Magma V2.19-8 Tue Aug 20 2013 23:47:51 on localhost [Seed = 627265358] Type ? for help. Type -D to quit. Loading file "K10a67__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K10a67 geometric_solution 11.63703523 oriented_manifold CS_known -0.0000000000000001 1 0 torus 0.000000000000 0.000000000000 13 1 1 2 3 0132 1302 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 -1 1 0 0 0 0 1 0 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.351729367694 0.512430940308 0 4 5 0 0132 0132 0132 2031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.949373740922 0.750440409485 6 7 8 0 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 2 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.392315177940 0.874941091836 5 9 0 8 0132 0132 0132 3012 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1.089489352798 1.326513706163 10 1 10 6 0132 0132 3012 0213 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.079524937548 0.823693000159 3 7 8 1 0132 2310 2310 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.630258649185 0.450180599133 2 11 7 4 0132 0132 1023 0213 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 -1 0 0 0 0 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.544541994678 0.412001815518 9 2 6 5 0321 0132 1023 3201 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.716490147189 0.882249147392 12 5 3 2 0132 3201 1230 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.848736164447 0.719492260524 7 3 11 12 0321 0132 1230 2031 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 -1 1 0 1 0 -2 1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.885791553236 0.688756444635 4 4 12 11 0132 1230 0321 2310 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.603295678268 0.539862998452 10 6 12 9 3201 0132 1230 3012 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 1 0 0 -1 0 -2 0 2 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.265024569999 0.862912938430 8 9 10 11 0132 1302 0321 3012 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.017471304969 0.714019492246 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : negation(d['c_1001_10']), 'c_1001_10' : d['c_1001_10'], 'c_1001_12' : d['c_0011_11'], 'c_1001_5' : negation(d['c_1001_2']), 'c_1001_4' : d['c_0011_0'], 'c_1001_7' : d['c_0101_0'], 'c_1001_6' : d['c_0101_7'], 'c_1001_1' : negation(d['c_0011_3']), 'c_1001_0' : d['c_0101_0'], 'c_1001_3' : d['c_0011_12'], 'c_1001_2' : d['c_1001_2'], 'c_1001_9' : negation(d['c_0101_8']), 'c_1001_8' : negation(d['c_0101_5']), 'c_1010_12' : negation(d['c_0101_11']), 'c_1010_11' : d['c_0101_7'], 'c_1010_10' : negation(d['c_0101_11']), 's_0_10' : negation(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' : d['c_0101_11'], '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_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' : negation(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_0011_11' : d['c_0011_11'], 'c_0011_10' : negation(d['c_0011_0']), 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_0011_12']), 'c_1100_4' : negation(d['c_1001_10']), 'c_1100_7' : d['c_0011_3'], 'c_1100_6' : negation(d['c_0011_3']), 'c_1100_1' : negation(d['c_0011_12']), 'c_1100_0' : d['c_0101_5'], 'c_1100_3' : d['c_0101_5'], 'c_1100_2' : d['c_0101_5'], 's_3_11' : d['1'], 'c_1100_11' : d['c_0101_8'], 'c_1100_10' : d['c_0011_11'], 's_0_11' : d['1'], 'c_1010_7' : d['c_1001_2'], 'c_1010_6' : negation(d['c_1001_10']), 'c_1010_5' : negation(d['c_0011_3']), 'c_1010_4' : negation(d['c_0011_3']), 'c_1010_3' : negation(d['c_0101_8']), 'c_1010_2' : d['c_0101_0'], 'c_1010_1' : d['c_0011_0'], 'c_1010_0' : d['c_0011_12'], 'c_1010_9' : d['c_0011_12'], 'c_1010_8' : d['c_1001_2'], 'c_1100_8' : d['c_0101_5'], 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : 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_1001_10'], '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' : d['1'], 's_1_1' : d['1'], 's_1_0' : d['1'], 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : negation(d['c_0011_3']), 'c_0011_8' : negation(d['c_0011_12']), 'c_0011_5' : negation(d['c_0011_3']), 'c_0011_4' : d['c_0011_0'], 'c_0011_7' : negation(d['c_0011_11']), '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' : d['c_0011_3'], 'c_0011_2' : d['c_0011_11'], 'c_0110_11' : d['c_0101_11'], 'c_0110_10' : negation(d['c_0101_11']), 'c_0110_12' : d['c_0101_8'], 'c_0101_12' : negation(d['c_0101_10']), 'c_0110_0' : d['c_0101_1'], 'c_0101_7' : d['c_0101_7'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : negation(d['c_0101_11']), 'c_0101_3' : d['c_0101_1'], 'c_0101_2' : negation(d['c_0101_10']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0101_7']), 'c_0101_8' : d['c_0101_8'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : negation(d['1']), 'c_0110_9' : d['c_0011_11'], 'c_0110_8' : negation(d['c_0101_10']), 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : d['c_0101_11'], 'c_0110_3' : d['c_0101_5'], 'c_0110_2' : d['c_0101_0'], 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : d['c_0011_3'], '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_11, c_0011_12, c_0011_3, c_0101_0, c_0101_1, c_0101_10, c_0101_11, c_0101_5, c_0101_7, c_0101_8, c_1001_10, c_1001_2 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 14 Groebner basis: [ t - 226184177/90895168*c_1001_2^13 - 359967963/45447584*c_1001_2^12 + 100290543/90895168*c_1001_2^11 + 1488645853/45447584*c_1001_2^10 + 3026885353/90895168*c_1001_2^9 - 36932855/873992*c_1001_2^8 - 8290221913/90895168*c_1001_2^7 - 984847225/90895168*c_1001_2^6 + 7812336359/90895168*c_1001_2^5 + 6598129691/90895168*c_1001_2^4 - 244991307/45447584*c_1001_2^3 - 662772979/12985024*c_1001_2^2 - 4633138927/90895168*c_1001_2 + 916866539/90895168, c_0011_0 - 1, c_0011_11 + 541/62428*c_1001_2^13 - 623/31214*c_1001_2^12 - 15685/62428*c_1001_2^11 - 8863/31214*c_1001_2^10 + 49511/62428*c_1001_2^9 + 26532/15607*c_1001_2^8 - 19629/62428*c_1001_2^7 - 200299/62428*c_1001_2^6 - 103655/62428*c_1001_2^5 + 150707/62428*c_1001_2^4 + 38593/15607*c_1001_2^3 - 7603/62428*c_1001_2^2 - 74207/62428*c_1001_2 - 42601/62428, c_0011_12 - 36611/62428*c_1001_2^13 - 28294/15607*c_1001_2^12 + 18693/62428*c_1001_2^11 + 226601/31214*c_1001_2^10 + 443019/62428*c_1001_2^9 - 287817/31214*c_1001_2^8 - 1182675/62428*c_1001_2^7 - 113355/62428*c_1001_2^6 + 1082063/62428*c_1001_2^5 + 900491/62428*c_1001_2^4 - 26437/31214*c_1001_2^3 - 642017/62428*c_1001_2^2 - 685691/62428*c_1001_2 + 166389/62428, c_0011_3 + 9882/15607*c_1001_2^13 + 31360/15607*c_1001_2^12 - 3473/15607*c_1001_2^11 - 128165/15607*c_1001_2^10 - 134340/15607*c_1001_2^9 + 160970/15607*c_1001_2^8 + 360760/15607*c_1001_2^7 + 54183/15607*c_1001_2^6 - 331584/15607*c_1001_2^5 - 287813/15607*c_1001_2^4 + 19238/15607*c_1001_2^3 + 193110/15607*c_1001_2^2 + 196856/15607*c_1001_2 - 42205/15607, c_0101_0 - 1, c_0101_1 - 76139/62428*c_1001_2^13 - 59654/15607*c_1001_2^12 + 32585/62428*c_1001_2^11 + 482931/31214*c_1001_2^10 + 980379/62428*c_1001_2^9 - 609757/31214*c_1001_2^8 - 2625715/62428*c_1001_2^7 - 330087/62428*c_1001_2^6 + 2408399/62428*c_1001_2^5 + 2051743/62428*c_1001_2^4 - 64913/31214*c_1001_2^3 - 1414457/62428*c_1001_2^2 - 1473115/62428*c_1001_2 + 335209/62428, c_0101_10 - 31591/62428*c_1001_2^13 - 25559/15607*c_1001_2^12 + 11161/62428*c_1001_2^11 + 212731/31214*c_1001_2^10 + 449863/62428*c_1001_2^9 - 268429/31214*c_1001_2^8 - 1212495/62428*c_1001_2^7 - 180003/62428*c_1001_2^6 + 1114815/62428*c_1001_2^5 + 974083/62428*c_1001_2^4 - 17179/31214*c_1001_2^3 - 651869/62428*c_1001_2^2 - 671403/62428*c_1001_2 + 162505/62428, c_0101_11 - 9127/31214*c_1001_2^13 - 29839/31214*c_1001_2^12 + 537/31214*c_1001_2^11 + 58017/15607*c_1001_2^10 + 125545/31214*c_1001_2^9 - 138785/31214*c_1001_2^8 - 313263/31214*c_1001_2^7 - 35853/31214*c_1001_2^6 + 137414/15607*c_1001_2^5 + 105200/15607*c_1001_2^4 - 3159/15607*c_1001_2^3 - 67170/15607*c_1001_2^2 - 86410/15607*c_1001_2 + 20169/31214, c_0101_5 + 9882/15607*c_1001_2^13 + 31360/15607*c_1001_2^12 - 3473/15607*c_1001_2^11 - 128165/15607*c_1001_2^10 - 134340/15607*c_1001_2^9 + 160970/15607*c_1001_2^8 + 360760/15607*c_1001_2^7 + 54183/15607*c_1001_2^6 - 331584/15607*c_1001_2^5 - 287813/15607*c_1001_2^4 + 19238/15607*c_1001_2^3 + 193110/15607*c_1001_2^2 + 196856/15607*c_1001_2 - 42205/15607, c_0101_7 + 6315/62428*c_1001_2^13 + 13441/31214*c_1001_2^12 + 16889/62428*c_1001_2^11 - 42413/31214*c_1001_2^10 - 156663/62428*c_1001_2^9 + 8122/15607*c_1001_2^8 + 315417/62428*c_1001_2^7 + 217915/62428*c_1001_2^6 - 177981/62428*c_1001_2^5 - 350451/62428*c_1001_2^4 - 33241/15607*c_1001_2^3 + 162579/62428*c_1001_2^2 + 221611/62428*c_1001_2 + 3073/62428, c_0101_8 + c_1001_2, c_1001_10 - 7833/62428*c_1001_2^13 - 7361/15607*c_1001_2^12 - 10035/62428*c_1001_2^11 + 54877/31214*c_1001_2^10 + 163597/62428*c_1001_2^9 - 46195/31214*c_1001_2^8 - 368579/62428*c_1001_2^7 - 174357/62428*c_1001_2^6 + 263485/62428*c_1001_2^5 + 365903/62428*c_1001_2^4 + 29124/15607*c_1001_2^3 - 183999/62428*c_1001_2^2 - 269855/62428*c_1001_2 + 20685/62428, c_1001_2^14 + 3*c_1001_2^13 - c_1001_2^12 - 13*c_1001_2^11 - 11*c_1001_2^10 + 19*c_1001_2^9 + 33*c_1001_2^8 - 2*c_1001_2^7 - 34*c_1001_2^6 - 22*c_1001_2^5 + 7*c_1001_2^4 + 19*c_1001_2^3 + 16*c_1001_2^2 - 8*c_1001_2 + 1 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_11, c_0011_12, c_0011_3, c_0101_0, c_0101_1, c_0101_10, c_0101_11, c_0101_5, c_0101_7, c_0101_8, c_1001_10, c_1001_2 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 18 Groebner basis: [ t - 288635568903321510026572188268/27094368020225772850849443563*c_1001\ _2^17 + 761326738071013948849042665910/2709436802022577285084944356\ 3*c_1001_2^16 - 3247451621032322719714005503766/2709436802022577285\ 0849443563*c_1001_2^15 + 326155059887606704422715934784/38706240028\ 89396121549920509*c_1001_2^14 - 14637947562653648408954830929210/27\ 094368020225772850849443563*c_1001_2^13 + 85503199719197668073131751980/351874909353581465595447319*c_1001_2^\ 12 - 70668159523780000510614396573264/27094368020225772850849443563\ *c_1001_2^11 - 2396041724907859968304964364387/24631243654750702591\ 68131233*c_1001_2^10 + 14103969358023771621525886273214/27094368020\ 225772850849443563*c_1001_2^9 - 90125001900163824407628104640876/27\ 094368020225772850849443563*c_1001_2^8 + 91266056273758123024592082109383/27094368020225772850849443563*c_10\ 01_2^7 + 548913258749828795558890956434/387062400288939612154992050\ 9*c_1001_2^6 + 50131295825854587151237823633714/2709436802022577285\ 0849443563*c_1001_2^5 + 2052819993913253979309834490968/24631243654\ 75070259168131233*c_1001_2^4 - 26486044189505633065464581560868/270\ 94368020225772850849443563*c_1001_2^3 - 20666418257619123144540589052535/27094368020225772850849443563*c_10\ 01_2^2 - 2641094303505871704999986463455/27094368020225772850849443\ 563*c_1001_2 - 1395115771147268330302840639687/27094368020225772850\ 849443563, c_0011_0 - 1, c_0011_11 - 88968868382555187717834/62600055035328494146139*c_1001_2^17 + 317357225279633377636512/62600055035328494146139*c_1001_2^16 - 1336299708075739916782485/62600055035328494146139*c_1001_2^15 + 2089049161615306196215333/62600055035328494146139*c_1001_2^14 - 7043219635176492382466756/62600055035328494146139*c_1001_2^13 + 9464314272003183250008261/62600055035328494146139*c_1001_2^12 - 33564905262142562844257060/62600055035328494146139*c_1001_2^11 + 27061842492605813477184950/62600055035328494146139*c_1001_2^10 - 35096197450018562004990026/62600055035328494146139*c_1001_2^9 + 15849047323289611544895784/62600055035328494146139*c_1001_2^8 + 1819256135906438116158635/62600055035328494146139*c_1001_2^7 + 4241546339135705146069938/62600055035328494146139*c_1001_2^6 + 12409154354826122516422782/62600055035328494146139*c_1001_2^5 - 135274515651792501415161/62600055035328494146139*c_1001_2^4 - 5636905144854409315076288/62600055035328494146139*c_1001_2^3 - 2478089303345752108746489/62600055035328494146139*c_1001_2^2 - 692570081877990178993602/62600055035328494146139*c_1001_2 - 114390607123913830409797/62600055035328494146139, c_0011_12 + 97280540165125927908841/62600055035328494146139*c_1001_2^17 - 317262063435258372238964/62600055035328494146139*c_1001_2^16 + 1339677694655455555386802/62600055035328494146139*c_1001_2^15 - 1778154653671706046905178/62600055035328494146139*c_1001_2^14 + 6755116361748600074499662/62600055035328494146139*c_1001_2^13 - 7562071840718110031522347/62600055035328494146139*c_1001_2^12 + 32200295538008555726481968/62600055035328494146139*c_1001_2^11 - 16352290077982264518082169/62600055035328494146139*c_1001_2^10 + 22973963695341480739663404/62600055035328494146139*c_1001_2^9 + 894043003926417559387475/62600055035328494146139*c_1001_2^8 - 15089173200669494279064036/62600055035328494146139*c_1001_2^7 - 348119893790889407599137/62600055035328494146139*c_1001_2^6 - 16001707587216799541694419/62600055035328494146139*c_1001_2^5 - 3115029955102127391441267/62600055035328494146139*c_1001_2^4 + 8019757339319635483989670/62600055035328494146139*c_1001_2^3 + 3926824696685408684039677/62600055035328494146139*c_1001_2^2 + 697089654235588281778412/62600055035328494146139*c_1001_2 + 207593031659572493314914/62600055035328494146139, c_0011_3 - 5060300992780256169/5170567030257577777*c_1001_2^17 + 18444734090661631180/5170567030257577777*c_1001_2^16 - 76899126810481450055/5170567030257577777*c_1001_2^15 + 122812220498727418383/5170567030257577777*c_1001_2^14 - 401827986560766604255/5170567030257577777*c_1001_2^13 + 556147637967859973944/5170567030257577777*c_1001_2^12 - 1908784030202392655854/5170567030257577777*c_1001_2^11 + 1627249078172331612791/5170567030257577777*c_1001_2^10 - 1915970053573841893832/5170567030257577777*c_1001_2^9 + 872184997950983821713/5170567030257577777*c_1001_2^8 + 247591491369784065745/5170567030257577777*c_1001_2^7 + 141197777129292240873/5170567030257577777*c_1001_2^6 + 665022784045674939339/5170567030257577777*c_1001_2^5 - 41637639756641987404/5170567030257577777*c_1001_2^4 - 398156275142626074138/5170567030257577777*c_1001_2^3 - 88107038076754811152/5170567030257577777*c_1001_2^2 - 1705212612475734768/5170567030257577777*c_1001_2 - 4394635534682111141/5170567030257577777, c_0101_0 + 8097638906847027533398/62600055035328494146139*c_1001_2^17 - 51168768945958904783583/62600055035328494146139*c_1001_2^16 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