# Manifold: Census Knot K5_3

# Number of Tetrahedra: 5

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

# Approximate Field Generator
0.00692142332638135 + 0.546500081101693*I

# Shape Parameters
11/8*y^6 - 33/8*y^5 + 17/8*y^4 - 29/8*y^3 - 31/4*y^2 - 29/8

-4*y^5 + 15*y^4 - 18*y^3 + 27*y^2 - 3*y + 8

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

-1/8*y^6 + 3/8*y^5 - 3/8*y^4 + 7/8*y^3 + 1/4*y^2 + y + 7/8

-1/8*y^6 + 3/8*y^5 - 3/8*y^4 + 7/8*y^3 + 1/4*y^2 + y + 7/8


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

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

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

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

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

# 1 Loop Invariant
-4*y^6 + 18*y^5 - 31*y^4 + 95/2*y^3 - 32*y^2 + 24*y - 8

# 2 Loop Invariant
356417476/19026275277603*y^6 - 2210037724/19026275277603*y^5 + 886433387/6342091759201*y^4 + 43069978595/19026275277603*y^3 - 1267027757455/76105101110412*y^2 + 1042960154117/6342091759201*y - 62152877366365/76105101110412

# 3 Loop Invariant
-3226214650087450/15971613123875597551*y^6 + 23392147152225240/15971613123875597551*y^5 - 155873955255463855/31943226247751195102*y^4 + 174255951059644660/15971613123875597551*y^3 + 13366445879123570/15971613123875597551*y^2 - 88838108359071860/15971613123875597551*y + 521391503948796/15971613123875597551

# 4 Loop Invariant
-321251202133711624881937083983/6077606158444678056437800639005060*y^6 - 4359709093354634314681770655873/9116409237667017084656700958507590*y^5 + 43261844982093391242545294998267/8103474877926237408583734185340080*y^4 - 185067697999374431950282686154909/18232818475334034169313401917015180*y^3 + 153208339114350585002926148231717/72931273901336136677253607668060720*y^2 - 94095144642299688052084467334301/18232818475334034169313401917015180*y + 1105236647772729687932913690017/4558204618833508542328350479253795

# 5 Loop Invariant
613047541761495797390217592471610195/765277277336265671405409583851951592803*y^6 - 46674750458233108505550925641997833/46380441050682767963964217203148581382*y^5 - 32798327791558819473656544989949843439/6122218218690125371243276670815612742424*y^4 + 4876970894010097419200623516407195173/1530554554672531342810819167703903185606*y^3 - 22609009472049173198128462666043175997/3061109109345062685621638335407806371212*y^2 + 2675958834927721141925692983013260127/3061109109345062685621638335407806371212*y - 144192911703375685081082236449446328/255092425778755223801803194617317197601