# Manifold: Rolfsen Knot 8_20

# Number of Tetrahedra: 5

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

# Approximate Field Generator
-0.812446514465027 + 0.173141871635952*I

# Shape Parameters
-y^4 + 3*y^3 - y^2 - 2*y

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

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

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

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


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

# 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
{2, 2, 0, 0, 2}

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

# f' Combinatorial flattening
{4, 4, 0, 0, 0}

# 1 Loop Invariant
7/2*y^4 - 12*y^3 + 15/2*y^2 + 10*y - 5

# 2 Loop Invariant
-9847085/51579744*y^4 + 8087149/17193248*y^3 + 921267/8596624*y^2 - 29511655/51579744*y - 3915215/6447468

# 3 Loop Invariant
11911466225/201642412544*y^4 - 29004010361/201642412544*y^3 - 333152517/3150662696*y^2 + 55112192591/201642412544*y + 20858292013/100821206272

# 4 Loop Invariant
-4726781500710150641/34668880061873029120*y^4 + 10061051292241047933/34668880061873029120*y^3 + 18091076674541680849/78004980139214315520*y^2 - 16062308543181248647/34668880061873029120*y - 5982491686868639207/17334440030936514560