# Manifold: Census Knot K6_2

# Number of Tetrahedra: 6

# Number Field
x^9 + 3*x^8 - 4*x^7 - 17*x^6 + x^5 + 29*x^4 + 8*x^3 - 14*x^2 - 3*x + 3 

# Approximate Field Generator
1.58168080149426 + 0.0433203177123449*I

# Shape Parameters
1/3*y^8 + 4/3*y^7 - 1/3*y^6 - 7*y^5 - 16/3*y^4 + 10*y^3 + 37/3*y^2 - 2*y - 14/3

43/49*y^8 + 88/49*y^7 - 39/7*y^6 - 514/49*y^5 + 614/49*y^4 + 902/49*y^3 - 83/7*y^2 - 57/7*y + 207/49

y^6 - 4*y^4 + 4*y^2

8/21*y^8 + y^7 - 32/21*y^6 - 103/21*y^5 + 23/21*y^4 + 142/21*y^3 + 16/21*y^2 - 34/21*y + 5/7

8/21*y^8 + y^7 - 32/21*y^6 - 103/21*y^5 + 23/21*y^4 + 142/21*y^3 + 16/21*y^2 - 34/21*y + 5/7

8/21*y^8 + y^7 - 32/21*y^6 - 103/21*y^5 + 23/21*y^4 + 142/21*y^3 + 16/21*y^2 - 34/21*y + 5/7


# A Gluing Matrix
{{1,2,-3,-4,-4,-4},{0,1,-1,-2,-2,-2},{2,4,-5,-6,-6,-6},{0,0,-1,0,-1,-1},{0,0,-1,-1,0,-1},{0,0,-1,-1,-1,0}}

# B Gluing Matrix
{{1,0,4,0,0,0},{0,1,2,0,0,0},{0,0,6,0,0,0},{0,0,0,1,0,0},{0,0,0,0,1,0},{0,0,0,0,0,1}}

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

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

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

# 1 Loop Invariant
9/2*y^8 + 12*y^7 - 14*y^6 - 51*y^5 + 5/2*y^4 + 58*y^3 + 12*y^2 - 14*y - 3/2

# 2 Loop Invariant
16163402486298235873/105426234769035244428*y^8 + 530711025458732771/1673432297921194356*y^7 - 39776647164849028451/52713117384517622214*y^6 - 167172105094181899541/105426234769035244428*y^5 + 108084036117518468143/105426234769035244428*y^4 + 234045154561592248451/105426234769035244428*y^3 - 13635496535875014509/52713117384517622214*y^2 - 33431483678234021353/52713117384517622214*y - 166223307995248129/35142078256345081476

# 3 Loop Invariant
-536816370606545104507066763/52081222632502051518460852194*y^7 - 112764753170203642796500091/17360407544167350506153617398*y^6 + 1381978169793051636243129694/26040611316251025759230426097*y^5 + 1298846363124154573136918851/52081222632502051518460852194*y^4 - 3963930594153901612388965907/52081222632502051518460852194*y^3 - 1261105455807289250588636503/52081222632502051518460852194*y^2 + 601661457954400447785030394/26040611316251025759230426097*y - 23750668321979933667310045/26040611316251025759230426097