Magma V2.19-8 Tue Aug 20 2013 16:08:57 on localhost [Seed = 3482210679] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation m219 geometric_solution 4.11285290 oriented_manifold CS_known 0.0000000000000001 1 0 torus 0.000000000000 0.000000000000 5 1 2 3 1 0132 0132 0132 1302 0 0 0 0 0 0 1 -1 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 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 0.874063109300 0.886621967461 0 3 0 2 0132 3012 2031 1230 0 0 0 0 0 -1 1 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 1 -1 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 0.157036645733 1.105570726967 1 0 4 4 3012 0132 3201 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 0.359416465887 0.474539071569 1 3 3 0 1230 1230 3012 0132 0 0 0 0 0 0 1 -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 1 -1 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 0.675518157523 0.989157595049 2 4 2 4 2310 2310 0132 3201 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.160626461198 0.576893433534 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 's_3_1' : negation(d['1']), 's_3_0' : negation(d['1']), 's_3_3' : d['1'], 's_3_2' : d['1'], 's_3_4' : d['1'], 's_2_0' : d['1'], 's_2_1' : negation(d['1']), 's_2_2' : d['1'], 's_2_3' : d['1'], 's_2_4' : 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_0_4' : d['1'], 's_0_2' : negation(d['1']), 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_1100_4' : negation(d['c_0011_4']), 'c_1100_1' : d['c_0101_4'], 'c_1100_0' : d['c_0011_3'], 'c_1100_3' : d['c_0011_3'], 'c_1100_2' : negation(d['c_0011_4']), 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : negation(d['c_0101_2']), 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0011_3'], 'c_0101_0' : negation(d['c_0011_0']), 'c_0011_4' : d['c_0011_4'], '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_1001_4' : negation(d['c_0101_2']), 'c_1001_1' : negation(d['c_0011_3']), 'c_1001_0' : negation(d['c_0101_2']), 'c_1001_3' : negation(d['c_0011_3']), 'c_1001_2' : negation(d['c_0101_4']), 'c_0110_1' : negation(d['c_0011_0']), 'c_0110_0' : d['c_0011_3'], 'c_0110_3' : negation(d['c_0011_0']), 'c_0110_2' : d['c_0101_4'], 'c_0110_4' : negation(d['c_0101_2']), 'c_1010_4' : d['c_0101_2'], 'c_1010_3' : negation(d['c_0101_2']), 'c_1010_2' : negation(d['c_0101_2']), 'c_1010_1' : d['c_0101_2'], 'c_1010_0' : negation(d['c_0101_4'])})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 6 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_3, c_0011_4, c_0101_2, c_0101_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 9 Groebner basis: [ t + 7/12*c_0101_4^8 + 19/12*c_0101_4^7 - 5/3*c_0101_4^6 - 13/2*c_0101_4^5 - 61/12*c_0101_4^4 + 35/12*c_0101_4^3 + 17/4*c_0101_4^2 - 115/12*c_0101_4 - 9/2, c_0011_0 - 1, c_0011_3 - 1/3*c_0101_4^8 - 7/12*c_0101_4^7 + 7/6*c_0101_4^6 + 2*c_0101_4^5 + 7/3*c_0101_4^4 - 23/12*c_0101_4^3 + c_0101_4^2 + 25/12*c_0101_4 + 2, c_0011_4 + 5/36*c_0101_4^8 + 1/4*c_0101_4^7 - 5/12*c_0101_4^6 - 8/9*c_0101_4^5 - 53/36*c_0101_4^4 + 3/4*c_0101_4^3 + 2/9*c_0101_4^2 - 5/36*c_0101_4 - 43/36, c_0101_2 + 11/36*c_0101_4^8 + 7/12*c_0101_4^7 - 13/12*c_0101_4^6 - 20/9*c_0101_4^5 - 77/36*c_0101_4^4 + 23/12*c_0101_4^3 - 4/9*c_0101_4^2 - 65/36*c_0101_4 - 49/36, c_0101_4^9 + 2*c_0101_4^8 - 3*c_0101_4^7 - 7*c_0101_4^6 - 9*c_0101_4^5 + 4*c_0101_4^4 - 2*c_0101_4^3 - 5*c_0101_4^2 - 7*c_0101_4 - 1 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.000 Total time: 0.200 seconds, Total memory usage: 32.09MB