Magma V2.19-8 Tue Aug 20 2013 23:44:16 on localhost [Seed = 139357684] Type ? for help. Type -D to quit. Loading file "K13n1779__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K13n1779 geometric_solution 10.69771592 oriented_manifold CS_known -0.0000000000000007 1 0 torus 0.000000000000 0.000000000000 12 1 2 3 4 0132 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 -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 -0.166323333204 0.830803082755 0 5 2 6 0132 0132 2031 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 -1 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 1.306520944029 1.069037691965 3 0 7 1 1023 0132 0132 1302 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -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 0.257634446317 1.724402577052 5 2 8 0 0132 1023 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.239153305754 0.600591161304 7 6 0 9 2031 1023 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.884826057854 1.777484792725 3 1 7 10 0132 0132 3012 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 0 11 -11 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 0.216234316505 0.581369349579 4 11 1 10 1023 0132 0132 0321 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.469148424205 0.451221173558 11 5 4 2 3120 1230 1302 0132 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 0 1 0 0 1 -1 0 0 0 0 11 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.491731975012 0.458383958687 11 11 9 3 2310 1023 0132 0132 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 -12 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.367774377757 0.971929629226 10 10 4 8 3120 3012 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 -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 11 1 0 -12 11 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.474349901726 0.746936184762 9 6 5 9 1230 0321 0132 3120 0 0 0 0 0 0 -1 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 0 11 -11 -1 0 1 0 11 0 0 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.562016023898 1.511040872456 8 6 8 7 1023 0132 3201 3120 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 12 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.236762925115 0.673458105288 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : negation(d['c_0011_9']), 'c_1001_10' : negation(d['c_0110_2']), 'c_1001_5' : negation(d['c_0011_7']), 'c_1001_4' : d['c_0101_0'], 'c_1001_7' : d['c_0101_9'], 'c_1001_6' : negation(d['c_0011_7']), 'c_1001_1' : negation(d['c_0110_2']), 'c_1001_0' : d['c_0110_2'], 'c_1001_3' : d['c_0101_2'], 'c_1001_2' : d['c_0101_0'], 'c_1001_9' : negation(d['c_0011_10']), 'c_1001_8' : negation(d['c_0101_10']), 'c_1010_11' : negation(d['c_0011_7']), 'c_1010_10' : negation(d['c_0011_9']), 's_3_11' : d['1'], 's_0_11' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : negation(d['c_0101_10']), 'c_0101_10' : d['c_0101_10'], 's_2_0' : negation(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_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' : negation(d['1']), 's_0_2' : d['1'], 's_0_3' : negation(d['1']), 's_0_0' : negation(d['1']), 's_0_1' : negation(d['1']), 'c_0011_11' : d['c_0011_11'], 'c_0011_10' : d['c_0011_10'], 'c_1100_5' : negation(d['c_0101_9']), 'c_1100_4' : d['c_1100_0'], 'c_1100_7' : d['c_0101_1'], 'c_1100_6' : negation(d['c_0110_2']), 'c_1100_1' : negation(d['c_0110_2']), 'c_1100_0' : d['c_1100_0'], 'c_1100_3' : d['c_1100_0'], 'c_1100_2' : d['c_0101_1'], 's_0_10' : d['1'], 'c_1100_11' : negation(d['c_0011_11']), 'c_1100_10' : negation(d['c_0101_9']), 's_3_10' : d['1'], 'c_1010_7' : d['c_0101_0'], 'c_1010_6' : negation(d['c_0011_9']), 'c_1010_5' : negation(d['c_0110_2']), 'c_1010_4' : negation(d['c_0011_10']), 'c_1010_3' : d['c_0110_2'], 'c_1010_2' : d['c_0110_2'], 'c_1010_1' : negation(d['c_0011_7']), 'c_1010_0' : d['c_0101_0'], 'c_1010_9' : negation(d['c_0101_10']), 'c_1010_8' : d['c_0101_2'], 'c_1100_8' : d['c_1100_0'], 's_3_1' : 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' : 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' : negation(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_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : d['c_0011_9'], 'c_0011_8' : d['c_0011_11'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_11']), 'c_0011_7' : d['c_0011_7'], 'c_0011_6' : negation(d['c_0011_11']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : negation(d['c_0011_0']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_2'], 'c_0110_10' : d['c_0011_9'], 'c_0110_0' : d['c_0101_1'], 'c_0101_7' : d['c_0011_11'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0101_10'], 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_9'], 'c_0101_8' : d['c_0011_9'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0011_9'], 'c_0110_8' : d['c_0101_10'], 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : d['c_1100_0'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0110_2'], 'c_0110_5' : d['c_0101_10'], 'c_0110_4' : d['c_0101_9'], 'c_0110_7' : d['c_0101_2'], 'c_0110_6' : negation(d['c_0011_10'])})} 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_7, c_0011_9, c_0101_0, c_0101_1, c_0101_10, c_0101_2, c_0101_9, c_0110_2, c_1100_0 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 6 Groebner basis: [ t - 32378233/2517242*c_1100_0^5 + 52140048/1258621*c_1100_0^4 + 5283285/179803*c_1100_0^3 - 91307617/179803*c_1100_0^2 - 2859521829/2517242*c_1100_0 - 1931514129/2517242, c_0011_0 - 1, c_0011_10 - 911/13831*c_1100_0^5 + 3984/13831*c_1100_0^4 - 3330/13831*c_1100_0^3 - 27191/13831*c_1100_0^2 - 55704/13831*c_1100_0 - 16275/13831, c_0011_11 - 1708/13831*c_1100_0^5 + 7515/13831*c_1100_0^4 - 5469/13831*c_1100_0^3 - 60195/13831*c_1100_0^2 - 80495/13831*c_1100_0 - 32897/13831, c_0011_7 - 76/13831*c_1100_0^5 + 302/13831*c_1100_0^4 - 794/13831*c_1100_0^3 - 735/13831*c_1100_0^2 - 11388/13831*c_1100_0 - 18210/13831, c_0011_9 - 1, c_0101_0 - 76/13831*c_1100_0^5 + 302/13831*c_1100_0^4 - 794/13831*c_1100_0^3 - 735/13831*c_1100_0^2 - 11388/13831*c_1100_0 - 4379/13831, c_0101_1 - 264/13831*c_1100_0^5 + 1777/13831*c_1100_0^4 - 4214/13831*c_1100_0^3 - 4737/13831*c_1100_0^2 + 11398/13831*c_1100_0 + 8811/13831, c_0101_10 + 1444/13831*c_1100_0^5 - 5738/13831*c_1100_0^4 + 1255/13831*c_1100_0^3 + 55458/13831*c_1100_0^2 + 91893/13831*c_1100_0 + 27877/13831, c_0101_2 - 76/13831*c_1100_0^5 + 302/13831*c_1100_0^4 - 794/13831*c_1100_0^3 - 735/13831*c_1100_0^2 - 11388/13831*c_1100_0 + 9452/13831, c_0101_9 - 188/13831*c_1100_0^5 + 1475/13831*c_1100_0^4 - 3420/13831*c_1100_0^3 - 4002/13831*c_1100_0^2 + 8955/13831*c_1100_0 + 13190/13831, c_0110_2 - 264/13831*c_1100_0^5 + 1777/13831*c_1100_0^4 - 4214/13831*c_1100_0^3 - 4737/13831*c_1100_0^2 + 11398/13831*c_1100_0 + 8811/13831, c_1100_0^6 - 3*c_1100_0^5 - 3*c_1100_0^4 + 39*c_1100_0^3 + 97*c_1100_0^2 + 79*c_1100_0 + 13 ], 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_7, c_0011_9, c_0101_0, c_0101_1, c_0101_10, c_0101_2, c_0101_9, c_0110_2, c_1100_0 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 14 Groebner basis: [ t - 14129191703030166336152684523479671814160697/4626454712169843326773\ 864258417218478000*c_1100_0^13 - 1321543010663354536026240508245634\ 10833647869/4626454712169843326773864258417218478000*c_1100_0^12 - 423721919345142336346358785400796735372120561/231322735608492166338\ 6932129208609239000*c_1100_0^11 - 224349813737148367170155792453781\ 760287280146/289153419510615207923366516151076154875*c_1100_0^10 - 12102325972057346646063404741103249697360648687/4626454712169843326\ 773864258417218478000*c_1100_0^9 - 1976404739118858105851724892842025106231541048/28915341951061520792\ 3366516151076154875*c_1100_0^8 - 3453858999434966945550119975288599\ 9640480854151/2313227356084921663386932129208609239000*c_1100_0^7 - 1070034498875854267411165229687315731329767781/40942077098848171033\ 397028835550606000*c_1100_0^6 - 44293817350227671481947724465029331\ 322348801379/1156613678042460831693466064604304619500*c_1100_0^5 - 104477175181269304899607324217566302497773368169/231322735608492166\ 3386932129208609239000*c_1100_0^4 - 206629951669679719469785585567791904820409837199/462645471216984332\ 6773864258417218478000*c_1100_0^3 - 40249129645772633841157297505007658685130992867/1156613678042460831\ 693466064604304619500*c_1100_0^2 - 74399511663319076571177866755312932969908111109/4626454712169843326\ 773864258417218478000*c_1100_0 - 9025711043283858956895564051148142\ 73708308099/289153419510615207923366516151076154875, c_0011_0 - 1, c_0011_10 - 183553541188924310023469417061/7180678937658623048107937779\ 1800*c_1100_0^13 - 198952927828794412482842115532/89758486720732788\ 10134922223975*c_1100_0^12 - 9990688410549094949636100440181/718067\ 89376586230481079377791800*c_1100_0^11 - 20146587768876401362890333594131/35903394688293115240539688895900*c\ _1100_0^10 - 26491014670093920617600751104151/143613578753172460962\ 15875558360*c_1100_0^9 - 66001412419358130823234722790269/143613578\ 75317246096215875558360*c_1100_0^8 - 70111262303841481730541698834943/7180678937658623048107937779180*c_\ 1100_0^7 - 231631834494641982212085708780479/1436135787531724609621\ 5875558360*c_1100_0^6 - 1643917444364286423423179894668767/71806789\ 376586230481079377791800*c_1100_0^5 - 901347922517245935579779254906099/35903394688293115240539688895900*\ c_1100_0^4 - 350343637745671160587170889190677/14361357875317246096\ 215875558360*c_1100_0^3 - 1251923793935210387333821001544781/718067\ 89376586230481079377791800*c_1100_0^2 - 472086688152785741469145885810229/71806789376586230481079377791800*\ c_1100_0 - 89808316667130474544256705518851/71806789376586230481079\ 377791800, c_0011_11 + 4884482240775446753639527793773/143613578753172460962158755\ 583600*c_1100_0^13 + 5680014893188753856287393571391/17951697344146\ 557620269844447950*c_1100_0^12 + 290806796867058294813970080297813/\ 143613578753172460962158755583600*c_1100_0^11 + 613697203948122139788469740599363/71806789376586230481079377791800*\ c_1100_0^10 + 825742211163576636041456115527687/2872271575063449219\ 2431751116720*c_1100_0^9 + 2150012913228860579043160296080789/28722\ 715750634492192431751116720*c_1100_0^8 + 2342105391260623200762032083333567/14361357875317246096215875558360\ *c_1100_0^7 + 1632623583095088516649000787334043/574454315012689843\ 8486350223344*c_1100_0^6 + 59588687670740770358956032781713551/1436\ 13578753172460962158755583600*c_1100_0^5 + 34919227383582345424608623937308107/7180678937658623048107937779180\ 0*c_1100_0^4 + 13742639300194312209733864159537853/2872271575063449\ 2192431751116720*c_1100_0^3 + 52996941822361603227684191062155813/1\ 43613578753172460962158755583600*c_1100_0^2 + 23798277208652402059827757710509757/1436135787531724609621587555836\ 00*c_1100_0 + 4288429205220096386355795131805603/143613578753172460\ 962158755583600, c_0011_7 - 47432423408550990555195835099/574454315012689843848635022334\ 4*c_1100_0^13 - 290036568107115440458136007991/35903394688293115240\ 53968889590*c_1100_0^12 - 15104723609219434103271675232267/28722715\ 750634492192431751116720*c_1100_0^11 - 32872520474045663619446158953717/14361357875317246096215875558360*c\ _1100_0^10 - 225178014690958368649944287693753/28722715750634492192\ 431751116720*c_1100_0^9 - 602812823007051105018587864845099/2872271\ 5750634492192431751116720*c_1100_0^8 - 669038748598594056450668604016491/14361357875317246096215875558360*\ c_1100_0^7 - 2406659163892734316177643194904781/2872271575063449219\ 2431751116720*c_1100_0^6 - 3593239356653006101685615395437913/28722\ 715750634492192431751116720*c_1100_0^5 - 437626878229812596946285842863209/2872271575063449219243175111672*c\ _1100_0^4 - 4412207327165449759481184412464699/28722715750634492192\ 431751116720*c_1100_0^3 - 3593752874795631202580347965243407/287227\ 15750634492192431751116720*c_1100_0^2 - 1863975252321380445914304994216219/28722715750634492192431751116720\ *c_1100_0 - 417352029448530381281581782257549/287227157506344921924\ 31751116720, c_0011_9 - 2368019691846886219585721821153/1436135787531724609621587555\ 83600*c_1100_0^13 - 2810445371301072041431098654801/179516973441465\ 57620269844447950*c_1100_0^12 - 144806689991904718852718035326493/1\ 43613578753172460962158755583600*c_1100_0^11 - 309284250410589807360463776985943/71806789376586230481079377791800*\ c_1100_0^10 - 418820767060590337493725544406267/2872271575063449219\ 2431751116720*c_1100_0^9 - 1101951850015585767576587863158769/28722\ 715750634492192431751116720*c_1100_0^8 - 1207990877725442706582596743406037/14361357875317246096215875558360\ *c_1100_0^7 - 852107505197509148419001569896819/5744543150126898438\ 486350223344*c_1100_0^6 - 31325312092801730320855590994745911/14361\ 3578753172460962158755583600*c_1100_0^5 - 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