(* ::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:: *)
<< KnotTheory`


(* ::Input::Initialization:: *)
Rot[pd_PD]:=Module[{n,xs,x,rots,Xp,Xm,front={1},k},
n=Length@pd;rots=Table[0,{2n}];
xs=Cases[pd,x_X:>\[Piecewise]{
 {Xp[x[[4]],x[[1]]], PositiveQ@x},
 {Xm[x[[2]],x[[1]]], True}
}];
For[k=1,k<=2n,++k,
If[FreeQ[front,-k],
front=Flatten@Replace[front,k->(xs/.{
Xp[k,l_]|Xm[l_,k]:>{l+1,k+1,-l},
Xp[l_,k]|Xm[k,l_]:>(++rots[[l]];{-l,k+1,l+1}),
_Xp|_Xm:>{}
}), {1}],
Cases[front,k|-k]/.{k,-k}:>--rots[[k]];
]
];
{xs/.{Xp[i_,j_]:>{+1,i,j}, Xm[i_,j_]:>{-1,i,j}},rots} ];
Rot[K_]:=Rot[PD[K]];


(* ::Input::Initialization:: *)
Subscript[R, 11][s_,i_,j_]=s(1/2-Subscript[g, 3\[InvisibleComma]i\[InvisibleComma]i]+\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(g\), \(1\[InvisibleComma]i\[InvisibleComma]i\)] 
\*SubscriptBox[\(g\), \(2\[InvisibleComma]j\[InvisibleComma]i\)]\)-Subscript[g, 1\[InvisibleComma]i\[InvisibleComma]i] Subscript[g, 2\[InvisibleComma]j\[InvisibleComma]j]-(\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] - 1\))Subscript[g, 2\[InvisibleComma]j\[InvisibleComma]i] Subscript[g, 3\[InvisibleComma]i\[InvisibleComma]i]+2Subscript[g, 2\[InvisibleComma]j\[InvisibleComma]j] Subscript[g, 3\[InvisibleComma]i\[InvisibleComma]i]-(1-\!\(\*SubsuperscriptBox[\(T\), \(3\), \(s\)]\))Subscript[g, 2\[InvisibleComma]j\[InvisibleComma]i] Subscript[g, 3\[InvisibleComma]j\[InvisibleComma]i]-Subscript[g, 2\[InvisibleComma]i\[InvisibleComma]i] Subscript[g, 3\[InvisibleComma]j\[InvisibleComma]j]-\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(g\), \(2\[InvisibleComma]j\[InvisibleComma]i\)] 
\*SubscriptBox[\(g\), \(3\[InvisibleComma]j\[InvisibleComma]j\)]\)+Subscript[g, 1\[InvisibleComma]i\[InvisibleComma]i] Subscript[g, 3\[InvisibleComma]j\[InvisibleComma]j]+((\!\(
\*SubsuperscriptBox[\(T\), \(1\), \(s\)] - 1\))Subscript[g, 1\[InvisibleComma]j\[InvisibleComma]i](\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(2  s\)] 
\*SubscriptBox[\(g\), \(2\[InvisibleComma]j\[InvisibleComma]i\)]\)-\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(g\), \(2\[InvisibleComma]j\[InvisibleComma]j\)]\)+\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(g\), \(3\[InvisibleComma]j\[InvisibleComma]j\)]\))+(\!\(
\*SubsuperscriptBox[\(T\), \(3\), \(s\)] - 1\))Subscript[g, 3\[InvisibleComma]j\[InvisibleComma]i](1-\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] 
\*SubscriptBox[\(g\), \(1\[InvisibleComma]i\[InvisibleComma]i\)]\)-(\!\(
\*SubsuperscriptBox[\(T\), \(1\), \(s\)] - 1\))(\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] + 1\)) Subscript[g, 1\[InvisibleComma]j\[InvisibleComma]i]+(\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] - 2\))Subscript[g, 2\[InvisibleComma]j\[InvisibleComma]j]+Subscript[g, 2\[InvisibleComma]i\[InvisibleComma]j]))/(\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s\)] - 1\)));


(* ::Input::Initialization:: *)
Subscript[R, 12][{s0_,i0_,j0_},{s1_,i1_,j1_}]=s1(\!\(
\*SubsuperscriptBox[\(T\), \(1\), \(s0\)] - 1\))(\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s1\)] - 1\))^-1 (\!\(
\*SubsuperscriptBox[\(T\), \(3\), \(s1\)] - 1\))Subscript[g, 1,j1,i0] Subscript[g, 3,j0,i1]( (\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s0\)] 
\*SubscriptBox[\(g\), \(2, i1, i0\)]\)-Subscript[g, 2,i1,j0])- (\!\(
\*SubsuperscriptBox[\(T\), \(2\), \(s0\)] 
\*SubscriptBox[\(g\), \(2, j1, i0\)]\)-Subscript[g, 2,j1,j0]));


(* ::Input::Initialization:: *)
Subscript[\[CapitalGamma], 1][\[CurlyPhi]_,k_]=-\[CurlyPhi]/2+\[CurlyPhi] Subscript[g, 3\[InvisibleComma]k\[InvisibleComma]k];


(* ::Input::Initialization:: *)
Subscript[T, 3]=Subscript[T, 1] Subscript[T, 2];
\[CapitalTheta][K_]:=Module[{Cs,\[CurlyPhi],n,A,s,i,j,k,\[CapitalDelta],G,\[Nu],\[Alpha],\[Beta],gEval,c,z},
{Cs,\[CurlyPhi]}=Rot[K]; n=Length[Cs];
A=IdentityMatrix[2n+1];
Cases[Cs,{s_,i_,j_}:>(A[[{i,j},{i+1,j+1}]]+=({
 {-T^s, T^s-1},
 {0, -1}
}))];
\[CapitalDelta]=T^((-Total[\[CurlyPhi]]-Total[Cs[[All,1]]])/2) Det[A];
G=Inverse[A];
gEval[\[ScriptCapitalE]_]:=Factor[\[ScriptCapitalE]/.Subscript[g, \[Nu]_,\[Alpha]_,\[Beta]_]:>(G[[\[Alpha],\[Beta]]]/.T->Subscript[T, \[Nu]])];
z=gEval[\!\(
\*SubsuperscriptBox[\(\[Sum]\), \(k = 1\), \(n\)]\(
\*SubscriptBox[\(R\), \(11\)] @@ Cs[[k]]\)\)];
z+=gEval[\!\(
\*SubsuperscriptBox[\(\[Sum]\), \(k1 = 1\), \(n\)]\(
\*SubsuperscriptBox[\(\[Sum]\), \(k2 = 1\), \(n\)]
\(\*SubscriptBox[\(R\), \(12\)]\)[Cs[\([k1]\)], Cs[\([k2]\)]]\)\)];
z+=gEval[\!\(
\*SubsuperscriptBox[\(\[Sum]\), \(k = 1\), \(2  n\)]\(
\(\*SubscriptBox[\(\[CapitalGamma]\), \(1\)]\)[\[CurlyPhi][[\(k\)\(]\)], k]\)\)];
{\[CapitalDelta],(\[CapitalDelta]/.T->Subscript[T, 1])(\[CapitalDelta]/.T->Subscript[T, 2])(\[CapitalDelta]/.T->Subscript[T, 3])z}//Factor ];


(* ::Input::Initialization:: *)
SetOptions[$FrontEndSession,PrintingStyleEnvironment->"Working"];
nb2tex[nb_String,opts___Rule]:=nb2tex[nb,nb,opts];


(* ::Input::Initialization:: *)
nb2tex[nb_String,tex_String, opts___Rule]:=Module[
{notebook,PDFCounter=0,type,tag,pdfname,cells,cell,c,cl,texfiles={},TeXOut,
PDFFolder=PDFFolder/. {opts}/.PDFFolder->nb
},
nb2tex$TeXFileName=tex<>".tex";
nb2tex$PDFWidth = PDFWidth /. {opts} /. PDFWidth->6.5;
TeXOut[s_String]:=(texfiles=texfiles\[Union]{nb2tex$TeXFileName};
WriteString[nb2tex$TeXFileName,s]);
notebook=NotebookGet[NotebookOpen@FileNameJoin[{Directory[],nb<>".nb"}]];
If[FileType[PDFFolder]===None, CreateDirectory[PDFFolder]];
DeleteFile/@FileNames["*.pdf",PDFFolder];
cells=Cases[notebook,c_Cell /; Length[c]>=2,\[Infinity]];
Do[
type=cell[[2]];
tag=CellTags /. Cases[cell,_Rule] /. CellTags->"";
Which[
type=="Text"\[And]tag=="tex", TeXOut[
StringReplace[cell[[1]],{"\[CloseCurlyQuote]"->"'", "\[CloseCurlyDoubleQuote]"->"\""}]<>"\n\n"],
StringMatchQ[tag,"pdf:"~~___], (
pdfname=PDFFolder<>"/"<>StringDrop[tag,4]<>type<>".pdf";
Export[pdfname, Join[cell, Cell[PageWidth -> 80nb2tex$PDFWidth/0.75]]];
cl="c:\\drorbn\\bin\\cpdf.exe -scale-page \"0.75 0.75\" "<>pdfname<>" -o "<>pdfname;
Close@OpenRead["!"<>cl];
),
StringMatchQ[tag,"pdf"~~___], (
pdfname=PDFFolder<>"/"<>ToString[++PDFCounter]<>".pdf";
Export[pdfname, Join[cell, Cell[PageWidth -> 80nb2tex$PDFWidth/0.75]]];
cl="c:\\drorbn\\bin\\cpdf.exe -scale-page \"0.75 0.75\" "<>pdfname<>" -o "<>pdfname;
Close@OpenRead["!"<>cl];
TeXOut[StringReplace[
"\\noindent\\nbpdfXXXType{pdfname}\n\n",
{"XXX"->StringDrop[tag,3], "Type"->type, "pdfname"->pdfname}
]]
),
type=="Input"\[And]tag=="exec", ToExpression[cell[[1]]],
True, Null
],
{cell,cells}
];
Close/@texfiles;
]
