Magma V2.19-8 Tue Aug 20 2013 16:16:40 on localhost [Seed = 3566553118] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation v0965 geometric_solution 4.85997549 oriented_manifold CS_known 0.0000000000000000 1 0 torus 0.000000000000 0.000000000000 7 1 1 2 2 0132 2310 0132 2310 0 0 0 0 0 -2 1 1 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 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 1.701482328764 1.916881021605 0 3 4 0 0132 0132 0132 3201 0 0 0 0 0 1 0 -1 0 0 0 0 0 -2 0 2 -1 1 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 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.488592349877 0.353538545904 0 2 2 0 3201 1230 3012 0132 0 0 0 0 0 1 0 -1 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 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 -0.240168697825 0.197107788516 5 1 5 6 0132 0132 1230 0132 0 0 0 0 0 -1 0 1 0 0 0 0 1 -1 0 0 -1 2 -1 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.506999931640 0.319597649211 5 6 6 1 2103 0132 2103 0132 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.586318132857 0.828926138712 3 6 4 3 0132 0321 2103 3012 0 0 0 0 0 -1 0 1 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 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 0.069909075289 1.726711555364 4 4 3 5 2103 0132 0132 0321 0 0 0 0 0 0 -1 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 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 0.740705936740 0.418471125826 ==TRIANGULATION=ENDS== PY=EVAL=SECTION=BEGINS=HERE {'variable_dict' : (lambda d, negation = (lambda x:-x): { 's_3_1' : d['1'], 's_3_3' : negation(d['1']), 's_3_2' : d['1'], 's_3_5' : negation(d['1']), 's_3_4' : d['1'], 's_3_0' : d['1'], 's_2_0' : d['1'], 's_2_1' : d['1'], 's_2_2' : d['1'], 's_2_3' : negation(d['1']), 's_2_4' : d['1'], 's_2_5' : d['1'], 's_2_6' : negation(d['1']), 's_1_6' : d['1'], 's_1_5' : negation(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' : d['c_0011_4'], 'c_1100_5' : negation(d['c_0101_1']), 'c_1100_4' : negation(d['c_0011_0']), 's_3_6' : negation(d['1']), 'c_1100_1' : negation(d['c_0011_0']), 'c_1100_0' : d['c_0011_2'], 'c_1100_3' : d['c_0011_4'], 'c_1100_2' : d['c_0011_2'], 'c_0101_6' : d['c_0101_4'], 'c_0101_5' : d['c_0101_4'], 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : d['c_0011_4'], 'c_0101_2' : negation(d['c_0101_1']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0011_5' : negation(d['c_0011_0']), 'c_0011_4' : d['c_0011_4'], 'c_0011_6' : negation(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_0'], 'c_0011_2' : d['c_0011_2'], 'c_1001_5' : d['c_0011_4'], 'c_1001_4' : negation(d['c_0011_4']), 'c_1001_6' : d['c_1001_1'], 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : negation(d['c_0101_1']), 'c_1001_3' : d['c_0101_1'], 'c_1001_2' : negation(d['c_0011_2']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_4'], 'c_0110_2' : d['c_0101_0'], 'c_0110_5' : d['c_0011_4'], 'c_0110_4' : d['c_0101_1'], 'c_0110_6' : d['c_0011_0'], 'c_1010_6' : negation(d['c_0011_4']), 'c_1010_5' : negation(d['c_0011_4']), 'c_1010_4' : d['c_1001_1'], 'c_1010_3' : d['c_1001_1'], 'c_1010_2' : negation(d['c_0101_1']), 'c_1010_1' : d['c_0101_1'], '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_2, c_0011_4, c_0101_0, c_0101_1, c_0101_4, c_1001_1 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 18 Groebner basis: [ t + 1427675/55956*c_1001_1^8 + 869263/13989*c_1001_1^7 + 7856205/74608*c_1001_1^6 + 15116515/111912*c_1001_1^5 + 135424681/895296*c_1001_1^4 + 58672745/447648*c_1001_1^3 + 90225517/895296*c_1001_1^2 + 58674451/895296*c_1001_1 + 10379509/895296, c_0011_0 - 1, c_0011_2 + 58808/13989*c_1001_1^8 + 162640/13989*c_1001_1^7 + 93042/4663*c_1001_1^6 + 375224/13989*c_1001_1^5 + 806885/27978*c_1001_1^4 + 361114/13989*c_1001_1^3 + 541823/27978*c_1001_1^2 + 353417/27978*c_1001_1 + 82409/27978, c_0011_4 - 74858/13989*c_0101_4*c_1001_1^8 - 56200/4663*c_0101_4*c_1001_1^7 - 522985/27978*c_0101_4*c_1001_1^6 - 110779/4663*c_0101_4*c_1001_1^5 - 2731975/111912*c_0101_4*c_1001_1^\ 4 - 1150627/55956*c_0101_4*c_1001_1^3 - 1643443/111912*c_0101_4*c_1001_1^2 - 940925/111912*c_0101_4*c_1001_1 + 78053/111912*c_0101_4, c_0101_0 + 2380/4663*c_1001_1^8 + 40304/13989*c_1001_1^7 + 74573/13989*c_1001_1^6 + 102874/13989*c_1001_1^5 + 477571/55956*c_1001_1^4 + 72381/9326*c_1001_1^3 + 330187/55956*c_1001_1^2 + 76931/18652*c_1001_1 + 114943/55956, c_0101_1 - 18884/13989*c_1001_1^8 - 37088/13989*c_1001_1^7 - 51109/13989*c_1001_1^6 - 60934/13989*c_1001_1^5 - 71577/18652*c_1001_1^4 - 78521/27978*c_1001_1^3 - 19009/18652*c_1001_1^2 - 19717/55956*c_1001_1 + 19247/18652, c_0101_4^2 - 9442/13989*c_1001_1^8 - 18544/13989*c_1001_1^7 - 51109/27978*c_1001_1^6 - 30467/13989*c_1001_1^5 - 71577/37304*c_1001_1^4 - 78521/55956*c_1001_1^3 - 19009/37304*c_1001_1^2 - 75673/111912*c_1001_1 - 18057/37304, c_1001_1^9 + 3*c_1001_1^8 + 21/4*c_1001_1^7 + 29/4*c_1001_1^6 + 131/16*c_1001_1^5 + 123/16*c_1001_1^4 + 97/16*c_1001_1^3 + 33/8*c_1001_1^2 + 11/8*c_1001_1 + 1/16 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.010 Total time: 0.210 seconds, Total memory usage: 32.09MB