# Manifold: Rolfsen Knot 8_16

# Number of Tetrahedra: 11

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

# Approximate Field Generator
None

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

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

-1/4*y^4 - 1/2*y^3 - 1/4*y^2 + 3/4*y + 5/4

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

-y^2 - y + 1

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

-y^2 - y + 1

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

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

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

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


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

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

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

# f Combinatorial flattening
{3, 4, -10, -13, -3, 7, -3, 1, 7, -6, 4}

# f' Combinatorial flattening
{-10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

# 1 Loop Invariant
-37/2*y^4 - 25/2*y^3 + 33/2*y^2 + 14*y + 15/2

# 2 Loop Invariant
-2592551115793/26624960163844*y^4 + 1545210041141/11410697213076*y^3 + 2201039302843/5705348606538*y^2 + 338173225591/79874880491532*y + 80549629106297/26624960163844

# 3 Loop Invariant
103225277401308288655/8054086799289673688021*y^4 + 14187445693656248539/1150583828469953384003*y^3 - 31448374275848310951/1150583828469953384003*y^2 + 284880358895408465367/8054086799289673688021*y + 678825669328926354990/8054086799289673688021

# 4 Loop Invariant
76968959289257980092152640873534739/4824894154212661227737150247752536290*y^4 + 27338428110131857464966300549672671/551416474767161283169960028314575576*y^3 + 6949318331615562747116557411138207/153171242990878134213877785642937660*y^2 - 26797848299216103560696190874429969/3216596102808440818491433498501690860*y - 315274564250769604697633575649801969/9649788308425322455474300495505072580