(* ::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:: *)
RVK::usage="RVK[xs, rots] represents a Rotational Virtual Knot with a list of n Xp/Xm crossings xs and a length 2n list of rotation numbers rots. Crossing sites are indexed 1 through 2n, and rots\[LeftDoubleBracket]k\[RightDoubleBracket] is the rotation between site k-1 and site k. RVK is also a casting operator converting to the RVK presentation from other knot presentations.";


(* ::Input::Initialization:: *)
RVK[pd_PD]:=Subscript[PP, RVK]@Module[{n,xs,x,rots,front={0},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=0,k<2n,++k,If[k==0\[Or]FreeQ[front,-k],
front=Flatten[front/.k->(xs/.{
Xp[k+1,l_]|Xm[l_,k+1]:>{l,k+1,1-l},
Xp[l_,k+1]|Xm[k+1,l_]:>(++rots[[l]];{1-l,k+1,l})
})],
Cases[front,k|-k]/.{k,-k}:>--rots[[k+1]];
]];
RVK[xs,rots] ];
RVK[K_]:=RVK[PD[K]];


(* ::Input::Initialization:: *)
rot[i_,0]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i}\)]\)[0,0,1];
rot[i_,n_]:=Module[{j},
rot[i,n]=If[n>0,rot[i,n-1]Subscript[kC, j],rot[i,n+1]Subscript[\!\(\*OverscriptBox[\(kC\), \(_\)]\), j]]//Subscript[km, i,j->i]];


(* ::Input::Initialization:: *)
Z[K_] := Z[RVK@K];
Z[rvk_RVK] := (*Z[rvk] =*)Monitor[ \!\(\*SubscriptBox[\(PP\), \("\<Z\>"\)]\)@Module[{todo,n,rots,\[Zeta],done,st,cx, \[Zeta]1, i,j,k,k1,k2,k3},
{todo,rots}=List@@rvk;
AppendTo[rots,0];
n=Length[todo];
\[Zeta]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {0}\)]\)[0,0,1];
done={0};
st=Range[0,2n+1];
While[{}=!=($M=todo),
{cx}=MaximalBy[todo, Length[done\[Intersection]{#[[1]], #[[2]], #[[1]]-1,#[[2]]-1}]&,1];
{i,j}=List@@cx;
\[Zeta]1=Switch[Head[cx],
 Xp, (Subscript[kR, i,j] Subscript[\!\(\*OverscriptBox[\(kKink\), \(_\)]\), k])//Subscript[km, j,k->j],
 Xm, (Subscript[\!\(\*OverscriptBox[\(kR\), \(_\)]\), i,j] Subscript[kKink, k])//Subscript[km, j,k->j]
];
\[Zeta]1=(rot[k,rots[[i]]]\[Zeta]1)//Subscript[km, k,i->i]; rots[[i]]=0;
\[Zeta]1=(\[Zeta]1 rot[k, rots[[i+1]]])//Subscript[km, i,k->i]; rots[[i+1]]=0;
\[Zeta]1=(rot[k,rots[[j]]]\[Zeta]1)//Subscript[km, k,j->j]; rots[[j]]=0;
\[Zeta]1=(\[Zeta]1 rot[k, rots[[j+1]]])//Subscript[km, j,k->j]; rots[[j+1]]=0;
\[Zeta]*=\[Zeta]1;
If[MemberQ[done, i], \[Zeta]=\[Zeta]//Subscript[km, i,i+1->i]; st=st/.st[[i+2]]->st[[i+1]]];
If[MemberQ[done, i-1],  \[Zeta]=\[Zeta]//Subscript[km, st[[i]],i->st[[i]]]; st=st/.st[[i+1]]->st[[i]]]; 
If[MemberQ[done, j],  \[Zeta]=\[Zeta]//Subscript[km, j,j+1->j]; st=st/.st[[j+2]]->st[[j+1]]]; 
If[MemberQ[done, j-1],  \[Zeta]=\[Zeta]//Subscript[km, st[[j]],j->st[[j]]]; st=st/.st[[j+1]]->st[[j]]];
done=done\[Union]{i-1,i,j-1,j};
todo=DeleteCases[todo, cx]
];
CF/@ (\[Zeta] /. {Subscript[x, 0]->x,Subscript[y, 0]->y,Subscript[a, 0]->a})
], $M]
