(* ::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:: *)
\[Gamma]2\[Beta]={Subscript[\[Gamma], i_]:>Subscript[\[Beta], i+1]-Subscript[\[Beta], i]}; \[Beta]2\[Gamma]={Subscript[\[Beta], j_]:>Sum[Subscript[\[Gamma], i],{i,j-1}]};
Subscript[\[Sigma], i_][x_]/;i>0:=Expand[x/.\[Gamma]2\[Beta]/.{Subscript[\[Beta], i]->Subscript[\[Beta], i+1],Subscript[\[Beta], i+1]->t Subscript[\[Beta], i]+(1-t)Subscript[\[Beta], i+1]}/.\[Beta]2\[Gamma]];
Subscript[\[Sigma], i_][x_]/;i<0:=Expand[x/.\[Gamma]2\[Beta]/.{Subscript[\[Beta], -i]->t^-1 Subscript[\[Beta], -i+1]+(1-t^-1)Subscript[\[Beta], -i],Subscript[\[Beta], -i+1]->Subscript[\[Beta], -i]}/.\[Beta]2\[Gamma]];


(* ::Input::Initialization:: *)
\[Xi][x_,y_]:=Expand[Expand[(x/.{t->t^-1})(y/.{Subscript[\[Gamma], i_]:>Subscript[\!\(\*OverscriptBox[\(\[Gamma]\), \(_\)]\), i]})]/.Subscript[\[Gamma], i_] Subscript[\!\(\*OverscriptBox[\(\[Gamma]\), \(_\)]\), j_]:>\!\(\*
TagBox[GridBox[{
{"\[Piecewise]", GridBox[{
{
RowBox[{"1", "-", 
SuperscriptBox["t", 
RowBox[{"-", "1"}]]}], 
RowBox[{"j", "==", 
RowBox[{"i", "-", "1"}]}]},
{
RowBox[{
SuperscriptBox["t", 
RowBox[{"-", "1"}]], "-", "t"}], 
RowBox[{"j", "==", "i"}]},
{
RowBox[{"t", "-", "1"}], 
RowBox[{"j", "==", 
RowBox[{"i", "+", "1"}]}]},
{"0", "True"}
},
AllowedDimensions->{2, Automatic},
Editable->True,
GridBoxAlignment->{"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxItemSize->{"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.84]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}},
Selectable->True]}
},
GridBoxAlignment->{"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxItemSize->{"Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.35]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}],
"Piecewise",
DeleteWithContents->True,
Editable->False,
SelectWithContents->True,
Selectable->False,
StripWrapperBoxes->True]\)]



