Magma V2.19-8 Tue Aug 20 2013 23:49:23 on localhost [Seed = 795428304] Type ? for help. Type -D to quit. Loading file "K11n26__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K11n26 geometric_solution 11.72890133 oriented_manifold CS_known 0.0000000000000002 1 0 torus 0.000000000000 0.000000000000 13 1 2 3 4 0132 0132 0132 0132 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 -1 0 1 -1 0 0 1 0 -2 0 2 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.278001300282 1.432417780112 0 5 4 6 0132 0132 0213 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 0 0 1 0 0 -1 1 0 0 -1 0 3 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.792340577526 0.691101496757 3 0 5 4 1023 0132 0132 1230 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 0 0 0 -1 0 1 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.171293573320 0.690722563456 5 2 7 0 0132 1023 0132 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 0 0 0 0 0 0 0 0 0 0 0 -3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.211658311969 0.958241227016 2 1 0 8 3012 0213 0132 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 1 0 -1 0 0 0 0 0 -1 3 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.350356626555 0.322252877896 3 1 8 2 0132 0132 1302 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 0 0 3 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.447372309685 0.819169903191 9 10 1 11 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 0 0 0 0 0 1 -1 0 1 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.345485855082 0.606124971457 10 12 8 3 3012 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 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.175355439886 0.864259605545 5 9 4 7 2031 0321 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 1.371831086778 0.941103161403 6 11 12 8 0132 2103 2103 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 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 0.737992551343 0.839194531835 11 6 12 7 0321 0132 0321 1230 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 -1 -1 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.822485148872 0.761677637152 10 9 6 12 0321 2103 0132 2103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.028209549165 1.848555899788 9 7 10 11 2103 0132 0321 2103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.737992551343 0.839194531835 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_0011_10'], 'c_1001_10' : d['c_0011_10'], 'c_1001_12' : d['c_0101_2'], 'c_1001_5' : d['c_0101_7'], 'c_1001_4' : d['c_1001_1'], 'c_1001_7' : d['c_1001_7'], 'c_1001_6' : d['c_0101_7'], 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_0011_4'], 'c_1001_3' : d['c_0101_2'], 'c_1001_2' : d['c_1001_1'], 'c_1001_9' : d['c_0011_11'], 'c_1001_8' : negation(d['c_0110_12']), 'c_1010_12' : d['c_1001_7'], 'c_1010_11' : negation(d['c_1001_7']), 'c_1010_10' : d['c_0101_7'], 's_3_11' : d['1'], 's_3_10' : d['1'], 's_0_12' : d['1'], 's_3_12' : 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_12' : 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_0011_12' : d['c_0011_11'], 'c_1100_5' : d['c_0101_8'], 'c_1100_4' : d['c_1100_0'], 'c_1100_7' : d['c_1100_0'], 'c_1100_6' : negation(d['c_0110_12']), 'c_1100_1' : negation(d['c_0110_12']), 'c_1100_0' : d['c_1100_0'], 'c_1100_3' : d['c_1100_0'], 'c_1100_2' : d['c_0101_8'], 's_0_10' : d['1'], 'c_1100_9' : negation(d['c_0110_12']), 'c_1100_11' : negation(d['c_0110_12']), 'c_1100_10' : d['c_0101_2'], 's_0_11' : d['1'], 'c_1010_7' : d['c_0101_2'], 'c_1010_6' : d['c_0011_10'], 'c_1010_5' : d['c_1001_1'], 'c_1010_4' : negation(d['c_0110_12']), 'c_1010_3' : d['c_0011_4'], 'c_1010_2' : d['c_0011_4'], 'c_1010_1' : d['c_0101_7'], 'c_1010_0' : d['c_1001_1'], 'c_1010_9' : d['c_1001_7'], 'c_1010_8' : d['c_1001_7'], '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'], 'c_1100_12' : d['c_0011_10'], '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_10'], 'c_0011_8' : d['c_0011_8'], 'c_0011_5' : d['c_0011_0'], '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' : negation(d['c_0011_0']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : negation(d['c_0011_10']), 'c_0110_10' : negation(d['c_0011_11']), 'c_0110_12' : d['c_0110_12'], 'c_0101_12' : negation(d['c_0101_10']), 'c_0101_7' : d['c_0101_7'], 'c_0101_6' : negation(d['c_0011_8']), 'c_0101_5' : negation(d['c_0011_8']), 'c_0101_4' : d['c_0011_4'], 'c_0101_3' : d['c_0101_2'], 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0011_4'], 'c_0101_0' : negation(d['c_0011_8']), 'c_0101_9' : negation(d['c_0101_10']), 'c_0101_8' : d['c_0101_8'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : negation(d['c_0011_8']), 'c_0110_8' : d['c_0101_7'], 'c_0110_1' : negation(d['c_0011_8']), 'c_0110_0' : d['c_0011_4'], 'c_0110_3' : negation(d['c_0011_8']), 'c_0110_2' : d['c_0011_4'], 'c_0110_5' : d['c_0101_2'], 'c_0110_4' : d['c_0101_8'], 'c_0110_7' : d['c_0101_2'], 'c_0110_6' : negation(d['c_0101_10'])})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_11, c_0011_4, c_0011_8, c_0101_10, c_0101_2, c_0101_7, c_0101_8, c_0110_12, c_1001_1, c_1001_7, c_1100_0 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 28 Groebner basis: [ t - 132199500213712664582170424895/83820973917224380137472*c_1100_0^27 + 270069198240962801639463753661/83820973917224380137472*c_1100_0^26 - 3713171284122614223861413283765/83820973917224380137472*c_1100_0^25 + 1160128959100246014559938113619/10477621739653047517184*c_1100_0^\ 24 - 34967529821506086606197528191031/41910486958612190068736*c_110\ 0_0^23 + 145378587538644290732644115859941/83820973917224380137472*\ c_1100_0^22 - 305788942332600181688902444778591/4191048695861219006\ 8736*c_1100_0^21 + 659601121623790175931585275669623/83820973917224\ 380137472*c_1100_0^20 - 2774611587039783430286401676600265/83820973\ 917224380137472*c_1100_0^19 + 147479091348670044773563685170525/523\ 8810869826523758592*c_1100_0^18 - 163058636540612567363333084324230\ 87/83820973917224380137472*c_1100_0^17 + 19062189129634956723584475049193945/83820973917224380137472*c_1100_\ 0^16 - 17907321240009408192070999757430345/20955243479306095034368*\ c_1100_0^15 + 21992425995307202351443771961218029/41910486958612190\ 068736*c_1100_0^14 - 36252399999939561952090709833769021/2095524347\ 9306095034368*c_1100_0^13 + 10416971824756110006772105829199955/419\ 10486958612190068736*c_1100_0^12 - 269608058101374304558890588183148257/83820973917224380137472*c_1100\ _0^11 + 36893279370001284021374383056631181/83820973917224380137472\ *c_1100_0^10 - 358160423565749930639990707498930179/838209739172243\ 80137472*c_1100_0^9 - 35478939840904644700607851462002891/419104869\ 58612190068736*c_1100_0^8 - 100672362787729354459897879080746247/41\ 910486958612190068736*c_1100_0^7 - 13308155611380525881588227838744783/83820973917224380137472*c_1100_\ 0^6 - 22702562800054558713178074328528695/41910486958612190068736*c\ _1100_0^5 + 8489377582215774752338026444951795/83820973917224380137\ 472*c_1100_0^4 - 138845260117649003978848715672439/8382097391722438\ 0137472*c_1100_0^3 - 256228098809332644545814074287109/419104869586\ 12190068736*c_1100_0^2 + 790606253196277995939958710037/19493249748\ 19171631104*c_1100_0 - 3051484518699534480267929138411/838209739172\ 24380137472, c_0011_0 - 1, c_0011_10 + 2318674019077/279918827012096*c_1100_0^27 - 3946251868861/279918827012096*c_1100_0^26 + 63556920467655/279918827012096*c_1100_0^25 - 70340059824281/139959413506048*c_1100_0^24 + 293102922799855/69979706753024*c_1100_0^23 - 2135092574637517/279918827012096*c_1100_0^22 + 4941063697391297/139959413506048*c_1100_0^21 - 7966942872663233/279918827012096*c_1100_0^20 + 44942211952813173/279918827012096*c_1100_0^19 - 6266463699120063/69979706753024*c_1100_0^18 + 272888218874536369/279918827012096*c_1100_0^17 - 237838601490571773/279918827012096*c_1100_0^16 + 71758703871249009/17494926688256*c_1100_0^15 - 175434044275474669/139959413506048*c_1100_0^14 + 576610246121566407/69979706753024*c_1100_0^13 + 240733329206109307/139959413506048*c_1100_0^12 + 4657213490493219247/279918827012096*c_1100_0^11 + 947749781084114251/279918827012096*c_1100_0^10 + 6155177566432371977/279918827012096*c_1100_0^9 + 838582891185560657/69979706753024*c_1100_0^8 + 1020080550642726965/69979706753024*c_1100_0^7 + 1435620039643702103/279918827012096*c_1100_0^6 + 468574090451612625/139959413506048*c_1100_0^5 + 111345616664235643/279918827012096*c_1100_0^4 - 37648412849266889/279918827012096*c_1100_0^3 + 1179158153957471/139959413506048*c_1100_0^2 + 49146433986109/6509740163072*c_1100_0 - 23015106681029/279918827012096, c_0011_11 + 85/2097152*c_1100_0^27 - 103/2097152*c_1100_0^26 + 2297/2097152*c_1100_0^25 - 2027/1048576*c_1100_0^24 + 20733/1048576*c_1100_0^23 - 58821/2097152*c_1100_0^22 + 171003/1048576*c_1100_0^21 - 137225/2097152*c_1100_0^20 + 1650779/2097152*c_1100_0^19 - 71607/1048576*c_1100_0^18 + 10267523/2097152*c_1100_0^17 - 3747801/2097152*c_1100_0^16 + 10581115/524288*c_1100_0^15 + 3446899/1048576*c_1100_0^14 + 24101625/524288*c_1100_0^13 + 32719395/1048576*c_1100_0^12 + 221221339/2097152*c_1100_0^11 + 153727325/2097152*c_1100_0^10 + 341668751/2097152*c_1100_0^9 + 39168413/262144*c_1100_0^8 + 180314781/1048576*c_1100_0^7 + 275532943/2097152*c_1100_0^6 + 109371587/1048576*c_1100_0^5 + 138104563/2097152*c_1100_0^4 + 79289429/2097152*c_1100_0^3 + 4719577/262144*c_1100_0^2 + 10484373/2097152*c_1100_0 - 105/2097152, c_0011_4 + 4059174737159/139959413506048*c_1100_0^27 - 8143667365467/139959413506048*c_1100_0^26 + 113718839119857/139959413506048*c_1100_0^25 - 140406540581769/69979706753024*c_1100_0^24 + 66787152836085/4373731672064*c_1100_0^23 - 4385790818751327/139959413506048*c_1100_0^22 + 9310069952333789/69979706753024*c_1100_0^21 - 19574974655157911/139959413506048*c_1100_0^20 + 84497981599163783/139959413506048*c_1100_0^19 - 17343620313352891/34989853376512*c_1100_0^18 + 498228833564206719/139959413506048*c_1100_0^17 - 567100987549796067/139959413506048*c_1100_0^16 + 272398375363328475/17494926688256*c_1100_0^15 - 635594983312445703/69979706753024*c_1100_0^14 + 1102130375519033971/34989853376512*c_1100_0^13 - 239547642055063435/69979706753024*c_1100_0^12 + 8266602805829217701/139959413506048*c_1100_0^11 - 829425747068151619/139959413506048*c_1100_0^10 + 10978799540358644671/139959413506048*c_1100_0^9 + 322868358731482017/17494926688256*c_1100_0^8 + 786737630085961337/17494926688256*c_1100_0^7 + 645825176643486045/139959413506048*c_1100_0^6 + 715927637442220269/69979706753024*c_1100_0^5 - 204151037186002403/139959413506048*c_1100_0^4 + 1622918154184333/139959413506048*c_1100_0^3 + 8025799826039885/69979706753024*c_1100_0^2 - 3087574964781/3254870081536*c_1100_0 + 23611662301309/139959413506048, c_0011_8 + 1021123157077/69979706753024*c_1100_0^27 - 1025701730609/34989853376512*c_1100_0^26 + 3576526981857/8747463344128*c_1100_0^25 - 17679753760789/17494926688256*c_1100_0^24 + 537812129396451/69979706753024*c_1100_0^23 - 1104742400491961/69979706753024*c_1100_0^22 + 1171725524631045/17494926688256*c_1100_0^21 - 4936915066145157/69979706753024*c_1100_0^20 + 41539799918197/136679114752*c_1100_0^19 - 17510463265219885/69979706753024*c_1100_0^18 + 62687791471642921/34989853376512*c_1100_0^17 - 143006893767459987/69979706753024*c_1100_0^16 + 274270990865496855/34989853376512*c_1100_0^15 - 160644949551059549/34989853376512*c_1100_0^14 + 69357929568613009/4373731672064*c_1100_0^13 - 61862725390322945/34989853376512*c_1100_0^12 + 2079576727489163389/69979706753024*c_1100_0^11 - 53727029020227011/17494926688256*c_1100_0^10 + 690395459231712001/17494926688256*c_1100_0^9 + 320578424125708907/34989853376512*c_1100_0^8 + 1580465584459991055/69979706753024*c_1100_0^7 + 156396112294680547/69979706753024*c_1100_0^6 + 89696635534475259/17494926688256*c_1100_0^5 - 53176756447813577/69979706753024*c_1100_0^4 + 186932624497415/34989853376512*c_1100_0^3 + 3953745118620971/69979706753024*c_1100_0^2 - 312986305061/813717520384*c_1100_0 + 6917709259617/69979706753024, c_0101_10 - 3873626415647/279918827012096*c_1100_0^27 + 7965654997481/279918827012096*c_1100_0^26 - 108993733137317/279918827012096*c_1100_0^25 + 68393897177659/69979706753024*c_1100_0^24 - 1027623651889025/139959413506048*c_1100_0^23 + 4293060219811793/279918827012096*c_1100_0^22 - 9011005223405143/139959413506048*c_1100_0^21 + 19655792104083231/279918827012096*c_1100_0^20 - 81942742804256221/279918827012096*c_1100_0^19 + 8825055950491407/34989853376512*c_1100_0^18 - 480453654910549367/279918827012096*c_1100_0^17 + 566228256657547309/279918827012096*c_1100_0^16 - 529185051961979955/69979706753024*c_1100_0^15 + 663871328708348777/139959413506048*c_1100_0^14 - 1077742099732172237/69979706753024*c_1100_0^13 + 344323197881685211/139959413506048*c_1100_0^12 - 7998266436399799817/279918827012096*c_1100_0^11 + 1185846662047729513/279918827012096*c_1100_0^10 - 10683791454650812579/279918827012096*c_1100_0^9 - 971309912014279389/139959413506048*c_1100_0^8 - 3051362548744332329/139959413506048*c_1100_0^7 - 394426146513998515/279918827012096*c_1100_0^6 - 733729048266301951/139959413506048*c_1100_0^5 + 237450991965434235/279918827012096*c_1100_0^4 - 38827898734131675/279918827012096*c_1100_0^3 - 6993552754107613/139959413506048*c_1100_0^2 + 43164805434973/6509740163072*c_1100_0 - 220268642695599/279918827012096, c_0101_2 + 1021123157077/69979706753024*c_1100_0^27 - 1025701730609/34989853376512*c_1100_0^26 + 3576526981857/8747463344128*c_1100_0^25 - 17679753760789/17494926688256*c_1100_0^24 + 537812129396451/69979706753024*c_1100_0^23 - 1104742400491961/69979706753024*c_1100_0^22 + 1171725524631045/17494926688256*c_1100_0^21 - 4936915066145157/69979706753024*c_1100_0^20 + 41539799918197/136679114752*c_1100_0^19 - 17510463265219885/69979706753024*c_1100_0^18 + 62687791471642921/34989853376512*c_1100_0^17 - 143006893767459987/69979706753024*c_1100_0^16 + 274270990865496855/34989853376512*c_1100_0^15 - 160644949551059549/34989853376512*c_1100_0^14 + 69357929568613009/4373731672064*c_1100_0^13 - 61862725390322945/34989853376512*c_1100_0^12 + 2079576727489163389/69979706753024*c_1100_0^11 - 53727029020227011/17494926688256*c_1100_0^10 + 690395459231712001/17494926688256*c_1100_0^9 + 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