(* ::Package:: *)

(************************************************************************)
(* This file was generated automatically by the Mathematica front end.  *)
(* It contains Initialization cells from a Notebook file, which         *)
(* typically will have the same name as this file except ending in      *)
(* ".nb" instead of ".m".                                               *)
(*                                                                      *)
(* This file is intended to be loaded into the Mathematica kernel using *)
(* the package loading commands Get or Needs.  Doing so is equivalent   *)
(* to using the Evaluate Initialization Cells menu command in the front *)
(* end.                                                                 *)
(*                                                                      *)
(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
(* automatically each time the parent Notebook file is saved in the     *)
(* Mathematica front end.  Any changes you make to this file will be    *)
(* overwritten.                                                         *)
(************************************************************************)



(* ::Input::Initialization:: *)
SetDirectory["C:\\drorbn\\AcademicPensieve\\2020-01"];
<< KnotTheory`
$k=2;


(* ::Input::Initialization:: *)
Subscript[\[DoubleStruckCapitalE][L_,Q_,P_], $k_]:=\[DoubleStruckCapitalE][L,Q,Series[Normal@P,{\[Epsilon],0,$k}]];
Subscript[Subscript[\[DoubleStruckCapitalE], d_->r_][L_,Q_,P_], $k_]:=Subscript[\[DoubleStruckCapitalE], d->r]@@Subscript[\[DoubleStruckCapitalE][L,Q,P], $k];


(* ::Input::Initialization:: *)
\[DoubleStruckCapitalE]3@\[DoubleStruckCapitalE][\[Omega]_,L_,Q_,Ps_]:=Simplify/@Subscript[\[DoubleStruckCapitalE][L,\[Omega]^-1 Q,\[Omega]^-1 (\[Omega]^-4 \[Epsilon])^(-1+Range@Length@Ps).Ps], $k];
\[DoubleStruckCapitalE]3@Subscript[\[DoubleStruckCapitalE], sp___][as___]:=\[DoubleStruckCapitalE]3@\[DoubleStruckCapitalE][as]/.\[DoubleStruckCapitalE]->Subscript[\[DoubleStruckCapitalE], sp];


(* ::Input::Initialization:: *)
Clear[QP,\[Omega]];
QP[Knot[n_,k_]] := QP[Knot[n,k]]=Module[{fname},
fname="../Projects/SL2Invariant/k=2/Data/"<>ToString[n]<>"_"<>ToString[k]<>".m";
Collect[\[DoubleStruckCapitalE]3[Get[fname][[2,2]]][[3]] // Normal, \[Epsilon], Simplify]
];
\[Omega][K_Knot]:=\[Omega][K]=Factor[(QP@K/.\[Epsilon]->0)^-1];
Subscript[c, k_,d_][K_Knot]:=Factor[SeriesCoefficient[QP[K],{y,0,0}, {\[Epsilon],0,k},{a,0,d}]\[Omega][K]^(1+2k-d)]


(* ::Input::Initialization:: *)
p1[K_Knot]:=p1[K]=Factor[(T(-Subscript[c, 1,0][K]+\[Omega][K]T \!\(
\*SubscriptBox[\(\[PartialD]\), \(T\)]\(\[Omega][K]\)\)))/(T-1)^2];


(* ::Input::Initialization:: *)
p2[K_Knot]:=p2[K]=Expand[-2Subscript[c, 2,0][K]+\[Omega][K]Subscript[c, 2,1][K]];



