(* ::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:: *)
K\[Delta]/:Subscript[K\[Delta], i_,j_]:=If[i===j,1,0];
{SuperStar[z],SuperStar[x],SuperStar[y]}={\[Zeta],\[Xi],\[Eta]}; {SuperStar[\[Zeta]],SuperStar[\[Xi]],SuperStar[\[Eta]]}={z,x,y};
SuperStar[(Subscript[u_, i_])]:=Subscript[(SuperStar[u]), i];
CF[\[ScriptCapitalE]_] := Module[
{vs=Cases[\[ScriptCapitalE],Subscript[(z|\[Zeta]|y|\[Eta]), _],\[Infinity]]\[Union]{z,\[Zeta],y,\[Eta]}},
Total[CoefficientRules[Expand[\[ScriptCapitalE]], vs] /. (ps_->c_) :> Simplify[c](Times@@(vs^ps))]
];
\[DoubleStruckCapitalE]/:\[DoubleStruckCapitalE][\[Omega]1_,Q1_]\[Congruent]\[DoubleStruckCapitalE][\[Omega]2_,Q2_]:=CF[\[Omega]1==\[Omega]2]\[And]CF[Q1==Q2];


(* ::Input::Initialization:: *)
\[DoubleStruckCapitalE] /: Subscript[Zip, \[Zeta]s_List]@\[DoubleStruckCapitalE][\[Omega]_,Q_] := Module[{\[Zeta],z,zs,c,ys,\[Eta]s,qt,zrule,\[Zeta]rule},
zs=Table[SuperStar[\[Zeta]],{\[Zeta],\[Zeta]s}];
c=Q/.Alternatives@@(\[Zeta]s\[Union]zs)->0;
ys=Table[\!\(
\*SubscriptBox[\(\[PartialD]\), \(\[Zeta]\)]\((Q /. Alternatives @@ zs -> 0)\)\),{\[Zeta],\[Zeta]s}];
\[Eta]s=Table[\!\(
\*SubscriptBox[\(\[PartialD]\), \(z\)]\((Q /. Alternatives @@ \[Zeta]s -> 0)\)\),{z,zs}];
qt=Inverse@Table[Subscript[K\[Delta], z,SuperStar[\[Zeta]]]-\!\(
\*SubscriptBox[\(\[PartialD]\), \(z, \[Zeta]\)]Q\),{\[Zeta],\[Zeta]s},{z,zs}];
zrule=Thread[zs->qt.(zs+ys)];
\[Zeta]rule=Thread[\[Zeta]s->\[Zeta]s+\[Eta]s.qt];
CF /@ \[DoubleStruckCapitalE][\[Omega] Det[qt],c+\[Eta]s.qt.ys] ];



