Magma V2.19-8 Tue Aug 20 2013 18:03:32 on localhost [Seed = 3600245582] Type ? for help. Type -D to quit. Loading file "9_28__sl2_c1.magma" ==TRIANGULATION=BEGINS== % Triangulation 9_28 geometric_solution 11.56317702 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 0 0 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 0 0 0 0.683682809084 0.688455786509 0 5 3 6 0132 0132 3120 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 -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 0.425764634340 0.156008786962 7 0 9 8 0132 0132 0132 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 0 0 0 -6 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.185815184877 0.743576362629 6 10 1 0 0132 0132 3120 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 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 0.503539378787 0.602736169814 8 10 0 8 1230 1230 0132 0213 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 -1 1 0 -1 0 1 0 6 0 0 -6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.236863612129 1.076892914586 9 1 6 10 1023 0132 0132 2103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0.500000000000 0.866025403784 3 11 1 5 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 1 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 0.429304013127 1.624770360560 2 9 11 12 0132 1023 2103 0132 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 0 0 0 0 0 -7 7 6 0 0 -6 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.500000000000 0.866025403784 12 4 2 4 3012 3012 0132 0213 0 0 0 0 0 0 0 0 0 0 -1 1 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 -6 6 -1 1 0 0 6 -6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.438061605041 0.618166616241 7 5 10 2 1023 1023 1302 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 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.448951572748 2.931392763311 9 3 4 5 2031 0132 3012 2103 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0.683682809084 1.265806055698 7 6 12 12 2103 0132 3012 3120 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 1 -1 0 0 0 -7 7 7 0 0 -7 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.121744414125 1.306622402750 11 11 7 8 3120 1230 0132 1230 0 0 0 0 0 1 -1 0 -1 0 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 7 -7 0 -7 0 6 1 7 -1 0 -6 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.121744414125 1.306622402750 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : negation(d['c_0011_12']), 'c_1001_10' : negation(d['c_0011_4']), 'c_1001_12' : d['c_0101_12'], 'c_1001_5' : negation(d['c_0011_12']), 'c_1001_4' : d['c_0110_5'], 'c_1001_7' : negation(d['c_0011_10']), 'c_1001_6' : negation(d['c_0011_12']), 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : negation(d['c_0011_4']), 'c_1001_3' : negation(d['c_1001_1']), 'c_1001_2' : d['c_0110_5'], 'c_1001_9' : d['c_0101_3'], 'c_1001_8' : negation(d['c_0011_4']), 'c_1010_12' : d['c_0101_11'], 'c_1010_11' : negation(d['c_0011_12']), 'c_1010_10' : negation(d['c_1001_1']), 's_3_11' : 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' : 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' : 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' : negation(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' : negation(d['1']), 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_0011_11' : negation(d['c_0011_10']), '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_1']), 'c_1100_7' : negation(d['c_0011_8']), 'c_1100_6' : negation(d['c_0101_3']), 'c_1100_1' : negation(d['c_0101_3']), 'c_1100_0' : negation(d['c_0101_1']), 'c_1100_3' : negation(d['c_0101_1']), 'c_1100_2' : d['c_0101_10'], 's_0_10' : d['1'], 'c_1100_11' : negation(d['c_0101_12']), 'c_1100_10' : negation(d['c_0110_5']), 's_0_11' : d['1'], 'c_1010_7' : d['c_0101_12'], 'c_1010_6' : negation(d['c_0011_12']), 'c_1010_5' : d['c_1001_1'], 'c_1010_4' : d['c_0101_10'], 'c_1010_3' : negation(d['c_0011_4']), 'c_1010_2' : negation(d['c_0011_4']), 'c_1010_1' : negation(d['c_0011_12']), 'c_1010_0' : d['c_0110_5'], 'c_1010_9' : d['c_0110_5'], 'c_1010_8' : negation(d['c_0101_1']), 'c_1100_8' : d['c_0101_10'], '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' : negation(d['1']), 's_3_8' : d['1'], 'c_1100_12' : negation(d['c_0011_8']), 's_1_7' : negation(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' : d['c_0011_0'], 'c_0011_8' : d['c_0011_8'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : d['c_0011_4'], 'c_0011_7' : d['c_0011_0'], 'c_0011_6' : d['c_0011_10'], '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_0011_8'], 'c_0110_10' : d['c_0101_3'], 'c_0110_12' : d['c_0011_8'], 'c_0101_12' : d['c_0101_12'], 'c_0110_0' : d['c_0101_1'], 'c_0101_7' : d['c_0101_11'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_3'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0101_12'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0011_10']), '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_12'], 'c_0110_8' : negation(d['c_0011_8']), 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : d['c_0101_10'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_11'], 'c_0110_5' : d['c_0110_5'], 'c_0110_4' : d['c_0011_8'], 'c_0110_7' : d['c_0101_12'], 'c_0110_6' : d['c_0101_3']})} 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_4, c_0011_8, c_0101_0, c_0101_1, c_0101_10, c_0101_11, c_0101_12, c_0101_3, c_0110_5, c_1001_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 4 Groebner basis: [ t - 697/273*c_0110_5*c_1001_1 - 41/273*c_0110_5 - 1018/273*c_1001_1 - 638/273, c_0011_0 - 1, c_0011_10 + c_0110_5*c_1001_1 + c_1001_1, c_0011_12 + c_0110_5*c_1001_1 + c_0110_5, c_0011_4 + c_0110_5*c_1001_1 - c_0110_5, c_0011_8 + c_0110_5, c_0101_0 + c_0110_5 + 2*c_1001_1 + 1, c_0101_1 - c_0110_5*c_1001_1 - c_0110_5 - c_1001_1, c_0101_10 - c_0110_5*c_1001_1 + c_0110_5 + c_1001_1, c_0101_11 + c_0110_5 + 1, c_0101_12 + c_0110_5*c_1001_1 + c_0110_5 + c_1001_1, c_0101_3 + c_0110_5 + c_1001_1 + 1, c_0110_5^2 + c_0110_5 + c_1001_1 + 1, c_1001_1^2 + c_1001_1 + 1 ], 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_4, c_0011_8, c_0101_0, c_0101_1, c_0101_10, c_0101_11, c_0101_12, c_0101_3, c_0110_5, c_1001_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 6 Groebner basis: [ t + 6039/32*c_1001_1^5 + 44441/32*c_1001_1^4 + 3037*c_1001_1^3 + 44953/32*c_1001_1^2 + 307/8*c_1001_1 + 6913/32, c_0011_0 - 1, c_0011_10 + 1/37*c_1001_1^5 + 15/37*c_1001_1^4 + 89/37*c_1001_1^3 + 198/37*c_1001_1^2 + 98/37*c_1001_1 + 21/37, c_0011_12 - 10/37*c_1001_1^5 - 76/37*c_1001_1^4 - 187/37*c_1001_1^3 - 130/37*c_1001_1^2 + 19/37*c_1001_1 + 12/37, c_0011_4 - 16/37*c_1001_1^5 - 129/37*c_1001_1^4 - 351/37*c_1001_1^3 - 356/37*c_1001_1^2 - 162/37*c_1001_1 - 3/37, c_0011_8 - 10/37*c_1001_1^5 - 76/37*c_1001_1^4 - 187/37*c_1001_1^3 - 167/37*c_1001_1^2 - 92/37*c_1001_1 - 25/37, c_0101_0 + 2/37*c_1001_1^5 + 30/37*c_1001_1^4 + 141/37*c_1001_1^3 + 248/37*c_1001_1^2 + 122/37*c_1001_1 + 5/37, c_0101_1 + 6/37*c_1001_1^5 + 53/37*c_1001_1^4 + 164/37*c_1001_1^3 + 189/37*c_1001_1^2 + 70/37*c_1001_1 + 15/37, c_0101_10 + 20/37*c_1001_1^5 + 152/37*c_1001_1^4 + 374/37*c_1001_1^3 + 297/37*c_1001_1^2 + 73/37*c_1001_1 - 24/37, c_0101_11 + 5/37*c_1001_1^5 + 38/37*c_1001_1^4 + 75/37*c_1001_1^3 - 9/37*c_1001_1^2 - 65/37*c_1001_1 - 43/37, c_0101_12 - 6/37*c_1001_1^5 - 53/37*c_1001_1^4 - 164/37*c_1001_1^3 - 189/37*c_1001_1^2 - 70/37*c_1001_1 - 15/37, c_0101_3 - 5/37*c_1001_1^5 - 38/37*c_1001_1^4 - 75/37*c_1001_1^3 + 9/37*c_1001_1^2 + 65/37*c_1001_1 + 6/37, c_0110_5 + 10/37*c_1001_1^5 + 76/37*c_1001_1^4 + 187/37*c_1001_1^3 + 167/37*c_1001_1^2 + 92/37*c_1001_1 + 25/37, c_1001_1^6 + 8*c_1001_1^5 + 21*c_1001_1^4 + 19*c_1001_1^3 + 7*c_1001_1^2 + c_1001_1 + 1 ], 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_4, c_0011_8, c_0101_0, c_0101_1, c_0101_10, c_0101_11, c_0101_12, c_0101_3, c_0110_5, c_1001_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 16 Groebner basis: [ t + 2467968108804571188711/74627364178721737*c_1001_1^15 + 18948195633400819510921/74627364178721737*c_1001_1^14 + 66278341439080617800050/74627364178721737*c_1001_1^13 + 133916175476420209442504/74627364178721737*c_1001_1^12 + 169138985946442532571703/74627364178721737*c_1001_1^11 + 129821264072546565268132/74627364178721737*c_1001_1^10 + 49143878485599157189537/74627364178721737*c_1001_1^9 - 3816374068015690129153/74627364178721737*c_1001_1^8 - 10627961888463421018287/74627364178721737*c_1001_1^7 - 3827295585695362930424/74627364178721737*c_1001_1^6 - 2855640425303397202674/74627364178721737*c_1001_1^5 - 2646645797087530129243/74627364178721737*c_1001_1^4 - 834180449458350941021/74627364178721737*c_1001_1^3 + 2531439781874788105/74627364178721737*c_1001_1^2 - 50573827118833027859/74627364178721737*c_1001_1 - 42097502823950130878/74627364178721737, c_0011_0 - 1, c_0011_10 - 11484001102709761150/74627364178721737*c_1001_1^15 - 95607628972525436473/74627364178721737*c_1001_1^14 - 362127944219592272433/74627364178721737*c_1001_1^13 - 798950801197826812005/74627364178721737*c_1001_1^12 - 1114221541353789370060/74627364178721737*c_1001_1^11 - 976523225780999407136/74627364178721737*c_1001_1^10 - 471908732236934529953/74627364178721737*c_1001_1^9 - 44663512024067388011/74627364178721737*c_1001_1^8 + 71672538803740263499/74627364178721737*c_1001_1^7 + 33724987539236139872/74627364178721737*c_1001_1^6 + 18817506991915508347/74627364178721737*c_1001_1^5 + 20736547359737585973/74627364178721737*c_1001_1^4 + 9303581919745476164/74627364178721737*c_1001_1^3 + 504634947076502844/74627364178721737*c_1001_1^2 + 219761233728014692/74627364178721737*c_1001_1 + 447547543330240867/74627364178721737, c_0011_12 + 8167333501642854721/74627364178721737*c_1001_1^15 + 67449934287378858712/74627364178721737*c_1001_1^14 + 253323593261671961177/74627364178721737*c_1001_1^13 + 553500269580578779675/74627364178721737*c_1001_1^12 + 763101852796717669388/74627364178721737*c_1001_1^11 + 658308000265725777903/74627364178721737*c_1001_1^10 + 308209804708575905189/74627364178721737*c_1001_1^9 + 19793720117957307411/74627364178721737*c_1001_1^8 - 54783577123685209965/74627364178721737*c_1001_1^7 - 26779347329850365045/74627364178721737*c_1001_1^6 - 14599801273124626374/74627364178721737*c_1001_1^5 - 13446541310492148499/74627364178721737*c_1001_1^4 - 5308314984530831842/74627364178721737*c_1001_1^3 - 139617289983788986/74627364178721737*c_1001_1^2 - 156679507520112620/74627364178721737*c_1001_1 - 210630030962048365/74627364178721737, c_0011_4 - 11749866800417280668/74627364178721737*c_1001_1^15 - 95727325851304485940/74627364178721737*c_1001_1^14 - 353321914361275094976/74627364178721737*c_1001_1^13 - 753503001020426719657/74627364178721737*c_1001_1^12 - 1002331482965236304598/74627364178721737*c_1001_1^11 - 813353142332164158536/74627364178721737*c_1001_1^10 - 327521854787222000704/74627364178721737*c_1001_1^9 + 23565907222194839140/74627364178721737*c_1001_1^8 + 77140277855642968674/74627364178721737*c_1001_1^7 + 23809144961880829759/74627364178721737*c_1001_1^6 + 14068113051174758696/74627364178721737*c_1001_1^5 + 17041862550083301013/74627364178721737*c_1001_1^4 + 5948535929473728491/74627364178721737*c_1001_1^3 - 580516550432505161/74627364178721737*c_1001_1^2 + 82109826618376557/74627364178721737*c_1001_1 + 386452686654288893/74627364178721737, c_0011_8 + 19850420661445339462/74627364178721737*c_1001_1^15 + 164497021406963239344/74627364178721737*c_1001_1^14 + 619690511563876512968/74627364178721737*c_1001_1^13 + 1357814308284191945047/74627364178721737*c_1001_1^12 + 1876276728086288747686/74627364178721737*c_1001_1^11 + 1621196260900912360174/74627364178721737*c_1001_1^10 + 759453260591270128680/74627364178721737*c_1001_1^9 + 49948725455529224536/74627364178721737*c_1001_1^8 - 129403756353649956512/74627364178721737*c_1001_1^7 - 57500904514867914320/74627364178721737*c_1001_1^6 - 30587788636928523650/74627364178721737*c_1001_1^5 - 32823754344760756652/74627364178721737*c_1001_1^4 - 14167380352909479221/74627364178721737*c_1001_1^3 - 655207739288729398/74627364178721737*c_1001_1^2 - 327435430625500947/74627364178721737*c_1001_1 - 676925367599734375/74627364178721737, c_0101_0 + 24345214952972566156/74627364178721737*c_1001_1^15 + 200081197517505915513/74627364178721737*c_1001_1^14 + 746735170643268088550/74627364178721737*c_1001_1^13 + 1617067468901193672037/74627364178721737*c_1001_1^12 + 2199385106321867051587/74627364178721737*c_1001_1^11 + 1852538577443269004507/74627364178721737*c_1001_1^10 + 817784286165205348479/74627364178721737*c_1001_1^9 + 9259652015330807520/74627364178721737*c_1001_1^8 - 162461122020033332365/74627364178721737*c_1001_1^7 - 61865858184230998688/74627364178721737*c_1001_1^6 - 33037273037892219421/74627364178721737*c_1001_1^5 - 37810238449581617312/74627364178721737*c_1001_1^4 - 15297973463016175798/74627364178721737*c_1001_1^3 + 208628085975319335/74627364178721737*c_1001_1^2 - 204694584451948127/74627364178721737*c_1001_1 - 812129084191666638/74627364178721737, c_0101_1 - 3524284746698112831/74627364178721737*c_1001_1^15 - 28751757512820904380/74627364178721737*c_1001_1^14 - 106611083508007339358/74627364178721737*c_1001_1^13 - 229626807126339725664/74627364178721737*c_1001_1^12 - 311862751973693425147/74627364178721737*c_1001_1^11 - 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