(* ::Package:: *)

(************************************************************************)\012(* This file was generated automatically by the Mathematica front end.  *)\012(* It contains Initialization cells from a Notebook file, which         *)\012(* typically will have the same name as this file except ending in      *)\012(* ".nb" instead of ".m".                                               *)\012(*                                                                      *)\012(* This file is intended to be loaded into the Mathematica kernel using *)\012(* the package loading commands Get or Needs.  Doing so is equivalent   *)\012(* to using the Evaluate Initialization Cells menu command in the front *)\012(* end.                                                                 *)\012(*                                                                      *)\012(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)\012(* automatically each time the parent Notebook file is saved in the     *)\012(* Mathematica front end.  Any changes you make to this file will be    *)\012(* overwritten.                                                         *)\012(************************************************************************)\012\012

(* ::Input::Initialization:: *)
SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\Theta"];


(* ::Input::Initialization:: *)
Do[
NumberOfKnots[n,Alternating]={0,0,1,1,2,3,7,18,41,123,367,1288,4878,19536,85263}[[n]];
NumberOfKnots[n,NonAlternating]={0,0,0,0,0,0,0,3,8,42,185,888,5110,27436,168030}[[n]],
{n,15}
];
NumberOfKnots[n_Integer]:=NumberOfKnots[n,Alternating]+NumberOfKnots[n,NonAlternating];
NumberOfKnots[{n_}]:=Sum[NumberOfKnots[n1],{n1,n}];
{NumberOfKnots[15,Alternating], NumberOfKnots[15,NonAlternating],NumberOfKnots[15],NumberOfKnots[{15}]}


(* ::Input::Initialization:: *)
Get["../../Projects/HigherRank/Data/HOMFLYPT3-15.m"]/.(K_->V_):>(H[K]=Expand@V);
H[Knot[3,1]]


(* ::Input::Initialization:: *)
Get["../../Projects/HigherRank/Data/Kh3-15.m"]/.(K_->V_):>(Kh[K]=Expand@V);
Kh[Knot[3,1]]


(* ::Input::Initialization:: *)
J[K_]:=J[K]=Kh[K]/.t->-1;
J[Knot[3,1]]


(* ::Input::Initialization:: *)
Get["../../Projects/HigherRank/Data/theta3-15.m"]/.(K_->V_):>(\[CapitalTheta][K]=Expand@V);
\[CapitalTheta][Knot[3,1]]


(* ::Input::Initialization:: *)
\[CapitalDelta][K_]:=\[CapitalDelta][K]=\[CapitalTheta][K][[1]];
Subscript[\[Rho], 1][K_]:=Subscript[\[Rho], 1][K]=-\[CapitalTheta][K][[2]]/.{T1->T, T2->1};
Factor@{\[CapitalDelta][Knot[3,1]], Subscript[\[Rho], 1][Knot[3,1]]}


(* ::Input::Initialization:: *)
(Join@@(Get["../../Talks/KnotTheoryCongress-2502/Rho2Data/"<>#]& /@ {"Rho2_3-10.m","Rho2_11.m","Rho2_12.m","Rho2_13.m","Rho2_14.m","Rho2_15.m"}))/.(K_->V_):>(Subscript[\[Rho], 2][K]=Expand@V);
Subscript[\[Rho], 2][Knot[3,1]]


(* ::Input::Initialization:: *)
Get["../../Projects/Theta/Vols/Vols.m"]/.(K_->v_):>(Vol[K]=v);
Vol[Knot[4,1]]
Vol[Knot[4,1]]//Precision


(* ::Input::Initialization:: *)
Get["../../Talks/ICERM-2305/TLSigData.m"]/.(K_->v_):>(\[Sigma][K]=v);
\[Sigma][Knot[3,1]]
\[Sigma][Knot[14,NonAlternating,27436]]


(* ::Input::Initialization:: *)
Knots[n_Integer]:=If[n<=10,
Table[Knot[n,k],{k,NumberOfKnots[n]}],
Join[
Table[Knot[n,Alternating,k],{k,NumberOfKnots[n,Alternating]}],
Table[Knot[n,NonAlternating,k],{k,NumberOfKnots[n,NonAlternating]}]
]
];
Knots[{n_}]:=Join@@Table[Knots[n1],{n1,n}];
Knots[{11}]//Short


(* ::Input::Initialization:: *)
Stats[{n_},\[Iota]s_List]:=NumberOfKnots[{n}]-CountDistinct@Table[\[Iota][K],{K,Knots[{n}]},{\[Iota],\[Iota]s}];
Stats[\[Iota]s_List]:=Monitor[
Table[def=Stats[{n},\[Iota]s], {n,10,15}],
{n-1,def}
];


(* ::Input::Initialization:: *)
Clear[TVol]
TVol[K_]:=TVol[K]=If[Vol@K<1,0,N[Vol@K,58]]



