# Manifold: Rolfsen Knot 8_21

# Number of Tetrahedra: 7

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

# Approximate Field Generator
None

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

y^2 - y + 1

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

y^2 - y + 1

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

1/2*y^2 - y + 1

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


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

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

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

# f Combinatorial flattening
{0, 0, 1, 0, 1, 0, 1}

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

# 1 Loop Invariant
4*y^3 - 21/2*y^2 + 10*y - 3

# 2 Loop Invariant
7633/189728*y^3 + 7939/81312*y^2 - 39189/189728*y + 29345/284592

# 3 Loop Invariant
79034101/2571193856*y^3 - 792999/52473344*y^2 - 388763/2571193856*y - 18669325/642798464

# 4 Loop Invariant
117102193557049/3991315646545920*y^3 - 15891783837463/443479516282880*y^2 + 26223172419679/1330438548848640*y - 1452881569291/41576204651520