Magma V2.19-8 Tue Aug 20 2013 23:54:29 on localhost [Seed = 3019233293] Type ? for help. Type -D to quit. Loading file "K12n549__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n549 geometric_solution 11.92906089 oriented_manifold CS_known -0.0000000000000003 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 0 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 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.866025403784 0 5 3 6 0132 0132 3120 0132 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 4 -4 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 -0.365175303435 0.491669789755 5 0 8 7 0132 0132 0132 0132 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 4 0 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.351597056402 1.498527583003 8 9 1 0 1302 0132 3120 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 0 0 0 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 1.108386179918 0.936441598517 10 11 0 10 0132 0132 0132 2103 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 1 0 -1 0 3 0 0 -3 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.878035573048 1.053755774241 2 1 6 11 0132 0132 2103 3120 0 0 0 0 0 1 -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 0 0 0 -4 4 0 -4 0 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.121964426952 1.053755774241 5 10 1 8 2103 3201 0132 2310 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 -1 0 1 0 -4 0 0 4 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.866025403784 8 12 2 12 2310 0132 0132 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.229632629450 0.820232549676 6 3 7 2 3201 2031 3201 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 -4 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.351597056402 1.498527583003 11 3 12 10 3120 0132 0132 2031 0 0 0 0 0 0 0 0 1 0 0 -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 0 0 0 -3 0 0 3 -1 4 0 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.526438516646 1.287278998807 4 9 6 4 0132 1302 2310 2103 0 0 0 0 0 1 0 -1 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 -3 0 3 -1 0 1 0 1 0 0 -1 -3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.878035573048 1.053755774241 5 4 12 9 3120 0132 0321 3120 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 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.251713962036 0.684232371983 7 7 11 9 3201 0132 0321 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 0.310965085165 0.491689567824 ==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_0101_2'], 'c_1001_12' : negation(d['c_0101_9']), 'c_1001_5' : d['c_0011_6'], 'c_1001_4' : d['c_0011_3'], 'c_1001_7' : d['c_1001_0'], 'c_1001_6' : d['c_0011_6'], 'c_1001_1' : negation(d['c_0011_10']), 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_0011_10'], 'c_1001_2' : d['c_0011_3'], 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : negation(d['c_0101_0']), 'c_1010_12' : d['c_1001_0'], 'c_1010_11' : d['c_0011_3'], 'c_1010_10' : negation(d['c_1001_11']), 's_0_10' : d['1'], 's_3_10' : d['1'], 's_0_12' : d['1'], 's_3_12' : d['1'], 's_2_8' : negation(d['1']), 's_2_9' : d['1'], 'c_0101_11' : d['c_0101_11'], 'c_0101_10' : negation(d['c_0011_6']), 's_2_0' : d['1'], 's_2_1' : d['1'], 's_2_2' : negation(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' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_1100_9' : d['c_1001_11'], 'c_0011_10' : d['c_0011_10'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_0101_11']), 'c_1100_4' : negation(d['c_0101_1']), 'c_1100_7' : d['c_0011_12'], 'c_1100_6' : d['c_0011_8'], 'c_1100_1' : d['c_0011_8'], 'c_1100_0' : negation(d['c_0101_1']), 'c_1100_3' : negation(d['c_0101_1']), 'c_1100_2' : d['c_0011_12'], 's_3_11' : d['1'], 'c_1100_11' : negation(d['c_0101_9']), 'c_1100_10' : d['c_0011_6'], 's_0_11' : d['1'], 'c_1010_7' : negation(d['c_0101_9']), 'c_1010_6' : negation(d['c_0101_2']), 'c_1010_5' : negation(d['c_0011_10']), '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_0011_6'], 'c_1010_0' : d['c_0011_3'], 'c_1010_9' : d['c_0011_10'], 'c_1010_8' : d['c_0011_3'], 'c_1100_8' : d['c_0011_12'], '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' : negation(d['1']), 'c_1100_12' : d['c_1001_11'], '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' : d['c_0011_8'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_10']), 'c_0011_7' : negation(d['c_0011_12']), '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_3'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_2'], 'c_0110_10' : d['c_0101_1'], 'c_0110_12' : d['c_0101_9'], 'c_0101_12' : negation(d['c_0101_11']), 'c_0110_0' : d['c_0101_1'], 'c_0101_7' : d['c_0101_0'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : negation(d['c_0011_8']), '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_9'], 'c_0101_8' : negation(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_2'], 'c_0110_8' : d['c_0101_2'], 'c_0110_1' : d['c_0101_0'], 'c_0011_11' : d['c_0011_10'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_0'], 'c_0110_5' : d['c_0101_2'], 'c_0110_4' : negation(d['c_0011_6']), 'c_0110_7' : d['c_0101_11'], 'c_0110_6' : d['c_0101_11']})} 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_0011_3, c_0011_6, c_0011_8, c_0101_0, c_0101_1, c_0101_11, c_0101_2, c_0101_9, c_1001_0, c_1001_11 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 4 Groebner basis: [ t + 1294/1365*c_1001_11^3 + 629/195*c_1001_11^2 + 12221/1365*c_1001_11 + 9859/1365, c_0011_0 - 1, c_0011_10 + 3/5*c_1001_11^3 + 11/5*c_1001_11^2 + 27/5*c_1001_11 + 28/5, c_0011_12 + 3/5*c_1001_11^3 + 11/5*c_1001_11^2 + 27/5*c_1001_11 + 28/5, c_0011_3 + 3/5*c_1001_11^3 + 11/5*c_1001_11^2 + 32/5*c_1001_11 + 28/5, c_0011_6 + 1/5*c_1001_11^3 + 2/5*c_1001_11^2 + 4/5*c_1001_11 + 1/5, c_0011_8 + 1, c_0101_0 - 1/5*c_1001_11^3 - 2/5*c_1001_11^2 - 4/5*c_1001_11 - 1/5, c_0101_1 + 1/5*c_1001_11^3 + 2/5*c_1001_11^2 + 4/5*c_1001_11 + 1/5, c_0101_11 - 3/5*c_1001_11^3 - 11/5*c_1001_11^2 - 32/5*c_1001_11 - 33/5, c_0101_2 - 3/5*c_1001_11^3 - 11/5*c_1001_11^2 - 32/5*c_1001_11 - 28/5, c_0101_9 - 2/5*c_1001_11^3 - 9/5*c_1001_11^2 - 28/5*c_1001_11 - 32/5, c_1001_0 - 3/5*c_1001_11^3 - 11/5*c_1001_11^2 - 32/5*c_1001_11 - 33/5, c_1001_11^4 + 5*c_1001_11^3 + 15*c_1001_11^2 + 23*c_1001_11 + 13 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_12, c_0011_3, c_0011_6, c_0011_8, c_0101_0, c_0101_1, c_0101_11, c_0101_2, c_0101_9, c_1001_0, c_1001_11 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 6 Groebner basis: [ t + 264853700864528/77129994375*c_1001_11^5 - 633507663334436/77129994375*c_1001_11^4 + 177406471035518/5141999625*c_1001_11^3 - 807671073746722/15425998875*c_1001_11^2 + 5796151100330953/154259988750*c_1001_11 - 902748074209139/77129994375, c_0011_0 - 1, c_0011_10 + 15112/47777*c_1001_11^5 - 49572/47777*c_1001_11^4 + 175752/47777*c_1001_11^3 - 358823/47777*c_1001_11^2 + 279424/47777*c_1001_11 - 97185/47777, c_0011_12 - 36208/47777*c_1001_11^5 + 102384/47777*c_1001_11^4 - 396716/47777*c_1001_11^3 + 689262/47777*c_1001_11^2 - 559624/47777*c_1001_11 + 162313/47777, c_0011_3 + 3248/47777*c_1001_11^5 - 21176/47777*c_1001_11^4 + 62864/47777*c_1001_11^3 - 166504/47777*c_1001_11^2 + 213757/47777*c_1001_11 - 120438/47777, c_0011_6 - 21856/47777*c_1001_11^5 + 69064/47777*c_1001_11^4 - 247912/47777*c_1001_11^3 + 472720/47777*c_1001_11^2 - 425418/47777*c_1001_11 + 163445/47777, c_0011_8 - 6744/47777*c_1001_11^5 + 19492/47777*c_1001_11^4 - 72160/47777*c_1001_11^3 + 113897/47777*c_1001_11^2 - 98217/47777*c_1001_11 + 18483/47777, c_0101_0 - 18608/47777*c_1001_11^5 + 47888/47777*c_1001_11^4 - 185048/47777*c_1001_11^3 + 306216/47777*c_1001_11^2 - 211661/47777*c_1001_11 + 43007/47777, c_0101_1 + 18608/47777*c_1001_11^5 - 47888/47777*c_1001_11^4 + 185048/47777*c_1001_11^3 - 306216/47777*c_1001_11^2 + 211661/47777*c_1001_11 - 43007/47777, c_0101_11 - 8368/47777*c_1001_11^5 + 30080/47777*c_1001_11^4 - 103592/47777*c_1001_11^3 + 244926/47777*c_1001_11^2 - 228984/47777*c_1001_11 + 78702/47777, c_0101_2 - 17848/47777*c_1001_11^5 + 31636/47777*c_1001_11^4 - 158100/47777*c_1001_11^3 + 163935/47777*c_1001_11^2 - 18666/47777*c_1001_11 - 55310/47777, c_0101_9 + 18360/47777*c_1001_11^5 - 70748/47777*c_1001_11^4 + 238616/47777*c_1001_11^3 - 525327/47777*c_1001_11^2 + 493181/47777*c_1001_11 - 169846/47777, c_1001_0 - 3248/47777*c_1001_11^5 + 21176/47777*c_1001_11^4 - 62864/47777*c_1001_11^3 + 166504/47777*c_1001_11^2 - 213757/47777*c_1001_11 + 72661/47777, c_1001_11^6 - 7/2*c_1001_11^5 + 13*c_1001_11^4 - 215/8*c_1001_11^3 + 61/2*c_1001_11^2 - 145/8*c_1001_11 + 41/8 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_12, c_0011_3, c_0011_6, c_0011_8, c_0101_0, c_0101_1, c_0101_11, c_0101_2, c_0101_9, c_1001_0, c_1001_11 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 6 Groebner basis: [ t - 5671003/22601250*c_1001_11^5 - 21739009/11300625*c_1001_11^4 - 31384391/7533750*c_1001_11^3 + 46048693/22601250*c_1001_11^2 + 190036211/11300625*c_1001_11 + 176142844/11300625, c_0011_0 - 1, c_0011_10 + 3/28*c_1001_11^5 + 15/28*c_1001_11^4 + 17/28*c_1001_11^3 - 1/7*c_1001_11^2 - 5/14*c_1001_11 - 9/28, c_0011_12 - 1/14*c_1001_11^5 - 5/14*c_1001_11^4 - 1/14*c_1001_11^3 + 10/7*c_1001_11^2 + 11/7*c_1001_11 + 31/14, c_0011_3 - 13/28*c_1001_11^5 - 107/28*c_1001_11^4 - 335/28*c_1001_11^3 - 255/14*c_1001_11^2 - 121/7*c_1001_11 - 311/28, c_0011_6 - 3/28*c_1001_11^5 - 29/28*c_1001_11^4 - 101/28*c_1001_11^3 - 75/14*c_1001_11^2 - 29/7*c_1001_11 - 89/28, c_0011_8 - 3/14*c_1001_11^5 - 29/14*c_1001_11^4 - 101/14*c_1001_11^3 - 82/7*c_1001_11^2 - 72/7*c_1001_11 - 103/14, c_0101_0 + 3/28*c_1001_11^5 + 29/28*c_1001_11^4 + 101/28*c_1001_11^3 + 75/14*c_1001_11^2 + 29/7*c_1001_11 + 89/28, c_0101_1 - 9/28*c_1001_11^5 - 73/28*c_1001_11^4 - 219/28*c_1001_11^3 - 81/7*c_1001_11^2 - 153/14*c_1001_11 - 169/28, c_0101_11 - 3/14*c_1001_11^5 - 11/7*c_1001_11^4 - 59/14*c_1001_11^3 - 73/14*c_1001_11^2 - 67/14*c_1001_11 - 13/7, c_0101_2 - 3/7*c_1001_11^5 - 51/14*c_1001_11^4 - 80/7*c_1001_11^3 - 237/14*c_1001_11^2 - 211/14*c_1001_11 - 129/14, c_0101_9 + 9/28*c_1001_11^5 + 59/28*c_1001_11^4 + 135/28*c_1001_11^3 + 71/14*c_1001_11^2 + 31/7*c_1001_11 + 43/28, c_1001_0 - 3/28*c_1001_11^5 - 15/28*c_1001_11^4 - 17/28*c_1001_11^3 + 1/7*c_1001_11^2 - 9/14*c_1001_11 - 19/28, c_1001_11^6 + 10*c_1001_11^5 + 40*c_1001_11^4 + 83*c_1001_11^3 + 102*c_1001_11^2 + 83*c_1001_11 + 41 ], Ideal of Polynomial ring of rank 14 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_12, c_0011_3, c_0011_6, c_0011_8, c_0101_0, c_0101_1, c_0101_11, c_0101_2, c_0101_9, c_1001_0, c_1001_11 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 6 Groebner basis: [ t - 3631/5040*c_1001_11^5 + 2321/840*c_1001_11^4 - 4619/720*c_1001_11^3 + 29251/5040*c_1001_11^2 - 11231/2520*c_1001_11 + 101/315, c_0011_0 - 1, c_0011_10 - 1/4*c_1001_11^5 + 1/2*c_1001_11^4 - 3/4*c_1001_11^3 - 3/4*c_1001_11^2 - 1/2*c_1001_11 - 2, c_0011_12 + c_1001_11^4 - 3*c_1001_11^3 + 7*c_1001_11^2 - 5*c_1001_11 + 6, c_0011_3 - 1/4*c_1001_11^5 + 1/2*c_1001_11^4 - 3/4*c_1001_11^3 - 3/4*c_1001_11^2 + 1/2*c_1001_11 - 2, c_0011_6 + 1/4*c_1001_11^5 - c_1001_11^4 + 11/4*c_1001_11^3 - 15/4*c_1001_11^2 + 4*c_1001_11 - 2, c_0011_8 + 1, c_0101_0 - 1/2*c_1001_11^4 + 2*c_1001_11^3 - 9/2*c_1001_11^2 + 9/2*c_1001_11 - 4, c_0101_1 + 1/4*c_1001_11^5 - c_1001_11^4 + 11/4*c_1001_11^3 - 15/4*c_1001_11^2 + 4*c_1001_11 - 2, c_0101_11 - 1/2*c_1001_11^5 + 3/2*c_1001_11^4 - 7/2*c_1001_11^3 + 2*c_1001_11^2 - 5/2*c_1001_11 - 2, c_0101_2 + 1/4*c_1001_11^5 - 1/2*c_1001_11^4 + 3/4*c_1001_11^3 + 3/4*c_1001_11^2 - 1/2*c_1001_11 + 2, c_0101_9 + 1/2*c_1001_11^4 - 2*c_1001_11^3 + 9/2*c_1001_11^2 - 7/2*c_1001_11 + 4, c_1001_0 - 1/2*c_1001_11^5 + 3/2*c_1001_11^4 - 7/2*c_1001_11^3 + 2*c_1001_11^2 - 5/2*c_1001_11 - 2, c_1001_11^6 - 4*c_1001_11^5 + 11*c_1001_11^4 - 15*c_1001_11^3 + 20*c_1001_11^2 - 12*c_1001_11 + 8 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 10.520 Total time: 10.730 seconds, Total memory usage: 141.00MB