(* ::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:: *)
Print["Loading Rot.m to compute rotation numbers."]


(* ::Input::Initialization:: *)
Rot::usage="Rot[K] where K is any n-crossing knot presentation returns {Cs, \[CurlyPhi]}, where Cs is a length n list of crossings as triples {s,i,j} and \[CurlyPhi] is a lengtth 2n list of rotation numbers.";


(* ::Input::Initialization:: *)
PD[epd_EPD]:=PD@@epd/.{Subscript[X, i_,j_]:>X[j,i+1,j+1,i],Subscript[\!\(\*OverscriptBox[\(X\), \(_\)]\), i_,j_]:>X[j,i,j+1,i+1]}


(* ::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]];
