(* ::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\\Projects\\Theta"];


(* ::Input::Initialization:: *)
<< KnotTheory`


(* ::Input::Initialization:: *)
(* Rot suppressed *)


(* ::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:: *)
(* PolyPlot suppressed *)


(* ::Input::Initialization:: *)
PolyPlot1[\[CapitalDelta]_]:=Module[{crs,m,maxc,minc,s,rect},
rect={{0,0},{1,0},{1,1},{0,1}};
If[Expand[\[CapitalDelta]]===0,Graphics[],
m=Max[-Exponent[\[CapitalDelta],T,Min], Exponent[\[CapitalDelta],T,Max]];
crs=CoefficientRules[T^m \[CapitalDelta],{T}];
maxc=N@Log@Max@Abs[Last/@crs];
minc=N@Log@Min@Select[Abs[Last/@crs],#>0&];
If[minc==maxc,s[_]=0,s[c_]:=s[c]=(maxc-Log@c)/(maxc-minc)];
Graphics[crs/.({x_}->c_):>{
Lighter[Which[c==0, White,c>0, Red,c<0,Blue], 0.88s[Abs@c]],
Tooltip[Polygon[({x+m-1/2,0}+#)&/@rect],c T^(x-m)]
},AspectRatio->Min[1/5 ,1/Sqrt[m+1]],ImagePadding->None,PlotRangePadding->None]
]];
Options[PolyPlot2]={Labeled->False};
PolyPlot2[\[Theta]_,OptionsPattern[]]:=Module[{crs,m1,m2,maxc,minc,s,hex,p},
If[Expand[\[Theta]]===0,Graphics[{White,Disk[]}],
hex=Table[{Cos[\[Alpha]],Sin[\[Alpha]]}/Cos[2\[Pi]/12]/2, {\[Alpha],2\[Pi]/12,2\[Pi],2\[Pi]/6}];
m1=Max[-Exponent[\[Theta],Subscript[T, 1],Min], Exponent[\[Theta],Subscript[T, 1],Max]];
m2=Max[-Exponent[\[Theta],Subscript[T, 2],Min], Exponent[\[Theta],Subscript[T, 2],Max]];
crs=CoefficientRules[\!\(
\*SubsuperscriptBox[\(T\), \(1\), \(m1\)] 
\*SubsuperscriptBox[\(T\), \(2\), \(m2\)] \[Theta]\),{Subscript[T, 1],Subscript[T, 2]}];
maxc=N@Log@Max@Abs[Last/@crs];
minc=N@Log@Min@Select[Abs[Last/@crs],#>0&];
If[minc==maxc,s[_]=0,s[c_]:=s[c]=(maxc-Log@c)/(maxc-minc)];
Graphics[{(*{Yellow,Disk[{0,0},1+Cos[2\[Pi]/12]Norm[{m1,m2}]/Sqrt[2]]},*)
crs/.({x1_,x2_}->c_):>{
Lighter[Which[c==0, White,c>0, Red,c<0,Blue], 0.88s[Abs@c]],
p=({
 {1, -1/2},
 {0, Sqrt[3]/2}
}) . {x1-m1,x2-m2};
Tooltip[Polygon[(p+#)&/@hex],c \!\(\*SubsuperscriptBox[\(T\), \(1\), \(x1 - m1\)]\) \!\(\*SubsuperscriptBox[\(T\), \(2\), \(x2 - m2\)]\)] ,
If[Not@OptionValue[Labeled],{},{Black, Text[Style[c \!\(\*SubsuperscriptBox[\(T\), \(1\), \(x1 - m1\)]\) \!\(\*SubsuperscriptBox[\(T\), \(2\), \(x2 - m2\)]\),30],p]}]
}
},ImagePadding->None,PlotRangePadding->None]
]];
PolyPlot[{\[CapitalDelta]_,\[Theta]_},opts___Rule]:=GraphicsColumn[
{PolyPlot1[\[CapitalDelta]],PolyPlot2[\[Theta],FilterRules[{opts},Options[PolyPlot2]]]},
Spacings -> Scaled@0.08,ImagePadding->None,PlotRangePadding->None,
FilterRules[{opts},Options[GraphicsColumn]]
];


(* ::Input::Initialization:: *)
Subscript[T, 3]=Subscript[T, 1] Subscript[T, 2];


(* ::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:: *)
\[CapitalTheta][K_]:=Module[{Cs,\[CurlyPhi],n,A,\[CapitalDelta],G,ev,\[Theta]},
{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];
ev[\[ScriptCapitalE]_]:=Factor[\[ScriptCapitalE]/.Subscript[g, \[Nu]_,\[Alpha]_,\[Beta]_]:>(G[[\[Alpha],\[Beta]]]/.T->Subscript[T, \[Nu]])];
\[Theta]=ev[\!\(
\*SubsuperscriptBox[\(\[Sum]\), \(k1 = 1\), \(n\)]\(
\*SubsuperscriptBox[\(\[Sum]\), \(k2 = 1\), \(n\)]
\(\*SubscriptBox[\(R\), \(12\)]\)[Cs[[\(k1\)\(]\)], Cs[[\(k2\)\(]\)]]\)\)];
\[Theta]+=ev[\!\(
\*SubsuperscriptBox[\(\[Sum]\), \(k = 1\), \(n\)]\(
\(\*SubscriptBox[\(R\), \(11\)]\)[Cs[[k]]]\)\)];
\[Theta]+=ev[\!\(
\*SubsuperscriptBox[\(\[Sum]\), \(k = 1\), \(2  n\)]\(
\(\*SubscriptBox[\(\[CapitalGamma]\), \(1\)]\)[\[CurlyPhi][[\(k\)\(]\)], k]\)\)];
Factor@{\[CapitalDelta],(\[CapitalDelta]/.T->Subscript[T, 1])(\[CapitalDelta]/.T->Subscript[T, 2])(\[CapitalDelta]/.T->Subscript[T, 3])\[Theta]}];



