# Manifold: Census Knot K5_20 # Number of Tetrahedra: 5 # Number Field x^6 - x^5 + 3*x^4 - 2*x^3 + 2*x^2 - x - 1 # Approximate Field Generator 0.408802480154171 + 1.27637696070335*I # Shape Parameters 1/3*y^5 - 2/3*y^4 + 2/3*y^3 - 1/3*y^2 + 2/3 y^2 + 2 -y^5 + y^4 - 2*y^3 + y^2 + 1 -y^5 - 2*y^3 - y 1/3*y^5 - 2/3*y^4 + 2/3*y^3 - 1/3*y^2 + 2/3 # A Gluing Matrix {{1,1,0,0,0},{1,2,1,0,1},{0,1,0,-1,0},{0,0,-1,-1,0},{0,1,0,0,1}} # B Gluing Matrix {{1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,0},{0,0,0,0,1}} # nu Gluing Vector {1, 2, 0, -1, 1} # f Combinatorial flattening {0, 1, 0, 1, 0} # f' Combinatorial flattening {0, 0, 0, 0, 0} # 1 Loop Invariant 1/2*y^5 - 7/2*y^4 + 4*y^3 - 7*y^2 + 4*y - 5/2 # 2 Loop Invariant -214339617/12262093202*y^5 - 10783752523/73572559212*y^4 + 8231438291/73572559212*y^3 - 20493483827/73572559212*y^2 + 2279838532/18393139803*y - 4716395027/73572559212 # 3 Loop Invariant 759007556255/480067079904901*y^5 - 759007556255/480067079904901*y^4 + 3078843477009/960134159809802*y^3 + 13620377006743/960134159809802*y^2 - 15302176859949/960134159809802*y + 10266116437167/480067079904901 # 4 Loop Invariant 3714523441141517585655521/1059592909861057924544940360*y^5 - 351784526966298157572491/141279054648141056605992048*y^4 + 4813818447103560465702487/529796454930528962272470180*y^3 - 2687932853694755530768295/423837163944423169817976144*y^2 + 3738132927318060986168677/353197636620352641514980120*y - 6620805825439690102717591/706395273240705283029960240 # 5 Loop Invariant -2091523954057284145299440968/691393203625255804581611459403*y^5 + 7525046358513597147244265755/2765572814501023218326445837612*y^4 - 8289200271403174142289473373/1843715209667348812217630558408*y^3 + 445847022866862720024644533/5531145629002046436652891675224*y^2 + 49964960063796701795502967/1843715209667348812217630558408*y - 167689178508184706813560098/230464401208418601527203819801