Magma V2.19-8 Tue Aug 20 2013 23:49:10 on localhost [Seed = 4071921789] Type ? for help. Type -D to quit. Loading file "K11n137__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K11n137 geometric_solution 12.36406126 oriented_manifold CS_known -0.0000000000000001 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 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 0 0 1 -1 12 -1 0 -11 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.520351933260 0.594992322144 0 4 6 5 0132 2103 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 1 -1 0 0 -12 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.801330308430 0.522093772832 5 0 5 7 0132 0132 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 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 0.167146404596 0.952319887871 7 8 9 0 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 -1 1 0 0 1 -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 0.665169886850 0.529574686013 10 1 0 7 0132 2103 0132 0213 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 1 -1 0 -1 0 1 0 0 0 0 0 -11 0 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.482854183249 1.150818000598 2 2 1 9 0132 1230 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 0.520351933260 0.594992322144 11 8 7 1 0132 0213 0213 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 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 0 0 1.069692352217 0.802523474840 3 6 2 4 0132 0213 0132 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.319322659629 0.682941659805 11 3 6 10 3012 0132 0213 3201 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 1 0 -12 11 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.428160361515 0.949972284749 12 12 5 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 -1 0 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 0.851438625943 0.753821775144 4 8 12 11 0132 2310 0321 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 1 0 -1 0 11 -11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.618686893602 0.861390725089 6 12 10 8 0132 3120 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 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 0.415814835498 0.444425716003 9 11 10 9 0132 3120 0321 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 -1 0 0 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 0.251663403176 1.276976297003 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_0110_6' : d['c_0101_1'], 'c_1001_11' : negation(d['c_0110_8']), 'c_1001_10' : d['c_1001_10'], 'c_1001_12' : d['c_0110_8'], 'c_1001_5' : d['c_1001_5'], 'c_1001_4' : negation(d['c_0011_0']), 'c_1001_7' : d['c_1001_0'], 'c_1001_6' : d['c_1001_0'], 'c_1001_1' : negation(d['c_0011_10']), 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : negation(d['c_1001_10']), 'c_1001_2' : negation(d['c_0011_0']), 'c_1001_9' : d['c_0101_2'], 'c_1001_8' : d['c_1001_0'], 'c_1010_12' : negation(d['c_0011_11']), 'c_1010_11' : negation(d['c_0011_11']), 'c_1010_10' : negation(d['c_0110_8']), 's_0_10' : 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_1'], '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' : negation(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' : negation(d['1']), 's_0_4' : d['1'], 's_0_5' : d['1'], 's_0_2' : d['1'], 's_0_3' : negation(d['1']), 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_0011_11' : d['c_0011_11'], 'c_1100_8' : negation(d['c_0011_10']), 'c_0011_12' : d['c_0011_11'], 'c_1100_5' : d['c_1010_7'], 'c_1100_4' : d['c_1010_7'], 'c_1100_7' : negation(d['c_1001_5']), 'c_1100_6' : d['c_1010_7'], 'c_1100_1' : d['c_1010_7'], 'c_1100_0' : d['c_1010_7'], 'c_1100_3' : d['c_1010_7'], 'c_1100_2' : negation(d['c_1001_5']), 's_3_11' : d['1'], 'c_1100_9' : d['c_1010_7'], 'c_1100_11' : d['c_0110_8'], 'c_1100_10' : d['c_0110_8'], 's_0_11' : d['1'], 'c_1010_7' : d['c_1010_7'], 'c_1010_6' : negation(d['c_0011_10']), 'c_1010_5' : d['c_0101_2'], 'c_1010_4' : negation(d['c_1001_5']), 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_1001_5'], 'c_1010_0' : negation(d['c_0011_0']), 'c_1010_9' : negation(d['c_1001_10']), 'c_1010_8' : negation(d['c_1001_10']), 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : negation(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'], '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' : 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_11']), 'c_0011_8' : negation(d['c_0011_3']), 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_10']), 'c_0011_7' : negation(d['c_0011_3']), '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' : negation(d['c_0011_0']), 'c_0110_11' : negation(d['c_0011_3']), 'c_0110_10' : d['c_0101_1'], 'c_0110_12' : d['c_0101_2'], 'c_0101_12' : negation(d['c_0101_10']), 'c_0101_7' : d['c_0101_0'], 'c_0101_6' : negation(d['c_0011_3']), 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : negation(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_2'], 'c_0101_8' : negation(d['c_0011_11']), 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : negation(d['c_0101_10']), 'c_0110_8' : d['c_0110_8'], '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_0101_0'], 'c_0110_5' : d['c_0101_2'], 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : negation(d['c_0101_10']), 'c_0011_10' : d['c_0011_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_3, c_0101_0, c_0101_1, c_0101_10, c_0101_2, c_0110_8, c_1001_0, c_1001_10, c_1001_5, c_1010_7 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 16 Groebner basis: [ t + 85904597/270336*c_1010_7^15 - 36472157/270336*c_1010_7^14 + 187248335/270336*c_1010_7^13 - 13781797/22528*c_1010_7^12 + 63099067/22528*c_1010_7^11 - 407182649/270336*c_1010_7^10 + 472614127/135168*c_1010_7^9 - 830445623/270336*c_1010_7^8 + 819722885/135168*c_1010_7^7 - 317659443/90112*c_1010_7^6 + 83646583/22528*c_1010_7^5 - 278265367/67584*c_1010_7^4 + 185471195/90112*c_1010_7^3 - 193243375/90112*c_1010_7^2 + 73299563/270336*c_1010_7 - 67658543/90112, c_0011_0 - 1, c_0011_10 + 1/8*c_1010_7^15 + 1/8*c_1010_7^14 + 1/8*c_1010_7^13 + 3/4*c_1010_7^11 + 7/8*c_1010_7^10 + 1/4*c_1010_7^9 - 3/8*c_1010_7^8 + c_1010_7^7 + 15/8*c_1010_7^6 - 1/2*c_1010_7^5 - 2*c_1010_7^4 - 3/8*c_1010_7^3 + 5/8*c_1010_7^2 - 3/8*c_1010_7 - 9/8, c_0011_11 + 7/8*c_1010_7^15 + 3/8*c_1010_7^14 + 9/8*c_1010_7^13 - 1/4*c_1010_7^12 + 23/4*c_1010_7^11 + 19/8*c_1010_7^10 + 13/4*c_1010_7^9 - 13/8*c_1010_7^8 + 17/2*c_1010_7^7 + 31/8*c_1010_7^6 - 3/2*c_1010_7^5 - 11/2*c_1010_7^4 - 13/8*c_1010_7^3 - 13/8*c_1010_7^2 - 19/8*c_1010_7 - 13/8, c_0011_3 - 1/8*c_1010_7^15 + 1/8*c_1010_7^14 - 1/8*c_1010_7^13 + 1/4*c_1010_7^12 - c_1010_7^11 + 7/8*c_1010_7^10 - 1/4*c_1010_7^9 + 7/8*c_1010_7^8 - 9/4*c_1010_7^7 + 11/8*c_1010_7^6 + c_1010_7^5 + 1/2*c_1010_7^4 - 9/8*c_1010_7^3 + 1/8*c_1010_7^2 + 15/8*c_1010_7 - 1/8, c_0101_0 - 1/8*c_1010_7^15 + 1/8*c_1010_7^14 - 1/8*c_1010_7^13 + 1/4*c_1010_7^12 - c_1010_7^11 + 7/8*c_1010_7^10 - 1/4*c_1010_7^9 + 7/8*c_1010_7^8 - 9/4*c_1010_7^7 + 11/8*c_1010_7^6 + c_1010_7^5 + 1/2*c_1010_7^4 - 17/8*c_1010_7^3 + 1/8*c_1010_7^2 + 15/8*c_1010_7 - 1/8, c_0101_1 - 1/8*c_1010_7^15 - 1/8*c_1010_7^14 - 1/8*c_1010_7^13 - 3/4*c_1010_7^11 - 7/8*c_1010_7^10 - 1/4*c_1010_7^9 + 3/8*c_1010_7^8 - c_1010_7^7 - 15/8*c_1010_7^6 + 1/2*c_1010_7^5 + 2*c_1010_7^4 + 3/8*c_1010_7^3 - 13/8*c_1010_7^2 + 3/8*c_1010_7 + 9/8, c_0101_10 + 1/2*c_1010_7^15 - 3/4*c_1010_7^14 + 3/4*c_1010_7^13 - 3/2*c_1010_7^12 + 17/4*c_1010_7^11 - 11/2*c_1010_7^10 + 3*c_1010_7^9 - 11/2*c_1010_7^8 + 35/4*c_1010_7^7 - 9*c_1010_7^6 + 3/2*c_1010_7^5 - 3*c_1010_7^4 + 4*c_1010_7^3 - 3/4*c_1010_7^2 + 5/4*c_1010_7 + 1, c_0101_2 + 1, c_0110_8 + 11/8*c_1010_7^15 - 3/8*c_1010_7^14 + 19/8*c_1010_7^13 - 7/4*c_1010_7^12 + 21/2*c_1010_7^11 - 25/8*c_1010_7^10 + 37/4*c_1010_7^9 - 53/8*c_1010_7^8 + 73/4*c_1010_7^7 - 33/8*c_1010_7^6 + 7/2*c_1010_7^5 - 7*c_1010_7^4 + 7/8*c_1010_7^3 - 7/8*c_1010_7^2 - 25/8*c_1010_7 - 9/8, c_1001_0 - c_1010_7, c_1001_10 + 1/8*c_1010_7^15 - 1/8*c_1010_7^14 + 1/8*c_1010_7^13 - 1/4*c_1010_7^12 + c_1010_7^11 - 7/8*c_1010_7^10 + 1/4*c_1010_7^9 - 7/8*c_1010_7^8 + 9/4*c_1010_7^7 - 11/8*c_1010_7^6 - 1/2*c_1010_7^4 + 17/8*c_1010_7^3 - 1/8*c_1010_7^2 + 9/8*c_1010_7 + 1/8, c_1001_5 - 1/8*c_1010_7^15 + 1/8*c_1010_7^14 - 1/8*c_1010_7^13 + 1/4*c_1010_7^12 - c_1010_7^11 + 7/8*c_1010_7^10 - 1/4*c_1010_7^9 + 7/8*c_1010_7^8 - 9/4*c_1010_7^7 + 11/8*c_1010_7^6 + c_1010_7^5 + 1/2*c_1010_7^4 - 17/8*c_1010_7^3 + 1/8*c_1010_7^2 + 7/8*c_1010_7 - 1/8, c_1010_7^16 + 2*c_1010_7^14 - c_1010_7^13 + 8*c_1010_7^12 - c_1010_7^11 + 9*c_1010_7^10 - 5*c_1010_7^9 + 15*c_1010_7^8 - 3*c_1010_7^7 + 7*c_1010_7^6 - 8*c_1010_7^5 + c_1010_7^4 - 4*c_1010_7^3 - 2*c_1010_7^2 - 2*c_1010_7 - 1 ], 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_3, c_0101_0, c_0101_1, c_0101_10, c_0101_2, c_0110_8, c_1001_0, c_1001_10, c_1001_5, c_1010_7 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 18 Groebner basis: [ t + 48043850638442122856552740168660456309/5838656528466712126841894189\ 30163825*c_1010_7^17 - 771496861057853611960092585743984753312/2919\ 328264233356063420947094650819125*c_1010_7^16 + 563993453683018132845262233569356672762/583865652846671212684189418\ 930163825*c_1010_7^15 - 1075435389788321250163208307674195989718/58\ 3865652846671212684189418930163825*c_1010_7^14 + 5085256932484485681622008503011167255661/97310942141111868780698236\ 4883606375*c_1010_7^13 - 744594985565778139638946427535284204009/94\ 171879491398582690998293375832875*c_1010_7^12 + 44862125090410532652293461005692946724634/2919328264233356063420947\ 094650819125*c_1010_7^11 - 1015667662680894839450156275056877248893\ 9/583865652846671212684189418930163825*c_1010_7^10 + 16971214243950635175289006697217503347601/5838656528466712126841894\ 18930163825*c_1010_7^9 - 26792373856801610244498759158558033857177/\ 973109421411118687806982364883606375*c_1010_7^8 + 11654929092100611596594738145818259493244/3243698071370395626023274\ 54961202125*c_1010_7^7 - 70748704732669040964405185862286803998842/\ 2919328264233356063420947094650819125*c_1010_7^6 + 81289991367574181571492927888984510838508/2919328264233356063420947\ 094650819125*c_1010_7^5 - 396300512093276809450114286573305811771/3\ 1390626497132860896999431125277625*c_1010_7^4 + 29044364745665312850193631960984037544669/2919328264233356063420947\ 094650819125*c_1010_7^3 + 2526318251485753440677796241320430155469/\ 2919328264233356063420947094650819125*c_1010_7^2 + 725300674486772278138364117168262522911/583865652846671212684189418\ 930163825*c_1010_7 - 3115219838543435281448583715911712127473/29193\ 28264233356063420947094650819125, c_0011_0 - 1, c_0011_10 + 5396808957687664248438320580/208771357840585471905129851*c_\ 1010_7^17 - 17372677967191976168752560333/2087713578405854719051298\ 51*c_1010_7^16 + 63535633970332803128097477292/20877135784058547190\ 5129851*c_1010_7^15 - 121495198178752518654206268477/20877135784058\ 5471905129851*c_1010_7^14 + 344391910508601174101640606773/20877135\ 7840585471905129851*c_1010_7^13 - 522798881468422056968122848589/20\ 8771357840585471905129851*c_1010_7^12 + 1015919535818205272213385848412/208771357840585471905129851*c_1010_\ 7^11 - 1156054791193828529093859837986/208771357840585471905129851*\ c_1010_7^10 + 1928025917118904229346363930437/208771357840585471905\ 129851*c_1010_7^9 - 1837830126145423918237213235269/208771357840585\ 471905129851*c_1010_7^8 + 2395195541915001149291208845420/208771357\ 840585471905129851*c_1010_7^7 - 1636697848884343317574945382579/208\ 771357840585471905129851*c_1010_7^6 + 1870502443105380517869844362497/208771357840585471905129851*c_1010_\ 7^5 - 869722334291073735195093935635/208771357840585471905129851*c_\ 1010_7^4 + 683439245417883992386685225452/2087713578405854719051298\ 51*c_1010_7^3 + 35104425172175684210380004087/208771357840585471905\ 129851*c_1010_7^2 + 88913968368697106608528390826/20877135784058547\ 1905129851*c_1010_7 - 70997364138485050492301631201/208771357840585\ 471905129851, c_0011_11 - 19396898448501184537235548785/208771357840585471905129851*c\ _1010_7^17 + 62438177061799822771507772411/208771357840585471905129\ 851*c_1010_7^16 - 228366981962610409364520361776/208771357840585471\ 905129851*c_1010_7^15 + 436691381541445953356403566222/208771357840\ 585471905129851*c_1010_7^14 - 1237909529184282921333456041279/20877\ 1357840585471905129851*c_1010_7^13 + 1879142674232073436120963595376/208771357840585471905129851*c_1010_\ 7^12 - 3651989102499473675591283222197/208771357840585471905129851*\ c_1010_7^11 + 4155613340183094669086757629138/208771357840585471905\ 129851*c_1010_7^10 - 6931271455369820043759116103194/20877135784058\ 5471905129851*c_1010_7^9 + 6606556195997790098371600131969/20877135\ 7840585471905129851*c_1010_7^8 - 8611676426134361984985329680537/20\ 8771357840585471905129851*c_1010_7^7 + 5884326309781059213433548085353/208771357840585471905129851*c_1010_\ 7^6 - 6725921144299308950109720266870/208771357840585471905129851*c\ _1010_7^5 + 3127120619547675720884795439966/20877135784058547190512\ 9851*c_1010_7^4 - 2458275359710557446149624911900/20877135784058547\ 1905129851*c_1010_7^3 - 126395210289189524390447384511/208771357840\ 585471905129851*c_1010_7^2 - 319648639237185967370509214954/2087713\ 57840585471905129851*c_1010_7 + 254506705261057415609841009739/2087\ 71357840585471905129851, c_0011_3 + 15483395664309925968026274210/208771357840585471905129851*c_\ 1010_7^17 - 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