# Manifold: H T Link Exterior K9a27

# Number of Tetrahedra: 5

# Number Field
x^7 + x^6 + 6*x^5 + 5*x^4 + 10*x^3 + 6*x^2 + 4*x + 1 

# Approximate Field Generator
-0.0231710276033201 + 1.82953243390828*I

# Shape Parameters
y^6 + y^5 + 6*y^4 + 5*y^3 + 10*y^2 + 6*y + 4

y^6 + y^5 + 6*y^4 + 5*y^3 + 10*y^2 + 6*y + 4

y^6 + y^5 + 6*y^4 + 5*y^3 + 10*y^2 + 6*y + 4

3*y^6 + y^5 + 17*y^4 + 4*y^3 + 26*y^2 + 3*y + 10

y^4 + 4*y^2 + 4


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

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

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

# f Combinatorial flattening
{6, 0, 0, 4, 2}

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

# 1 Loop Invariant
3*y^6 + 3*y^5 + 35/2*y^4 + 27/2*y^3 + 28*y^2 + 31/2*y + 10

# 2 Loop Invariant
758260004644/6342091759201*y^6 + 3229290716701/25368367036804*y^5 + 18448989018081/25368367036804*y^4 + 8200345695715/12684183518402*y^3 + 31641086004925/25368367036804*y^2 + 30678975743917/38052550555206*y + 18643630271932/19026275277603

# 3 Loop Invariant
735156588537120165/15971613123875597551*y^6 + 450811246095789540/15971613123875597551*y^5 + 4139142119950086015/15971613123875597551*y^4 + 3997778709452036385/31943226247751195102*y^3 + 12064489168496606665/31943226247751195102*y^2 + 1743722478973088685/15971613123875597551*y + 3019715252502539267/31943226247751195102

# 4 Loop Invariant
-8296145688619619366474433549353/810347487792623740858373418534008*y^6 - 41398580029867204717886272466767/4862084926755742445150240511204048*y^5 - 265739715700204080059266355437661/4862084926755742445150240511204048*y^4 - 2822366335483953924961530193840327/72931273901336136677253607668060720*y^3 - 163028713774030587354574936851347/2431042463377871222575120255602024*y^2 - 337081158256808934195616336600273/9116409237667017084656700958507590*y + 7479522641229439205471087741029/4862084926755742445150240511204048