# Manifold: Census Knot K6_33 # Number of Tetrahedra: 6 # Number Field x^7 - 4*x^6 + 3*x^5 - 9*x^4 + 7*x^3 - 10*x^2 + x - 1 # Approximate Field Generator 0.598811055194181 - 0.932972818443548*I # Shape Parameters -121/124*y^6 + 489/124*y^5 - 177/62*y^4 + 995/124*y^3 - 421/62*y^2 + 513/62*y + 39/124 -18/31*y^6 + 73/31*y^5 - 46/31*y^4 + 106/31*y^3 - 63/31*y^2 + 106/31*y + 14/31 -35/186*y^6 + 77/93*y^5 - 74/93*y^4 + 337/186*y^3 - 139/62*y^2 + 275/186*y - 26/93 3/124*y^6 - 7/124*y^5 + 9/62*y^4 - 121/124*y^3 + 13/62*y^2 - 45/62*y + 39/124 11/93*y^6 - 67/93*y^5 + 128/93*y^4 - 175/93*y^3 + 271/93*y^2 - 299/93*y + 89/31 3/124*y^6 - 7/124*y^5 + 9/62*y^4 - 121/124*y^3 + 13/62*y^2 - 45/62*y + 39/124 # A Gluing Matrix {{5,2,1,5,4,3},{2,1,1,2,2,1},{1,1,0,2,2,2},{5,2,2,5,3,2},{4,2,2,3,2,1},{3,1,2,2,1,1}} # B Gluing Matrix {{1,0,0,0,0,0},{0,1,0,0,0,0},{0,0,1,0,0,0},{0,0,0,1,0,0},{0,0,0,0,1,0},{0,0,0,0,0,1}} # nu Gluing Vector {5, 3, 2, 5, 4, 3} # f Combinatorial flattening {20, -10, -14, -15, 6, 5} # f' Combinatorial flattening {-25, 0, 0, 0, 0, 0} # 1 Loop Invariant -91/31*y^6 + 683/62*y^5 - 255/62*y^4 + 1213/62*y^3 - 1071/62*y^2 + 281/31*y + 119/31 # 2 Loop Invariant -32900228252231/1834018923615552*y^6 + 59350610928527/611339641205184*y^5 - 43440978226427/305669820602592*y^4 + 115575092181655/611339641205184*y^3 - 62301584854351/229252365451944*y^2 + 1525710520933/9552181893831*y + 114217649327731735/1834018923615552 # 3 Loop Invariant 5850726577570127/1368362997957082392*y^6 - 538994481623636065/21893807967313318272*y^5 + 236432522827735697/5473451991828329568*y^4 - 536448508228601573/10946903983656659136*y^3 + 1491634755013846393/21893807967313318272*y^2 - 1200902173915017569/21893807967313318272*y + 46094718857434487/810881776567159936