# Manifold: Census Knot K5_19

# Number of Tetrahedra: 5

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

# Approximate Field Generator
0.276511073487284 + 0.728236608887858*I

# Shape Parameters
-y^3 + y^2 + 1

y^2 + 1

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

-y^4 - y^2 + y

y^2 + 1


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

# 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, 1, 1, 0, 1}

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

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

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

# 2 Loop Invariant
-1581190/9473187*y^4 + 604947/3157729*y^3 - 1633861/37892748*y^2 + 2559381/12630916*y + 1333939/18946374

# 3 Loop Invariant
55937569/5611284433*y^4 - 52375693/11222568866*y^3 + 52375693/11222568866*y^2 - 325863959/11222568866*y - 610293/5611284433

# 4 Loop Invariant
29364390679867867/12757619218559513040*y^4 + 10516818263721329/6378809609279756520*y^3 - 14028860232566039/6378809609279756520*y^2 + 72145666168424189/12757619218559513040*y + 3891565942728863/637880960927975652

# 5 Loop Invariant
-1639694337305074676/94459538964084394467*y^4 + 11223919041543342809/755676311712675155736*y^3 - 11439268860106741883/755676311712675155736*y^2 + 5144743432866649345/755676311712675155736*y - 320991097069112703/62973025976056262978