(* ::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:: *)
SetAttributes[Define, HoldAll];
Define[def_,defs__] := (Define[def]; Define[defs];);
Define[Subscript[op_, is__]=\[ScriptCapitalE]_] := Module[{SD,ii,jj,kk,isp,nis,nisp,sis},Block[{i,j,k},
ReleaseHold[Hold[
SD[Subscript[op, nisp,$k_Integer],Block[{i,j,k},Subscript[op, isp,$k]=\[ScriptCapitalE];Subscript[op, nis,$k]]];
SD[Subscript[op, isp],\!\(\*SubscriptBox[\(op\), \({is}, $k\)]\)]; SD[Subscript[op, sis__],\!\(\*SubscriptBox[\(op\), \({sis}\)]\)];
]/. {SD->SetDelayed,
isp->{is}/.{i->i_,j->j_,k->k_},
nis->{is}/.{i->ii,j->jj,k->kk},
nisp->{is}/.{i->ii_,j->jj_,k->kk_}
}]  ]]


(* ::Input::Initialization:: *)
Define[Subscript[m, i,j->k]=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({i, j} \[Rule] {k}\)]\)[1,-Subscript[\[Xi], i] Subscript[\[Eta], j]+(Subscript[\[Eta], i]+Subscript[\[Eta], j])Subscript[y, k]+(Subscript[\[Xi], i]+Subscript[\[Xi], j])Subscript[x, k],\[Epsilon]Series[0]]]


(* ::Input::Initialization:: *)
AllMonomials[{},0]={1};
AllMonomials[{},d_Integer] /; d>0 := {};
AllMonomials[{v_,vs___},d_Integer] := Join@@Table[v^(d-k) AllMonomials[{vs},k],{k,0,d}];
AllMonomials[vs_List, {d_}] := Join@@Table[AllMonomials[vs,k],{k,0,d}];


(* ::Input::Initialization:: *)
Basis[js_List,m_]:=Flatten@Outer[Times,AllMonomials[Table[Subscript[y, j],{j,js}],m],AllMonomials[Table[Subscript[x, j],{j,js}],m]];
Basis[js_List,{m_}]:=Flatten@Table[Basis[js,k],{k,0,m}]


(* ::Input::Initialization:: *)
GenericCombination[bas_,c_]:=bas . Table[Subscript[c, j],{j,Length@bas}];
GenericCombination[bas_,Subscript[c_, k_]]:=bas . Table[Subscript[c, k,j],{j,Length@bas}];


(* ::Input::Initialization:: *)
Subscript[R, i_,j_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i, j}\)]\)[1,(-1+T) Subscript[x, j] (Subscript[y, i]-Subscript[y, j]),\[Epsilon]Series@@Prepend[0]@Table[GenericCombination[Basis[{i,j},{k+1}],Subscript[c, k]],{k,$k}]];
Subscript[\!\(\*OverscriptBox[\(R\), \(_\)]\), i_,j_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i, j}\)]\)[1,(-1+1/T) Subscript[x, j] (Subscript[y, i]-Subscript[y, j]),\[Epsilon]Series@@Prepend[0]@Table[GenericCombination[Basis[{i,j},{k+1}],Subscript[d, k]],{k,$k}]];
Subscript[CC, i_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i}\)]\)[Sqrt[T],0,\[Epsilon]Series@@Prepend[0]@Table[GenericCombination[Basis[{i},{k+1}],Subscript[e, k]],{k,$k}]];
Subscript[\!\(\*OverscriptBox[\(CC\), \(_\)]\), i_]:=\!\(\*SubscriptBox[\(\[DoubleStruckCapitalE]\), \({} \[Rule] {i}\)]\)[1/Sqrt[T],0,\[Epsilon]Series@@Prepend[0]@Table[GenericCombination[Basis[{i},{k+1}],Subscript[f, k]],{k,$k}]];


(* ::Input::Initialization:: *)
{Subscript[c, 1,1],Subscript[c, 1,2],Subscript[c, 1,3],Subscript[c, 1,4],Subscript[c, 1,5],Subscript[c, 1,6],Subscript[c, 1,7],Subscript[c, 1,8],Subscript[c, 1,9],Subscript[c, 1,10],Subscript[c, 1,11],Subscript[c, 1,12],Subscript[c, 1,13],Subscript[c, 1,14],Subscript[d, 1,1],Subscript[d, 1,2],Subscript[d, 1,3],Subscript[d, 1,4],Subscript[d, 1,5],Subscript[d, 1,6],Subscript[d, 1,7],Subscript[d, 1,8],Subscript[d, 1,9],Subscript[d, 1,10],Subscript[d, 1,11],Subscript[d, 1,12],Subscript[d, 1,13],Subscript[d, 1,14],Subscript[e, 1,1],Subscript[e, 1,2],Subscript[e, 1,3],Subscript[f, 1,1],Subscript[f, 1,2],Subscript[f, 1,3]}={0,0,0,0,0,0,0,1/2 (-1+T),0,1,1/2 (1-3 T),0,0,0,0,0,0,0,0,0,-((-1+T)/T^2),-((1-T)/(2 T^3)),0,-(1/T^2),-((-1-T)/(2 T^3)),0,0,0,0,-(1/T),0,0,1/T,0};


(* ::Input::Initialization:: *)
{Subscript[c, 2,1],Subscript[c, 2,2],Subscript[c, 2,3],Subscript[c, 2,4],Subscript[c, 2,5],Subscript[c, 2,6],Subscript[c, 2,7],Subscript[c, 2,8],Subscript[c, 2,9],Subscript[c, 2,10],Subscript[c, 2,11],Subscript[c, 2,12],Subscript[c, 2,13],Subscript[c, 2,14],Subscript[c, 2,15],Subscript[c, 2,16],Subscript[c, 2,17],Subscript[c, 2,18],Subscript[c, 2,19],Subscript[c, 2,20],Subscript[c, 2,21],Subscript[c, 2,22],Subscript[c, 2,23],Subscript[c, 2,24],Subscript[c, 2,25],Subscript[c, 2,26],Subscript[c, 2,27],Subscript[c, 2,28],Subscript[c, 2,29],Subscript[c, 2,30],Subscript[d, 2,1],Subscript[d, 2,2],Subscript[d, 2,3],Subscript[d, 2,4],Subscript[d, 2,5],Subscript[d, 2,6],Subscript[d, 2,7],Subscript[d, 2,8],Subscript[d, 2,9],Subscript[d, 2,10],Subscript[d, 2,11],Subscript[d, 2,12],Subscript[d, 2,13],Subscript[d, 2,14],Subscript[d, 2,15],Subscript[d, 2,16],Subscript[d, 2,17],Subscript[d, 2,18],Subscript[d, 2,19],Subscript[d, 2,20],Subscript[d, 2,21],Subscript[d, 2,22],Subscript[d, 2,23],Subscript[d, 2,24],Subscript[d, 2,25],Subscript[d, 2,26],Subscript[d, 2,27],Subscript[d, 2,28],Subscript[d, 2,29],Subscript[d, 2,30],Subscript[e, 2,1],Subscript[e, 2,2],Subscript[e, 2,3],Subscript[e, 2,4],Subscript[f, 2,1],Subscript[f, 2,2],Subscript[f, 2,3],Subscript[f, 2,4]}={0,0,0,0,0,0,0,0,0,0,-(1/2),0,0,0,0,0,0,-((-1+4 T-3 T^2)/(6 T)),0,-(1/(2 T)),-((1-3 T)/(2 T)),-((1-11 T+16 T^2)/(6 T)),0,0,-(1/2),1/6 (-1+7 T),0,0,0,0,0,0,0,0,0,0,-((1-T)/T^3),-((-1+T)/(2 T^4)),0,1/T^3,-(1/(2 T^4)),0,0,0,0,-((-1+T)/(2 T^3)),-((3-4 T+T^2)/(2 T^4)),-((-3+4 T-T^2)/(6 T^5)),0,-(1/(2 T^3)),2/T^4,-((4+T+T^2)/(6 T^5)),0,0,-(1/(2 T^4)),-((-1+T)/(6 T^5)),0,0,0,0,0,0,0,0,0,-(1/T^2),0,0};


(* ::Input::Initialization:: *)
{Subscript[c, 3,1],Subscript[c, 3,2],Subscript[c, 3,3],Subscript[c, 3,4],Subscript[c, 3,5],Subscript[c, 3,6],Subscript[c, 3,7],Subscript[c, 3,8],Subscript[c, 3,9],Subscript[c, 3,10],Subscript[c, 3,11],Subscript[c, 3,12],Subscript[c, 3,13],Subscript[c, 3,14],Subscript[c, 3,15],Subscript[c, 3,16],Subscript[c, 3,17],Subscript[c, 3,18],Subscript[c, 3,19],Subscript[c, 3,20],Subscript[c, 3,21],Subscript[c, 3,22],Subscript[c, 3,23],Subscript[c, 3,24],Subscript[c, 3,25],Subscript[c, 3,26],Subscript[c, 3,27],Subscript[c, 3,28],Subscript[c, 3,29],Subscript[c, 3,30],Subscript[c, 3,31],Subscript[c, 3,32],Subscript[c, 3,33],Subscript[c, 3,34],Subscript[c, 3,35],Subscript[c, 3,36],Subscript[c, 3,37],Subscript[c, 3,38],Subscript[c, 3,39],Subscript[c, 3,40],Subscript[c, 3,41],Subscript[c, 3,42],Subscript[c, 3,43],Subscript[c, 3,44],Subscript[c, 3,45],Subscript[c, 3,46],Subscript[c, 3,47],Subscript[c, 3,48],Subscript[c, 3,49],Subscript[c, 3,50],Subscript[c, 3,51],Subscript[c, 3,52],Subscript[c, 3,53],Subscript[c, 3,54],Subscript[c, 3,55],Subscript[d, 3,1],Subscript[d, 3,2],Subscript[d, 3,3],Subscript[d, 3,4],Subscript[d, 3,5],Subscript[d, 3,6],Subscript[d, 3,7],Subscript[d, 3,8],Subscript[d, 3,9],Subscript[d, 3,10],Subscript[d, 3,11],Subscript[d, 3,12],Subscript[d, 3,13],Subscript[d, 3,14],Subscript[d, 3,15],Subscript[d, 3,16],Subscript[d, 3,17],Subscript[d, 3,18],Subscript[d, 3,19],Subscript[d, 3,20],Subscript[d, 3,21],Subscript[d, 3,22],Subscript[d, 3,23],Subscript[d, 3,24],Subscript[d, 3,25],Subscript[d, 3,26],Subscript[d, 3,27],Subscript[d, 3,28],Subscript[d, 3,29],Subscript[d, 3,30],Subscript[d, 3,31],Subscript[d, 3,32],Subscript[d, 3,33],Subscript[d, 3,34],Subscript[d, 3,35],Subscript[d, 3,36],Subscript[d, 3,37],Subscript[d, 3,38],Subscript[d, 3,39],Subscript[d, 3,40],Subscript[d, 3,41],Subscript[d, 3,42],Subscript[d, 3,43],Subscript[d, 3,44],Subscript[d, 3,45],Subscript[d, 3,46],Subscript[d, 3,47],Subscript[d, 3,48],Subscript[d, 3,49],Subscript[d, 3,50],Subscript[d, 3,51],Subscript[d, 3,52],Subscript[d, 3,53],Subscript[d, 3,54],Subscript[d, 3,55],Subscript[e, 3,1],Subscript[e, 3,2],Subscript[e, 3,3],Subscript[e, 3,4],Subscript[e, 3,5],Subscript[f, 3,1],Subscript[f, 3,2],Subscript[f, 3,3],Subscript[f, 3,4],Subscript[f, 3,5]}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-((1-T)/(6 T)),0,0,1/(2 T),-((-2+5 T)/(2 T)),0,0,0,5/6,0,0,0,0,0,0,0,0,-((1-12 T+27 T^2-16 T^3)/(24 T^2)),0,1/(6 T^2),-((-1+3 T)/(4 T^2)),-((-1+11 T-16 T^2)/(6 T^2)),-((-1+31 T-131 T^2+125 T^3)/(24 T^2)),0,0,1/T,-((-5+23 T)/(6 T)),-((-5+69 T-142 T^2)/(24 T)),0,0,0,1/6,1/24 (1-15 T),0,0,0,0,0,0,0,0,0,0,0,-((-1+T)/T^4),-((1-T)/(2 T^5)),0,-(1/T^4),1/(2 T^5),0,0,0,0,-((1-T)/T^4),-((-7+9 T-2 T^2)/(2 T^5)),-((7-9 T+2 T^2)/(6 T^6)),0,1/T^4,-((9-T)/(2 T^5)),3/(2 T^6),0,0,1/T^5,-(1/(3 T^6)),0,0,0,0,0,-((-1+T)/(6 T^4)),-((2-3 T+T^2)/T^5),-((-16+27 T-12 T^2+T^3)/(6 T^6)),-((16-27 T+12 T^2-T^3)/(24 T^7)),0,-(1/(6 T^4)),-((-3+T)/T^5),(3 (-3+T))/(2 T^6),-((-27+5 T-T^2-T^3)/(24 T^7)),0,0,-(1/T^5),2/T^6,-((12-T-5 T^2)/(24 T^7)),0,0,0,-(1/(6 T^6)),-((-1-T)/(24 T^7)),0,0,0,0,0,0,0,0,0,0,0,1/T^3,0,0,0};



