# Manifold: Rolfsen Knot 8_5 # Number of Tetrahedra: 8 # Number Field x^5 - x^4 - 3*x^3 + 2*x^2 + 2*x + 1 # Approximate Field Generator None # Shape Parameters -y^3 + y^2 + y + 1 1/2*y^4 - y^3 - 3/2*y^2 + 5/2*y + 3/2 y^4 - 2*y^3 - 2*y^2 + 4*y + 1 -1/2*y^3 + 1/2*y^2 + 1/2 -1/2*y^4 + 3/2*y^2 - 1/2*y + 1/2 -y^3 + 2*y + 1 -y^2 + 2*y -y^4 + y^3 + 2*y^2 - 2*y # A Gluing Matrix {{0,-1,0,0,-1,0,0,0},{0,-1,-1,-1,-1,-1,0,0},{0,-1,0,0,-1,0,0,0},{-1,-2,0,1,-2,0,0,0},{0,-1,-1,-1,-1,-1,1,0},{0,-1,0,0,-1,0,0,0},{0,0,0,0,1,0,-1,0},{0,-1,0,0,-1,-1,-1,1}} # B Gluing Matrix {{1,0,0,1,0,0,0,0},{0,1,0,0,0,0,0,1},{0,0,1,0,0,0,0,0},{0,0,0,2,0,0,0,0},{0,0,0,0,1,0,0,1},{0,0,0,0,0,1,0,1},{0,0,0,0,0,0,1,1},{0,0,0,0,0,0,0,2}} # nu Gluing Vector {0, -1, 0, 0, -1, 0, 1, 0} # f Combinatorial flattening {0, -1, 1, 0, 1, 0, 0, 0} # f' Combinatorial flattening {0, 0, 0, 0, 0, 0, 0, 0} # 1 Loop Invariant -1/2*y^4 - 5/2*y^3 + y^2 + 25/2*y + 5/2 # 2 Loop Invariant 588537460/14027883483*y^4 - 18841009857/74815378576*y^3 + 1090748117/224446135728*y^2 + 15721341137/28055766966*y - 20552461183/74815378576 # 3 Loop Invariant -212681322917257343/4993167592747725056*y^4 + 32613277521989719/624145949093465632*y^3 + 502802690396106291/4993167592747725056*y^2 - 36013714914736959/262798294355143424*y + 30135649776642709/4993167592747725056 # 4 Loop Invariant 162829251470189300849393186555/13448366054814083116586428809216*y^4 - 6191112314911800041313179707/210130719606470048696662950144*y^3 - 180473311122887234529324237767/13448366054814083116586428809216*y^2 + 794165577599960959694388706753/13448366054814083116586428809216*y - 1465512374507289825044858570629/67241830274070415582932144046080