(***********************************************************************
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 Initialiation 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.
***********************************************************************)







Off[General::"spell",General::"spell1",Remove::"rmnsm",UpSet::"write"];

Unprotect["Global`*"];ClearAll["Global`*"];Remove["Global`*"];Unprotect[$];
ClearAll[Wedge,K,$];Protect[$];Unprotect[In,Out];Clear[In,Out];
Protect[In,Out];$Line=0;$RecursionLimit=256;$IterationLimit=4096;

Forms[i_]:={};AllScalForms={};matForms[i_]:={};AllMatForms={};AllDifForms={};
AllMatrices={};AllSymbols={};FormVars={_Wedge,_d};ZeroVars={_Wedge,_tr};
HeadList={};ScalHeadList={};MatFormHeadList={};ZeroHeads={};AllMatHeads={};
nodHeads={tr,Bar,Pattern,Condition,RuleDelayed,SeriesData};$EDCversion=370;

zeroQ[0]=True;zeroQ[x_List]:=And@@(zeroQ/@Union[Flatten[x]]);
zeroQ[x_SeriesData]:=If[x[[3]]==={},True,False];zeroQ[x_]:=False;

SetAttributes[Bar,{Listable}];Bar[Bar[x_]]=x;
Bar[Complex[x_,y_]]:=Complex[x,-y];
Bar[x_Plus|x_Times|x_Wedge|x_Power|x_Rule|x_Equal]:=Bar/@x;
Bar[x_?NumericQ]:=x;
Bar[x_RuleDelayed]:=Rule[Bar[x[[1]]],Bar[x[[2]]]]/.Rule\[Rule]RuleDelayed;
Bar[x_SeriesData]:=
  x/.{First[x]->Bar[First[x]],x[[2]]->Bar[x[[2]]],x[[3]]->Bar/@x[[3]]};
Bar[DirectedInfinity[x_]]:=DirectedInfinity[Bar[x]];
Bar[HoldPattern[tr[x_]]]:=tr[Bar[x]];Bar[d[x_]]:=d[Bar[x]];
Bar[x_Condition]:=Condition[Bar[x[[1]]],x[[2]]];
Bar[Derivative[x__][y_][z__]]:=
  If[Union[Bar[{z}]]===Union[{z}],
    Derivative[Sequence@@Coefficient[{x}.{z},Bar[{z}]]][Bar[y]][z],
    Derivative[x][Bar[y]][Sequence@@Bar[{z}]]];
Bar[h_[y__]/;FreeQ[nodHeads,h]]:=
  If[Union[Bar[{y}]]===Union[{y}],Bar[h][y],Bar[h][Sequence@@Bar[{y}]]]/;
    FreeQ[{Integer,Blank,Pattern,Condition},Head[First[{y}]]];

Qvalue[x_List]:=
  Length[Select[OrderedQ/@Transpose[{Drop[x,-1],Rest[x]}],#===False&]]

AllCaseTable[x_List]:=
  With[{rvstr=Reverse[Map[Transpose,x]/.-z_\[Rule]z]},
    If[traceOption===2,
      Join[Table[{Qvalue[RotateLeft[x,i]],RotateLeft[x,i],i},{i,0,
            Length[x]-1}],
        Table[{Qvalue[RotateRight[rvstr,i]],RotateRight[rvstr,i],-i-1},{i,0,
            Length[x]-1}]],
      Table[{Qvalue[RotateLeft[x,i]],RotateLeft[x,i],i},{i,0,Length[x]-1}]]]

bestOrd[x_List]:=
  Block[{tmp=Sort[AllCaseTable[x]]},tmp=Select[tmp,First[#1]===tmp[[1,1]]&];
    If[Length[tmp]>1,
      First[Sort[Select[tmp,#1[[2]]===tmp[[1,2]]&],
          Abs[Last[#1]]<Abs[Last[#2]]&]],First[tmp]]];

splitFDprod[n_,FDx_List]:=(Plus@@Take[FDx,n])(Plus@@Drop[FDx,n]);
allFDprods[FDx_List]:=Sum[FDx[[i]]*(Plus@@Drop[FDx,i]),{i,Length[FDx]-1}];

traceOption=2;tr[x_]:=FacSimp[Plus@@Transpose[x,{1,1}]]/;MatrixQ[x];
tr[x_Plus]:=tr/@x;
tr[x_SeriesData]:=(x/.x[[3]]->tr/@x[[3]])+(x/.x[[3]]\[Rule]{});
tr[x__ y_]:=(x tr[y])/;!MatQ[x];tr[d[x_]]:=d[tr[x]];
tr[x__\[Wedge]y__]:=(x\[Wedge]tr[Wedge[y]])/;ScalFormQ[x];
tr[x_]:=(tr[x]=0)/;AntisymQ[x];
tr[Bar[x_]]:=With[{evalHx=tr[x]},Bar[evalHx]/;Head[evalHx]=!=tr];
tr[x_Wedge/;Union[Head/@Level[x,1]]==={Bar}]:=
  With[{evalHx=tr[Bar/@x]},Bar[evalHx]/;Head[evalHx]=!=tr];
tr[x_Wedge]:=
  Block[{inpList=List@@x,resList,FDx},resList=bestOrd[inpList];
      FDx=FormDegree/@inpList;
      Which[ Last[resList]>
          0,(-1)^splitFDprod[ Last[resList],FDx]tr[Wedge@@resList[[2]]], 
        Last[resList]===-1,(-1)^(
              allFDprods[FDx]+Length[Select[inpList,AntisymQ]])tr[
            Wedge@@resList[[2]]], 
        Last[resList]<-1,(-1)^(
              allFDprods[FDx]+splitFDprod[Abs[1+ Last[resList]],FDx]+
                Length[Select[inpList,AntisymQ]])tr[Wedge@@resList[[2]]]]]/;
    traceOption>0&&bestOrd[List@@x][[2]]=!=List@@x;
tr[x__\[Wedge]y__]:=(tr[x\[Wedge]y]=0)/;(
      SymQ[Wedge[x]]&&AntisymQ[Wedge[y]]||SymQ[Wedge[y]]&&AntisymQ[Wedge[x]]);
tr[x_]:=x matDimension/;!MatQ[x];

toComponents[x_+y_,rul_]:=toComponents[x,rul]+toComponents[y,rul];
toComponents[x_.*y_,rul_]:=
  If[MatQ[x*y],reWrite[x*y/.rul],
    reWrite[(x*y*
            IdentityMatrix[
              Length[Select[Part[#,2]&/@rul,MatrixQ][[1]]]])/.rul]];
toComponents[x_\[Wedge]y_,rul_]:=
  If[MatQ[x\[Wedge]y],reWrite[x\[Wedge]y/.rul],
    reWrite[(x\[Wedge]y*
            IdentityMatrix[
              Length[Select[Part[#,2]&/@rul,MatrixQ][[1]]]])/.rul]];

FormDegree[x_Plus]:=FormDegree[First[x]];
FormDegree[x_Times]:=Plus@@FormDegree/@List@@x;
FormDegree[x_Wedge]:=Plus@@FormDegree/@List@@x;
FormDegree[d[x_]]:=FormDegree[d[x]]=1+FormDegree[x];
FormDegree[x_List]:=FormDegree[Last[Union[Flatten[x]]]];
FormDegree[tr[x_]]:=FormDegree[x];
FormDegree[Bar[x_]]:=FormDegree[Bar[x]]=FormDegree[x];
FormDegree[x_SeriesData]:=If[x[[3]]==={},0,FormDegree[x[[3]]]];
FormDegree[x_]:=0;

DeclareMatrixForms[z__]:=
  Block[{x={{z}},xi,rxi,h,ht,k,min1,oldHeads,newHeads},
    While[Head[x[[1,1]]]===List,x=First[x]];Unprotect[Transpose];
    Do[xi=x[[i]];
      If[xi[[3]]===xi[[2]]||xi[[3]]===-xi[[2]],rxi={xi[[2]]},rxi=Rest[xi]];
      matForms[First[xi]]=Union[matForms[First[xi]],rxi];
      \[IndentingNewLine]AllMatrices=Union[AllMatrices,rxi];h=Head[xi[[2]]];
      If[First[xi]>0,AllMatForms=Union[AllMatForms,rxi],
        If[h=!=Symbol,ZeroHeads=Union[{h},ZeroHeads];
          If[Head[xi[[3]]]=!=Times,
            ZeroHeads=Union[{Head[xi[[3]]]},ZeroHeads]]]];
      If[h===Symbol,FormDegree[xi[[2]]]=First[xi];BasicMatQ[xi[[2]]]=True;
        BasicScalFormQ[xi[[2]]]=False;Transpose[xi[[2]]]=xi[[3]];
        If[xi[[3]]===-xi[[2]],tr[xi[[2]]]=0,
          If[xi[[3]]=!=xi[[2]],FormDegree[xi[[3]]]=First[xi];
            BasicMatQ[xi[[3]]]=True;BasicScalFormQ[xi[[3]]]=False;
            Transpose[xi[[3]]]=xi[[2]];tr[xi[[3]]]=tr[xi[[2]]]]],
        FormDegree[_h]=First[xi];BasicMatQ[_h]=True;BasicScalFormQ[_h]=False;
        ht=Head[xi[[3]]];
        If[ht===Times,min1=-1;ht=h;tr[h[k_]]=0,min1=1;
          If[ht=!=h,FormDegree[_ht]=First[xi];BasicMatQ[_ht]=True;
            BasicScalFormQ[_ht]=False;tr[ht[k_]]=tr[h[k]]]];
        Transpose[h[k_]]=min1 ht[k];Transpose[ht[k_]]=min1 h[k]],{i,
        Length[x]}];Protect[Transpose];
    \[IndentingNewLine]AllDifForms=Union[AllScalForms,AllMatForms];
    AllSymbols=Union[AllDifForms,AllMatrices];
    MatFormHeadList=
      Complement[Union[Head/@AllMatForms,MatFormHeadList],{Symbol}];
    oldHeads=AllMatHeads;AllMatHeads=Union[ZeroHeads,MatFormHeadList];
    newHeads=Complement[AllMatHeads,oldHeads];
    \[IndentingNewLine]HeadList=Union[Head/@AllSymbols];
    DifFormSymbols=
      Drop[AllDifForms,-Length[Union[ScalHeadList,MatFormHeadList]]];
    nodHeads=Union[nodHeads,ZeroHeads];
    k=Thread[Blank[Union[ScalHeadList,MatFormHeadList]]];
    FormVars=Flatten[{_Wedge,_d,Union[k,Bar[k]],
          y_|Bar[y_]/;MemberQ[DifFormSymbols,y],_tr}];
    ZeroMatSymbols=Drop[matForms[0],-Length[ZeroHeads]];
    ZeroVars=Flatten[{_Wedge,
          Union[Thread[Blank[ZeroHeads]],Bar[Thread[Blank[ZeroHeads]]]],
          y_|Bar[y_]/;MemberQ[ZeroMatSymbols,y],_tr}];];

DeclareForms[z__]:=
  Block[{h,x={{z}},xi,rxi,k,oldHeads,newHeads},
    While[Head[x[[1,1]]]===List,x=First[x]];
    Do[xi=x[[i]];rxi=Rest[xi];Forms[First[xi]]=Union[Forms[First[xi]],rxi];
      \[IndentingNewLine]AllScalForms=Union[AllScalForms,rxi];
      \[IndentingNewLine]Do[h=Head[rxi[[j]]];
        If[h===Symbol,FormDegree[rxi[[j]]]=First[xi];
          BasicScalFormQ[rxi[[j]]]=True;BasicMatQ[rxi[[j]]]=False;,
          FormDegree[_h]=First[xi];BasicScalFormQ[_h]=True;
          BasicMatQ[_h]=False;],{j,Length[rxi]}],{i,Length[x]}];
    \[IndentingNewLine]AllDifForms=Union[AllScalForms,AllMatForms];
    oldHeads=ScalHeadList;
    ScalHeadList=Complement[Union[Head/@AllScalForms,ScalHeadList],{Symbol}];
    newHeads=Complement[ScalHeadList,oldHeads];
    AllSymbols=Union[AllDifForms,AllMatrices];
    \[IndentingNewLine]HeadList=Union[Head/@AllSymbols];
    DifFormSymbols=
      Drop[AllDifForms,-Length[Union[ScalHeadList,MatFormHeadList]]];
    k=Thread[Blank[Union[ScalHeadList,MatFormHeadList]]];
    FormVars=Flatten[{_Wedge,_d,Union[k,Bar[k]],
          y_|Bar[y_]/;MemberQ[DifFormSymbols,y],_tr}];];

NoDif[z__]:=(nodHeads=Union[nodHeads,Flatten[{z}]];)

BasicMatQ[Bar[x_]]:=BasicMatQ[x];BasicMatQ[d[x_]]:=BasicMatQ[x];
BasicMatQ[x_List]=True;BasicMatQ[x_]:=False;

MatQ[x_Times|x_Wedge|x_Plus]:=Or@@MatQ/@List@@x;
MatQ[x_SeriesData]:=Or@@MatQ/@x[[3]];MatQ[x_]:=BasicMatQ[x];

BasicScalFormQ[HoldPattern[tr[x_]]]:=FormDegree[x]>0;
BasicScalFormQ[Bar[x_]]:=BasicScalFormQ[x];
BasicScalFormQ[d[x_]]:=!BasicMatQ[x];BasicScalFormQ[x_]:=False;

ScalFormQ[x_Times]:=Or@@ScalFormQ/@List@@x;
ScalFormQ[x_Wedge|x_Plus]:=And@@ScalFormQ/@List@@x;
ScalFormQ[x_]:=BasicScalFormQ[x];

Unprotect[Transpose];Transpose[x_Plus]:=Transpose/@x;
Transpose[x_SeriesData]:=x/.x[[3]]->Transpose/@x[[3]];
Transpose[x__ y_]:=x Transpose[y]/;!MatQ[x];
Transpose[x__\[Wedge]y__]:=(x\[Wedge]Transpose[Wedge[y]])/;ScalFormQ[x];
Transpose[
    x_Wedge]:=(-1)^allFDprods[FormDegree/@(List@@x)]Wedge@@
      Map[Transpose,Reverse[List@@x]];Transpose[d[x_]]:=d[Transpose[x]];
HoldPattern[Transpose[Bar[x_]]]:=Bar[Transpose[x]];Transpose[x_]:=x/;!MatQ[x];
Protect[Transpose];

SymQ[Bar[x_]]:=Union[Flatten[{reWrite[Transpose[x]-x]}]]==={0};
AntisymQ[Bar[x_]]:=Union[Flatten[{reWrite[Transpose[x]+x]}]]==={0};
SymQ[x_]:=Union[Flatten[{reWrite[Transpose[x]-x]}]]==={0};
AntisymQ[x_]:=Union[Flatten[{reWrite[Transpose[x]+x]}]]==={0};

SetAttributes[d,{Listable}];
d[x_Times|x_Wedge]:=
  d[First[x]]\[Wedge]Rest[x]+(-1)^FormDegree[First[x]]*
      First[x]\[Wedge]d[Rest[x]];d[x_?NumericQ|x_d]=0;d[matDimension]=0;
d[Power[y_,n_]]:=n y^(n-1) d[y]+y^n Log[y]d[n];d[x_Plus]:=d/@x;
HoldPattern[d[tr[x_]]]:=With[{evalHx=d[x]},tr[evalHx]/;Head[evalHx]=!=d];
HoldPattern[d[Bar[x_]]]:=With[{evalHx=d[x]},Bar[evalHx]/;Head[evalHx]=!=d];
d[x_Rule|x_Equal]:=reWrite[d/@x];
d[x_SeriesData]:=(x/.x[[3]]->d[x[[3]]])+Wedge[d[First[x]],D[x,First[x]]];
d[h_[y__]/;FreeQ[nodHeads,h]]:=
  Sum[(Derivative[
                Sequence@@RotateRight[Append[Table[0,{Length[{y}]-1}],1],i]][
              h][y])d[{y}[[i]]],{i,Length[{y}]}]/;
    FormDegree[h[y]]===0&&
      FreeQ[{Integer,Blank,Pattern,Condition},Head[First[{y}]]];

newSer$[x_SeriesData,k_]:=
  SeriesData[First[x],x[[2]],
    Flatten[Transpose[
        Prepend[Table[Table[0,{Length[x[[3]]]}],{k-1}],x[[3]]]]],k x[[4]],
    k x[[5]],k Last[x]]

Wedge[x_]:=x/;Length[{x}]<2&&Head[{x}[[1]]]=!=Pattern

Default[Wedge]:=1;SetAttributes[Wedge,{Flat,OneIdentity}];Wedge[0,y__]=0;
Wedge[x__,0]=0;
Wedge[x_SeriesData,y_SeriesData]:=
  Block[{x$,y$,r1,r2,res,x3,y3},
      If[Last[x]===Last[y],x$=x;y$=y,
        x$=newSer$[x,LCM[Last[x],Last[y]]/Last[x]];
        y$=newSer$[y,LCM[Last[x],Last[y]]/Last[y]]];r1=x$[[-3]]+y$[[-3]];
      r2=Min[x$[[-2]]+y$[[-3]],x$[[-3]]+y$[[-2]]];
      If[Length[x$[[3]]]<x$[[-2]]-x$[[-3]],
        x3=Join[x$[[3]],Table[0,{x$[[-2]]-x$[[-3]]-Length[x$[[3]]]}]],
        x3=x$[[3]]];
      If[Length[y$[[3]]]<y$[[-2]]-y$[[-3]],
        y3=Join[y$[[3]],Table[0,{y$[[-2]]-y$[[-3]]-Length[y$[[3]]]}]],
        y3=y$[[3]]];
      Which[r2===r1,res={},r2-r1===x$[[-2]]-x$[[-3]],
        res=Sum[Map[Wedge[x3[[i]],#]&,Join[Table[0,{i-1}],Drop[y3,-i+1]]],{i,
              Length[x3]}],True,
        res=Sum[Map[Wedge[#,y3[[i]]]&,Join[Table[0,{i-1}],Drop[x3,-i+1]]],{i,
              Length[y3]}]];
      SeriesData[First[x$],x$[[2]],res,r1,r2,Last[x$]]]/;
    First[x]===First[y]&&x[[2]]===y[[2]];
Wedge[y_,x_SeriesData]:=x/.x[[3]]->Map[Wedge[y,#]&,x[[3]]];
Wedge[x_SeriesData,y_]:=x/.x[[3]]->Map[Wedge[#,y]&,x[[3]]];
Wedge[x__,y_Plus]:=Plus@@Map[Wedge[x,#]&,List@@y];
Wedge[x_Plus,y__]:=Plus@@Map[Wedge[#,y]&,List@@x];
Wedge[z__,Times[x_,y_]]:=
  Times[x,Wedge[z,y]]/;NumericQ[x]||(FormDegree[x]===0&&!MatQ[x]);
Wedge[Times[x_,y_],z__]:=
  Times[x,Wedge[y,z]]/;NumericQ[x]||(FormDegree[x]===0&&!MatQ[x]);
Wedge[x_^n_.,y_]:=x^n*y/;FormDegree[x]===0&&!MatQ[x];
Wedge[y_,x_^n_.]:=x^n*y/;FormDegree[x]===0&&!MatQ[x];
Wedge[x_,y___,x_]:=0/;OddQ[FormDegree[x]]&&ScalFormQ[x];
Wedge[x__,y__]:=(-1)^(FormDegree[x]*FormDegree[y])*y\[Wedge]x/;
    MatQ[x]&&ScalFormQ[y];
Wedge[x__]:=
  Block[{doubL=Transpose[{FormDegree/@{x},{x}}]},
      Signature[Select[doubL,OddQ[First[#]]&]]Wedge@@
          Map[Last[#1]&,Sort[doubL]]]/;
    Union[BasicScalFormQ/@{x}]==={True}&&
      Map[Last[#1]&,Sort[Transpose[{FormDegree/@{x},{x}}]]]=!={x};
Wedge[x_List,y_List]:=
  If[(FormDegree[x]===0&&!MatQ[Last[Union[Flatten[x]]]])||(
        FormDegree[y]===0&&!MatQ[Last[Union[Flatten[y]]]]),Dot[x,y],
    Inner[Wedge,x,y]];
Wedge[x_,y_List]:=
  If[FormDegree[x]===0||(FormDegree[y]===0&&!MatQ[Last[Union[Flatten[y]]]]),
      x *y,Map[Wedge[x,#]&,y]]/;!BasicMatQ[x];
Wedge[x_List,y_]:=
  If[FormDegree[y]===0||(FormDegree[x]===0&&!MatQ[Last[Union[Flatten[x]]]]),
      x*y,Map[Wedge[#,y]&,x]]/;!BasicMatQ[y];

simpRules = {Cos[z_]^2*(x_.)+(x_.)*Sin[z_]^2 -> x};varList={};

coll[x_]:=Collect[x,{_Wedge,_tr},Factor]/.simpRules;

SetAttributes[reWrite,{Listable}];reWrite[0]=0;
reWrite[x_Equal]:=Equal[reWrite[First[x]-Last[x]],0];
reWrite[x_Rule]:=Rule[First[x],reWrite[Last[x]]];
reWrite[x_RuleDelayed]:=Rule[First[x],reWrite[x[[2]]]]/.Rule->RuleDelayed;
reWrite[x_SeriesData]:=(x/.x[[3]]->reWrite[x[[3]]]);
reWrite[x_Condition]:=Condition[reWrite[x[[1]]],x[[2]]];
reWrite[x_]:=(Collect[coll[x/.simpRules],FormVars,bestFacRul]/.simpRules)/;
    FormDegree[x]>0;
reWrite[x_]:=(Collect[x/.simpRules,ZeroVars,bestFacRul]/.simpRules)/;MatQ[x];
reWrite[x_]:=bestFacRul[x/.simpRules]/.simpRules;

FreeALLQ[x_,y_List]:=And@@(FreeQ[x,#]&/@y);

bestFacRul[x_]:=
  If[varList==={}||FreeALLQ[x,varList],minFacRul[x],varFacRul[x]];
varFacRul[x_]:=Collect[Expand[x]/.simpRules,varList,Factor]/.simpRules;
minFacRul[x_]:=Factor[Expand[x]/.simpRules]/.simpRules;

Unprotect[SeriesData];If[$VersionNumber<5,Times[x_SeriesData,0]^=0];
SeriesData[x1_,x2_,x3_,x4_,x5_,x6_]:= 
  Plus@@If[x2===Infinity,
        Map[First[#]/x1^((x4+Last[#]-1)/x6)&,
            Transpose[{x3,Range[Length[x3]]}]]+SeriesData[x1,x2,{},x4,x5,x6],
           Map[First[#]*(x1-x2)^((x4+Last[#]-1)/x6)&,
            Transpose[{x3,Range[Length[x3]]}]]+
          SeriesData[x1,x2,{},x4,x5,x6]]/;!FreeQ[x3,x1];Protect[SeriesData];

CHcoef[x_,0]=1;CHcoef[x_,1]:=tr[x];
CHcoef[x_,n_]:=CHcoef[x,n]=reWrite[tr[CHeq[x,n]]/n];

CHeq[x_,n_]:=
  reWrite[CHcoef[x,n-1]\[Wedge] x+
      Sum[(-1)^(i-1)CHcoef[x,n-i]\[Wedge]Wedge@@Table[x,{i}],{i,2,n}]];

subMatDR[m_,p_,q_]:=Transpose[Drop[Transpose[Drop[m,p]],q]];
subMatTK[m_,p_,q_]:=Transpose[Take[Transpose[Take[m,p]],q]];

DeclareMatrixForms[{0,$,$t}]

CHrul[n_,x_:$]:=
  Block[{cn=CHeq[x,n],cn0,rul,tmp,r1,r2},
    If[FormDegree[x]>0,Print[x," is not a 0-form matrix"];Return[]]; 
    matDimension=n;
    rul=First[Solve[cn==cn0,Wedge@@Table[x,{n}]]]/.cn0->tr[cn]/n;
    rul=reWrite[rul];
    If[x===$,tmp=MapAt[HoldPattern,rul/.Rule->RuleDelayed,{1,1}];
      r1=tmp[[1,1]];r2=r1/.$->Pattern[$,Blank[]];
      tmp={Rule[r2,
              tmp[[1,2]]/;
                MatQ[$]&&FormDegree[$]===0&&matDimension===n]}/.Rule->
            RuleDelayed,tmp=rul]];

On[General::"spell",General::"spell1",UpSet::"write"];