(* ::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:: *)
\[Omega]2[v_][p_]:=Module[{q=Expand[p],n,c},
If[q===0,0,c=Coefficient[q,\[Omega],n=Exponent[q,\[Omega]]];c v^n+\[Omega]2v[q-c (\[Omega]+\[Omega]^-1)^n,v]]];


(* ::Input::Initialization:: *)
\[Omega]2u[f_]:=Factor@Module[{num,den,v},
{num,den}=NumeratorDenominator[f];{num,den}/=\[Omega]^(Exponent[num,\[Omega]]/2);
Times@@(\[Omega]2[v]/@{num,den})/.v->(2u^2-1)/2 ]



