Magma V2.19-8 Tue Aug 20 2013 23:38:17 on localhost [Seed = 1831536960] Type ? for help. Type -D to quit. Loading file "K12n523__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n523 geometric_solution 8.62358496 oriented_manifold CS_known 0.0000000000000002 1 0 torus 0.000000000000 0.000000000000 10 1 2 3 4 0132 0132 0132 0132 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 0 0 0 0 -1 0 1 2 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.783227847770 0.497582454441 0 5 3 6 0132 0132 0213 0132 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 0 0 0 0 0 0 0 -2 0 0 2 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.714183143089 0.802111577718 7 0 5 8 0132 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 -2 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 0.261299968005 1.136475222803 6 1 9 0 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 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 0.640292220338 0.646998270017 8 9 0 5 3201 0132 0132 1230 0 0 0 0 0 0 0 0 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 0 0 -1 1 -1 0 2 -1 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.958997937412 1.653937930362 4 1 9 2 3012 0132 3201 0132 0 0 0 0 0 0 1 -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 0 -2 2 -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 0.041951917522 0.665227344378 3 8 1 7 0132 3012 0132 3012 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 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.105123276844 0.435929225495 2 8 6 9 0132 3120 1230 3012 0 0 0 0 0 0 1 -1 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 -2 2 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 1.268392329118 0.899497073839 6 7 2 4 1230 3120 0132 2310 0 0 0 0 0 0 1 -1 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 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.315365421780 0.785952609786 5 4 7 3 2310 0132 1230 0132 0 0 0 0 0 0 0 0 1 0 -1 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 0 -1 0 0 1 2 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.290882562713 0.739453975606 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_5' : negation(d['c_0011_8']), 'c_1001_4' : d['c_1001_1'], 'c_1001_7' : negation(d['c_1001_0']), 'c_1001_6' : negation(d['c_0011_8']), 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_1001_1'], 'c_1001_2' : d['c_1001_1'], 'c_1001_9' : negation(d['c_0101_3']), 'c_1001_8' : d['c_1001_0'], 's_2_8' : negation(d['1']), 's_2_9' : 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_2_7' : d['1'], 's_0_8' : d['1'], 's_0_9' : d['1'], 's_0_6' : d['1'], 's_0_7' : negation(d['1']), 's_0_4' : d['1'], 's_0_5' : d['1'], 's_0_2' : negation(d['1']), 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_1100_9' : d['c_0101_2'], 'c_1100_8' : d['c_0011_4'], 'c_1100_5' : d['c_0011_4'], 'c_1100_4' : d['c_0101_2'], 'c_1100_7' : d['c_0101_3'], 'c_1100_6' : d['c_1001_0'], 'c_1100_1' : d['c_1001_0'], 'c_1100_0' : d['c_0101_2'], 'c_1100_3' : d['c_0101_2'], 'c_1100_2' : d['c_0011_4'], 'c_1010_7' : negation(d['c_0011_8']), 'c_1010_6' : negation(d['c_0101_7']), 'c_1010_5' : d['c_1001_1'], 'c_1010_4' : negation(d['c_0101_3']), 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : negation(d['c_0011_8']), 'c_1010_0' : d['c_1001_1'], 'c_1010_9' : d['c_1001_1'], 'c_1010_8' : negation(d['c_0011_0']), 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : d['1'], 's_3_2' : negation(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' : negation(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_1_9' : d['1'], 's_1_8' : negation(d['1']), 'c_0011_9' : negation(d['c_0011_4']), 'c_0011_8' : d['c_0011_8'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : d['c_0011_4'], 'c_0011_7' : d['c_0011_0'], 'c_0011_6' : negation(d['c_0011_3']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_3'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0101_7' : d['c_0101_7'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : negation(d['c_0101_3']), 'c_0101_4' : d['c_0011_3'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0011_3'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0011_8'], 'c_0101_8' : d['c_0101_7'], 'c_0110_9' : d['c_0101_3'], 'c_0110_8' : negation(d['c_0011_3']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0011_3'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_7'], 'c_0110_5' : d['c_0101_2'], 'c_0110_4' : d['c_0011_0'], 'c_0110_7' : d['c_0101_2'], 'c_0110_6' : d['c_0101_3']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 11 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_3, c_0011_4, c_0011_8, c_0101_0, c_0101_2, c_0101_3, c_0101_7, c_1001_0, c_1001_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 15 Groebner basis: [ t + 4549493096257776985489/10131502419040216248*c_1001_1^14 - 17667945929322319022899/14352961760306973018*c_1001_1^13 + 76842170978416850613655/86117770561841838108*c_1001_1^12 - 89669302288714037136053/86117770561841838108*c_1001_1^11 + 112948352505412475806030/21529442640460459527*c_1001_1^10 - 37063796768182274523376/7176480880153486509*c_1001_1^9 + 115275798997464059101/1872125446996561698*c_1001_1^8 - 1069013399825002147645445/172235541123683676216*c_1001_1^7 - 168686824213814561873287/57411847041227892072*c_1001_1^6 - 584193324404283382789333/172235541123683676216*c_1001_1^5 - 4490227459519146554177/3377167473013405416*c_1001_1^4 - 70994973918823071282185/86117770561841838108*c_1001_1^3 - 2853570508181568878137/14352961760306973018*c_1001_1^2 - 1411892926332798473441/19137282347075964024*c_1001_1 + 1827814148188043640125/86117770561841838108, c_0011_0 - 1, c_0011_3 + 209332123612992/70322494440559*c_1001_1^14 - 1865944934187141/140644988881118*c_1001_1^13 + 1357303638008051/70322494440559*c_1001_1^12 - 1118468729268250/70322494440559*c_1001_1^11 + 6662511270978511/140644988881118*c_1001_1^10 - 13325249868846689/140644988881118*c_1001_1^9 + 7503290397186279/140644988881118*c_1001_1^8 - 2876277072436449/70322494440559*c_1001_1^7 + 4383294426702734/70322494440559*c_1001_1^6 + 2235881448332899/140644988881118*c_1001_1^5 + 4937295262588103/140644988881118*c_1001_1^4 + 1937440013266167/140644988881118*c_1001_1^3 + 1678763066344247/140644988881118*c_1001_1^2 + 242993908592059/70322494440559*c_1001_1 + 156956544691531/70322494440559, c_0011_4 + 650300590657221/140644988881118*c_1001_1^14 - 3024636422785607/281289977762236*c_1001_1^13 + 679809161549175/140644988881118*c_1001_1^12 - 1200002420810053/140644988881118*c_1001_1^11 + 3437620932545005/70322494440559*c_1001_1^10 - 4317413012993701/140644988881118*c_1001_1^9 - 1906933347088635/140644988881118*c_1001_1^8 - 8861329752888193/140644988881118*c_1001_1^7 - 19279514418877129/281289977762236*c_1001_1^6 - 16060362181081217/281289977762236*c_1001_1^5 - 13836827357663797/281289977762236*c_1001_1^4 - 6801348672496449/281289977762236*c_1001_1^3 - 2275651244071295/140644988881118*c_1001_1^2 - 848883173433329/140644988881118*c_1001_1 - 559762853975903/281289977762236, c_0011_8 - 582175884047683/140644988881118*c_1001_1^14 + 2490932945711925/281289977762236*c_1001_1^13 - 708900546360321/281289977762236*c_1001_1^12 + 2118697629981177/281289977762236*c_1001_1^11 - 12590673628256883/281289977762236*c_1001_1^10 + 6101029492963733/281289977762236*c_1001_1^9 + 4424451690337411/281289977762236*c_1001_1^8 + 18922726443153635/281289977762236*c_1001_1^7 + 8256535556689405/140644988881118*c_1001_1^6 + 18103751358883603/281289977762236*c_1001_1^5 + 3425396631798340/70322494440559*c_1001_1^4 + 8460353999648917/281289977762236*c_1001_1^3 + 4568300836176551/281289977762236*c_1001_1^2 + 1721959546770783/281289977762236*c_1001_1 + 177902726470513/70322494440559, c_0101_0 + 813965403361056/70322494440559*c_1001_1^14 - 1838073276058973/70322494440559*c_1001_1^13 + 1331960103597145/140644988881118*c_1001_1^12 - 3113947648259465/140644988881118*c_1001_1^11 + 9139245883174513/70322494440559*c_1001_1^10 - 5195704865731869/70322494440559*c_1001_1^9 - 2924220316187199/70322494440559*c_1001_1^8 - 27427427470981467/140644988881118*c_1001_1^7 - 9634418943372251/70322494440559*c_1001_1^6 - 9548239246735402/70322494440559*c_1001_1^5 - 11673812485963197/140644988881118*c_1001_1^4 - 3213012997547613/70322494440559*c_1001_1^3 - 1589330271085749/70322494440559*c_1001_1^2 - 1006533647126321/140644988881118*c_1001_1 - 149864849426313/70322494440559, c_0101_2 - 1351936855891409/140644988881118*c_1001_1^14 + 3380168709597981/140644988881118*c_1001_1^13 - 1003619366862220/70322494440559*c_1001_1^12 + 1493382526093875/70322494440559*c_1001_1^11 - 7589457988000044/70322494440559*c_1001_1^10 + 11913683127532881/140644988881118*c_1001_1^9 + 720035208623154/70322494440559*c_1001_1^8 + 9940471312398746/70322494440559*c_1001_1^7 + 14945478894763107/140644988881118*c_1001_1^6 + 7232460445602658/70322494440559*c_1001_1^5 + 4770097551387712/70322494440559*c_1001_1^4 + 4822267449658213/140644988881118*c_1001_1^3 + 1222205476708590/70322494440559*c_1001_1^2 + 425768879816672/70322494440559*c_1001_1 + 90569239837661/70322494440559, c_0101_3 + 863127433236819/70322494440559*c_1001_1^14 - 4174177384735677/140644988881118*c_1001_1^13 + 2166270889917083/140644988881118*c_1001_1^12 - 3746159818963155/140644988881118*c_1001_1^11 + 19788154993114903/140644988881118*c_1001_1^10 - 7124244472218480/70322494440559*c_1001_1^9 - 2912216247326421/140644988881118*c_1001_1^8 - 14136473764110687/70322494440559*c_1001_1^7 - 17068864974014991/140644988881118*c_1001_1^6 - 20066730712166617/140644988881118*c_1001_1^5 - 5117191090680161/70322494440559*c_1001_1^4 - 7092781214849549/140644988881118*c_1001_1^3 - 2528258113255581/140644988881118*c_1001_1^2 - 603451572900532/70322494440559*c_1001_1 - 123178620309901/140644988881118, c_0101_7 - 750598155119819/140644988881118*c_1001_1^14 + 2378513750827533/140644988881118*c_1001_1^13 - 2181722872531947/140644988881118*c_1001_1^12 + 1970484967203629/140644988881118*c_1001_1^11 - 9549239551097063/140644988881118*c_1001_1^10 + 12426997778181285/140644988881118*c_1001_1^9 - 1941391247580519/140644988881118*c_1001_1^8 + 4841514183310249/70322494440559*c_1001_1^7 - 1999371323768649/140644988881118*c_1001_1^6 + 943254526755106/70322494440559*c_1001_1^5 - 2377666373045391/140644988881118*c_1001_1^4 - 264175937585503/140644988881118*c_1001_1^3 - 1068278308740185/140644988881118*c_1001_1^2 - 84411904542668/70322494440559*c_1001_1 - 106699990543776/70322494440559, c_1001_0 - 454205293184319/281289977762236*c_1001_1^14 + 244956075238881/70322494440559*c_1001_1^13 - 96236629261073/70322494440559*c_1001_1^12 + 689852411088277/140644988881118*c_1001_1^11 - 1434678121880621/70322494440559*c_1001_1^10 + 1327406443173061/140644988881118*c_1001_1^9 + 262245992451235/140644988881118*c_1001_1^8 + 11435498273105569/281289977762236*c_1001_1^7 + 5127225105743131/281289977762236*c_1001_1^6 + 5022585404001227/281289977762236*c_1001_1^5 + 2101353150187887/281289977762236*c_1001_1^4 + 101397428217345/70322494440559*c_1001_1^3 - 37984298388647/140644988881118*c_1001_1^2 - 211267222778375/281289977762236*c_1001_1 - 92108405544557/140644988881118, c_1001_1^15 - 36/17*c_1001_1^14 + 14/17*c_1001_1^13 - 43/17*c_1001_1^12 + 191/17*c_1001_1^11 - 93/17*c_1001_1^10 - 13/17*c_1001_1^9 - 332/17*c_1001_1^8 - 258/17*c_1001_1^7 - 328/17*c_1001_1^6 - 207/17*c_1001_1^5 - 151/17*c_1001_1^4 - 72/17*c_1001_1^3 - 36/17*c_1001_1^2 - 11/17*c_1001_1 - 3/17 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.090 Total time: 0.290 seconds, Total memory usage: 32.09MB