# Manifold: Census Knot K5_5

# Number of Tetrahedra: 5

# Number Field
x^7 - x^6 - 4*x^5 + 13*x^4 - 14*x^3 + 11*x^2 - 6*x + 1 

# Approximate Field Generator
1.32513238111104 + 1.00443434866126*I

# Shape Parameters
y^6 - y^5 - 4*y^4 + 13*y^3 - 14*y^2 + 11*y - 5

-45/31*y^6 + 33/31*y^5 + 195/31*y^4 - 533/31*y^3 + 461/31*y^2 - 308/31*y + 161/31

-45/31*y^6 + 33/31*y^5 + 195/31*y^4 - 533/31*y^3 + 461/31*y^2 - 308/31*y + 161/31

64/31*y^6 - 18/31*y^5 - 267/31*y^4 + 643/31*y^3 - 429/31*y^2 + 385/31*y - 85/31

-113/31*y^6 + 25/31*y^5 + 469/31*y^4 - 1098/31*y^3 + 725/31*y^2 - 688/31*y + 168/31


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

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

# nu Gluing Vector
{0, 6, 6, 4, -1}

# f Combinatorial flattening
{5, -1, 5, -5, -7}

# f' Combinatorial flattening
{-6, 6, 0, 2, 0}

# 1 Loop Invariant
613/31*y^6 - 526/31*y^5 - 2584/31*y^4 + 7623/31*y^3 - 7256/31*y^2 + 5178/31*y - 2446/31

# 2 Loop Invariant
-256920805880777/3727448070222064*y^6 + 328154191726361/11182344210666192*y^5 + 3288722736241403/11182344210666192*y^4 - 8094796466158661/11182344210666192*y^3 + 1590436910847479/2795586052666548*y^2 - 284568446053945/698896513166637*y + 28113454962574781/5591172105333096

# 3 Loop Invariant
37159750686159630855/2554562737411866453148*y^6 - 479396851983750668477/40873003798589863250368*y^5 - 2416001275946238716211/40873003798589863250368*y^4 + 1865537579348459006835/10218250949647465812592*y^3 - 7073780056479521412147/40873003798589863250368*y^2 + 4627502544799387924559/40873003798589863250368*y - 92866766774198554605/2554562737411866453148

# 4 Loop Invariant
1801918630005785052618555641090246339/221156127774047724981790917748920560640*y^6 - 1062868675509046480976128457430731293/221156127774047724981790917748920560640*y^5 - 7069241211050328124284968972956397939/221156127774047724981790917748920560640*y^4 + 5058258513004339072548343959955887971/55289031943511931245447729437230140160*y^3 - 19890775219566676970604690466541244931/221156127774047724981790917748920560640*y^2 + 1150479851583331446167886834230602013/13822257985877982811361932359307535040*y - 7391858463259325631862324232618878409/221156127774047724981790917748920560640

# 5 Loop Invariant
-64282378601987758128502649702363342346123/53890401274823915824178442466111700059746304*y^6 - 138442737995302243767881077560438121744871/161671203824471747472535327398335100179238912*y^5 + 232790254305437473616177307978034953371423/53890401274823915824178442466111700059746304*y^4 - 171644560106960035403409628491328322485169/26945200637411957912089221233055850029873152*y^3 + 16881640419149594477921849782760059238553/53890401274823915824178442466111700059746304*y^2 - 698351848826396943299627818716006287542835/80835601912235873736267663699167550089619456*y - 138403112584059211058995804927393697002871/53890401274823915824178442466111700059746304