Magma V2.19-8 Tue Aug 20 2013 16:19:23 on localhost [Seed = 1966401650] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v3483 geometric_solution 6.72322290 oriented_manifold CS_known -0.0000000000000004 1 0 torus 0.000000000000 0.000000000000 7 1 2 0 0 0132 0132 1230 3012 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 0 1 -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 0.075951720033 0.446437566620 0 3 2 4 0132 0132 1230 0132 0 0 0 0 0 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 -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 0.378729922507 1.392718345204 5 0 6 1 0132 0132 0132 3012 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 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 0.378729922507 1.392718345204 5 1 5 6 1023 0132 0132 2031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.434466155008 0.933437656654 5 6 1 6 2031 0213 0132 3120 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 0 0 0 0 0 -1 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 0.317454980988 0.811094139253 2 3 4 3 0132 1023 1302 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 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 0.434466155008 0.933437656654 4 3 4 2 3120 1302 0213 0132 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 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 0.317454980988 0.811094139253 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 's_3_1' : d['1'], 's_3_3' : d['1'], 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : d['1'], 's_3_0' : negation(d['1']), 's_2_0' : negation(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_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_0_6' : 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_6' : negation(d['c_0011_6']), 'c_1100_5' : d['c_0101_0'], 'c_1100_4' : negation(d['c_0011_4']), 's_3_6' : d['1'], 'c_1100_1' : negation(d['c_0011_4']), 'c_1100_0' : d['c_0101_1'], 'c_1100_3' : d['c_0101_0'], 'c_1100_2' : negation(d['c_0011_6']), 'c_0101_6' : d['c_0011_4'], 'c_0101_5' : negation(d['c_0011_4']), 'c_0101_4' : d['c_0101_0'], 'c_0101_3' : d['c_0101_2'], 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : d['c_0011_4'], '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_0'], 'c_0011_2' : negation(d['c_0011_0']), 'c_1001_5' : d['c_0101_2'], 'c_1001_4' : d['c_0110_3'], 'c_1001_6' : d['c_0110_3'], 'c_1001_1' : d['c_0011_6'], 'c_1001_0' : negation(d['c_0101_1']), 'c_1001_3' : d['c_0110_3'], 'c_1001_2' : negation(d['c_0101_0']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0110_3'], 'c_0110_2' : negation(d['c_0011_4']), 'c_0110_5' : d['c_0101_2'], 'c_0110_4' : d['c_0101_2'], 'c_0110_6' : d['c_0101_2'], 'c_1010_6' : negation(d['c_0101_0']), 'c_1010_5' : d['c_0110_3'], 'c_1010_4' : negation(d['c_0011_6']), 'c_1010_3' : d['c_0011_6'], 'c_1010_2' : negation(d['c_0101_1']), 'c_1010_1' : d['c_0110_3'], 'c_1010_0' : negation(d['c_0101_0'])})} PY=EVAL=SECTION=ENDS=HERE PRIMARY=DECOMPOSITION=BEGINS=HERE [ Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_4, c_0011_6, c_0101_0, c_0101_1, c_0101_2, c_0110_3 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 8 Groebner basis: [ t - 90765/203422*c_0110_3^7 - 121099/101711*c_0110_3^6 + 470814/101711*c_0110_3^5 + 1727501/101711*c_0110_3^4 + 329556/101711*c_0110_3^3 - 218279/6562*c_0110_3^2 + 480673/203422*c_0110_3 + 13451125/203422, c_0011_0 - 1, c_0011_4 + 1143/203422*c_0110_3^7 + 1713/101711*c_0110_3^6 + 1480/101711*c_0110_3^5 - 49659/203422*c_0110_3^4 - 141903/203422*c_0110_3^3 - 16353/101711*c_0110_3^2 + 40044/101711*c_0110_3 - 321/6562, c_0011_6 + 3765/203422*c_0110_3^7 + 5679/203422*c_0110_3^6 - 52985/203422*c_0110_3^5 - 99505/203422*c_0110_3^4 + 128427/203422*c_0110_3^3 + 309523/203422*c_0110_3^2 - 98989/203422*c_0110_3 - 7051/6562, c_0101_0 - 2454/101711*c_0110_3^7 - 9105/203422*c_0110_3^6 + 50025/203422*c_0110_3^5 + 74582/101711*c_0110_3^4 + 6738/101711*c_0110_3^3 - 276817/203422*c_0110_3^2 + 18901/203422*c_0110_3 + 3686/3281, c_0101_1 + 93/3281*c_0110_3^7 + 325/6562*c_0110_3^6 - 982/3281*c_0110_3^5 - 4955/6562*c_0110_3^4 - 127/3281*c_0110_3^3 + 9171/6562*c_0110_3^2 - 304/3281*c_0110_3 - 5107/6562, c_0101_2 + 2670/101711*c_0110_3^7 + 1596/101711*c_0110_3^6 - 56915/203422*c_0110_3^5 - 71027/203422*c_0110_3^4 + 15299/101711*c_0110_3^3 + 51740/101711*c_0110_3^2 - 208071/203422*c_0110_3 + 2143/6562, c_0110_3^8 - 12*c_0110_3^6 - 8*c_0110_3^5 + 32*c_0110_3^4 + 24*c_0110_3^3 - 88*c_0110_3^2 + 16*c_0110_3 + 31 ], Ideal of Polynomial ring of rank 8 over Rational Field Order: Lexicographical Variables: t, c_0011_0, c_0011_4, c_0011_6, c_0101_0, c_0101_1, c_0101_2, c_0110_3 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 9 Groebner basis: [ t + 40104/145*c_0110_3^8 + 5957/290*c_0110_3^7 - 14397/145*c_0110_3^6 - 9311/145*c_0110_3^5 - 1625/58*c_0110_3^4 + 4736/145*c_0110_3^3 - 12849/145*c_0110_3^2 - 578/145*c_0110_3 + 11721/290, c_0011_0 - 1, c_0011_4 + 3087/145*c_0110_3^8 + 148/145*c_0110_3^7 - 891/145*c_0110_3^6 - 958/145*c_0110_3^5 - 51/29*c_0110_3^4 + 338/145*c_0110_3^3 - 842/145*c_0110_3^2 + 1/145*c_0110_3 + 429/145, c_0011_6 + 3087/145*c_0110_3^8 + 148/145*c_0110_3^7 - 891/145*c_0110_3^6 - 958/145*c_0110_3^5 - 51/29*c_0110_3^4 + 338/145*c_0110_3^3 - 842/145*c_0110_3^2 + 1/145*c_0110_3 + 429/145, c_0101_0 + 1224/145*c_0110_3^8 - 824/145*c_0110_3^7 - 757/145*c_0110_3^6 - 431/145*c_0110_3^5 + 1/29*c_0110_3^4 + 156/145*c_0110_3^3 - 199/145*c_0110_3^2 + 257/145*c_0110_3 + 343/145, c_0101_1 + 279/29*c_0110_3^8 - 65/29*c_0110_3^7 + 49/29*c_0110_3^6 - 75/29*c_0110_3^5 - 14/29*c_0110_3^4 - 25/29*c_0110_3^3 - 75/29*c_0110_3^2 + 17/29*c_0110_3 + 14/29, c_0101_2 + c_0110_3, c_0110_3^9 + 4/9*c_0110_3^8 - 5/9*c_0110_3^7 - 5/9*c_0110_3^6 - 2/9*c_0110_3^5 + 1/9*c_0110_3^4 - 2/9*c_0110_3^3 - 1/9*c_0110_3^2 + 2/9*c_0110_3 + 1/9 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.020 Total time: 0.220 seconds, Total memory usage: 32.09MB