# Manifold: Census Knot K8_70 # Number of Tetrahedra: 8 # Number Field x^8 + 2*x^7 + 9*x^6 + 36*x^5 + 124*x^4 + 240*x^3 + 288*x^2 + 192*x + 64 # Approximate Field Generator -0.726947067197103 + 0.639841305445870*I # Shape Parameters 1/16*y^7 + 1/16*y^6 + 1/2*y^5 + 7/4*y^4 + 6*y^3 + 9*y^2 + 9*y + 4 1/320*y^7 + 9/320*y^5 + 9/160*y^4 + 11/40*y^3 + 1/5*y^2 + 1/2*y + 3/5 y + 2 -1/8*y^6 - 7/8*y^4 - 11/4*y^3 - 33/4*y^2 - 8*y - 3 1/64*y^7 + 1/32*y^6 + 9/64*y^5 + 9/16*y^4 + 31/16*y^3 + 15/4*y^2 + 9/2*y + 3 1/8*y^7 + 3/16*y^6 + y^5 + 63/16*y^4 + 53/4*y^3 + 89/4*y^2 + 21*y + 8 5/16*y^7 + 1/4*y^6 + 37/16*y^5 + 67/8*y^4 + 109/4*y^3 + 149/4*y^2 + 29*y + 6 3/16*y^7 + 1/16*y^6 + 21/16*y^5 + 71/16*y^4 + 14*y^3 + 15*y^2 + 8*y # A Gluing Matrix {{-3,-2,0,0,-2,-2,-2,-2},{-2,0,0,0,-2,-2,0,-1},{0,0,1,0,0,-2,0,-1},{0,0,0,0,0,0,2,1},{-2,-2,0,0,0,-2,-2,-2},{-2,-2,-2,0,-2,1,-2,-1},{-2,0,0,2,-2,-2,-3,-3},{-2,-1,-1,1,-2,-1,-3,-2}} # B Gluing Matrix {{1,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0},{0,0,1,0,0,0,0,0},{0,0,0,1,0,0,0,0},{0,0,0,0,1,0,0,0},{0,0,0,0,0,1,0,0},{0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,1}} # nu Gluing Vector {-5, -2, -1, 2, -4, -3, -5, -4} # f Combinatorial flattening {-9, -15, 45, 4, -15, 11, -11, 24} # f' Combinatorial flattening {-44, -4, 0, 0, -4, 0, 0, 0} # 1 Loop Invariant 77/16*y^7 + 27/4*y^6 + 601/16*y^5 + 1197/8*y^4 + 989/2*y^3 + 815*y^2 + 753*y + 284 # 2 Loop Invariant -735606472657099/719631349126374400*y^7 - 211083122037811/215889404737912320*y^6 - 18722375642649053/2158894047379123200*y^5 - 219190739939983/7937110468305600*y^4 - 8782903494711169/89953918640796800*y^3 - 59010882241677781/269861755922390400*y^2 - 1204008878652911/26986175592239040*y - 4079980741466074327/67465438980597600 # 3 Loop Invariant 419165867547062807922439/381544439408113686545920000*y^7 - 43577229955693335217/9538610985202842163648000*y^6 + 217351605842565348833583/22443790553418452149760000*y^5 + 5066453332388655805101331/190772219704056843272960000*y^4 + 1691270587040734124880917/23846527463007105409120000*y^3 + 397774124711016256227167/2980815932875888176140000*y^2 + 1114355430583783347401339/9538610985202842163648000*y + 681335385309452660423249/11923263731503552704560000 # 4 Loop Invariant -15413937790044255552780318821888417795827/9085081092449792538902435811896979456000000*y^7 + 6036028121585040132772836116768543051/37854504551874135578760149216237414400000*y^6 - 32797449021110736145426953846891328260241/3028360364149930846300811937298993152000000*y^5 - 194561437739363477540532062548722360454783/4542540546224896269451217905948489728000000*y^4 - 26343607096037529113902848001066645928953/283908784139056016840701119121780608000000*y^3 - 141187141298486064873036694702704911832121/1135635136556224067362804476487122432000000*y^2 - 5262903350631881489331728814646613466413/56781756827811203368140223824356121600000*y - 1065627291647726150201959057318835539573/31545420459895112982300124346864512000000