(d['c_0011_3']), 'c_0110_1' : negation(d['c_0011_3']), 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : negation(d['c_0101_4']), 'c_0110_2' : negation(d['c_0101_2']), 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : d['c_0110_4'], 'c_0110_6' : d['c_0101_4'], 'c_1010_6' : d['c_0101_1'], 'c_1010_5' : negation(d['c_0101_4']), 'c_1010_4' : negation(d['c_0101_4']), 'c_1010_3' : negation(d['c_0110_4']), 'c_1010_2' : d['c_0101_2'], 'c_1010_1' : negation(d['c_0110_4']), 'c_1010_0' : negation(d['c_0011_3'])})} 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_3, c_0011_5, c_0101_1, c_0101_2, c_0101_4, c_0110_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 33 Groebner basis: [ t - 3525238771697330777968653765150838163652376284834208889/15575276422\ 0584742810803867247524701363251505398655207*c_0110_4^32 + 44364324744912668982855039700811852262329191291860097828/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^31 - 143624623505706507772560119101496148246981017458083281747/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^30 + 230552989924439635273710973438389456469225995514179539685/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^29 - 427352141845711229921288317244109526175533434971586215678/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^28 + 59952645651775008534338951232702243433429926657057997838/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^27 + 876076681208871053737914808165830659456308858475458150630/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^26 - 12293796912748869553164856293003640951339979910170471558/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^25 + 2138660646676435630143441306411080442655364527709889274054/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^24 - 5776152180178163149259263628230078246387679946755243157803/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^23 + 5863604564242266270362097810846012702238876933817516910846/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^22 - 10438714933002502376886137308180197628427760202354427051297/1557527\ 64220584742810803867247524701363251505398655207*c_0110_4^21 + 4270256106612001189553177231260417228575103227568408984866/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^20 + 5883823049439228508340198789250144329001740255798134471753/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^19 - 10579382176245960762817112099539470115657090547147665388699/1557527\ 64220584742810803867247524701363251505398655207*c_0110_4^18 + 22625763800774108719138308359628354038623403880929330684723/1557527\ 64220584742810803867247524701363251505398655207*c_0110_4^17 - 16845416448467982566983700943486514064824526523968279616146/1557527\ 64220584742810803867247524701363251505398655207*c_0110_4^16 + 9447629187356726688172219161418387550738757271886473020681/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^15 - 4211047650414277952856216164882135356361494912172240333965/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^14 - 5999271713613241139031583798964730670368099669565341443881/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^13 + 4400771687071273920289008890033553144509457296387636644878/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^12 - 4283588699256153539057632235886365255831541680924817777203/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^11 + 2707563276458904196975327228274524661556995271165602731231/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^10 - 449823700405390160511153432076128001046148732478116270318/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^9 + 961338514302997249437707670752895456181324122329769813367/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^8 - 624114775489287034567298475169413767483865721941461185286/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^7 + 833053089141324217965536741829827298918327213062664181957/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^6 - 726495245779355551666541676915304796150180111283454711839/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^5 + 422307269259633742918685929876229907446792645767942911376/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^4 - 243564319149319204749789377585018877376083422965238742394/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^3 + 85958290037485997533221642378989383215175607065596494416/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^2 - 29361011243096405043367174620905456871840550491816476311/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4 + 6705222813873878211360061545838778766005241051410865378/15575276422\ 0584742810803867247524701363251505398655207, c_0011_0 - 1, c_0011_3 + 245138508602807044665435472567982288231341181516644054/15575\ 2764220584742810803867247524701363251505398655207*c_0110_4^32 - 2980765612964547983662393020062556405723335345485104340/15575276422\ 0584742810803867247524701363251505398655207*c_0110_4^31 + 8650925096446873391268833860191487012249057066069950413/15575276422\ 0584742810803867247524701363251505398655207*c_0110_4^30 - 11496280269462904146666356638754967925346963454806051917/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^29 + 22172168512599239416743600815814557543456463405481375554/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^28 + 9029130929272547411959929433525366400657535823168985037/15575276422\ 0584742810803867247524701363251505398655207*c_0110_4^27 - 63808766907581077679317844968397100230019617534645825919/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^26 - 27517362078173343589700665924366870182453252100651467474/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^25 - 140874981568163675010375864530116135421208690540530248320/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^24 + 345207976603916282926328701675425618971513543843154660890/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^23 - 227142929941371256069806931409726804918767905923327109161/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^22 + 518872290926749941136803097864662259300328803157386901514/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^21 + 9084061299733714751164383104365377986288388705284958064/15575276422\ 0584742810803867247524701363251505398655207*c_0110_4^20 - 551697374770008278089819354540713964620338900720784218044/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^19 + 532731307571448594320230574612729811695679319133500878148/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^18 - 1173106189477251284401777471227477469031128311850742463965/15575276\ 4220584742810803867247524701363251505398655207*c_0110_4^17 + 486361783637445998315158619000939676851153934449796530335/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^16 - 112776390571124764256210734923433587130841598605397802409/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^15 + 36047580604911659335361182042599412592765214103053948425/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^14 + 460560545502785158857128826179157823889132427595825625668/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^13 - 121909005281044058005588649393792709834836123808519685467/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^12 + 132632074093446535660489687701067062454440141294145449822/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^11 - 64341869629005061997494981982322891992247903260161912538/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^10 - 24836851507895866272223766343691297497306291768328978572/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^9 - 50253576947096272634723060659605314309242723917089320862/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^8 + 24155472592595306514471460307893300744899371209085587234/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^7 - 36483862437267396775000583078375874385057568395734995781/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^6 + 22471385856211363364142806930192032462952314312424085889/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^5 - 9811624054937710163288311745297487873170656442785537165/15575276422\ 0584742810803867247524701363251505398655207*c_0110_4^4 + 4413183256257948865071094432023345012287894081759669975/15575276422\ 0584742810803867247524701363251505398655207*c_0110_4^3 - 539916468920798143310424539397384968424275593083861805/155752764220\ 584742810803867247524701363251505398655207*c_0110_4^2 + 288950860850777808357003722292107439094109944272772971/155752764220\ 584742810803867247524701363251505398655207*c_0110_4 + 80056870710327441703651047471901267489370046714514175/1557527642205\ 84742810803867247524701363251505398655207, c_0011_5 - 307772390932083399671385038941789872199247397441291509/15575\ 2764220584742810803867247524701363251505398655207*c_0110_4^32 + 3667778983558472230826371574857472193062747291954584885/15575276422\ 0584742810803867247524701363251505398655207*c_0110_4^31 - 10078378441417281529119303121497275010738056637513253345/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^30 + 13282281522125889696066282071024551461176483355321106516/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^29 - 28397507402139556638854252018859251048170147200909867425/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^28 - 13079476482296242609890360177793864405744620598339909692/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^27 + 67062418906185206377968870177300882575787927836601944552/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^26 + 47312485129002380914851649577465487968924974987313985216/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^25 + 215590343670928863040347533576081019192483990599856364159/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^24 - 370557566472189771610168832878255060380466861800123392860/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^23 + 257184044374782381483218983981078879983056267277051352081/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^22 - 738218396338778344086553392849049754353773431742244990220/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^21 - 83565754334084701197011878335148498782180322655935404798/1557527642\ 20584742810803867247524701363251505398655207*c_0110_4^20 + 440039044543203640147363892944199867067357277265187595323/155752764\ 220584742810803867247524701363251505398655207*c_0110_4^19 - 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