Magma V2.19-8 Tue Aug 20 2013 23:42:18 on localhost [Seed = 1495219208] Type ? for help. Type -D to quit. Loading file "K12n821__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n821 geometric_solution 10.09281296 oriented_manifold CS_known -0.0000000000000004 1 0 torus 0.000000000000 0.000000000000 12 1 0 0 2 0132 3201 2310 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.266102595027 0.816135661746 0 2 4 3 0132 2310 0132 0132 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 -6 6 0 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 1.239202708360 1.222256581406 5 6 0 1 0132 0132 0132 3201 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 -1 1 0 0 0 0 0 -6 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.125690541195 0.769471542364 7 5 1 4 0132 3201 0132 0321 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 7 0 -7 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 0.599866720874 0.085392717234 8 3 9 1 0132 0321 0132 0132 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 7 -1 -6 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 0.425497018952 0.754343167426 2 10 3 8 0132 0132 2310 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 -1 1 0 0 0 0 0 0 0 0 0 7 -7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.425497018952 0.754343167426 9 2 9 7 2031 0132 3012 1023 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 1 -1 0 0 0 0 -6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.766257399709 1.520099840562 3 11 8 6 0132 0132 0213 1023 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0.735577631317 0.524560546663 4 7 5 11 0132 0213 0132 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 -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 0.237452824815 0.976014046559 10 6 6 4 0213 1230 1302 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 -1 0 1 -7 0 6 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 0.735577631317 0.524560546663 9 5 11 11 0213 0132 0132 2310 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 0 7 -7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.143840268979 0.490384058220 10 7 8 10 3201 0132 0132 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.221999334481 1.617284348498 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_0110_6'], 'c_1001_10' : d['c_1001_10'], 'c_1001_5' : negation(d['c_0011_9']), 'c_1001_4' : d['c_0101_6'], 'c_1001_7' : d['c_1001_10'], 'c_1001_6' : negation(d['c_0011_9']), 'c_1001_1' : d['c_0011_9'], 'c_1001_0' : negation(d['c_0101_0']), 'c_1001_3' : negation(d['c_0101_5']), 'c_1001_2' : d['c_0101_0'], 'c_1001_9' : d['c_0110_6'], 'c_1001_8' : d['c_1001_10'], 'c_1010_11' : d['c_1001_10'], 'c_1010_10' : negation(d['c_0011_9']), 's_0_10' : d['1'], 's_3_10' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0101_11'], 'c_0101_10' : d['c_0011_9'], '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' : d['1'], 's_2_5' : d['1'], 's_2_6' : d['1'], 's_2_7' : d['1'], 's_2_10' : d['1'], 's_2_11' : d['1'], 's_0_8' : d['1'], 's_0_9' : d['1'], 's_0_6' : d['1'], 's_0_7' : 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_9' : d['c_0101_6'], 'c_1100_8' : d['c_0011_11'], 'c_1100_5' : d['c_0011_11'], 'c_1100_4' : d['c_0101_6'], 'c_1100_7' : d['c_0110_6'], 'c_1100_6' : negation(d['c_0110_6']), 'c_1100_1' : d['c_0101_6'], 'c_1100_0' : d['c_0011_0'], 'c_1100_3' : d['c_0101_6'], 'c_1100_2' : d['c_0011_0'], 's_3_11' : d['1'], 'c_1100_11' : d['c_0011_11'], 'c_1100_10' : d['c_0011_11'], 's_0_11' : d['1'], 'c_1010_7' : d['c_0110_6'], 'c_1010_6' : d['c_0101_0'], 'c_1010_5' : d['c_1001_10'], 'c_1010_4' : d['c_0011_9'], 'c_1010_3' : d['c_0011_9'], 'c_1010_2' : negation(d['c_0011_9']), 'c_1010_1' : negation(d['c_0101_5']), 'c_1010_0' : d['c_0101_0'], 'c_1010_9' : d['c_0101_6'], 'c_1010_8' : d['c_0110_6'], 's_3_1' : negation(d['1']), 's_3_0' : d['1'], 's_3_3' : negation(d['1']), 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : negation(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' : d['1'], 's_1_5' : d['1'], 's_1_4' : negation(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' : d['c_0011_9'], 'c_0011_8' : negation(d['c_0011_4']), 'c_0011_5' : negation(d['c_0011_10']), 'c_0011_4' : d['c_0011_4'], 'c_0011_7' : negation(d['c_0011_11']), 'c_0011_6' : negation(d['c_0011_10']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_11'], 'c_0011_2' : d['c_0011_10'], 'c_0110_11' : d['c_0011_9'], 'c_0110_10' : negation(d['c_0101_11']), 'c_0110_0' : d['c_0101_1'], 'c_0101_7' : negation(d['c_0011_4']), 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : d['c_0101_11'], 'c_0101_3' : d['c_0101_0'], 'c_0101_2' : d['c_0101_1'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0011_10'], 'c_0101_8' : d['c_0101_1'], 'c_0011_10' : d['c_0011_10'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_11'], 'c_0110_8' : d['c_0101_11'], 'c_0110_1' : d['c_0101_0'], 'c_0011_11' : d['c_0011_11'], 'c_0110_3' : negation(d['c_0011_4']), 'c_0110_2' : d['c_0101_5'], 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : d['c_0101_1'], 'c_0110_7' : d['c_0101_0'], 'c_0110_6' : d['c_0110_6']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 13 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_4, c_0011_9, c_0101_0, c_0101_1, c_0101_11, c_0101_5, c_0101_6, c_0110_6, c_1001_10 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 12 Groebner basis: [ t + 206692788/4031*c_0101_5*c_1001_10^5 + 910568601/4031*c_0101_5*c_1001_10^4 - 1078355323/4031*c_0101_5*c_1001_10^3 - 129210770/139*c_0101_5*c_1001_10^2 + 2825331898/4031*c_0101_5*c_1001_10 + 536871571/4031*c_0101_5 + 40836829/4031*c_1001_10^5 + 179069266/4031*c_1001_10^4 - 216595963/4031*c_1001_10^3 - 25359088/139*c_1001_10^2 + 572551346/4031*c_1001_10 + 92396749/4031, c_0011_0 - 1, c_0011_10 + 28/139*c_0101_5*c_1001_10^5 + 145/139*c_0101_5*c_1001_10^4 - 40/139*c_0101_5*c_1001_10^3 - 515/139*c_0101_5*c_1001_10^2 + 125/139*c_0101_5*c_1001_10 + 108/139*c_0101_5 - 67/139*c_1001_10^5 - 342/139*c_1001_10^4 + 56/139*c_1001_10^3 + 999/139*c_1001_10^2 - 314/139*c_1001_10 - 40/139, c_0011_11 + 12/139*c_0101_5*c_1001_10^5 + 82/139*c_0101_5*c_1001_10^4 + 102/139*c_0101_5*c_1001_10^3 - 181/139*c_0101_5*c_1001_10^2 - 284/139*c_0101_5*c_1001_10 + 86/139*c_0101_5 - 73/139*c_1001_10^5 - 383/139*c_1001_10^4 + 5/139*c_1001_10^3 + 1020/139*c_1001_10^2 - 311/139*c_1001_10 - 83/139, c_0011_4 + 12/139*c_0101_5*c_1001_10^5 + 82/139*c_0101_5*c_1001_10^4 + 102/139*c_0101_5*c_1001_10^3 - 181/139*c_0101_5*c_1001_10^2 - 284/139*c_0101_5*c_1001_10 + 86/139*c_0101_5 - 24/139*c_1001_10^5 - 164/139*c_1001_10^4 - 204/139*c_1001_10^3 + 223/139*c_1001_10^2 + 151/139*c_1001_10 - 33/139, c_0011_9 + 28/139*c_0101_5*c_1001_10^5 + 145/139*c_0101_5*c_1001_10^4 - 40/139*c_0101_5*c_1001_10^3 - 515/139*c_0101_5*c_1001_10^2 + 125/139*c_0101_5*c_1001_10 + 108/139*c_0101_5 + 10/139*c_1001_10^5 + 22/139*c_1001_10^4 - 193/139*c_1001_10^3 - 313/139*c_1001_10^2 + 273/139*c_1001_10 - 21/139, c_0101_0 - 50/139*c_1001_10^5 - 249/139*c_1001_10^4 + 131/139*c_1001_10^3 + 1009/139*c_1001_10^2 - 253/139*c_1001_10 - 173/139, c_0101_1 + 28/139*c_1001_10^5 + 145/139*c_1001_10^4 - 40/139*c_1001_10^3 - 515/139*c_1001_10^2 + 125/139*c_1001_10 - 31/139, c_0101_11 - 44/139*c_1001_10^5 - 208/139*c_1001_10^4 + 182/139*c_1001_10^3 + 988/139*c_1001_10^2 - 117/139*c_1001_10 - 130/139, c_0101_5^2 + 10/139*c_0101_5*c_1001_10^5 + 22/139*c_0101_5*c_1001_10^4 - 193/139*c_0101_5*c_1001_10^3 - 313/139*c_0101_5*c_1001_10^2 + 273/139*c_0101_5*c_1001_10 - 21/139*c_0101_5 - 26/139*c_1001_10^5 - 85/139*c_1001_10^4 + 335/139*c_1001_10^3 + 786/139*c_1001_10^2 - 265/139*c_1001_10 - 1/139, c_0101_6 + 22/139*c_1001_10^5 + 104/139*c_1001_10^4 - 91/139*c_1001_10^3 - 494/139*c_1001_10^2 - 11/139*c_1001_10 + 65/139, c_0110_6 + 28/139*c_1001_10^5 + 145/139*c_1001_10^4 - 40/139*c_1001_10^3 - 515/139*c_1001_10^2 + 125/139*c_1001_10 - 31/139, c_1001_10^6 + 4*c_1001_10^5 - 7*c_1001_10^4 - 16*c_1001_10^3 + 21*c_1001_10^2 - 3*c_1001_10 - 1 ], Ideal of Polynomial ring of rank 13 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_4, c_0011_9, c_0101_0, c_0101_1, c_0101_11, c_0101_5, c_0101_6, c_0110_6, c_1001_10 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 13 Groebner basis: [ t + 15021456518173726797648852039814797405264/1716540245519853204506623\ 064653717*c_1001_10^12 + 6743003891980972408327691360721445228650/1\ 716540245519853204506623064653717*c_1001_10^11 - 15709201073322642547946563752481900305001/6866160982079412818026492\ 258614868*c_1001_10^10 - 482381476019870051693941181026506992262097\ /54929287856635302544211938068918944*c_1001_10^9 - 125949981942265291450153360914941601694353/686616098207941281802649\ 2258614868*c_1001_10^8 + 253214589082028505729252523033616115354123\ /27464643928317651272105969034459472*c_1001_10^7 - 19554360053787588495080719474546782110125/5492928785663530254421193\ 8068918944*c_1001_10^6 + 33043099904365033592482955200265865747603/\ 2496785811665241024736906275859952*c_1001_10^5 + 21301594742910649169535951339043838220255/1373232196415882563605298\ 4517229736*c_1001_10^4 - 75688726388903844254229109168176723149147/\ 27464643928317651272105969034459472*c_1001_10^3 - 49570702170058415431355270710770071020037/2746464392831765127210596\ 9034459472*c_1001_10^2 + 30558390703405579146156866441455596774095/\ 54929287856635302544211938068918944*c_1001_10 + 5539764086800694612846599506158670467539/27464643928317651272105969\ 034459472, c_0011_0 - 1, c_0011_10 - 964537639344216950684566668528/80733195696763030063162453*c\ _1001_10^12 - 434269570226491590248515910396/8073319569676303006316\ 2453*c_1001_10^11 + 1005321301117710850305934894445/322932782787052\ 120252649812*c_1001_10^10 + 1935892879157869502390093673363/1614663\ 91393526060126324906*c_1001_10^9 + 4046092567017521064782560051505/161466391393526060126324906*c_1001_\ 10^8 - 4052941531273119718460010516399/322932782787052120252649812*\ c_1001_10^7 + 38643775950084756155840838290/80733195696763030063162\ 453*c_1001_10^6 - 1458276576998305756438309122879/80733195696763030\ 063162453*c_1001_10^5 - 345822805579184087521599312585/161466391393\ 526060126324906*c_1001_10^4 + 606272391083048833877357885645/161466\ 391393526060126324906*c_1001_10^3 + 795466878769241826597151190505/322932782787052120252649812*c_1001_1\ 0^2 - 61197202372798268324527520616/80733195696763030063162453*c_10\ 01_10 - 22210018666381586340116310666/80733195696763030063162453, c_0011_11 + 160002489794911520128525373552/80733195696763030063162453*c\ _1001_10^12 + 72204446031399015366936077980/80733195696763030063162\ 453*c_1001_10^11 - 166061840639590424349827598805/32293278278705212\ 0252649812*c_1001_10^10 - 321179595053058473438992186381/1614663913\ 93526060126324906*c_1001_10^9 - 671399571765936652188681538319/1614\ 66391393526060126324906*c_1001_10^8 + 670872222444362925651260209327/322932782787052120252649812*c_1001_1\ 0^7 - 6417030065318016758644730821/80733195696763030063162453*c_100\ 1_10^6 + 242016224954623671512783683469/80733195696763030063162453*\ c_1001_10^5 + 57436557301817610932346014731/16146639139352606012632\ 4906*c_1001_10^4 - 100118850855347970889744299929/16146639139352606\ 0126324906*c_1001_10^3 - 132292504228911827510564713977/32293278278\ 7052120252649812*c_1001_10^2 + 10146070560976816088766510236/807331\ 95696763030063162453*c_1001_10 + 3684929689733549865514372510/80733\ 195696763030063162453, c_0011_4 + 176799206879087900181648846768/80733195696763030063162453*c_\ 1001_10^12 + 79678144966040721958817562604/807331956967630300631624\ 53*c_1001_10^11 - 183279070052829379743132123185/322932782787052120\ 252649812*c_1001_10^10 - 354708711949852233007632434493/16146639139\ 3526060126324906*c_1001_10^9 - 741716812822096641415899054393/16146\ 6391393526060126324906*c_1001_10^8 + 741810327281458836321122898091/322932782787052120252649812*c_1001_1\ 0^7 - 7427321609932460829231159401/80733195696763030063162453*c_100\ 1_10^6 + 267511528511795007505159923602/80733195696763030063162453*\ c_1001_10^5 + 63207095881048837003060271647/16146639139352606012632\ 4906*c_1001_10^4 - 110426652315536382484306055813/16146639139352606\ 0126324906*c_1001_10^3 - 145508197223470424414876236361/32293278278\ 7052120252649812*c_1001_10^2 + 11170941420398576679712490177/807331\ 95696763030063162453*c_1001_10 + 4087010201584376155858516396/80733\ 195696763030063162453, c_0011_9 - 402894330959747543261743693040/80733195696763030063162453*c_\ 1001_10^12 - 181083706311514647899299694524/80733195696763030063162\ 453*c_1001_10^11 + 419968051084544774516515012141/32293278278705212\ 0252649812*c_1001_10^10 + 808460692422196763514117798677/1614663913\ 93526060126324906*c_1001_10^9 + 1689634134265956329657202076863/161\ 466391393526060126324906*c_1001_10^8 - 1695075572688268214092576447135/322932782787052120252649812*c_1001_\ 10^7 + 16701496317096567607609967537/80733195696763030063162453*c_1\ 001_10^6 - 609404277747542008657481786296/8073319569676303006316245\ 3*c_1001_10^5 - 143495513457763450932083284881/16146639139352606012\ 6324906*c_1001_10^4 + 252971826426580489187313311429/16146639139352\ 6060126324906*c_1001_10^3 + 331815740519740782486904208529/32293278\ 2787052120252649812*c_1001_10^2 - 25536959930078756899525532145/807\ 33195696763030063162453*c_1001_10 - 9237660396774741732918461716/80733195696763030063162453, c_0101_0 + 265865601899276093784779190256/80733195696763030063162453*c_\ 1001_10^12 + 118911920792860450266955653724/80733195696763030063162\ 453*c_1001_10^11 - 278345744845881201267784401117/32293278278705212\ 0252649812*c_1001_10^10 - 266548473524143182548040532073/8073319569\ 6763030063162453*c_1001_10^9 - 1113556764094388692589992730079/1614\ 66391393526060126324906*c_1001_10^8 + 1123633854689673966132400621927/322932782787052120252649812*c_1001_\ 10^7 - 23147567356416991807179871289/161466391393526060126324906*c_\ 1001_10^6 + 401991554266255234576383368707/807331956967630300631624\ 53*c_1001_10^5 + 92845664341263318671067734255/16146639139352606012\ 6324906*c_1001_10^4 - 167158128890098385840992126367/16146639139352\ 6060126324906*c_1001_10^3 - 218520459665453838893716072757/32293278\ 2787052120252649812*c_1001_10^2 + 34178154716394392288729082751/161\ 466391393526060126324906*c_1001_10 + 6069786113313342660423271406/80733195696763030063162453, c_0101_1 - 516647622958916031389750512048/80733195696763030063162453*c_\ 1001_10^12 - 232455493167928904756011872748/80733195696763030063162\ 453*c_1001_10^11 + 537557829244197017622846937745/32293278278705212\ 0252649812*c_1001_10^10 + 1036812604937043026221965639761/161466391\ 393526060126324906*c_1001_10^9 + 2166930579443625944697699062491/16\ 1466391393526060126324906*c_1001_10^8 - 2171534794710067799384573761255/322932782787052120252649812*c_1001_\ 10^7 + 21356051919120828794623263597/80733195696763030063162453*c_1\ 001_10^6 - 781688635849418155432285505368/8073319569676303006316245\ 3*c_1001_10^5 - 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