# Manifold: Rolfsen Knot 9_42

# Number of Tetrahedra: 5

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

# Approximate Field Generator
-1.18667684088225 + 0.190224801204598*I

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

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

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

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

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


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

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

# nu Gluing Vector
{0, 1, 1, 2, 0}

# f Combinatorial flattening
{0, -2, -3, -3, -4}

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

# 1 Loop Invariant
-2*y^4 + 8*y^3 - 5*y^2 - 23/2*y + 10

# 2 Loop Invariant
6988531/209518347*y^4 + 36440745/558715592*y^3 - 55661288/209518347*y^2 - 124983353/558715592*y - 557405323/1676146776

# 3 Loop Invariant
-193276811371/18676744809376*y^4 - 6557123725/2334593101172*y^3 + 595474657509/18676744809376*y^2 + 638217254395/18676744809376*y + 60076346063/4669186202344

# 4 Loop Invariant
-14913673986281624627813/469574483976154754576640*y^4 + 17249169250416349856957/469574483976154754576640*y^3 + 58746297268386548309279/469574483976154754576640*y^2 - 3082858946092958576599/46957448397615475457664*y - 65548415833714968420661/469574483976154754576640