Magma V2.19-8 Tue Aug 20 2013 16:09:04 on localhost [Seed = 559988651] Type ? for help. Type -D to quit. ==TRIANGULATION=BEGINS== % Triangulation m363 geometric_solution 4.74293835 oriented_manifold CS_known 0.0000000000000000 1 0 torus 0.000000000000 0.000000000000 5 1 2 3 4 0132 0132 0132 0132 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 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 0.705822086719 1.029205514005 0 2 1 1 0132 1302 1230 3012 0 0 0 0 0 -1 1 0 0 0 1 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.729928076359 0.994360275962 3 0 4 1 0213 0132 2031 2031 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 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 0.546808804873 0.660827828571 2 3 3 0 0213 1230 3012 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 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.192080578164 0.872139830999 4 4 0 2 1302 2031 0132 1302 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 -1 1 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 0.473336489064 0.376424693641 ==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_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' : d['1'], 's_2_4' : d['1'], 's_1_4' : negation(d['1']), 's_1_3' : d['1'], 's_1_2' : d['1'], 's_1_1' : d['1'], 's_1_0' : d['1'], 's_0_4' : negation(d['1']), 's_0_2' : d['1'], 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_1100_4' : d['c_0011_3'], 'c_1100_1' : d['c_0101_0'], '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' : negation(d['c_0011_4']), 'c_0101_3' : negation(d['c_0011_0']), 'c_0101_2' : d['c_0011_3'], 'c_0101_1' : negation(d['c_0011_4']), 'c_0101_0' : d['c_0101_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_0110_4']), 'c_1001_1' : negation(d['c_0101_0']), 'c_1001_0' : negation(d['c_0011_0']), 'c_1001_3' : negation(d['c_0011_3']), 'c_1001_2' : negation(d['c_0110_4']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : negation(d['c_0011_4']), 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : negation(d['c_0101_0']), 'c_0110_4' : d['c_0110_4'], 'c_1010_4' : d['c_0011_4'], 'c_1010_3' : negation(d['c_0011_0']), 'c_1010_2' : negation(d['c_0011_0']), 'c_1010_1' : d['c_0011_4'], 'c_1010_0' : negation(d['c_0110_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_0, c_0110_4 Inhomogeneous, Dimension 0, Radical, Prime Size of variety over algebraically closed field: 15 Groebner basis: [ t - 1594253/10915544*c_0110_4^14 - 7505119/5457772*c_0110_4^13 - 15031535/5457772*c_0110_4^12 - 1019981/2728886*c_0110_4^11 + 29503693/10915544*c_0110_4^10 + 54918781/10915544*c_0110_4^9 + 116756445/10915544*c_0110_4^8 + 36662583/2728886*c_0110_4^7 + 35572831/5457772*c_0110_4^6 + 44515103/5457772*c_0110_4^5 + 192265723/10915544*c_0110_4^4 + 133100605/10915544*c_0110_4^3 - 137079643/10915544*c_0110_4^2 - 141258151/5457772*c_0110_4 - 12892428/1364443, c_0011_0 - 1, c_0011_3 - 361221/2728886*c_0110_4^14 - 2037173/2728886*c_0110_4^13 - 1062922/1364443*c_0110_4^12 + 1169148/1364443*c_0110_4^11 + 3423019/2728886*c_0110_4^10 + 2597925/1364443*c_0110_4^9 + 5691421/1364443*c_0110_4^8 + 7761423/2728886*c_0110_4^7 - 625185/1364443*c_0110_4^6 + 5343087/1364443*c_0110_4^5 + 16488175/2728886*c_0110_4^4 - 1348296/1364443*c_0110_4^3 - 13460431/1364443*c_0110_4^2 - 17985297/2728886*c_0110_4 + 4682427/1364443, c_0011_4 - 681707/2728886*c_0110_4^14 - 1613909/2728886*c_0110_4^13 + 140568/1364443*c_0110_4^12 + 980042/1364443*c_0110_4^11 + 2004031/2728886*c_0110_4^10 + 2596642/1364443*c_0110_4^9 + 3293138/1364443*c_0110_4^8 - 173549/2728886*c_0110_4^7 + 725788/1364443*c_0110_4^6 + 4342925/1364443*c_0110_4^5 + 3788127/2728886*c_0110_4^4 - 5787503/1364443*c_0110_4^3 - 8034738/1364443*c_0110_4^2 + 141707/2728886*c_0110_4 + 1773151/1364443, c_0101_0 + 3227789/5457772*c_0110_4^14 + 4270717/2728886*c_0110_4^13 + 423293/2728886*c_0110_4^12 - 2305435/1364443*c_0110_4^11 - 11824549/5457772*c_0110_4^10 - 26993045/5457772*c_0110_4^9 - 36917213/5457772*c_0110_4^8 - 2528981/1364443*c_0110_4^7 - 4360085/2728886*c_0110_4^6 - 22795729/2728886*c_0110_4^5 - 35516259/5457772*c_0110_4^4 + 46597699/5457772*c_0110_4^3 + 89871187/5457772*c_0110_4^2 + 7484659/2728886*c_0110_4 - 3989361/1364443, c_0110_4^15 + 2*c_0110_4^14 - 2*c_0110_4^13 - 4*c_0110_4^12 - c_0110_4^11 - 5*c_0110_4^10 - 5*c_0110_4^9 + 8*c_0110_4^8 + 2*c_0110_4^7 - 14*c_0110_4^6 + c_0110_4^5 + 27*c_0110_4^4 + 19*c_0110_4^3 - 22*c_0110_4^2 - 16*c_0110_4 + 8 ] ] PRIMARY=DECOMPOSITION=ENDS=HERE CPUTIME : 0.010 Total time: 0.210 seconds, Total memory usage: 32.09MB