# Manifold: Census Knot K5_1

# Number of Tetrahedra: 5

# Number Field
x^7 + 2*x^6 - 6*x^4 - 3*x^3 + 6*x^2 - 1 

# Approximate Field Generator
-1.31477233485861 - 1.38950954106388*I

# Shape Parameters
5/7*y^6 + 2*y^5 + y^4 - 30/7*y^3 - 39/7*y^2 + 17/7*y + 15/7

1/3*y^6 + 4/3*y^5 + 5/3*y^4 - 2/3*y^3 - 10/3*y^2 - 2/3*y + 5/3

4/7*y^6 + 2*y^5 + 2*y^4 - 17/7*y^3 - 41/7*y^2 - 6/7*y + 19/7

-9/7*y^6 - 2*y^5 + y^4 + 54/7*y^3 + 10/7*y^2 - 53/7*y + 22/7

-22/21*y^6 - 7/3*y^5 - 2/3*y^4 + 125/21*y^3 + 103/21*y^2 - 79/21*y - 17/21


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

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

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

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

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

# 1 Loop Invariant
-30/7*y^6 - 11*y^5 - 10*y^4 + 117/7*y^3 + 150/7*y^2 - 11/7*y - 41/7

# 2 Loop Invariant
49564123181591/431565594284328*y^6 + 10041109800055/30826113877452*y^5 + 5582434718849/20550742584968*y^4 - 146434627283919/287710396189552*y^3 - 690857977476497/863131188568656*y^2 + 267023383303/143855198094776*y - 262955734470307/863131188568656

# 3 Loop Invariant
-110658454464296546387/1844524009228650212288*y^6 - 21051886788292431625/131751714944903586592*y^5 - 24761821045016392615/263503429889807173184*y^4 + 577069651378933039265/1844524009228650212288*y^3 + 715107579446022414661/1844524009228650212288*y^2 - 143146449454479356829/922262004614325106144*y - 83102890408214469795/922262004614325106144

# 4 Loop Invariant
3062037698104712341268457902968729/121841801053235775486774562749707520*y^6 + 5935247236077954227037081285549631/97473440842588620389419650199766016*y^5 + 1933085661335366616039350755760959/81227867368823850324516375166471680*y^4 - 69528166687566026583738510573228157/487367204212943101947098250998830080*y^3 - 13386327241126537117594390359411749/97473440842588620389419650199766016*y^2 + 46912288704949278412614245000618213/487367204212943101947098250998830080*y + 6553125470349155746432033638430733/162455734737647700649032750332943360

# 5 Loop Invariant
-8406262166450327147422143951671986937639/729057604418771505751844263877860171327488*y^6 - 3703563122736614078889480788448494263249/208302172691077573071955503965102906093568*y^5 + 24823660340252087408713597041412280801/26037771586384696633994437995637863261696*y^4 + 99188981107737016245686572566390805256125/1458115208837543011503688527755720342654976*y^3 + 28823811285885256161225590298230658109403/1458115208837543011503688527755720342654976*y^2 - 16174205367167025170267485326973337144995/486038402945847670501229509251906780884992*y - 13290813742833946201380709520257160289451/486038402945847670501229509251906780884992