(* ::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:: *)
ME=MatrixExp; MF=MatrixForm;
Simp[sol_] := Flatten[sol]/. ConditionalExpression[\[ScriptCapitalE]_,_]:> \[ScriptCapitalE]/. (var_->val_) :> (var -> Simplify[PowerExpand@val]);


(* ::Input::Initialization:: *)
\[Rho]t=({
 {1, 0},
 {0, 1}
});  \[Rho]y=({
 {0, 0},
 {-\[Epsilon], 0}
});  \[Rho]a=({
 {(1+1/\[Epsilon])/2, 0},
 {0, -(1-1/\[Epsilon])/2}
}); \[Rho]x=({
 {0, 1},
 {0, 0}
});
Simplify@{\[Rho]a.\[Rho]x-\[Rho]x.\[Rho]a==\[Rho]x, \[Rho]a.\[Rho]y-\[Rho]y.\[Rho]a==-\[Rho]y, \[Rho]x.\[Rho]y-\[Rho]y.\[Rho]x==\[Rho]t-2\[Epsilon] \[Rho]a}



