Magma V2.19-8 Tue Aug 20 2013 23:38:59 on localhost [Seed = 509115006] Type ? for help. Type -D to quit. Loading file "K12n457__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n457 geometric_solution 9.90530132 oriented_manifold CS_known 0.0000000000000001 1 0 torus 0.000000000000 0.000000000000 11 1 2 3 4 0132 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 -1 0 1 0 0 0 0 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.286207024643 1.732142286294 0 4 6 5 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 1 -1 0 0 0 0 0 0 0 0 0 4 -3 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.471376593108 0.677947064998 7 0 3 8 0132 0132 1023 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 1 0 -1 0 0 0 0 -1 0 0 1 0 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.033390404201 0.930285733228 5 9 2 0 0132 0132 1023 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 3 1 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.263476623820 0.658399115471 1 9 0 8 1023 0321 0132 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 -1 1 -1 0 0 1 0 0 0 0 3 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.129655427678 0.462296173983 3 10 1 9 0132 0132 0132 3012 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 0 0 0 0 0 0 0 -3 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.385879014393 0.730463785154 10 7 8 1 3012 0213 3012 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 0.424545787142 1.189296490843 2 9 6 10 0132 3012 0213 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 1.117138047179 0.748661502451 10 6 2 4 0132 1230 0132 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 1 0 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 0.350598333085 1.419708721205 7 3 5 4 1230 0132 1230 0321 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 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.578993056565 0.949218603158 8 5 7 6 0132 0132 0132 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.754582909666 0.558900771078 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_10' : negation(d['c_0101_9']), 'c_1001_5' : d['c_0101_6'], 'c_1001_4' : d['c_0101_3'], 'c_1001_7' : d['c_0011_10'], 'c_1001_6' : d['c_0011_10'], 'c_1001_1' : d['c_0101_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_0101_10'], 'c_1001_2' : d['c_0101_3'], 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : d['c_1001_0'], 'c_1010_10' : d['c_0101_6'], 's_0_10' : d['1'], 's_3_10' : d['1'], 's_2_8' : negation(d['1']), 's_2_9' : d['1'], 'c_0101_10' : d['c_0101_10'], 's_2_0' : d['1'], 's_2_1' : d['1'], 's_2_2' : d['1'], 's_2_3' : d['1'], 's_2_4' : negation(d['1']), 's_2_5' : d['1'], 's_2_6' : d['1'], 's_2_7' : d['1'], 's_2_10' : 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_3'], 'c_0011_10' : d['c_0011_10'], 'c_1100_5' : negation(d['c_1001_0']), 'c_1100_4' : d['c_1100_0'], 'c_1100_7' : d['c_0101_1'], 'c_1100_6' : negation(d['c_1001_0']), 'c_1100_1' : negation(d['c_1001_0']), 'c_1100_0' : d['c_1100_0'], 'c_1100_3' : d['c_1100_0'], 'c_1100_2' : negation(d['c_1100_0']), 'c_1100_10' : d['c_0101_1'], 'c_1010_7' : negation(d['c_0101_9']), 'c_1010_6' : d['c_0101_1'], 'c_1010_5' : negation(d['c_0101_9']), 'c_1010_4' : d['c_0101_10'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_0101_6'], 'c_1010_0' : d['c_0101_3'], 'c_1010_9' : d['c_0101_10'], 'c_1010_8' : d['c_0101_6'], 'c_1100_8' : negation(d['c_1100_0']), 's_3_1' : d['1'], 's_3_0' : negation(d['1']), 's_3_3' : d['1'], 's_3_2' : negation(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' : negation(d['1']), 's_1_7' : 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' : negation(d['1']), 's_1_1' : d['1'], 's_1_0' : negation(d['1']), 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : negation(d['c_0011_10']), 'c_0011_8' : negation(d['c_0011_10']), 'c_0011_5' : negation(d['c_0011_10']), 'c_0011_4' : negation(d['c_0011_0']), 'c_0011_7' : d['c_0011_0'], 'c_0011_6' : d['c_0011_6'], 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_10'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_10' : d['c_0011_6'], 'c_0101_7' : d['c_0011_6'], 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0101_10'], '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_6'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0011_0'], 'c_0110_8' : d['c_0101_10'], 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0011_6'], 'c_0110_5' : d['c_0101_3'], 'c_0110_4' : d['c_0101_6'], 'c_0110_7' : d['c_0101_10'], 'c_0110_6' : d['c_0101_1']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 12 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_6, c_0101_0, c_0101_1, c_0101_10, c_0101_3, c_0101_6, c_0101_9, c_1001_0, c_1100_0 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 14 Groebner basis: [ t - 4158775405313/26448987240*c_1100_0^13 + 10195334470171/8816329080*c_1100_0^12 - 753118353601/278410392*c_1100_0^11 + 763408760459/508634370*c_1100_0^10 + 8244565714367/5289797448*c_1100_0^9 - 34974206214847/13224493620*c_1100_0^8 + 13327659193201/2204082270*c_1100_0^7 - 2066498627419/1763265816*c_1100_0^6 - 52794985508101/13224493620*c_1100_0^5 - 109478072823311/13224493620*c_1100_0^4 - 7510268746829/2034537480*c_1100_0^3 - 25696607719261/26448987240*c_1100_0^2 + 4469241650077/3306123405*c_1100_0 - 4149210231499/26448987240, c_0011_0 - 1, c_0011_10 + 2437813/1586384*c_1100_0^13 - 18726973/1586384*c_1100_0^12 + 47683215/1586384*c_1100_0^11 - 4505221/198298*c_1100_0^10 - 18982763/1586384*c_1100_0^9 + 25425221/793192*c_1100_0^8 - 26661121/396596*c_1100_0^7 + 46598257/1586384*c_1100_0^6 + 31018499/793192*c_1100_0^5 + 52527365/793192*c_1100_0^4 + 13321037/1586384*c_1100_0^3 - 9584335/1586384*c_1100_0^2 - 3763053/198298*c_1100_0 + 8047599/1586384, c_0011_6 - 216181/1586384*c_1100_0^13 + 1523263/1586384*c_1100_0^12 - 3197503/1586384*c_1100_0^11 + 359907/793192*c_1100_0^10 + 3087105/1586384*c_1100_0^9 - 1413817/793192*c_1100_0^8 + 863003/198298*c_1100_0^7 + 739011/1586384*c_1100_0^6 - 393900/99149*c_1100_0^5 - 857343/99149*c_1100_0^4 - 8386959/1586384*c_1100_0^3 - 776937/1586384*c_1100_0^2 + 1747189/793192*c_1100_0 + 442563/1586384, c_0101_0 + 2157115/1586384*c_1100_0^13 - 16734025/1586384*c_1100_0^12 + 43335193/1586384*c_1100_0^11 - 17112693/793192*c_1100_0^10 - 16504743/1586384*c_1100_0^9 + 23769875/793192*c_1100_0^8 - 6018637/99149*c_1100_0^7 + 46112939/1586384*c_1100_0^6 + 3480206/99149*c_1100_0^5 + 11080023/198298*c_1100_0^4 + 258017/1586384*c_1100_0^3 - 15580185/1586384*c_1100_0^2 - 13176927/793192*c_1100_0 + 8520451/1586384, c_0101_1 - 2809891/1586384*c_1100_0^13 + 21590395/1586384*c_1100_0^12 - 55007253/1586384*c_1100_0^11 + 10444481/396596*c_1100_0^10 + 21072189/1586384*c_1100_0^9 - 28546045/793192*c_1100_0^8 + 7622377/99149*c_1100_0^7 - 54697027/1586384*c_1100_0^6 - 34458267/793192*c_1100_0^5 - 62520183/793192*c_1100_0^4 - 12809119/1586384*c_1100_0^3 + 11743449/1586384*c_1100_0^2 + 4445527/198298*c_1100_0 - 9554405/1586384, c_0101_10 - 2799895/1586384*c_1100_0^13 + 21625611/1586384*c_1100_0^12 - 55629737/1586384*c_1100_0^11 + 2718542/99149*c_1100_0^10 + 20129613/1586384*c_1100_0^9 - 29084741/793192*c_1100_0^8 + 7682937/99149*c_1100_0^7 - 57630999/1586384*c_1100_0^6 - 34274553/793192*c_1100_0^5 - 60827733/793192*c_1100_0^4 - 6496183/1586384*c_1100_0^3 + 13636773/1586384*c_1100_0^2 + 8506417/396596*c_1100_0 - 10213149/1586384, c_0101_3 - 216181/1586384*c_1100_0^13 + 1523263/1586384*c_1100_0^12 - 3197503/1586384*c_1100_0^11 + 359907/793192*c_1100_0^10 + 3087105/1586384*c_1100_0^9 - 1413817/793192*c_1100_0^8 + 863003/198298*c_1100_0^7 + 739011/1586384*c_1100_0^6 - 393900/99149*c_1100_0^5 - 857343/99149*c_1100_0^4 - 8386959/1586384*c_1100_0^3 - 776937/1586384*c_1100_0^2 + 1747189/793192*c_1100_0 + 442563/1586384, c_0101_6 + 214319/198298*c_1100_0^13 - 3244335/396596*c_1100_0^12 + 4009443/198298*c_1100_0^11 - 5433515/396596*c_1100_0^10 - 3974217/396596*c_1100_0^9 + 2142106/99149*c_1100_0^8 - 8917801/198298*c_1100_0^7 + 1537771/99149*c_1100_0^6 + 11633897/396596*c_1100_0^5 + 19752579/396596*c_1100_0^4 + 4489643/396596*c_1100_0^3 - 567231/198298*c_1100_0^2 - 5177181/396596*c_1100_0 + 878629/396596, c_0101_9 - 2307821/1586384*c_1100_0^13 + 18023635/1586384*c_1100_0^12 - 47329435/1586384*c_1100_0^11 + 19683819/793192*c_1100_0^10 + 14517309/1586384*c_1100_0^9 - 24982999/793192*c_1100_0^8 + 26327801/396596*c_1100_0^7 - 56228049/1586384*c_1100_0^6 - 6829107/198298*c_1100_0^5 - 23618555/396596*c_1100_0^4 + 4021457/1586384*c_1100_0^3 + 17467911/1586384*c_1100_0^2 + 14624375/793192*c_1100_0 - 9561221/1586384, c_1001_0 - 3283297/1586384*c_1100_0^13 + 25356375/1586384*c_1100_0^12 - 65133447/1586384*c_1100_0^11 + 25174243/793192*c_1100_0^10 + 25253177/1586384*c_1100_0^9 - 34927251/793192*c_1100_0^8 + 36169433/396596*c_1100_0^7 - 66873285/1586384*c_1100_0^6 - 5242625/99149*c_1100_0^5 - 35023749/396596*c_1100_0^4 - 8187651/1586384*c_1100_0^3 + 20157107/1586384*c_1100_0^2 + 20735063/793192*c_1100_0 - 11361185/1586384, c_1100_0^14 - 8*c_1100_0^13 + 22*c_1100_0^12 - 21*c_1100_0^11 - 3*c_1100_0^10 + 23*c_1100_0^9 - 50*c_1100_0^8 + 33*c_1100_0^7 + 19*c_1100_0^6 + 36*c_1100_0^5 - 9*c_1100_0^4 - 6*c_1100_0^3 - 11*c_1100_0^2 + 7*c_1100_0 - 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.150 Total time: 0.350 seconds, Total memory usage: 32.09MB