# Manifold: Rolfsen Knot 8_3

# Number of Tetrahedra: 6

# Number Field
x^8 + 4/5*x^7 + 11/5*x^6 + 7/5*x^5 + 6/5*x^4 + 3/5*x^3 - 1/5*x^2 + 1/5*x + 1/5 

# Approximate Field Generator
-0.344576162603336 + 1.04314509104556*I

# Shape Parameters
-195/122*y^7 - 68/61*y^6 - 274/61*y^5 - 56/61*y^4 - 393/122*y^3 + 86/61*y^2 + 37/122*y + 123/122

-8/61*y^7 + 171/610*y^6 - 583/610*y^5 + 819/610*y^4 - 119/610*y^3 + 74/61*y^2 + 103/305*y + 27/610

985/122*y^7 + 163/122*y^6 + 1997/122*y^5 + 23/122*y^4 + 521/61*y^3 - 156/61*y^2 - 165/122*y + 114/61

-165/61*y^7 - 19/122*y^6 - 735/122*y^5 + 153/122*y^4 - 407/122*y^3 + 108/61*y^2 + 36/61*y - 3/122

-295/122*y^7 - 151/122*y^6 - 621/122*y^5 - 293/122*y^4 - 248/61*y^3 - 92/61*y^2 + 81/122*y + 25/61

-291/122*y^7 - 1179/610*y^6 - 2883/610*y^5 - 1441/610*y^4 - 577/305*y^3 - 19/61*y^2 + 811/610*y + 236/305


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

# B Gluing Matrix
{{1,0,0,0,0,0},{0,1,0,0,0,0},{0,0,1,0,0,0},{0,0,0,1,0,0},{0,0,0,0,1,1},{0,0,0,0,0,2}}

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

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

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

# 1 Loop Invariant
-1875/122*y^7 - 205/122*y^6 - 3519/122*y^5 + 400/61*y^4 - 531/61*y^3 + 889/122*y^2 + 947/122*y - 326/61

# 2 Loop Invariant
-940377709985/1493800084536*y^7 - 37072876781/497933361512*y^6 - 1708274956201/1493800084536*y^5 + 7462091735/29290197736*y^4 - 76402174219/248966680756*y^3 + 203569545283/746900042268*y^2 + 168661594043/497933361512*y - 16343327872/62241670189

# 3 Loop Invariant
246497721770905/1988185670847227*y^7 + 93887147435364/1988185670847227*y^6 + 534417516559323/1988185670847227*y^5 + 149676720144316/1988185670847227*y^4 + 289287544627635/1988185670847227*y^3 + 1275235718809/116952098285131*y^2 - 85013681905106/1988185670847227*y + 28682274921001/1988185670847227

# 4 Loop Invariant
7003965130847564735535/1909322997868757032041904*y^7 - 20530659874857687405297/477330749467189258010476*y^6 - 3884545149592504526506351/85919534904094066441885680*y^5 - 307876655406555360785159/2527045144238060777702520*y^4 - 2911146718150904859907841/28639844968031355480628560*y^3 - 2072762228536004911835453/21479883726023516610471420*y^2 - 4297720980391753625216299/85919534904094066441885680*y - 14517810776636593098843/9546614989343785160209520