Magma V2.19-8 Wed Aug 21 2013 00:52:48 on localhost [Seed = 38016907] Type ? for help. Type -D to quit. Loading file "L12n109__sl2_c2.magma" ==TRIANGULATION=BEGINS== % Triangulation L12n109 geometric_solution 12.49616960 oriented_manifold CS_known -0.0000000000000001 2 0 torus 0.000000000000 0.000000000000 torus 0.000000000000 0.000000000000 13 1 2 3 4 0132 0132 0132 0132 1 0 1 1 0 0 0 0 0 0 1 -1 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 -1 0 0 1 -6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.620401922751 1.196780723756 0 5 7 6 0132 0132 0132 0132 1 0 1 1 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 0 0 1 0 -1 6 0 -6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.500000000000 8 0 6 5 0132 0132 0132 0132 1 0 1 1 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 0 0 0 0 0 -6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.658591323253 0.658591323253 9 10 7 0 0132 0132 3120 0132 1 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 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 0.240803845502 0.759196154498 5 10 0 11 0132 0321 0132 0132 1 0 1 1 0 0 0 0 -1 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 0 0 -1 1 1 0 -1 0 -1 0 0 1 7 -7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.341408676747 0.658591323253 4 1 2 12 0132 0132 0132 0132 1 0 1 1 0 0 0 0 1 0 0 -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 0 1 -1 -1 0 0 1 -7 0 0 7 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.000000000000 1.000000000000 9 10 1 2 2103 0213 0132 0132 1 0 1 1 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 -1 7 0 -6 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.759196154498 0.759196154498 11 12 3 1 3120 0132 3120 0132 1 0 1 1 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 -1 1 1 -7 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.000000000000 1.000000000000 2 10 11 12 0132 3012 2103 3120 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.658591323253 0.658591323253 3 11 6 12 0132 0132 2103 2103 1 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 0 0 0 0 -1 1 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 0.379598077249 1.196780723756 8 3 6 4 1230 0132 0213 0321 1 1 1 1 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 -7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.335574955504 0.942013507992 8 9 4 7 2103 0132 0132 3120 1 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 0 0 0 1 -1 0 0 0 0 0 0 1 0 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.379598077249 1.196780723756 8 7 5 9 3120 0132 0132 2103 1 0 1 1 0 0 0 0 0 0 1 -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 0 1 -1 0 0 -1 1 0 0 0 0 0 7 -7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.500000000000 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_1001_11'], 'c_1001_10' : d['c_1001_0'], 'c_1001_12' : d['c_1001_1'], 'c_1001_5' : d['c_1001_0'], 'c_1001_4' : d['c_1001_2'], 'c_1001_7' : negation(d['c_1001_11']), 'c_1001_6' : d['c_1001_0'], 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_1001_11'], 'c_1001_2' : d['c_1001_2'], 'c_1001_9' : d['c_0011_12'], 'c_1001_8' : negation(d['c_0011_10']), 'c_1010_12' : negation(d['c_1001_11']), 'c_1010_11' : d['c_0011_12'], 'c_1010_10' : d['c_1001_11'], 's_3_11' : d['1'], 's_3_10' : d['1'], 's_0_12' : negation(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_0011_12'], '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_2_12' : negation(d['1']), 's_2_10' : d['1'], 's_2_11' : d['1'], 's_0_8' : negation(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' : negation(d['1']), 's_0_3' : d['1'], 's_0_0' : negation(d['1']), 's_0_1' : negation(d['1']), 'c_1100_9' : negation(d['c_0101_2']), 'c_0011_10' : d['c_0011_10'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_0101_3']), 'c_1100_4' : negation(d['c_0101_7']), 'c_1100_7' : negation(d['c_0101_3']), 'c_1100_6' : negation(d['c_0101_3']), 'c_1100_1' : negation(d['c_0101_3']), 'c_1100_0' : negation(d['c_0101_7']), 'c_1100_3' : negation(d['c_0101_7']), 'c_1100_2' : negation(d['c_0101_3']), 's_0_10' : d['1'], 'c_1100_11' : negation(d['c_0101_7']), 'c_1100_10' : d['c_1001_2'], 's_0_11' : d['1'], 'c_1010_7' : d['c_1001_1'], 'c_1010_6' : d['c_1001_2'], 'c_1010_5' : d['c_1001_1'], 'c_1010_4' : d['c_1001_11'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_1001_0'], 'c_1010_0' : d['c_1001_2'], 'c_1010_9' : d['c_1001_11'], 'c_1010_8' : negation(d['c_0011_12']), 'c_1100_8' : negation(d['c_0101_1']), 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : d['1'], 's_3_2' : d['1'], 's_3_5' : negation(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' : negation(d['1']), 'c_1100_12' : negation(d['c_0101_3']), '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' : negation(d['1']), 's_1_1' : negation(d['1']), 's_1_0' : negation(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_0'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_0']), 'c_0011_7' : negation(d['c_0011_12']), 'c_0011_6' : d['c_0011_12'], 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : negation(d['c_0011_10']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_1'], 'c_0110_10' : d['c_0011_0'], 'c_0110_12' : d['c_0101_2'], 'c_0101_12' : d['c_0101_1'], '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_11'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0101_3'], '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_0'], 'c_0101_8' : d['c_0101_11'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_3'], 'c_0110_8' : d['c_0101_2'], 'c_0110_1' : d['c_0101_0'], 'c_0011_11' : negation(d['c_0011_10']), 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_11'], 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : d['c_0101_11'], 'c_0110_7' : d['c_0101_1'], 'c_0110_6' : d['c_0101_2']})} 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_12, c_0101_0, c_0101_1, c_0101_11, c_0101_2, c_0101_3, c_0101_7, c_1001_0, c_1001_1, c_1001_11, c_1001_2 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 6 Groebner basis: [ t - 209/288*c_1001_2^5 - 647/144*c_1001_2^4 - 691/96*c_1001_2^3 + 217/72*c_1001_2^2 - 187/96*c_1001_2 + 889/72, c_0011_0 - 1, c_0011_10 + 1/9*c_1001_2^5 + 2/3*c_1001_2^4 + 10/9*c_1001_2^3 + 11/9*c_1001_2 - 16/9, c_0011_12 + 1/3*c_1001_2^2 + 2/3*c_1001_2 - 1/3, c_0101_0 - 1, c_0101_1 - 1/18*c_1001_2^5 - 1/3*c_1001_2^4 - 7/18*c_1001_2^3 + 2/3*c_1001_2^2 + 7/18*c_1001_2 + 5/9, c_0101_11 + 1/18*c_1001_2^5 + 4/9*c_1001_2^4 + 7/6*c_1001_2^3 + 8/9*c_1001_2^2 + 1/6*c_1001_2 - 1/9, c_0101_2 + 1/3*c_1001_2^2 + 2/3*c_1001_2 - 1/3, c_0101_3 + 1/9*c_1001_2^5 + 2/3*c_1001_2^4 + 10/9*c_1001_2^3 + 11/9*c_1001_2 - 7/9, c_0101_7 - 1/18*c_1001_2^5 - 1/3*c_1001_2^4 - 7/18*c_1001_2^3 + 2/3*c_1001_2^2 - 11/18*c_1001_2 + 5/9, c_1001_0 + 1, c_1001_1 + 1/6*c_1001_2^5 + c_1001_2^4 + 3/2*c_1001_2^3 - 2/3*c_1001_2^2 + 5/6*c_1001_2 - 4/3, c_1001_11 - 1/3*c_1001_2^2 - 2/3*c_1001_2 + 1/3, c_1001_2^6 + 6*c_1001_2^5 + 9*c_1001_2^4 - 4*c_1001_2^3 + 9*c_1001_2^2 - 12*c_1001_2 + 8 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_12, c_0101_0, c_0101_1, c_0101_11, c_0101_2, c_0101_3, c_0101_7, c_1001_0, c_1001_1, c_1001_11, c_1001_2 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t - 1567534097/577148*c_1001_2^7 - 15336136271/4184323*c_1001_2^6 - 47877544849/8368646*c_1001_2^5 - 35204206737/8368646*c_1001_2^4 - 38935900207/8368646*c_1001_2^3 - 6730269391/4184323*c_1001_2^2 - 14468611771/16737292*c_1001_2 - 982482395/4184323, c_0011_0 - 1, c_0011_10 + 41760/13117*c_1001_2^7 + 74320/13117*c_1001_2^6 + 71303/13117*c_1001_2^5 + 50142/13117*c_1001_2^4 + 24936/13117*c_1001_2^3 + 9502/13117*c_1001_2^2 - 31815/13117*c_1001_2 + 314/13117, c_0011_12 - 2394356/144287*c_1001_2^7 - 3415902/144287*c_1001_2^6 - 4964926/144287*c_1001_2^5 - 3390664/144287*c_1001_2^4 - 3601034/144287*c_1001_2^3 - 980365/144287*c_1001_2^2 - 404102/144287*c_1001_2 + 3931/144287, c_0101_0 - 1, c_0101_1 + 2853716/144287*c_1001_2^7 + 4233422/144287*c_1001_2^6 + 5749259/144287*c_1001_2^5 + 3942226/144287*c_1001_2^4 + 3875330/144287*c_1001_2^3 + 1084887/144287*c_1001_2^2 - 90150/144287*c_1001_2 - 144764/144287, c_0101_11 - 2265074/144287*c_1001_2^7 - 6102166/144287*c_1001_2^6 - 9507677/144287*c_1001_2^5 - 10155634/144287*c_1001_2^4 - 8771948/144287*c_1001_2^3 - 5803036/144287*c_1001_2^2 - 2185671/144287*c_1001_2 - 351770/144287, c_0101_2 + 2953882/144287*c_1001_2^7 + 3946762/144287*c_1001_2^6 + 5194243/144287*c_1001_2^5 + 3392765/144287*c_1001_2^4 + 3555186/144287*c_1001_2^3 + 934935/144287*c_1001_2^2 - 139408/144287*c_1001_2 + 81638/144287, c_0101_3 + 371287/13117*c_1001_2^7 + 681910/13117*c_1001_2^6 + 1047348/13117*c_1001_2^5 + 941907/13117*c_1001_2^4 + 907943/13117*c_1001_2^3 + 485844/13117*c_1001_2^2 + 214350/13117*c_1001_2 + 45003/13117, c_0101_7 + 13833/144287*c_1001_2^7 + 2877566/144287*c_1001_2^6 + 4269674/144287*c_1001_2^5 + 5781695/144287*c_1001_2^4 + 3974185/144287*c_1001_2^3 + 3892502/144287*c_1001_2^2 + 1092519/144287*c_1001_2 + 56999/144287, c_1001_0 + 3872834/144287*c_1001_2^7 + 4779163/144287*c_1001_2^6 + 7130654/144287*c_1001_2^5 + 4727464/144287*c_1001_2^4 + 5403374/144287*c_1001_2^3 + 1407392/144287*c_1001_2^2 + 600076/144287*c_1001_2 + 219572/144287, c_1001_1 + 4070324/144287*c_1001_2^7 + 4623444/144287*c_1001_2^6 + 7251154/144287*c_1001_2^5 + 4579282/144287*c_1001_2^4 + 6013188/144287*c_1001_2^3 + 1451782/144287*c_1001_2^2 + 1121044/144287*c_1001_2 + 438034/144287, c_1001_11 - 3772668/144287*c_1001_2^7 - 5065823/144287*c_1001_2^6 - 7685670/144287*c_1001_2^5 - 5276925/144287*c_1001_2^4 - 5723518/144287*c_1001_2^3 - 1557344/144287*c_1001_2^2 - 649334/144287*c_1001_2 - 137457/144287, c_1001_2^8 + 50/29*c_1001_2^7 + 76/29*c_1001_2^6 + 68/29*c_1001_2^5 + 67/29*c_1001_2^4 + 36/29*c_1001_2^3 + 16/29*c_1001_2^2 + 6/29*c_1001_2 + 1/29 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.120 Total time: 0.330 seconds, Total memory usage: 32.09MB