# Manifold: H T Link Exterior K8a15

# Number of Tetrahedra: 12

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

# Approximate Field Generator
None

# Shape Parameters
-y^2

1/2*y + 1/2

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

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

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

-11/2*y^4 + 8*y^3 - 19/2*y^2 + 9/2*y - 25/2

1/14*y^4 + 1/7*y^3 - 1/2*y^2 + 1/2*y + 9/14

-3*y^4 + 5*y^3 - 6*y^2 + 3*y - 7

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

3/7*y^4 - 1/7*y^3 + 6/7

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

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


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

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

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

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

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

# 1 Loop Invariant
-25/2*y^4 + 17*y^3 - 3*y^2 - 20*y - 7

# 2 Loop Invariant
-325823475969/6656240040961*y^4 + 1125663388733/26624960163844*y^3 - 505797712769/3803565737692*y^2 + 922817337047/2852674303269*y + 2741603949355/19968720122883

# 3 Loop Invariant
374417571168395154675/16108173598579347376042*y^4 - 487417756152310493795/8054086799289673688021*y^3 + 195543271234032891885/2301167656939906768006*y^2 - 55163010177454308263/2301167656939906768006*y + 1498242224766988088651/16108173598579347376042

# 4 Loop Invariant
-34134469405403334289132099563317732/804149025702110204622858374625422715*y^4 + 1103933731216350310278253937486102627/19299576616850644910948600991010145160*y^3 - 5146496950218993701184413914087813/91902745794526880528326671385762596*y^2 + 11174995982628954604922909646727547/344635296729475801981225017696609735*y - 114347340347394470004100002959797889/1608298051404220409245716749250845430