# Manifold: Census Knot K6_9 # Number of Tetrahedra: 6 # Number Field x^9 - 9*x^8 + 40*x^7 - 24*x^6 - 5*x^5 + 82*x^4 + 55*x^3 + 28*x^2 + 7*x + 1 # Approximate Field Generator -0.204194008191348 - 0.183659262284871*I # Shape Parameters 33035/2205781*y^8 - 336507/2205781*y^7 + 1675287/2205781*y^6 - 2417530/2205781*y^5 + 1270691/2205781*y^4 + 748776/2205781*y^3 + 850605/2205781*y^2 - 801280/2205781*y + 875387/2205781 -957549/35292496*y^8 + 1035933/4411562*y^7 - 2229793/2205781*y^6 + 1662441/4411562*y^5 - 4886583/35292496*y^4 - 52044097/35292496*y^3 - 22312043/8823124*y^2 - 11054923/4411562*y + 428989/35292496 -1330394/2205781*y^8 + 11940511/2205781*y^7 - 52879253/2205781*y^6 + 30254169/2205781*y^5 + 9069500/2205781*y^4 - 110362999/2205781*y^3 - 73920446/2205781*y^2 - 38101637/2205781*y - 6305697/2205781 -1330394/2205781*y^8 + 11940511/2205781*y^7 - 52879253/2205781*y^6 + 30254169/2205781*y^5 + 9069500/2205781*y^4 - 110362999/2205781*y^3 - 73920446/2205781*y^2 - 38101637/2205781*y - 6305697/2205781 -5309261/8823124*y^8 + 12654064/2205781*y^7 - 59622656/2205781*y^6 + 61588358/2205781*y^5 - 66306051/8823124*y^4 - 435160465/8823124*y^3 - 13787224/2205781*y^2 - 9502496/2205781*y + 7370645/8823124 -24920119/44115620*y^8 + 11385602/2205781*y^7 - 51340499/2205781*y^6 + 181771994/11028905*y^5 + 81171199/44115620*y^4 - 2102000287/44115620*y^3 - 265670477/11028905*y^2 - 109312311/11028905*y - 60635369/44115620 # A Gluing Matrix {{1,0,2,0,0,2},{0,1,2,0,0,2},{1,2,3,0,1,1},{0,0,0,1,-1,1},{0,0,1,-1,1,1},{1,2,1,1,1,0}} # B Gluing Matrix {{2,0,0,0,0,0},{0,1,0,0,0,0},{0,0,1,0,0,0},{0,0,0,1,0,0},{0,0,0,0,1,0},{0,0,0,0,0,1}} # nu Gluing Vector {4, 3, 3, 1, 1, 2} # f Combinatorial flattening {6, 5, -4, -6, -4, 3} # f' Combinatorial flattening {0, 0, 0, 0, 0, 0} # 1 Loop Invariant -127780923/17646248*y^8 + 148112786/2205781*y^7 - 678773578/2205781*y^6 + 563704373/2205781*y^5 - 413768641/17646248*y^4 - 10507822591/17646248*y^3 - 983444873/4411562*y^2 - 264242338/2205781*y - 272382717/17646248 # 2 Loop Invariant -60989023997300723076832/3150813550549309750828047*y^8 + 2933986282048075783973949/16804338936262985337749584*y^7 - 39377507972462114453267675/50413016808788956013248752*y^6 + 12934636491287991560182571/25206508404394478006624376*y^5 - 3651389536780603769369167/50413016808788956013248752*y^4 - 35291866795237466092060591/25206508404394478006624376*y^3 - 17771167075716865376322773/16804338936262985337749584*y^2 - 39901504985196776414641027/50413016808788956013248752*y + 2279572563186056780660509/3877924369906842770249904 # 3 Loop Invariant 43342044437738333465006302390561/23191079106639474301940171404482464*y^8 - 35390612705271829779909644591467/1783929162049190330918474723421728*y^7 + 4744424061546066775309615799752419/46382158213278948603880342808964928*y^6 - 3908663583512529228385491344054871/23191079106639474301940171404482464*y^5 + 53709228542907846351291608418793/724721222082483571935630356390077*y^4 + 4059650348593407403921910199442511/23191079106639474301940171404482464*y^3 - 7557241090535087182211036971860037/46382158213278948603880342808964928*y^2 - 2055266709350587348784310255050877/23191079106639474301940171404482464*y - 80443973474170995007713501521555/5797769776659868575485042851120616