# Manifold: Rolfsen Knot 9_3 # Number of Tetrahedra: 6 # Number Field x^9 + x^8 + 4*x^7 + 3*x^6 + 5*x^5 + 3*x^4 - 3*x - 1 # Approximate Field Generator -0.460882238780116 + 1.29533393643152*I # Shape Parameters -y^2 - 1 -1/7*y^8 - 3/7*y^7 - 10/7*y^6 - 9/7*y^5 - 16/7*y^4 - y^3 - y^2 + 10/7 -y^8 - y^7 - 3*y^6 - 2*y^5 - 2*y^4 - y^3 + 2*y^2 + y + 2 2*y^7 + 2*y^6 + 5*y^5 + 4*y^4 + 3*y^3 + 2*y^2 - 4*y - 2 -y^5 - 2*y^3 - y + 1 1/11*y^8 - 2/11*y^7 - 1/11*y^6 - 5/11*y^5 - 2/11*y^4 - 2/11*y^3 - 5/11*y^2 + 4/11*y + 7/11 # A Gluing Matrix {{1,0,0,0,0,1},{0,3,0,-1,2,1},{0,0,0,0,0,-1},{0,-1,0,0,0,1},{0,2,0,0,2,0},{1,1,-1,1,0,-1}} # B Gluing Matrix {{1,0,0,0,0,0},{0,1,0,0,0,0},{0,0,1,0,0,0},{0,0,0,1,0,0},{0,0,0,0,1,0},{0,0,0,0,0,1}} # nu Gluing Vector {1, 3, 0, 0, 2, 1} # f Combinatorial flattening {1, 0, -3, -3, 0, 0} # f' Combinatorial flattening {0, 0, 0, 0, 2, 0} # 1 Loop Invariant 5*y^8 + 4*y^7 + 33/2*y^6 + 19/2*y^5 + 27/2*y^4 + 15/2*y^3 - 9*y^2 - 3/2*y - 11 # 2 Loop Invariant -11723382750890356717/72205144472045183052*y^8 - 2983470320830320560/18051286118011295763*y^7 - 34104415711704806495/72205144472045183052*y^6 - 5849471891477640416/18051286118011295763*y^5 - 3392345003753896973/12034190745340863842*y^4 - 5474842677506864065/36102572236022591526*y^3 + 24456123904097067811/72205144472045183052*y^2 + 12304421498387622155/72205144472045183052*y - 31367871175057912379/144410288944090366104 # 3 Loop Invariant 78515937279854669787743703/29519591174429286164678555438*y^8 + 264106377370688957817569751/14759795587214643082339277719*y^7 + 365526839544086494353532389/29519591174429286164678555438*y^6 + 1153135738579930933002721115/29519591174429286164678555438*y^5 + 495505867248608979343833669/29519591174429286164678555438*y^4 + 725473329766982861809678253/29519591174429286164678555438*y^3 + 238323838354881087396520108/14759795587214643082339277719*y^2 - 451326439095986827754297269/14759795587214643082339277719*y + 168919624081371388663935925/14759795587214643082339277719 # 4 Loop Invariant -55159456295614874014375530481740023713245713209/12788798073032259269348993150088916742817840220656*y^8 + 71479139894757103134463053537685981581428532727/63943990365161296346744965750444583714089201103280*y^7 - 1258850092809050054076896162425455302769289019483/63943990365161296346744965750444583714089201103280*y^6 - 75141405877265987715453175779077650153089281929/63943990365161296346744965750444583714089201103280*y^5 - 442251167769670019341264390489888164852632683157/15985997591290324086686241437611145928522300275820*y^4 - 260085935782296983410665222455751627815008295657/63943990365161296346744965750444583714089201103280*y^3 - 3771581483976601518821811441320672324380597249/2664332931881720681114373572935190988087050045970*y^2 - 694875290267075355156400297152516218948151513511/63943990365161296346744965750444583714089201103280*y + 81681923107506662656278899114354196110010822489/3552443909175627574819164763913587984116066727960