# Manifold: Census Knot K5_8

# Number of Tetrahedra: 5

# Number Field
x^5 - 4*x^4 + 4*x^3 - 4*x^2 + 3*x - 1 

# Approximate Field Generator
-0.0844626122601329 - 0.905094122066272*I

# Shape Parameters
-3/4*y^4 + 5/2*y^3 - 5/4*y^2 + 7/4*y - 1/4

-1/2*y^4 + 3/2*y^3 + 1/2*y

-2*y^4 + 7*y^3 - 4*y^2 + 4*y - 2

-y + 1

-y + 1


# A Gluing Matrix
{{-1,2,3,1,-1},{0,0,-1,-1,1},{1,-1,0,0,1},{0,0,1,1,0},{-2,4,4,1,-1}}

# B Gluing Matrix
{{1,0,0,0,2},{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,1},{0,0,0,0,4}}

# nu Gluing Vector
{3, 0, 0, 1, 4}

# f Combinatorial flattening
{-3, -2, 2, -1, 1}

# f' Combinatorial flattening
{0, 0, 0, 0, 0}

# 1 Loop Invariant
9/2*y^4 - 15*y^3 + 5*y^2 - 5/2*y + 3

# 2 Loop Invariant
-163259799/558715592*y^4 + 1790874263/1676146776*y^3 - 616624441/838073388*y^2 + 1191772631/1676146776*y - 269737325/279357796

# 3 Loop Invariant
371112154781/9338372404688*y^4 - 751427501163/4669186202344*y^3 + 1320162462459/9338372404688*y^2 - 1105514352645/9338372404688*y + 1081882307959/9338372404688

# 4 Loop Invariant
32588698335726413001577/469574483976154754576640*y^4 - 33033449594315875907837/156524827992051584858880*y^3 + 1500830058805292484953/29348405248509672161040*y^2 - 83760819697637564578891/469574483976154754576640*y + 2034526593314126163527/78262413996025792429440

# 5 Loop Invariant
-161418295006853183280026609/1046462390023660075732528128*y^4 + 40688531408882523729395653/87205199168638339644377344*y^3 - 44301061613639240391032231/348820796674553358577509376*y^2 + 137082531603244577185645015/348820796674553358577509376*y - 70920983119775700126489061/1046462390023660075732528128