(* ::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\\Classes\\21-1350-KnotTheory\\Preps"];
<< ../Common.m


(* ::Input::Initialization:: *)
MT=\!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{" ", "a", "b", "c", "d"},
{"a", "a", "b", "0", "0"},
{"b", "0", "0", "a", "b"},
{"c", "c", "d", "0", "0"},
{"d", "0", "0", "c", "d"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}}], "", ")"}],
Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\);
\[ScriptCapitalE]_//Subscript[m, i_,j_->k_]:=Expand[\[ScriptCapitalE]]/.Flatten@Table[Subscript[MT[[\[Alpha],1]], i] Subscript[MT[[1,\[Beta]]], j]->(MT[[\[Alpha],\[Beta]]]/.v:(a|b|c|d):>Subscript[v, k]),{\[Alpha],2,5},{\[Beta],2,5}];
Subscript[\[Eta], i_]:=Subscript[a, i]+Subscript[d, i];


(* ::Input::Initialization:: *)
KBasis[i_]:={Subscript[a, i],Subscript[b, i],Subscript[c, i],Subscript[d, i]};
KBasis[i_,is__]:=Flatten@Outer[Times,KBasis[i],KBasis[is]]


(* ::Input::Initialization:: *)
Subscript[R, i_,j_]:=T^(-1/2) (Subscript[a, i] Subscript[a, j]+T Subscript[a, i] Subscript[d, j]+(1-T) Subscript[b, j] Subscript[c, i]+Subscript[d, i] Subscript[a, j]-T Subscript[d, i] Subscript[d, j]);
Subscript[\!\(\*OverscriptBox[\(R\), \(_\)]\), i_,j_]:=T^(1/2) (Subscript[a, i] Subscript[a, j]+T^-1 Subscript[a, i] Subscript[d, j]+(1-T^-1) Subscript[b, j] Subscript[c, i]+Subscript[d, i] Subscript[a, j]-T^-1 Subscript[d, i] Subscript[d, j]);
Subscript[C, i_]:=T^(-1/2) (Subscript[a, i]-Subscript[d, i]); Subscript[\!\(\*OverscriptBox[\(C\), \(_\)]\), i_]:=T^(1/2) (Subscript[a, i]-Subscript[d, i]);



