# Manifold: Rolfsen Knot 8_9

# Number of Tetrahedra: 8

# Number Field
x^12 + 3*x^11 + 9*x^10 + 11*x^9 + 25*x^8 + 18*x^7 + 35*x^6 + 18*x^5 + 25*x^4 + 11*x^3 + 9*x^2 + 3*x + 1 

# Approximate Field Generator
0.362904146481346 + 0.931826475512821*I

# Shape Parameters
46/13*y^11 + 119/13*y^10 + 26*y^9 + 272/13*y^8 + 759/13*y^7 + 131/13*y^6 + 857/13*y^5 - 70/13*y^4 + 417/13*y^3 - 3*y^2 + 63/13*y + 19/13

-y^10 - 3*y^9 - 8*y^8 - 8*y^7 - 17*y^6 - 10*y^5 - 18*y^4 - 8*y^3 - 7*y^2 - 3*y - 1

34/13*y^11 + 71/13*y^10 + 13*y^9 - 42/13*y^8 + 132/13*y^7 - 556/13*y^6 - 120/13*y^5 - 769/13*y^4 - 322/13*y^3 - 32*y^2 - 149/13*y - 47/13

4/13*y^11 - 23/13*y^10 - 7*y^9 - 320/13*y^8 - 402/13*y^7 - 798/13*y^6 - 593/13*y^5 - 846/13*y^4 - 460/13*y^3 - 30*y^2 - 133/13*y - 43/13

20/13*y^11 + 67/13*y^10 + 14*y^9 + 207/13*y^8 + 356/13*y^7 + 196/13*y^6 + 272/13*y^5 + 60/13*y^4 + 40/13*y^3 - 3*y^2 - 28/13*y - 7/13

32/13*y^11 + 76/13*y^10 + 16*y^9 + 105/13*y^8 + 398/13*y^7 - 131/13*y^6 + 404/13*y^5 - 320/13*y^4 + 168/13*y^3 - 16*y^2 + 28/13*y - 32/13

-y^10 - 3*y^9 - 8*y^8 - 8*y^7 - 17*y^6 - 10*y^5 - 18*y^4 - 8*y^3 - 7*y^2 - 3*y - 1

20/13*y^11 + 67/13*y^10 + 14*y^9 + 207/13*y^8 + 356/13*y^7 + 196/13*y^6 + 272/13*y^5 + 60/13*y^4 + 40/13*y^3 - 3*y^2 - 28/13*y - 7/13


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

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

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

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

# 1 Loop Invariant
-38/13*y^11 - 135/26*y^10 - 13*y^9 + 113/26*y^8 - 565/26*y^7 + 901/26*y^6 - 145/13*y^5 + 1163/26*y^4 + 381/26*y^3 + 29/2*y^2 + 239/26*y + 89/26

# 2 Loop Invariant
1054866942500/1868754115839*y^11 + 10163943024685/7475016463356*y^10 + 755523827313/191667088804*y^9 + 7044244851751/2491672154452*y^8 + 23318231920657/2491672154452*y^7 + 1510230969430/1868754115839*y^6 + 84782291153959/7475016463356*y^5 - 7498360309489/3737508231678*y^4 + 45864761002831/7475016463356*y^3 - 750117149479/575001266412*y^2 + 2292096905837/1868754115839*y - 860770077497/2491672154452

# 3 Loop Invariant
-30106340700426289/20977867036053398*y^11 - 96481084639552561/20977867036053398*y^10 - 140748625770955251/10488933518026699*y^9 - 9636212593947376/552049132527721*y^8 - 378479821265142299/10488933518026699*y^7 - 632657045388320665/20977867036053398*y^6 - 12027238801655314/255827646781139*y^5 - 339408973290267089/10488933518026699*y^4 - 610200318233691053/20977867036053398*y^3 - 5280796318937643/255827646781139*y^2 - 82731472150001155/10488933518026699*y - 118400830817353107/20977867036053398

# 4 Loop Invariant
-111041352600392943379098679918/5158220442782640962563364595*y^11 - 13223232399394489666387243812157/247594581253566766203041500560*y^10 - 3094115630758068287649310527811/19045737019505135861772423120*y^9 - 11871429574470684590610470382383/82531527084522255401013833520*y^8 - 2405289745048033627805400236009/5502101805634817026734255568*y^7 - 6864743240551160767237127076109/49518916250713353240608300112*y^6 - 37791262355293265926932839757011/61898645313391691550760375140*y^5 - 12942577316819218358217925470757/247594581253566766203041500560*y^4 - 25444790601496460930332080935819/61898645313391691550760375140*y^3 - 1139096921516702483287253567/55689289530716771525650360*y^2 - 1586267530561059740746944517293/13755254514087042566835638920*y - 142147045008395893702186750253/30949322656695845775380187570