# Manifold: Census Knot K8_245

# Number of Tetrahedra: 8

# Number Field
x^5 + 5*x^4 + 9*x^3 + 8*x^2 + 5*x + 1 

# Approximate Field Generator
-0.300688981009262 - 0.811268404497123*I

# Shape Parameters
-y

-y

-y^4 - 4*y^3 - 6*y^2 - 5*y - 2

-y^2 - 2*y

y^4 + 5*y^3 + 8*y^2 + 5*y + 3

-y^3 - 3*y^2 - 3*y - 1

-y^2 - 3*y - 1

2*y^4 + 9*y^3 + 14*y^2 + 10*y + 6


# A Gluing Matrix
{{3,-1,0,1,3,-1,3,3},{-1,1,0,-1,-1,1,-1,-1},{0,0,1,0,0,-1,1,0},{1,-1,0,1,2,0,2,2},{3,-1,0,2,4,-1,3,4},{-1,1,-1,0,-1,1,-1,-1},{3,-1,1,2,3,-1,4,4},{3,-1,0,2,4,-1,4,5}}

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

# nu Gluing Vector
{5, -1, 1, 3, 6, -1, 6, 7}

# f Combinatorial flattening
{6, 13, 6, -12, 16, 9, 4, -9}

# f' Combinatorial flattening
{-12, -18, 0, 0, -6, 0, 0, 0}

# 1 Loop Invariant
4*y^4 + 15*y^3 + 15*y^2 - 4*y - 5

# 2 Loop Invariant
3936879091/15036220848*y^4 + 18015802139/15036220848*y^3 + 745367185/455643056*y^2 + 1234111895/1253018404*y + 201842560621/3759055212

# 3 Loop Invariant
136483105661899/1951591200450848*y^4 + 1542469065735523/3903182400901696*y^3 + 266330822157475/354834763718336*y^2 + 2168493603320629/3903182400901696*y + 168463642569897/487897800112712

# 4 Loop Invariant
1314083531017192318346011/4001530403862598322301696*y^4 + 5198170945638852129175765/4001530403862598322301696*y^3 + 298740253062518382583807/161677996115660538274816*y^2 + 7449307828718809482304079/5335373871816797763068928*y + 11234169677248312209315595/16006121615450393289206784