# Manifold: H T Link Exterior K9n3

# Number of Tetrahedra: 7

# Number Field
x^8 + 1/2*x^7 - 13/4*x^6 - 2*x^5 + 15/4*x^4 + 5/2*x^3 - 5/4*x^2 - 5/4*x - 1/4 

# Approximate Field Generator
1.04703610721125 + 0.264552844248341*I

# Shape Parameters
-4*y^6 - 2*y^5 + 9*y^4 + 6*y^3 - 6*y^2 - 4*y

20*y^7 + 6*y^6 - 67*y^5 - 27*y^4 + 83*y^3 + 35*y^2 - 35*y - 19

-32*y^7 + 4*y^6 + 102*y^5 + y^4 - 121*y^3 - 5*y^2 + 44*y + 13

8*y^7 - 4*y^6 - 30*y^5 + 6*y^4 + 40*y^3 - 3*y^2 - 17*y - 3

-32*y^7 + 4*y^6 + 102*y^5 + y^4 - 121*y^3 - 5*y^2 + 43*y + 13

-4*y^7 + 6*y^6 + 21*y^5 - 8*y^4 - 32*y^3 + 2*y^2 + 16*y + 5

12*y^7 + 2*y^6 - 41*y^5 - 11*y^4 + 53*y^3 + 15*y^2 - 23*y - 9


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

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

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

# f Combinatorial flattening
{2, -1, 2, -4, -1, 0, 3}

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

# 1 Loop Invariant
20*y^7 - 14*y^6 - 91*y^5 + 13*y^4 + 275/2*y^3 + 35/2*y^2 - 65*y - 26

# 2 Loop Invariant
23017507784287054/5920734776508721*y^7 - 586833811371484/17762204329526163*y^6 - 230880988854937436/17762204329526163*y^5 - 30858856699437019/23682939106034884*y^4 + 382214005317894775/23682939106034884*y^3 + 139496290848251951/71048817318104652*y^2 - 453228668769339065/71048817318104652*y - 141382955946284021/71048817318104652

# 3 Loop Invariant
1190606810077430567389740/455578699461755540278231*y^7 - 81149388802292751270402/455578699461755540278231*y^6 - 3815468064375685427368693/455578699461755540278231*y^5 - 223416606080746245376804/455578699461755540278231*y^4 + 4578516077654416832183277/455578699461755540278231*y^3 + 827648188398865679853741/911157398923511080556462*y^2 - 3455425050533120363428221/911157398923511080556462*y - 1045069869371568444134635/911157398923511080556462

# 4 Loop Invariant
-414668678752778692028610365020330246652/1037446403592242677271105668333514597135*y^7 + 2928417923524432322499179466935866729369/37348070529320736381759804060006525496860*y^6 + 92734646205729242258963093608156831396621/74696141058641472763519608120013050993720*y^5 - 10208451379803182501747218080542185252673/149392282117282945527039216240026101987440*y^4 - 52045140183071356395078429424436413474991/37348070529320736381759804060006525496860*y^3 - 10524540095936513168555938526787852927959/149392282117282945527039216240026101987440*y^2 + 8400119647772464521704895502491976878401/16599142457475882836337690693336233554160*y + 12438622764383424058987081008670773827209/74696141058641472763519608120013050993720