# Manifold: H T Link Exterior K9a39

# Number of Tetrahedra: 9

# Number Field
x^6 - 3*x^5 + x^4 + 3*x^3 - 2*x^2 - 3*x - 1 

# Approximate Field Generator
None

# Shape Parameters
y^5 - 4*y^4 + 4*y^3 + y^2 - 3*y - 1

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

1/8*y^5 - 3/4*y^4 + 11/8*y^3 - 3/4*y^2 + 5/8

-3/8*y^5 + 5/4*y^4 - 9/8*y^3 + 1/4*y^2 + 9/8

2*y^5 - 7*y^4 + 5*y^3 + 5*y^2 - 7*y - 3

-y^5 + 3*y^4 - y^3 - 3*y^2 + 3*y + 3

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

2*y^5 - 7*y^4 + 5*y^3 + 5*y^2 - 7*y - 3

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


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

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

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

# f Combinatorial flattening
{5, -3, -7, -2, -4, -2, -2, 3, -2}

# f' Combinatorial flattening
{0, -4, 0, 0, 0, 0, 0, 0, 0}

# 1 Loop Invariant
-17/2*y^5 + 65/2*y^4 - 32*y^3 - 1/2*y^2 + 17*y + 4

# 2 Loop Invariant
-4272346797910465/34969932762220036*y^5 + 26414566684661587/52454899143330054*y^4 - 24577697726232797/34969932762220036*y^3 + 11187348654163424/26227449571665027*y^2 + 829515255935945/3746778510237861*y - 493141354047991211/209819596573320216

# 3 Loop Invariant
-26520693710751221428981864/417708303978843733397669953*y^5 + 92361351502755249020859516/417708303978843733397669953*y^4 - 66505171493998626263408505/417708303978843733397669953*y^3 - 49366175234925424793601573/417708303978843733397669953*y^2 + 9425849154757158320439356/59672614854120533342524279*y + 53151879779579223152939964/417708303978843733397669953

# 4 Loop Invariant
-1369251376982659699016780582251529484562745/87643387826166799750775165541597539350669848*y^5 + 20549635312190857794591705550851126514479919/328662704348125499065406870780990772565011930*y^4 - 49205516419867626859373351112080490833163943/657325408696250998130813741561981545130023860*y^3 + 20943371849571023348803366889605474685751911/1314650817392501996261627483123963090260047720*y^2 + 957134463438877335807298220366269903181851/37561451925500057036046499517827516864572792*y + 8845019109642112967325867722842053243029491/438216939130833998753875827707987696753349240