Magma V2.19-8 Tue Aug 20 2013 16:18:42 on localhost [Seed = 105356151] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v2867 geometric_solution 6.08655061 oriented_manifold CS_known 0.0000000000000004 1 0 torus 0.000000000000 0.000000000000 7 0 0 1 2 1302 2031 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 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 0.551573805004 0.779048812903 2 3 4 0 1302 0132 0132 0132 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 -1 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 0.539789233352 0.476439456281 5 1 0 4 0132 2031 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 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.539789233352 0.476439456281 6 1 4 5 0132 0132 3120 1302 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 1 0 -1 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 0.505162520225 0.858657241436 2 5 3 1 3201 1302 3120 0132 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 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 1.783038823246 0.492170017699 2 6 3 4 0132 0132 2031 2031 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.505162520225 0.858657241436 3 5 6 6 0132 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 1 -1 -1 0 1 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 1.110817624753 1.294506592134 ==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_6'], 'c_1100_5' : negation(d['c_1001_1']), 'c_1100_4' : d['c_0011_4'], 's_3_6' : d['1'], 'c_1100_1' : d['c_0011_4'], 'c_1100_0' : d['c_0011_4'], 'c_1100_3' : negation(d['c_0101_4']), 'c_1100_2' : d['c_0011_4'], 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : negation(d['c_0101_4']), 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : negation(d['c_0011_4']), 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : negation(d['c_0011_1']), 'c_0101_0' : negation(d['c_0011_0']), 'c_0011_5' : negation(d['c_0011_1']), 'c_0011_4' : d['c_0011_4'], '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' : negation(d['c_0101_6']), 'c_1001_4' : d['c_0101_2'], 'c_1001_6' : d['c_0011_4'], 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : negation(d['c_0101_2']), 'c_1001_3' : negation(d['c_0101_2']), 'c_1001_2' : d['c_0011_0'], 'c_0110_1' : negation(d['c_0011_0']), 'c_0110_0' : d['c_0101_2'], 'c_0110_3' : d['c_0101_6'], 'c_0110_2' : negation(d['c_0101_4']), 'c_0110_5' : d['c_0101_2'], 'c_0110_4' : negation(d['c_0011_1']), 'c_0110_6' : negation(d['c_0011_4']), 'c_1010_6' : negation(d['c_0101_6']), 'c_1010_5' : d['c_0011_4'], 'c_1010_4' : d['c_1001_1'], 'c_1010_3' : d['c_1001_1'], 'c_1010_2' : d['c_0011_1'], 'c_1010_1' : negation(d['c_0101_2']), 'c_1010_0' : d['c_0011_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_0011_4, c_0101_2, c_0101_4, c_0101_6, c_1001_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 21 Groebner basis: [ t + 14280314858041480359521019471/397250047464689063613889525*c_1001_1^\ 20 + 112880985107736524608506894301/397250047464689063613889525*c_1\ 001_1^19 + 173218210215864271911618497521/3972500474646890636138895\ 25*c_1001_1^18 + 40741821289813719579250472513/39725004746468906361\ 3889525*c_1001_1^17 + 1038897070522602367194494642724/3972500474646\ 89063613889525*c_1001_1^16 - 2444629025721719900605021621646/397250\ 047464689063613889525*c_1001_1^15 - 5357851702302772247114892075376/397250047464689063613889525*c_1001_\ 1^14 + 20000800146916686284024367444881/397250047464689063613889525\ *c_1001_1^13 - 13599058082022285899790441629887/3972500474646890636\ 13889525*c_1001_1^12 - 2839868294975967043890896407944/361136406786\ 08096692171775*c_1001_1^11 + 64745794722353297164334119500519/39725\ 0047464689063613889525*c_1001_1^10 - 25655547447835932030034480965359/397250047464689063613889525*c_1001\ _1^9 - 50348310475355167317376724738253/397250047464689063613889525\ *c_1001_1^8 + 72127789477195769857253257411743/39725004746468906361\ 3889525*c_1001_1^7 - 25135407600059452725104694934164/3972500474646\ 89063613889525*c_1001_1^6 - 19491158569137643123403229623373/397250\ 047464689063613889525*c_1001_1^5 + 21002459774697573573456271629469/397250047464689063613889525*c_1001\ _1^4 - 576333168045529886966433004457/36113640678608096692171775*c_\ 1001_1^3 + 9732262464895552866462924040/15890001898587562544555581*\ c_1001_1^2 + 66499589241991113671072406868/397250047464689063613889\ 525*c_1001_1 + 23948321878732804308326226652/3972500474646890636138\ 89525, c_0011_0 - 1, c_0011_1 + 420182204582510646563955906/36113640678608096692171775*c_100\ 1_1^20 + 3561357341365808969537606206/36113640678608096692171775*c_\ 1001_1^19 + 7156929227441747184824196736/36113640678608096692171775\ *c_1001_1^18 + 5508482630431307085107438728/36113640678608096692171\ 775*c_1001_1^17 + 34143255265679369670096917254/3611364067860809669\ 2171775*c_1001_1^16 - 52230416568712471988902811531/361136406786080\ 96692171775*c_1001_1^15 - 185738561767932095268048627781/3611364067\ 8608096692171775*c_1001_1^14 + 478486622315712659913353056736/36113\ 640678608096692171775*c_1001_1^13 - 140142992312144491313178929677/36113640678608096692171775*c_1001_1^\ 12 - 969138690283338195537584746724/36113640678608096692171775*c_10\ 01_1^11 + 1348497854510581110970610947404/3611364067860809669217177\ 5*c_1001_1^10 - 52684590127868084291134446459/361136406786080966921\ 71775*c_1001_1^9 - 1433203873099816770165992070443/3611364067860809\ 6692171775*c_1001_1^8 + 1324039137541640267307493231358/36113640678\ 608096692171775*c_1001_1^7 - 81988063584191296170355935239/36113640\ 678608096692171775*c_1001_1^6 - 556665795271273421671682517888/3611\ 3640678608096692171775*c_1001_1^5 + 319090281157428836713051628619/36113640678608096692171775*c_1001_1^\ 4 - 41184771763706107184145392037/36113640678608096692171775*c_1001\ _1^3 - 1788134063505940078094029552/7222728135721619338434355*c_100\ 1_1^2 - 733198607239532964146812432/36113640678608096692171775*c_10\ 01_1 + 910114413835506710761262117/36113640678608096692171775, c_0011_4 + 376514277810291102395487841/36113640678608096692171775*c_100\ 1_1^20 + 3184401723129156824570905796/36113640678608096692171775*c_\ 1001_1^19 + 6349625598575591504029278066/36113640678608096692171775\ *c_1001_1^18 + 4768209864511857403147619073/36113640678608096692171\ 775*c_1001_1^17 + 30371485714013416757978818954/3611364067860809669\ 2171775*c_1001_1^16 - 47533571546213355538498514441/361136406786080\ 96692171775*c_1001_1^15 - 166175299052492079432719427921/3611364067\ 8608096692171775*c_1001_1^14 + 432016273182411502885342932051/36113\ 640678608096692171775*c_1001_1^13 - 130749601834568845691929262277/36113640678608096692171775*c_1001_1^\ 12 - 870498441606811582291009374789/36113640678608096692171775*c_10\ 01_1^11 + 1222732883406296199999353602199/3611364067860809669217177\ 5*c_1001_1^10 - 57374262564619811254601154239/361136406786080966921\ 71775*c_1001_1^9 - 1292411102613564607047651065963/3611364067860809\ 6692171775*c_1001_1^8 + 1203631330629620236766366437403/36113640678\ 608096692171775*c_1001_1^7 - 80519569331220746362011577494/36113640\ 678608096692171775*c_1001_1^6 - 504029859346687323397677588358/3611\ 3640678608096692171775*c_1001_1^5 + 290851221033501144372361345224/36113640678608096692171775*c_1001_1^\ 4 - 37694884464207485263601926092/36113640678608096692171775*c_1001\ _1^3 - 323811127812276361286030131/1444545627144323867686871*c_1001\ _1^2 - 711060223546839683163618647/36113640678608096692171775*c_100\ 1_1 + 829802233226389575079589667/36113640678608096692171775, c_0101_2 + 296155827549748094539690281/36113640678608096692171775*c_100\ 1_1^20 + 2507826024932784543093616616/36113640678608096692171775*c_\ 1001_1^19 + 5026536873760443395033963701/36113640678608096692171775\ *c_1001_1^18 + 3860929967335727805640869458/36113640678608096692171\ 775*c_1001_1^17 + 24092092890778689302726674299/3611364067860809669\ 2171775*c_1001_1^16 - 36903562260128610905123970981/361136406786080\ 96692171775*c_1001_1^15 - 130379150992043817653684043916/3611364067\ 8608096692171775*c_1001_1^14 + 338370184535962501296397153921/36113\ 640678608096692171775*c_1001_1^13 - 102278096615565676402838603537/36113640678608096692171775*c_1001_1^\ 12 - 681734577351793347102008488799/36113640678608096692171775*c_10\ 01_1^11 + 957128535199173297674017717014/36113640678608096692171775\ *c_1001_1^10 - 47408570273365507348465804089/3611364067860809669217\ 1775*c_1001_1^9 - 1010047917861226960787469915398/36113640678608096\ 692171775*c_1001_1^8 + 944139525025469634196841165588/3611364067860\ 8096692171775*c_1001_1^7 - 67092608138054792461062863419/3611364067\ 8608096692171775*c_1001_1^6 - 392724305409703962778812510568/361136\ 40678608096692171775*c_1001_1^5 + 229494360801677098430236932074/36\ 113640678608096692171775*c_1001_1^4 - 30671783763378023544771812332/36113640678608096692171775*c_1001_1^3 - 1265871565059536115252724463/7222728135721619338434355*c_1001_1^2 - 558013734324708507189690347/36113640678608096692171775*c_1001_1 + 663349530241072071336180802/36113640678608096692171775, c_0101_4 - c_1001_1, c_0101_6 + 52305949128560528775322559/36113640678608096692171775*c_1001\ _1^20 + 462979615172142624463575649/36113640678608096692171775*c_10\ 01_1^19 + 1064296671126934053871383189/36113640678608096692171775*c\ _1001_1^18 + 1080835137996487145513228337/3611364067860809669217177\ 5*c_1001_1^17 + 4646147499229872804423995736/3611364067860809669217\ 1775*c_1001_1^16 - 4765284609504668247852983884/3611364067860809669\ 2171775*c_1001_1^15 - 24955263809150160096455815574/361136406786080\ 96692171775*c_1001_1^14 + 50248080651228916916073727669/36113640678\ 608096692171775*c_1001_1^13 + 1686307093069268131824211832/36113640\ 678608096692171775*c_1001_1^12 - 120566630895817008776586041586/361\ 13640678608096692171775*c_1001_1^11 + 122581689275847339564460918071/36113640678608096692171775*c_1001_1^\ 10 + 40788001389469405013575434754/36113640678608096692171775*c_100\ 1_1^9 - 164492111466090243906183484422/36113640678608096692171775*c\ _1001_1^8 + 102603518766686788908891039832/361136406786080966921717\ 75*c_1001_1^7 + 30234346556321904959882291534/361136406786080966921\ 71775*c_1001_1^6 - 59149738188643325050805025327/361136406786080966\ 92171775*c_1001_1^5 + 17154376800564116040897655836/361136406786080\ 96692171775*c_1001_1^4 + 2094890554162061064431328627/3611364067860\ 8096692171775*c_1001_1^3 - 112704298363572710285654737/722272813572\ 1619338434355*c_1001_1^2 - 337048683593746713110132208/361136406786\ 08096692171775*c_1001_1 + 4396747752957181133150203/361136406786080\ 96692171775, c_1001_1^21 + 8*c_1001_1^20 + 13*c_1001_1^19 + 5*c_1001_1^18 + 75*c_1001_1^17 - 163*c_1001_1^16 - 383*c_1001_1^15 + 1349*c_1001_1^14 - 875*c_1001_1^13 - 2148*c_1001_1^12 + 4306*c_1001_1^11 - 1651*c_1001_1^10 - 3351*c_1001_1^9 + 4772*c_1001_1^8 - 1693*c_1001_1^7 - 1231*c_1001_1^6 + 1388*c_1001_1^5 - 459*c_1001_1^4 + 26*c_1001_1^3 + 8*c_1001_1^2 + 3*c_1001_1 - 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.030 Total time: 0.230 seconds, Total memory usage: 32.09MB