# Manifold: Census Knot K8_231

# Number of Tetrahedra: 8

# Number Field
x^5 + x^4 + 8*x^3 + 4*x^2 + 7*x - 5 

# Approximate Field Generator
None

# Shape Parameters
-1/40*y^4 - 3/20*y^3 - 9/20*y^2 - 17/20*y + 3/40

1/4*y^2 + 3/4

1/8*y^4 + y^2 + 15/8

1/8*y^4 + 3/4*y^2 - 1/2*y + 5/8

1/8*y^4 + y^2 - 1/2*y + 11/8

1/8*y^4 + y^2 + 15/8

-3/8*y^4 - 1/2*y^3 - 3*y^2 - 3*y - 25/8

-1/8*y^4 - 1/4*y^3 - 5/4*y^2 - 7/4*y - 13/8


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

# 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
{1, 0, 1, 1, 0, 0, 1, 1}

# f Combinatorial flattening
{0, 2, 2, 0, 1, 1, 2, 2}

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

# 1 Loop Invariant
-3/2*y^4 - 2*y^3 - 41/4*y^2 - 23/2*y - 1/4

# 2 Loop Invariant
866571733/897784542912*y^4 - 551345099/149630757152*y^3 + 5743478071/74815378576*y^2 - 35452659859/448892271456*y + 216896441957/299261514304

# 3 Loop Invariant
49807836059020355/9986335185495450112*y^4 - 25116589944545313/9986335185495450112*y^3 + 288338000061042415/9986335185495450112*y^2 + 4315373553971/525596588710286848*y + 204665148782796239/4993167592747725056

# 4 Loop Invariant
21202585571043356453146192709/26896732109628166233172857618432*y^4 + 26854341696489791073848580383/8965577369876055411057619206144*y^3 + 397072102766558146422479122421/26896732109628166233172857618432*y^2 + 104866126860224110494180175465/8965577369876055411057619206144*y + 713987480945977257041633179991/67241830274070415582932144046080