# Manifold: Census Knot K4_1 # Number of Tetrahedra: 4 # Number Field x^4 + 2*x^3 + x^2 - 3*x + 1 # Approximate Field Generator -1.50410836415074 + 1.22685163774658*I # Shape Parameters 3/2*y^3 + 7/2*y^2 + 3*y - 5/2 2*y^3 + 5*y^2 + 5*y - 3 -1/2*y^3 - 3/2*y^2 - y + 3/2 1/2*y^3 + 3/2*y^2 + 2*y + 1/2 # A Gluing Matrix {{1,0,-1,0},{-1,1,1,1},{-1,1,1,0},{-1,1,0,1}} # B Gluing Matrix {{1,0,0,1},{0,1,0,1},{0,0,1,0},{0,0,0,2}} # nu Gluing Vector {1, 2, 1, 2} # f Combinatorial flattening {1, 2, 0, 1} # f' Combinatorial flattening {0, 0, 0, 0} # 1 Loop Invariant -7/2*y^3 - 17/2*y^2 - 17/2*y + 6 # 2 Loop Invariant 46490/198147*y^3 + 231209/396294*y^2 + 473191/792588*y - 62777/264196 # 3 Loop Invariant 570416/16974593*y^3 + 2833463/33949186*y^2 + 1122215/16974593*y - 1386486/16974593 # 4 Loop Invariant -2255130587026/50451970187565*y^3 - 91695358340911/807231523001040*y^2 - 85651263871967/807231523001040*y + 1596902056811/20180788075026 # 5 Loop Invariant -37040877003091/1728820845093894*y^3 - 330280282463219/6915283380375576*y^2 - 53499149965837/1728820845093894*y + 72838757049049/1152547230062596 # 6 Loop Invariant 1449319256564305241317/17984434859623040256945*y^3 + 23592842410230239076799/115100383101587457644448*y^2 + 110567432832899754708187/575501915507937288222240*y - 20008494585620168748319/143875478876984322055560