Magma V2.19-8 Tue Aug 20 2013 23:39:00 on localhost [Seed = 2968966359] Type ? for help. Type -D to quit. Loading file "K12n519__sl2_c0.magma" ==TRIANGULATION=BEGINS== % Triangulation K12n519 geometric_solution 10.59468665 oriented_manifold CS_known 0.0000000000000004 1 0 torus 0.000000000000 0.000000000000 11 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 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 1 -1 -3 1 0 2 0 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.603158383351 0.793060791788 0 5 7 6 0132 0132 0132 0132 0 0 0 0 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 -2 2 0 0 0 0 0 0 0 0 0 3 0 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.812849046806 1.044246741108 4 0 7 3 0321 0132 3201 1230 0 0 0 0 0 0 0 0 -1 0 0 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 -2 0 0 2 2 -2 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.504612334997 1.008433191353 2 8 9 0 3012 0132 0132 0132 0 0 0 0 0 0 0 0 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 0 0 0 1 0 0 -1 -2 0 0 2 0 -3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.719880926691 0.528991843257 2 5 0 10 0321 1302 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 1 0 -1 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 -2 2 0 0 2 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.790058965638 0.671818831811 10 1 9 4 0213 0132 3012 2031 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 2 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.435033011360 0.814180953905 7 8 1 9 1302 1023 0132 0132 0 0 0 0 0 0 0 0 0 0 0 0 -1 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 0 -3 3 0 0 3 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.689502299961 0.451045241607 2 6 10 1 2310 2031 0132 0132 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 3 -1 -2 0 0 0 0 0 -3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.535826444483 0.596312100706 6 3 9 10 1023 0132 1302 2031 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 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 -3 3 0 0 3 0 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.913094243710 0.821414136204 8 5 6 3 2031 1230 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 0 0 0 0 0 0 3 0 0 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.913094243710 0.821414136204 5 8 4 7 0213 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.575276915150 0.829038717224 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_0110_6' : d['c_0101_9'], 'c_1001_10' : d['c_0110_8'], 'c_1001_5' : negation(d['c_0011_9']), 'c_1001_4' : negation(d['c_0101_7']), 'c_1001_7' : negation(d['c_0101_9']), 'c_1001_6' : negation(d['c_0011_9']), 'c_1001_1' : negation(d['c_0011_3']), 'c_1001_0' : d['c_0101_3'], 'c_1001_3' : d['c_0011_10'], 'c_1001_2' : negation(d['c_0101_7']), 'c_1001_9' : d['c_0110_8'], 'c_1001_8' : d['c_0101_3'], 'c_1010_10' : negation(d['c_0101_9']), 's_0_10' : d['1'], 's_3_10' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_10' : d['c_0011_0'], '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_10' : 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' : 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_1100_0'], 'c_1100_8' : d['c_0101_9'], 'c_1100_5' : negation(d['c_0110_8']), 'c_1100_4' : d['c_1100_0'], 'c_1100_7' : d['c_1100_0'], 'c_1100_6' : d['c_1100_0'], 'c_1100_1' : d['c_1100_0'], 'c_1100_0' : d['c_1100_0'], 'c_1100_3' : d['c_1100_0'], 'c_1100_2' : negation(d['c_0011_7']), 'c_1100_10' : d['c_1100_0'], 'c_1010_7' : negation(d['c_0011_3']), 'c_1010_6' : d['c_0110_8'], 'c_1010_5' : negation(d['c_0011_3']), 'c_1010_4' : d['c_0110_8'], 'c_1010_3' : d['c_0101_3'], 'c_1010_2' : d['c_0101_3'], 'c_1010_1' : negation(d['c_0011_9']), 'c_1010_0' : negation(d['c_0101_7']), 'c_1010_9' : d['c_0011_10'], 'c_1010_8' : d['c_0011_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' : d['1'], 's_3_8' : d['1'], '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' : d['c_0011_9'], 'c_0011_8' : negation(d['c_0011_3']), 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_3']), 'c_0011_7' : d['c_0011_7'], 'c_0011_6' : negation(d['c_0011_3']), '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_10' : d['c_0101_7'], 'c_0101_7' : d['c_0101_7'], 'c_0101_6' : negation(d['c_0011_7']), 'c_0101_5' : d['c_0011_10'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : negation(d['c_0101_1']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : negation(d['c_0011_7']), 'c_0101_9' : d['c_0101_9'], 'c_0101_8' : negation(d['c_0011_9']), 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_3'], 'c_0110_8' : d['c_0110_8'], 'c_0110_1' : negation(d['c_0011_7']), 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : negation(d['c_0011_7']), 'c_0110_2' : d['c_0011_3'], 'c_0110_5' : negation(d['c_0101_7']), 'c_0110_4' : d['c_0011_0'], 'c_0110_7' : d['c_0101_1'], 'c_0011_10' : d['c_0011_10']})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 12 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_3, c_0011_7, c_0011_9, c_0101_1, c_0101_3, c_0101_7, c_0101_9, c_0110_8, c_1100_0 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 7 Groebner basis: [ t - 6293909/187663*c_1100_0^6 - 465315/187663*c_1100_0^5 - 47672951/187663*c_1100_0^4 - 13902017/187663*c_1100_0^3 - 28554912/187663*c_1100_0^2 - 29007526/187663*c_1100_0 - 678377/26809, c_0011_0 - 1, c_0011_10 - 47/83*c_1100_0^6 + 6/83*c_1100_0^5 - 369/83*c_1100_0^4 - 24/83*c_1100_0^3 - 310/83*c_1100_0^2 - 85/83*c_1100_0 - 19/83, c_0011_3 - c_1100_0, c_0011_7 + 21/83*c_1100_0^6 - 38/83*c_1100_0^5 + 179/83*c_1100_0^4 - 263/83*c_1100_0^3 + 248/83*c_1100_0^2 - 98/83*c_1100_0 - 18/83, c_0011_9 - 11/83*c_1100_0^6 + 12/83*c_1100_0^5 - 74/83*c_1100_0^4 + 35/83*c_1100_0^3 + 44/83*c_1100_0^2 - 87/83*c_1100_0 + 45/83, c_0101_1 + 48/83*c_1100_0^6 + 8/83*c_1100_0^5 + 338/83*c_1100_0^4 + 134/83*c_1100_0^3 + 57/83*c_1100_0^2 + 191/83*c_1100_0 - 53/83, c_0101_3 + 24/83*c_1100_0^6 + 4/83*c_1100_0^5 + 169/83*c_1100_0^4 + 67/83*c_1100_0^3 - 13/83*c_1100_0^2 + 137/83*c_1100_0 - 68/83, c_0101_7 + 1, c_0101_9 + 11/83*c_1100_0^6 - 12/83*c_1100_0^5 + 74/83*c_1100_0^4 - 35/83*c_1100_0^3 - 44/83*c_1100_0^2 + 87/83*c_1100_0 - 45/83, c_0110_8 - 30/83*c_1100_0^6 - 5/83*c_1100_0^5 - 232/83*c_1100_0^4 - 63/83*c_1100_0^3 - 129/83*c_1100_0^2 - 26/83*c_1100_0 + 2/83, c_1100_0^7 - c_1100_0^6 + 8*c_1100_0^5 - 6*c_1100_0^4 + 6*c_1100_0^3 - 2*c_1100_0 + 1 ], Ideal of Polynomial ring of rank 12 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_10, c_0011_3, c_0011_7, c_0011_9, c_0101_1, c_0101_3, c_0101_7, c_0101_9, c_0110_8, c_1100_0 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t + 290849166/235501*c_1100_0^7 + 11430831893/2590511*c_1100_0^6 + 13382144771/2590511*c_1100_0^5 + 1572649807/2590511*c_1100_0^4 - 548093194/235501*c_1100_0^3 - 1550993926/2590511*c_1100_0^2 + 1687937320/2590511*c_1100_0 + 65343932/370073, c_0011_0 - 1, c_0011_10 + 38742/1979*c_1100_0^7 + 144164/1979*c_1100_0^6 + 181910/1979*c_1100_0^5 + 40332/1979*c_1100_0^4 - 74365/1979*c_1100_0^3 - 30326/1979*c_1100_0^2 + 20187/1979*c_1100_0 + 9943/1979, c_0011_3 - 8338/1979*c_1100_0^7 - 24883/1979*c_1100_0^6 - 24059/1979*c_1100_0^5 - 599/1979*c_1100_0^4 + 10052/1979*c_1100_0^3 + 6266/1979*c_1100_0^2 + 318/1979*c_1100_0 - 1133/1979, c_0011_7 - 3619/1979*c_1100_0^7 - 12552/1979*c_1100_0^6 - 19301/1979*c_1100_0^5 - 14502/1979*c_1100_0^4 - 5083/1979*c_1100_0^3 + 2798/1979*c_1100_0^2 + 1339/1979*c_1100_0 + 127/1979, c_0011_9 + 5379/1979*c_1100_0^7 + 20906/1979*c_1100_0^6 + 30071/1979*c_1100_0^5 + 8634/1979*c_1100_0^4 - 18954/1979*c_1100_0^3 - 13765/1979*c_1100_0^2 + 2437/1979*c_1100_0 + 2488/1979, c_0101_1 + 15499/1979*c_1100_0^7 + 58057/1979*c_1100_0^6 + 71219/1979*c_1100_0^5 + 10515/1979*c_1100_0^4 - 35953/1979*c_1100_0^3 - 13992/1979*c_1100_0^2 + 8317/1979*c_1100_0 + 4166/1979, c_0101_3 - 15499/1979*c_1100_0^7 - 58057/1979*c_1100_0^6 - 71219/1979*c_1100_0^5 - 10515/1979*c_1100_0^4 + 35953/1979*c_1100_0^3 + 13992/1979*c_1100_0^2 - 8317/1979*c_1100_0 - 4166/1979, c_0101_7 + 4125/1979*c_1100_0^7 + 15498/1979*c_1100_0^6 + 20171/1979*c_1100_0^5 + 4800/1979*c_1100_0^4 - 7542/1979*c_1100_0^3 + 456/1979*c_1100_0^2 + 4892/1979*c_1100_0 - 241/1979, c_0101_9 - 22583/1979*c_1100_0^7 - 77532/1979*c_1100_0^6 - 85378/1979*c_1100_0^5 - 7280/1979*c_1100_0^4 + 34593/1979*c_1100_0^3 + 6037/1979*c_1100_0^2 - 12433/1979*c_1100_0 - 4549/1979, c_0110_8 + 29898/1979*c_1100_0^7 + 116335/1979*c_1100_0^6 + 156981/1979*c_1100_0^5 + 49435/1979*c_1100_0^4 - 51688/1979*c_1100_0^3 - 27314/1979*c_1100_0^2 + 12295/1979*c_1100_0 + 6945/1979, c_1100_0^8 + 43/11*c_1100_0^7 + 61/11*c_1100_0^6 + 26/11*c_1100_0^5 - 15/11*c_1100_0^4 - 14/11*c_1100_0^3 + 2/11*c_1100_0^2 + 4/11*c_1100_0 + 1/11 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.480 Total time: 0.690 seconds, Total memory usage: 32.09MB