Magma V2.19-8 Tue Aug 20 2013 16:16:07 on localhost [Seed = 1646526125] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v0375 geometric_solution 4.43100833 oriented_manifold CS_known 0.0000000000000007 1 0 torus 0.000000000000 0.000000000000 7 1 1 2 2 0132 2310 0132 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.460567347412 0.540573731347 0 1 1 0 0132 3201 2310 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.532726100628 0.041357681067 0 3 3 0 3201 0132 3201 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 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 -0.588817997903 0.461365566638 2 2 4 5 2310 0132 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 1 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 0.197047480202 0.470646786868 6 5 5 3 0132 3012 2031 0132 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 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 0.772671501595 0.846130484205 4 6 3 4 1230 2310 0132 1302 0 0 0 0 0 0 -1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.772671501595 0.846130484205 4 6 6 5 0132 3201 2310 3201 0 0 0 0 0 -1 0 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 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 0.296149092738 1.102284918052 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 's_3_1' : d['1'], 's_3_3' : negation(d['1']), 's_3_2' : d['1'], 's_3_5' : negation(d['1']), 's_3_4' : negation(d['1']), 's_3_0' : d['1'], 's_2_0' : d['1'], 's_2_1' : negation(d['1']), 's_2_2' : d['1'], 's_2_3' : negation(d['1']), 's_2_4' : negation(d['1']), 's_2_5' : negation(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' : negation(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_4']), 'c_1100_5' : d['c_0101_4'], 'c_1100_4' : d['c_0101_4'], 's_3_6' : d['1'], 'c_1100_1' : negation(d['c_0011_0']), 'c_1100_0' : d['c_0011_2'], 'c_1100_3' : d['c_0101_4'], 'c_1100_2' : d['c_0011_2'], 'c_0101_6' : d['c_0101_3'], 'c_0101_5' : d['c_0101_1'], 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : negation(d['c_0101_1']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0011_5' : d['c_0011_4'], 'c_0011_4' : d['c_0011_4'], 'c_0011_6' : negation(d['c_0011_4']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : negation(d['c_0011_2']), 'c_0011_2' : d['c_0011_2'], 'c_1001_5' : negation(d['c_0101_3']), 'c_1001_4' : negation(d['c_0011_4']), 'c_1001_6' : negation(d['c_0101_3']), 'c_1001_1' : negation(d['c_0101_1']), 'c_1001_0' : negation(d['c_0101_1']), 'c_1001_3' : negation(d['c_0101_1']), 'c_1001_2' : negation(d['c_0101_3']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_1'], 'c_0110_2' : d['c_0101_0'], 'c_0110_5' : d['c_0011_4'], 'c_0110_4' : d['c_0101_3'], 'c_0110_6' : d['c_0101_4'], 'c_1010_6' : d['c_0101_3'], 'c_1010_5' : negation(d['c_0101_4']), 'c_1010_4' : negation(d['c_0101_1']), 'c_1010_3' : negation(d['c_0101_3']), 'c_1010_2' : negation(d['c_0101_1']), 'c_1010_1' : d['c_0101_1'], '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_2, c_0011_4, c_0101_0, c_0101_1, c_0101_3, c_0101_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 19 Groebner basis: [ t - 239894636262989802239004356/5413240851127726041618625*c_0101_4^18 + 686788004464942065876215828/1082648170225545208323725*c_0101_4^17 - 19552487069997521170876351302/5413240851127726041618625*c_0101_4^16 + 48146331125982850226559741452/5413240851127726041618625*c_0101_4^\ 15 - 627657150611468480118834086/5413240851127726041618625*c_0101_4\ ^14 - 251742857369100580574516112251/5413240851127726041618625*c_01\ 01_4^13 + 391204303050309559185538674919/5413240851127726041618625*\ c_0101_4^12 + 273610295282336089141249268004/5413240851127726041618\ 625*c_0101_4^11 - 1083553065590160298486002479591/54132408511277260\ 41618625*c_0101_4^10 + 92930699180180414210061736418/10826481702255\ 45208323725*c_0101_4^9 + 686032836452753298688320391497/54132408511\ 27726041618625*c_0101_4^8 - 630290900960511585253465107182/54132408\ 51127726041618625*c_0101_4^7 - 20029685505987351618904150193/108264\ 8170225545208323725*c_0101_4^6 + 6088505827543554281448186781/13203\ 0264661651854673625*c_0101_4^5 + 29504293078461116588238033979/5413\ 240851127726041618625*c_0101_4^4 - 46472482592759851520110613457/5413240851127726041618625*c_0101_4^3 - 12520467792798774446687334342/5413240851127726041618625*c_0101_4^2 + 3475876120742914463299698692/5413240851127726041618625*c_0101_4 + 1068523038076808337465958431/5413240851127726041618625, c_0011_0 - 1, c_0011_2 + 274003304990137242/2929203258141922345*c_0101_4^18 - 872288767104680191/585840651628384469*c_0101_4^17 + 28566609733271329614/2929203258141922345*c_0101_4^16 - 90108290240011874159/2929203258141922345*c_0101_4^15 + 85662439108930404372/2929203258141922345*c_0101_4^14 + 290710148288768581987/2929203258141922345*c_0101_4^13 - 892726477073202597708/2929203258141922345*c_0101_4^12 + 349513139958073087557/2929203258141922345*c_0101_4^11 + 1744028778063754064447/2929203258141922345*c_0101_4^10 - 467967546573883952592/585840651628384469*c_0101_4^9 - 72241052421482265544/2929203258141922345*c_0101_4^8 + 1763355308539669298504/2929203258141922345*c_0101_4^7 - 157159555045459428199/585840651628384469*c_0101_4^6 - 10408735129604932782/71443981905900545*c_0101_4^5 + 265826870098854657197/2929203258141922345*c_0101_4^4 + 133721846069678514614/2929203258141922345*c_0101_4^3 - 24014029192713619406/2929203258141922345*c_0101_4^2 - 21574500574005547594/2929203258141922345*c_0101_4 + 154679400902409888/2929203258141922345, c_0011_4 - 225803194138563789195242/1082648170225545208323725*c_0101_4^\ 18 + 648940856671670416705421/216529634045109041664745*c_0101_4^17 - 18633027184469674321522864/1082648170225545208323725*c_0101_4^16 + 47054508667448654286637039/1082648170225545208323725*c_0101_4^15 - 7172390379703391654300227/1082648170225545208323725*c_0101_4^14 - 226932394987834023272014532/1082648170225545208323725*c_0101_4^13 + 381177508172664000591992933/1082648170225545208323725*c_0101_4^12 + 185706059700432552658434128/1082648170225545208323725*c_0101_4^11 - 954846379623332588952901237/1082648170225545208323725*c_0101_4^10 + 109625973930863327744967661/216529634045109041664745*c_0101_4^9 + 408365080384485981961009354/1082648170225545208323725*c_0101_4^8 - 534475935545861199868888374/1082648170225545208323725*c_0101_4^7 + 11357719577323218899980389/216529634045109041664745*c_0101_4^6 + 3072465754511546401850917/26406052932330370934725*c_0101_4^5 + 6048496332878576438063928/1082648170225545208323725*c_0101_4^4 - 9298390826831022522532574/1082648170225545208323725*c_0101_4^3 - 4669424966071881946732544/1082648170225545208323725*c_0101_4^2 - 227440579233756618304906/1082648170225545208323725*c_0101_4 - 322146865492893412801008/1082648170225545208323725, c_0101_0 + 768422637098673067629361/1082648170225545208323725*c_0101_4^\ 18 - 2208547994360411343212993/216529634045109041664745*c_0101_4^17 + 63239797632351152176423012/1082648170225545208323725*c_0101_4^16 - 157616554406924259802960337/1082648170225545208323725*c_0101_4^15 + 9967758085174582885363666/1082648170225545208323725*c_0101_4^14 + 808031158105675700062406406/1082648170225545208323725*c_0101_4^13 - 1298745446247665813019452739/1082648170225545208323725*c_0101_4^12 - 813662468104745845400526549/1082648170225545208323725*c_0101_4^11 + 3532346264495693633860231496/1082648170225545208323725*c_0101_4^10 - 335729052155043203932027973/216529634045109041664745*c_0101_4^9 - 2137544322614705361642082132/1082648170225545208323725*c_0101_4^8 + 2158958818699962963773617617/1082648170225545208323725*c_0101_4^7 + 39978389260106289448437953/216529634045109041664745*c_0101_4^6 - 19936882597330407140654386/26406052932330370934725*c_0101_4^5 - 41246002010188992899208224/1082648170225545208323725*c_0101_4^4 + 143080654358180203146045467/1082648170225545208323725*c_0101_4^3 + 35444720835864703226050377/1082648170225545208323725*c_0101_4^2 - 9555583214871099555111902/1082648170225545208323725*c_0101_4 - 3165295386999820801392586/1082648170225545208323725, c_0101_1 - 206795167081229759554216/1082648170225545208323725*c_0101_4^\ 18 + 601773225470999574826213/216529634045109041664745*c_0101_4^17 - 17519750714001788780349097/1082648170225545208323725*c_0101_4^16 + 45011623484109663392852322/1082648170225545208323725*c_0101_4^15 - 7688132940183146844196721/1082648170225545208323725*c_0101_4^14 - 223390889335366685990246661/1082648170225545208323725*c_0101_4^13 + 388827841864274398947389759/1082648170225545208323725*c_0101_4^12 + 188691058412088469320966219/1082648170225545208323725*c_0101_4^11 - 1040516543415421496854114126/1082648170225545208323725*c_0101_4^10 + 117879620334303436555801373/216529634045109041664745*c_0101_4^9 + 626931910421654883440375442/1082648170225545208323725*c_0101_4^8 - 744417922534540124569689402/1082648170225545208323725*c_0101_4^7 - 3404722868153019144005143/216529634045109041664745*c_0101_4^6 + 7174288911526421190459616/26406052932330370934725*c_0101_4^5 - 24422858940895873098868606/1082648170225545208323725*c_0101_4^4 - 59205212508964844477187952/1082648170225545208323725*c_0101_4^3 - 8134337676251604233390337/1082648170225545208323725*c_0101_4^2 + 6230156464994095419392862/1082648170225545208323725*c_0101_4 + 1663196897513897344752991/1082648170225545208323725, c_0101_3 + 447893681799662067703104/1082648170225545208323725*c_0101_4^\ 18 - 1287470199139992309451887/216529634045109041664745*c_0101_4^17 + 36897577673454907925209393/1082648170225545208323725*c_0101_4^16 - 92302292790676434233104118/1082648170225545208323725*c_0101_4^15 + 8121998710904414980378374/1082648170225545208323725*c_0101_4^14 + 465266529612876991823913434/1082648170225545208323725*c_0101_4^13 - 755742275774800942052139071/1082648170225545208323725*c_0101_4^12 - 448238279175532584883406436/1082648170225545208323725*c_0101_4^11 + 2011826262794725497031290769/1082648170225545208323725*c_0101_4^10 - 198396478881377420472528802/216529634045109041664745*c_0101_4^9 - 1135323862898505474436292848/1082648170225545208323725*c_0101_4^8 + 1175758888826706722355388738/1082648170225545208323725*c_0101_4^7 + 17076938096286516809875842/216529634045109041664745*c_0101_4^6 - 10023305760184022025575004/26406052932330370934725*c_0101_4^5 - 40171260676360472328226086/1082648170225545208323725*c_0101_4^4 + 70503082149019067908609388/1082648170225545208323725*c_0101_4^3 + 21080226694619003573267178/1082648170225545208323725*c_0101_4^2 - 3334262310741063404038303/1082648170225545208323725*c_0101_4 - 1295303322404693697085379/1082648170225545208323725, c_0101_4^19 - 14*c_0101_4^18 + 77*c_0101_4^17 - 175*c_0101_4^16 - 61*c_0101_4^15 + 1052*c_0101_4^14 - 1303*c_0101_4^13 - 1658*c_0101_4^12 + 4177*c_0101_4^11 - 529*c_0101_4^10 - 3502*c_0101_4^9 + 1785*c_0101_4^8 + 1237*c_0101_4^7 - 951*c_0101_4^6 - 425*c_0101_4^5 + 163*c_0101_4^4 + 104*c_0101_4^3 - 8*c_0101_4 - 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.030 Total time: 0.220 seconds, Total memory usage: 32.09MB