RS 5d - infinite radius!

-- modified Δ!!

Print["hmm"]

GRSetup2.nb - modified

(* Latest Version *)

metric={gtt,grr,gθθ,gϕϕ,gzz}

Gd=DiagonalMatrix[metric]

Gd[[1,2]]=grt

Gd[[2,1]]=grt

BuildMetric:=(Gu=FullSimplify[Inverse[Gd]];G={{u,d},IdentityMatrix[Nind]};)

BuildMetric

ind={t,r,θ,ϕ,z}

Nind=Length[ind]

getind[i1_]:=(If[IntegerQ[i1],i1,Position[ind,i1][[1,1]]])

lstind[i1_]:=(lsttmp2={};Do[AppendTo[lsttmp2,getind[i1[[lsttmp1,1]]]],{lsttmp1,1,Length[i1]}];lsttmp2)

up[i1_,i2_]:=(lsttmp2={};Do[AppendTo[lsttmp2,If[i1[[lsttmp1,2]]=!=i2[[lsttmp1]],If[i1[[lsttmp1,2]]===d,d,u],0]],{lsttmp1,1,Length[i1]}];lsttmp2)

MT[t1_,dim_,indpos_]:=(MTtmp1=0;If[Length[indpos]=!=dim,Print["Error in index position"]];Do[MTtmp1=Table[MTtmp1,{MTtmp3,1,Nind}],{MTtmp2,1,dim}];t1={indpos,MTtmp1})

ST[t1_,tind_,val_]:=(STtmp1=t1;If[up[tind,t1[[1]]]=!=Table[0,{Length[tind]}],Print["Error in Index Assignment!!"];];STtmp1[[2]]=ReplacePart[t1[[2]],val,lstind[tind]];STtmp1)

Edited the expression below as 7.0 seems to complain about Sum[x] whereas 6.0 would just return x (ie. if there is no sum index!)

GT[t1_,tind_]:=(GTtmp2=up[tind,t1[[1]]];GTtmp3="";GTtmp4="";GTtmp5="";GTtmp6=t1;
		Do[
			Switch[GTtmp2[[GTtmp1]],
				0,
				(GTtmp3=GTtmp3<>","<>ToString[getind[tind[[GTtmp1,1]]]];),
				u,
				(GTtmp3=GTtmp3<>","<>"tmpind"<>ToString[GTtmp1];
					GTtmp4=GTtmp4<>" Gu[["<>ToString[getind[tind[[GTtmp1,1]]]]<>", tmpind"<>ToString[GTtmp1]<>"]] ";
					GTtmp5=GTtmp5<>",{tmpind"<>ToString[GTtmp1]<>",1,Nind}"),
				d,
				(GTtmp3=GTtmp3<>","<>"tmpind"<>ToString[GTtmp1];
					GTtmp4=GTtmp4<>" Gd[["<>ToString[getind[tind[[GTtmp1,1]]]]<>", tmpind"<>ToString[GTtmp1]<>"]] ";
					GTtmp5=GTtmp5<>",{tmpind"<>ToString[GTtmp1]<>",1,Nind}";)];
			,{GTtmp1,1,Length[t1[[1]]]}];If[GTtmp4===""&&GTtmp5==="",ToExpression["GTtmp6[[2"<>GTtmp3<>"]]"],ToExpression["Sum[GTtmp6[[2"<>GTtmp3<>"]]"<>GTtmp4<>GTtmp5<>"]"]])

Trace, Outer Product and Covariant Derivative! - GREinstein.nb

Syntax:   trT[tensor,{{1,4},{2,3}}]   -  ie. contract 1 and 4 plus 2 and 3 positions

trT[t1_,lst_]:=(

dimt1=Length[Dimensions[t1[[2]]]];
tmpt1=t1;
Clear[tracetmp];

If[dimt1===2,

tracetmp=Sum[GT[tmpt1,{{s1,d},{s1,u}}],{s1,1,Nind}];

,

MT[tracetmp,dimt1-2Length[lst],Table[d,{ii,1,dimt1-2Length[lst]}]];

tmpstring1="";tmpstring2="";tmpstring3="";

Do[

If[{}===Position[lst,indno],
tmpstring1=tmpstring1<>"{i"<>ToString[indno]<>",d},";
tmpstring3=tmpstring3<>"{i"<>ToString[indno]<>",1,Nind},";
];

tmpstring2=tmpstring2<>"{i"<>ToString[indno]<>",d},";

,{indno,1,dimt1}];

tmpstring4="";

Do[

tmpstring4=tmpstring4<>"{s"<>ToString[indno]<>",1,Nind},";

tmpstring2=StringReplace[tmpstring2,"i"<>ToString[lst[[indno,1]]]->"s"<>ToString[indno]];

tmpstring2=StringReplace[tmpstring2,"i"<>ToString[lst[[indno,2]]]<>",d}"->"s"<>ToString[indno]<>",u}"];

,{indno,1,Length[lst]}];

tmpeval="Do[tracetmp=ST[tracetmp,{"<>StringDrop[tmpstring1,-1]<>"},Sum[GT[tmpt1,{"<>StringDrop[tmpstring2,-1]<>"}],"<>StringDrop[tmpstring4,-1]<>"]],"<>StringDrop[tmpstring3,-1]<>"]";

ToExpression[tmpeval];

];

tracetmp
)

Syntax:   outerT[tensor1,tensor2]

outerT[t1_,t2_]:=(

dimt1=Length[Dimensions[t1[[2]]]];dimt2=Length[Dimensions[t2[[2]]]];
tmpt1=t1;tmpt2=t2;
Clear[outertmp];

MT[outertmp,dimt1+dimt2,Table[d,{ii,1,dimt1+dimt2}]];

tmpstring1="";tmpstring2="";

Do[

tmpstring1=tmpstring1<>"{i"<>ToString[indno]<>",d},";
tmpstring2=tmpstring2<>"{i"<>ToString[indno]<>",1,Nind},";

,{indno,1,dimt1}];

tmpstring3="";tmpstring4="";

Do[

tmpstring3=tmpstring3<>"{j"<>ToString[indno]<>",d},";
tmpstring4=tmpstring4<>"{j"<>ToString[indno]<>",1,Nind},";

,{indno,1,dimt2}];

tmpeval="Do[outertmp=ST[outertmp,{"<>tmpstring1<>StringDrop[tmpstring3,-1]<>"},GT[tmpt1,{"<>StringDrop[tmpstring1,-1]<>"}]GT[tmpt2,{"<>StringDrop[tmpstring3,-1]<>"}]],"<>tmpstring2<>StringDrop[tmpstring4,-1]<>"]";

ToExpression[tmpeval];

outertmp

)

scalarDT[t1_]:=(

tmpt1=t1;
Clear[covDTtmp];
MT[covDTtmp,1,{d}];

tmpeval="Do[covDTtmp=ST[covDTtmp,{{i1,d}},D[tmpt1,ind[[i1]]]],{i1,1,Nind}]";

ToExpression[tmpeval];

covDTtmp

)

covDT[t1_]:=(

dimt1=Length[Dimensions[t1[[2]]]];
tmpt1=t1;
Clear[covDTtmp];
MT[covDTtmp,dimt1+1,Table[d,{ii,1,dimt1+1}]];

(* Build expression *)

tmpstring1="";tmpstring2="";tmpstring3="";

Do[

tmpstring1=tmpstring1<>"{i"<>ToString[indno]<>",d},";

tmpstring2=tmpstring2<>"{i"<>ToString[indno]<>",1,Nind},";

,{indno,1,dimt1}];

Do[
tmpstring4="-Sum[GT[tmpt1,{"<>StringDrop[tmpstring1,-1]<>"}]GT[Γ,{{REPL,d},{s1,d},{s2,u}}],{s2,1,Nind}]";

tmpstring4=StringReplace[tmpstring4,"i"<>ToString[indno]-> "s2"];

tmpstring4=StringReplace[tmpstring4,"REPL"->"i"<>ToString[indno]];

tmpstring3=tmpstring3<>tmpstring4;

,{indno,1,dimt1}];

tmpeval="Do[covDTtmp=ST[covDTtmp,{"<>tmpstring1<>"{s1,d}},D[GT[tmpt1,{"<>StringDrop[tmpstring1,-1]<>"}],ind[[s1]]]"<>tmpstring3<>"],"<>tmpstring2<>"{s1,1,Nind}]";


ToExpression[tmpeval];

covDTtmp

);

.

Buildmetric

Print["\n\n   Δ[r_,a_]=(\!\(\*FractionBox[\(\(\\ \)\(1\)\), \(\((1 - a^2)\) + eps\\ \((1 - r^2)\)\)]\))^2\n   f[r_]  =(1-r^2)\n   g[a_]   =2-a^2\n\n\n\n"];

(*
Gd=Δ[r,a](({{r^2f[r]^2Exp[T[l,r,a]], 0, 0, 0, 0}, {0, (4/(f[r]^2))Exp[T[l,r,a]+r^2f[r]A[l,r,a]], a r (1/(f[r]))F[l,r,a], 0, 0}, {0, a r (1/(f[r]))F[l,r,a], Exp[S[l,r,a]+a^2 B[l,r,a]](4/(g[a])), 0, 0}, {0, 0, 0, ((Exp[S[l,r,a]]g[a]a^2)/(1-θ1^2)), 0}, {0, 0, 0, 0,  Exp[S[l,r,a]]g[a]a^2(1-θ1^2)}}))
*)

Gd=Δ[r,a](({{4r^2f[r]^2Exp[T[l,r,a]], 0, 0, 0, 0}, {0, (4/(f[r]^2))Exp[T[l,r,a]+r^2A[l,r,a]], a r (1/(f[r]))F[l,r,a], 0, 0}, {0, a r (1/(f[r]))F[l,r,a], Exp[S[l,r,a]+a^2 B[l,r,a]](4/(g[a])), 0, 0}, {0, 0, 0, ((Exp[S[l,r,a]]g[a]a^2)/(1-θ1^2)), 0}, {0, 0, 0, 0,  Exp[S[l,r,a]]g[a]a^2(1-θ1^2)}}))

ind={t,r,a,θ1,θ2}

Nind=Length[ind]

BuildMetric;

Gd

Gu

detg=Simplify[Det[Gd]]

GRrun2.nb

Clear[Γ]

MT[Γ,3,{d,d,u}];

Clear[R4]

MT[R4,4,{d,d,d,u}];

Clear[R2]

MT[R2,2,{d,d}];

Clear[G2]

MT[G2,2,{d,d}];

Do[Γ=ST[Γ,{{ind[[i1]],d},{ind[[i2]],d},{ind[[i3]],u}},Sum[(1/2)GT[G,{{ind[[i3]],u},{ind[[ss1]],u}}](D[GT[G,{{ind[[i1]],d},{ind[[ss1]],d}}],ind[[i2]]]+D[GT[G,{{ind[[ss1]],d},{ind[[i2]],d}}],ind[[i1]]]-D[GT[G,{{ind[[i1]],d},{ind[[i2]],d}}],ind[[ss1]]]),{ss1,1,Nind}]],{i1,1,Nind},{i2,1,Nind},{i3,1,Nind}]

(* FullSimplify[Γ] *)

Γ=FullSimplify[Γ];

Do[
	R4=ST[R4,
			{{ind[[i1]],d},{ind[[i2]],d},{ind[[i3]],d},{ind[[i4]],u}},
	
			D[GT[Γ,{{ind[[i1]],d},{ind[[i3]],d},{ind[[i4]],u}}],ind[[i2]]]-D[GT[Γ,{{ind[[i2]],d},{ind[[i3]],d},{ind[[i4]],u}}],ind[[i1]]]+
			Sum[GT[Γ,{{ind[[i1]],d},{ind[[i3]],d},{ind[[ss1]],u}}]GT[Γ,{{ind[[i2]],d},{ind[[ss1]],d},{ind[[i4]],u}}]-GT[Γ,{{ind[[i2]],d},{ind[[i3]],d},{ind[[ss1]],u}}]GT[Γ,{{ind[[i1]],d},{ind[[ss1]],d},{ind[[i4]],u}}],{ss1,1,Nind}]
		
		]
		,
	{i1,1,Nind},{i2,1,Nind},{i3,1,Nind},{i4,1,Nind}]

(* FullSimplify[R4] *)

Do[R2=ST[R2,
			{{ind[[i1]],d},{ind[[i2]],d}},
			Sum[GT[R4,{{ind[[i1]],d},{ind[[ss1]],u},{ind[[i2]],d},{ind[[ss1]],d}}],{ss1,1,Nind}]
		]
	,{i1,1,Nind},{i2,1,Nind}]

(* FullSimplify[R2] *)

Ricci=Sum[GT[R2,{{ind[[ss1]],u},{ind[[ss1]],d}}],{ss1,1,Nind}];

Do[G2=ST[G2,
			{{ind[[i1]],d},{ind[[i2]],d}},
			GT[R2,{{ind[[i1]],d},{ind[[i2]],d}}]-(1/2)GT[G,{{ind[[i1]],d},{ind[[i2]],d}}]Ricci]
	,{i1,1,Nind},{i2,1,Nind}]

(* FullSimplify[G2] *)

(* FullSimplify[Ricci] *)

Einstein equations

Δ[r_,a_]:=((( 1)/((1-a^2)+rh(1-r^2))))^2

f[r_]:=(1-r^2)

g[a_]:=2-a^2

CForm[Simplify[Δ[r,a]]]

CForm[Simplify[D[Δ[r,a],r]]]

CForm[Simplify[D[Δ[r,a],a]]]

CForm[Simplify[D[Δ[r,a],{r,2}]]]

CForm[Simplify[D[Δ[r,a],{a,2}]]]

CForm[Simplify[D[D[Δ[r,a],r],a]]]

CForm[Simplify[f[r]]]

CForm[Simplify[f'[r]]]

CForm[Simplify[f''[r]]]

CForm[Simplify[g[a]]]

CForm[Simplify[g'[a]]]

CForm[Simplify[g''[a]]]

Clear[Δ,f,g,T,A,B,S,F]

Γ0=Γ/.{T->T0,A->A0,B->B0,F->F0,S->S0};

T0[l_,r_,a_]:=0;

A0[l_,r_,a_]:=0;

B0[l_,r_,a_]:=0;

F0[l_,r_,a_]:=0;

S0[l_,r_,a_]:=0;

Γ0=FullSimplify[Γ0];

Clear[dΓ]

MT[dΓ,3,{d,d,u}];

Do[dΓ=ST[dΓ,{{ind[[i1]],d},{ind[[i2]],d},{ind[[i3]],u}},
GT[Γ,{{ind[[i1]],d},{ind[[i2]],d},{ind[[i3]],u}}]-GT[Γ0,{{ind[[i1]],d},{ind[[i2]],d},{ind[[i3]],u}}]
],{i1,1,Nind},{i2,1,Nind},{i3,1,Nind}]

Clear[H]

MT[H,1,{d}];

Do[
H=ST[H,{{i1,d}},
- Sum[GT[dΓ,{{s1,d},{s1,u},{i1,d}}],{s1,1,Nind}]
];,
{i1,1,Nind}];

H=Simplify[H]

Htmp={{d},{0,hr,ha,0,0}};

phi=Simplify[trT[outerT[Htmp,Htmp],{{1,2}}]]

Clear[dH]

MT[dH,2,{d,d}];

Do[
dH=ST[dH,{{i1,d},{i2,d}},
(1/2)(D[GT[H,{{i1,d}}],ind[[i2]]]-Sum[GT[Γ,{{i1,d},{i2,d},{s1,u}}]GT[H,{{s1,d}}],{s1,1,Nind}]
+D[GT[H,{{i2,d}}],ind[[i1]]]-Sum[GT[Γ,{{i2,d},{i1,d},{s1,u}}]GT[H,{{s1,d}}],{s1,1,Nind}])
];,
{i1,1,Nind},{i2,1,Nind}];

Clear[RF1]

MT[RF1,2,{d,d}];

Do[
RF1=ST[RF1,{{i1,d},{i2,d}},
D[GT[G,{{i1,d},{i2,d}}],l]+2( GT[R2,{{i1,d},{i2,d}}]-Λ GT[G,{{i1,d},{i2,d}}]+ GT[dH,{{i1,d},{i2,d}}] )
];,
{i1,1,Nind},{i2,1,Nind}];

repl={T[l,r,a]->T,Derivative[1,0,0][T][l,r,a]->Tl,Derivative[0,1,0][T][l,r,a]->Tr,Derivative[0,0,1][T][l,r,a]->Ta,Derivative[0,2,0][T][l,r,a]->Trr,Derivative[0,0,2][T][l,r,a]->Taa,Derivative[0,1,1][T][l,r,a]->Tra,A[l,r,a]->A,Derivative[1,0,0][A][l,r,a]->Al,Derivative[0,1,0][A][l,r,a]->Ar,Derivative[0,0,1][A][l,r,a]->Aa,Derivative[0,2,0][A][l,r,a]->Arr,Derivative[0,0,2][A][l,r,a]->Aaa,Derivative[0,1,1][A][l,r,a]->Ara,B[l,r,a]->B,Derivative[1,0,0][B][l,r,a]->Bl,Derivative[0,1,0][B][l,r,a]->Br,Derivative[0,0,1][B][l,r,a]->Ba,Derivative[0,2,0][B][l,r,a]->Brr,Derivative[0,0,2][B][l,r,a]->Baa,Derivative[0,1,1][B][l,r,a]->Bra,F[l,r,a]->F,Derivative[1,0,0][F][l,r,a]->Fl,Derivative[0,1,0][F][l,r,a]->Fr,Derivative[0,0,1][F][l,r,a]->Fa,Derivative[0,2,0][F][l,r,a]->Frr,Derivative[0,0,2][F][l,r,a]->Faa,Derivative[0,1,1][F][l,r,a]->Fra,S[l,r,a]->S,Derivative[1,0,0][S][l,r,a]->Sl,Derivative[0,1,0][S][l,r,a]->Sr,Derivative[0,0,1][S][l,r,a]->Sa,Derivative[0,2,0][S][l,r,a]->Srr,Derivative[0,0,2][S][l,r,a]->Saa,Derivative[0,1,1][S][l,r,a]->Sra,Δ[r,a]->L,Derivative[1,0][Δ][r,a]->Lr,Derivative[2,0][Δ][r,a]->Lrr,Derivative[0,1][Δ][r,a]->La,Derivative[0,2][Δ][r,a]->Laa,Derivative[1,1][Δ][r,a]->Lra,f[r]->f,f'[r]->fr,f''[r]->frr,g[a]->g,g'[a]->ga,g''[a]->gaa};

CForm[H[[2,2]]/.{Exp[x_]->exp[x]}//.repl]

CForm[H[[2,3]]/.{Exp[x_]->exp[x]}//.repl]

CForm[phi/.{Exp[x_]->exp[x]}//.repl]

dlistλ={Tl,Al,Bl,Fl,Sl};

dlistrr={Trr,Arr,Brr,Frr,Srr};

dlistaa={Taa,Aaa,Baa,Faa,Saa};

dlistra={Tra,Ara,Bra,Fra,Sra};

dlist={Tr,Ar,Br,Fr,Sr,Ta,Aa,Ba,Fa,Sa};

zerodlist=Thread[dlist->Table[0,{ii,1,Length[dlist]}]];

allderiv=Join[dlistλ,dlistrr,dlistaa,dlistra,dlist];

allvar=Join[{r,a,θ1,T,A,B,F,S,L,Lr,La,Lrr,Laa,Lra,f,fr,frr,g,ga,gaa,Λ},allderiv];

zeroallderiv=Thread[allderiv->Table[0,{ii,1,Length[allderiv]}]];

dlist2=Flatten[Table[dlist[[ii]]dlist[[jj]],{ii,1,Length[dlist]},{jj,ii,Length[dlist]}]];

randlist=Table[Thread[allvar->Table[Random[],{ii,1,Length[allvar]}]],{ii,1,20}];

extract[expr_]:=(

derivλ=Simplify[Coefficient[expr,dlistλ]];

derivrr=Simplify[Coefficient[expr,dlistrr]];

derivaa=Simplify[Coefficient[expr,dlistaa]];

derivra=Simplify[Coefficient[expr,dlistra]];

deriv1=Simplify[Coefficient[expr,dlist]//.zerodlist];

deriv2=Simplify[Coefficient[expr,dlist2]];

noderiv=Simplify[expr//.zeroallderiv];

Print[N[expr-(derivλ.dlistλ+derivrr.dlistrr+derivaa.dlistaa+derivra.dlistra+deriv1.dlist+deriv2.dlist2+noderiv)/.randlist]];

{derivλ,derivrr,derivaa,derivra,deriv1,deriv2,noderiv}

);

tmp=RF1[[2,1,1]]//.repl;

coefftt=extract[tmp];

tmp=RF1[[2,2,2]]//.repl;

coeffrr=extract[tmp];

tmp=RF1[[2,3,3]]//.repl;

coeffaa=extract[tmp];

tmp=RF1[[2,2,3]]//.repl;

coeffra=extract[tmp];

tmp=RF1[[2,4,4]]//.repl;

coeffθθ=extract[tmp];

coeffs={coefftt,coeffrr,coeffaa,coeffra,coeffθθ};

coeffλ=coeffs[[All,1]]

Inverse[coeffλ].coeffs[[All,1]]

newcoeffrr=Simplify[Inverse[coeffλ].coeffs[[All,2]]]

newcoeffaa=Simplify[Inverse[coeffλ].coeffs[[All,3]]]

newcoeffra=Simplify[Inverse[coeffλ].coeffs[[All,4]]]

newcoeffderiv1=Simplify[Inverse[coeffλ].coeffs[[All,5]]]

newcoeffderiv2=Simplify[Inverse[coeffλ].coeffs[[All,6]]]

newcoeffnoderiv=Simplify[Inverse[coeffλ].coeffs[[All,7]]]

Load

dlistrr={Trr,Arr,Brr,Frr,Srr};

dlistaa={Taa,Aaa,Baa,Faa,Saa};

dlistra={Tra,Ara,Bra,Fra,Sra};

dlist={Tr,Ar,Br,Fr,Sr,Ta,Aa,Ba,Fa,Sa};

dlist2={(Tr^2),Ar Tr,Br Tr,Fr Tr,Sr Tr,Ta Tr,Aa Tr,Ba Tr,Fa Tr,Sa Tr,(Ar^2),Ar Br,Ar Fr,Ar Sr,Ar Ta,Aa Ar,Ar Ba,Ar Fa,Ar Sa,(Br^2),Br Fr,Br Sr,Br Ta,Aa Br,Ba Br,Br Fa,Br Sa,(Fr^2),Fr Sr,Fr Ta,Aa Fr,Ba Fr,Fa Fr,Fr Sa,(Sr^2),Sr Ta,Aa Sr,Ba Sr,Fa Sr,Sa Sr,(Ta^2),Aa Ta,Ba Ta,Fa Ta,Sa Ta,(Aa^2),Aa Ba,Aa Fa,Aa Sa,(Ba^2),Ba Fa,Ba Sa,(Fa^2),Fa Sa,(Sa^2)};

newcoeffrr={{-((4 (E^((a^2) B+S)) (f^2))/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0,0,0,0},{0,-((4 (E^((a^2) B+S)) (f^2))/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0,0,0},{0,0,-((4 (E^((a^2) B+S)) (f^2))/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0,0},{0,0,0,-((4 (E^((a^2) B+S)) (f^2))/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0},{0,0,0,0,-((4 (E^((a^2) B+S)) (f^2))/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2)))}};

newcoeffaa={{-((4 (E^(A (r^2)+T)) g)/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0,0,0,0},{0,-((4 (E^(A (r^2)+T)) g)/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0,0,0},{0,0,-((4 (E^(A (r^2)+T)) g)/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0,0},{0,0,0,-((4 (E^(A (r^2)+T)) g)/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0},{0,0,0,0,-((4 (E^(A (r^2)+T)) g)/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2)))}};

newcoeffra={{((2 a f F g r)/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0,0,0,0},{0,((2 a f F g r)/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0,0,0},{0,0,((2 a f F g r)/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0,0},{0,0,0,((2 a f F g r)/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2))),0},{0,0,0,0,((2 a f F g r)/(16 (E^((a^2) B+A (r^2)+S+T)) L-(a^2) (F^2) g L (r^2)))}};

newcoeffderiv1={{-(1/(8 (L^2) (16 (E^((a^2) B+A (r^2)+S+T)) r-(a^2) (F^2) g (r^3))))(E^(-S-T)) f (16 (E^(A (r^2)+S+2 T)) f Lr r+32 (E^((a^2) B+A (r^2)+S+2 T)) f Lr r+16 (E^((a^2) B+2 S+T)) (2 fr L-f Lr) r+8 a (E^(S+T)) F g La (r^2)-2 (a^2) (E^T) f (F^2) g Lr (r^3)+16 (E^((a^2) B+A (r^2)+2 S+T)) (2 f L+2 fr L r+f Lr r)-(a^2) (E^S) (F^2) g (r^2) (2 f L+2 fr L r+f Lr r)),0,0,0,0,-(1/(8 (L^2) (16 a (E^((a^2) B+A (r^2)+S+T))-(a^3) (F^2) g (r^2))))(E^(-S-T)) (16 a (E^((a^2) B+2 S+T)) g La+16 a (E^((a^2) B+A (r^2)+2 S+T)) g La+16 a (E^(A (r^2)+S+2 T)) (ga L-g La)+32 (E^((a^2) B+A (r^2)+S+2 T)) (2 g L+a ga L+a g La)+8 (a^2) (E^(S+T)) f F g Lr r-(a^3) (E^S) (F^2) (g^2) La (r^2)-2 (a^2) (E^T) (F^2) g (2 g L+a ga L+a g La) (r^2)),0,0,0,0},{((E^(-A (r^2)-2 T)) f (256 a (E^(2 ((a^2) B+A (r^2)+S+T))) F g La (r^2)+512 a (E^((a^2) B+2 A (r^2)+S+3 T)) F g La (r^2)+256 a (E^(2 (a^2) B+A (r^2)+2 (S+T))) F g La (r^2)+64 (a^2) (E^(2 A (r^2)+3 T)) f (F^2) g Lr (r^3)-32 (a^3) (E^((a^2) B+A (r^2)+S+T)) (F^3) (g^2) La (r^4)-16 (a^2) (E^(A (r^2)+2 T)) (F^3) g (-2 g L-a ga L+a g La) (r^4)+(a^5) (F^5) (g^3) La (r^6)+64 (a^2) (E^((a^2) B+A (r^2)+S+2 T)) (F^2) g (r^3) (4 fr L+3 f Lr+4 A f L r)+1024 (E^(2 (a^2) B+3 A (r^2)+2 S+3 T)) (2 f L+2 fr L r+f Lr r)-128 (a^2) (E^((a^2) B+2 A (r^2)+S+2 T)) (F^2) g (r^2) (2 f L+2 fr L r+f Lr r)-4 (a^4) (E^T) (F^4) (g^2) (r^4) (2 f L+2 fr L r+f Lr r)+4 (a^4) (E^(A (r^2)+T)) (F^4) (g^2) (r^4) (2 f L+2 fr L r+f Lr r)+1024 (E^(2 (a^2) B+2 A (r^2)+2 S+3 T)) (-2 fr L r-f (Lr r+L (2-2 A (r^2))))))/(16 (L^2) (r^3) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),((E^(-S-T)) f (-256 (E^((a^2) B+2 A (r^2)+2 S+3 T)) f Lr r-512 (E^(2 (a^2) B+2 A (r^2)+2 S+3 T)) f Lr r+128 a (E^(2 (a^2) B+3 S+T)) F g La (r^2)+128 a (E^((a^2) B+A (r^2)+2 (S+T))) F g La (r^2)+48 (a^2) (E^(A (r^2)+S+2 T)) f (F^2) g Lr (r^3)+64 (a^2) (E^((a^2) B+A (r^2)+S+2 T)) f (F^2) g Lr (r^3)+8 (a^2) (E^(S+T)) (F^3) g (2 g+a ga) L (r^4)-2 (a^4) (E^T) f (F^4) (g^2) Lr (r^5)-256 (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) (2 f L+2 fr L r+f Lr r)+32 (a^2) (E^((a^2) B+A (r^2)+2 S+T)) (F^2) g (r^2) (2 f L+2 fr L r+f Lr r)-(a^4) (E^S) (F^4) (g^2) (r^4) (2 f L+2 fr L r+f Lr r)+16 (a^2) (E^((a^2) B+2 S+T)) (F^2) g (r^3) (2 fr L+f (Lr+8 A L r))+256 (E^(2 (a^2) B+A (r^2)+3 S+2 T)) (-2 fr L r+f (Lr r+4 L (-2+A (r^2))))))/(8 (L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),(1/((L^2) (r^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)))(a^2) (E^((a^2) B-A (r^2)+S-T)) f (64 (E^(3 (A (r^2)+T))) f Lr-64 (E^((a^2) B+2 A (r^2)+S+2 T)) f Lr+16 (E^(2 (A (r^2)+T))) F (2 g L+a ga L+a g La) r+(a^3) (F^3) (g^2) La (r^3)+8 (a^2) (E^(A (r^2)+T)) f (F^2) g (r^2) (Lr+A L r)),-(a (E^(-A (r^2)-T)) f g (64 (E^((a^2) B+2 A (r^2)+S+2 T)) La+4 (a^2) (F^2) ((E^(A (r^2)+T)) ga L+(E^((a^2) B+S)) g La) (r^2)+(a^3) f (F^3) g Lr (r^3)+8 a (E^(A (r^2)+T)) F (2 (E^(A (r^2)+T)) f Lr r+F g L (r^2)+4 (E^((a^2) B+S)) f L (-1+2 A (r^2)))))/(2 (L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),((E^(-A (r^2)-S-T)) f (-1536 (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) f Lr+512 (E^((a^2) B+3 A (r^2)+2 S+3 T)) f Lr+1024 (E^(2 (a^2) B+3 A (r^2)+2 S+3 T)) f Lr+256 (E^(2 ((a^2) B+A (r^2)+S+T))) F (2 g L+a ga L+a g La) r+128 (E^((a^2) B+2 (A (r^2)+S+T))) F (2 g L+a ga L+a g La) r-128 (a^2) (E^((a^2) B+2 A (r^2)+S+2 T)) f (F^2) g Lr (r^2)+8 (a^3) (E^((a^2) B+2 S)) (F^3) (g^2) La (r^3)-32 (a^2) (E^((a^2) B+A (r^2)+S+T)) (F^3) g (2 g L+a ga L+a g La) (r^3)-4 (a^4) (E^S) f (F^4) (g^2) Lr (r^4)+4 (a^4) (E^(A (r^2)+T)) f (F^4) (g^2) Lr (r^4)+(a^4) (F^5) (g^2) (2 g L+a ga L+a g La) (r^5)+64 (a^2) (E^((a^2) B+A (r^2)+2 S+T)) f (F^2) g (r^2) (3 Lr+A L r)))/(8 (L^2) (r^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),((2 a f F g (-16 (E^((a^2) B+A (r^2)+S+T)) Lr+(a^2) (F^2) g r (Lr r+L (2-2 A (r^2)))))/((L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),-((E^(-S-T)) (256 a (E^(2 (a^2) B+A (r^2)+3 S+2 T)) g La+256 a (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) g La+256 a (E^((a^2) B+2 A (r^2)+2 S+3 T)) (ga L-g La)+512 (E^(2 (a^2) B+2 A (r^2)+2 S+3 T)) (2 g L+a ga L+a g La)-16 (a^3) (E^((a^2) B+2 S+T)) (F^2) (g^2) La (r^2)-32 (a^3) (E^((a^2) B+A (r^2)+2 S+T)) (F^2) (g^2) La (r^2)+16 (a^3) (E^(A (r^2)+S+2 T)) (F^2) g (-ga L+g La) (r^2)-64 (a^2) (E^((a^2) B+A (r^2)+S+2 T)) (F^2) g (2 g L+a ga L+a g La) (r^2)+(a^5) (E^S) (F^4) (g^3) La (r^4)+2 (a^4) (E^T) (F^4) (g^2) (2 g L+a ga L+a g La) (r^4)+8 (a^4) (E^(S+T)) f (F^3) (g^2) (r^3) (-3 Lr+4 A L r)-128 (a^2) (E^((a^2) B+A (r^2)+2 (S+T))) f F g (4 L-3 Lr r)))/(8 a (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),0,((2 a f g (16 (E^((a^2) B+A (r^2)+S+T)) Lr+(a^2) (F^2) g r (-Lr r+2 L (-1+A (r^2)))))/((L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),0},{0,0,-((E^(-S-T)) f (256 (E^((a^2) B+2 A (r^2)+2 S+3 T)) f Lr r+512 (E^(2 (a^2) B+2 A (r^2)+2 S+3 T)) f Lr r+256 (E^(2 (a^2) B+A (r^2)+3 S+2 T)) (2 fr L-f Lr) r-128 (E^((a^2) B+A (r^2)+2 (S+T))) F g (4 L-3 a La) (r^2)-16 (a^2) (E^(A (r^2)+S+2 T)) f (F^2) g Lr (r^3)-64 (a^2) (E^((a^2) B+A (r^2)+S+2 T)) f (F^2) g Lr (r^3)-16 (a^2) (E^((a^2) B+2 S+T)) (F^2) g (2 fr L-f Lr) (r^3)+8 (a^3) (E^(S+T)) (F^3) g (4 a B g L-2 ga L-3 g La) (r^4)+2 (a^4) (E^T) f (F^4) (g^2) Lr (r^5)+256 (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) (2 f L+2 fr L r+f Lr r)-32 (a^2) (E^((a^2) B+A (r^2)+2 S+T)) (F^2) g (r^2) (2 f L+2 fr L r+f Lr r)+(a^4) (E^S) (F^4) (g^2) (r^4) (2 f L+2 fr L r+f Lr r)))/(8 (L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),-((2 f g r (-16 (E^((a^2) B+A (r^2)+S+T)) La+a (F^2) (a ga L+g (2 L-2 (a^2) B L+a La)) (r^2)))/(a (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),((2 f F g r (-16 (E^((a^2) B+A (r^2)+S+T)) La+a (F^2) (a ga L+g (2 L-2 (a^2) B L+a La)) (r^2)))/(a (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),((E^(-(a^2) B-S-T)) g (-1024 (E^(2 (a^2) B+A (r^2)+2 (S+T))) (-(E^((a^2) B+S))-(E^((a^2) B+A (r^2)+S))+2 (E^(A (r^2)+T))) La+128 (a^2) (E^((a^2) B+A (r^2)+S+T)) (-(E^((a^2) B+S))+2 (E^T)) (F^2) g La (r^2)+4 (a^4) ((E^((a^2) B+S))-(E^T)) (F^4) (g^2) La (r^4)+(a^5) (F^5) (g^2) (r^4) (2 f L+2 fr L r+f Lr r)+256 a (E^(2 (a^2) B+A (r^2)+2 (S+T))) F (2 (E^(A (r^2))) fr L r+(1+(E^(A (r^2)))) f (2 L+Lr r))+16 (a^3) (E^(A (r^2)+T)) (F^2) g (r^2) (8 B (E^((a^2) B+S+T)) L-F (-(E^T) f Lr r+2 (E^((a^2) B+S)) (2 f L+2 fr L r+f Lr r)))))/(16 (a^2) (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),(((E^(-(a^2) B+A (r^2)-S+T)) g (r^2) (64 (E^(2 ((a^2) B+S))) ((E^((a^2) B+S))-(E^(A (r^2)+T))) La+8 (a^2) (E^((a^2) B+S)) (F^2) g La (r^2)+16 a (E^(2 ((a^2) B+S))) f F (2 L+Lr r)+(a^3) (F^2) g (r^2) (8 B (E^((a^2) B+S)) L+f F Lr r)))/((a^2) (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),((E^(-S-T)) (-256 a (E^(2 (a^2) B+A (r^2)+3 S+2 T)) g La-256 a (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) g La-512 (E^(2 (a^2) B+2 A (r^2)+2 S+3 T)) (2 g L+a ga L+a g La)+256 (E^((a^2) B+2 A (r^2)+2 S+3 T)) (-a ga L+g (4 (-2+(a^2) B) L+a La))+128 (a^2) (E^(2 A (r^2)+S+3 T)) f F g Lr r+128 (a^2) (E^((a^2) B+A (r^2)+2 (S+T))) f F g Lr r+16 (a^4) (E^(S+T)) f (F^3) (g^2) L (r^2)+48 (a^3) (E^((a^2) B+2 S+T)) (F^2) (g^2) La (r^2)+32 (a^3) (E^((a^2) B+A (r^2)+2 S+T)) (F^2) (g^2) La (r^2)+16 (a^3) (E^(A (r^2)+S+2 T)) (F^2) g (8 a B g L-3 ga L+g La) (r^2)+64 (a^2) (E^((a^2) B+A (r^2)+S+2 T)) (F^2) g (2 g L+a ga L+a g La) (r^2)-(a^5) (E^S) (F^4) (g^3) La (r^4)-2 (a^4) (E^T) (F^4) (g^2) (2 g L+a ga L+a g La) (r^4)))/(8 a (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),-((E^(-(a^2) B-S)) g r (64 (E^(2 (a^2) B+A (r^2)+2 S+T)) f Lr+8 (a^2) (E^((a^2) B+S)) f (F^2) g L r+16 (E^((a^2) B+A (r^2)+S+T)) F ((-2+4 (a^2) B) g-a ga) L r+16 a (E^(2 ((a^2) B+S))) F g La r+4 (a^2) (E^(A (r^2)+T)) f (F^2) g Lr (r^2)+(a^3) (F^3) (g^2) La (r^3)))/(2 a (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),((E^(-(a^2) B-2 S)) (1024 (E^(3 (a^2) B+2 A (r^2)+3 S+2 T)) (2 g L+a ga L+a g La)+1024 (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) (-a ga L+g (-2 L+(a^2) B L-a La))+256 (a^2) (E^(2 ((a^2) B+A (r^2)+S+T))) f F g Lr r+256 (a^2) (E^(2 (a^2) B+A (r^2)+3 S+T)) f F g Lr r+128 (a^2) (E^((a^2) B+2 (A (r^2)+S+T))) f F g Lr r+32 (a^3) (E^(2 (a^2) B+3 S)) (F^2) (g^2) La (r^2)-128 (a^2) (E^(2 (a^2) B+A (r^2)+2 S+T)) (F^2) g (2 g L+a ga L+a g La) (r^2)+32 (a^2) (E^((a^2) B+A (r^2)+2 S+T)) (F^2) g (2 a ga L+g (4 L+4 (a^2) B L+5 a La)) (r^2)-32 (a^4) (E^((a^2) B+A (r^2)+S+T)) f (F^3) (g^2) Lr (r^3)-4 (a^4) (E^S) (F^4) (g^2) (2 g L+a ga L+a g La) (r^4)+4 (a^4) (E^((a^2) B+S)) (F^4) (g^2) (2 g L+a ga L+a g La) (r^4)+(a^6) f (F^5) (g^3) Lr (r^5)-8 (a^4) (E^((a^2) B+2 S)) f (F^3) (g^2) (r^2) (-2 L+Lr r)))/(8 (a^3) (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))},{((E^(-T)) f (1024 (E^(3 (a^2) B+A (r^2)+3 S+2 T)) (1+(E^(A (r^2)))) La-128 (a^2) (E^((a^2) B+A (r^2)+S+T)) (F^2) ((E^((a^2) B+S)) g La+(E^T) (ga L-g La)) (r^2)+4 (a^4) ((E^((a^2) B+S))-(E^T)) (F^4) (g^2) La (r^4)+(a^5) (F^5) (g^2) (r^4) (2 f L+2 fr L r+f Lr r)+256 a (E^((a^2) B+A (r^2)+S+2 T)) F (-F g L (r^2)+(E^((a^2) B+S)) f (2 L+Lr r)+(E^((a^2) B+A (r^2)+S)) (2 f L+2 fr L r+f Lr r))+16 (a^3) (E^(A (r^2)+T)) (F^2) g (r^2) (24 B (E^((a^2) B+S+T)) L-F (-(E^T) f Lr r+2 (E^((a^2) B+S)) (2 f L+2 fr L r+f Lr r)))))/(8 a (L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),(1/(a (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)))2 (E^(A (r^2)+T)) f r (64 (E^(2 ((a^2) B+S))) ((E^((a^2) B+S))+(E^(A (r^2)+T))) La-8 (a^2) (E^((a^2) B+S)) (F^2) ga L (r^2)+(a^3) (F^2) g (r^2) (24 B (E^((a^2) B+S)) L+f F Lr r)+16 a (E^((a^2) B+S)) F (-F g L (r^2)+(E^((a^2) B+S)) f (2 L+Lr r))),(1/((L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)))2 a (E^((a^2) B+S)) f (-128 (E^((a^2) B+2 A (r^2)+S+2 T)) La+4 (a^2) ((E^((a^2) B+S))+3 (E^(A (r^2)+T))) (F^2) g La (r^2)+(a^3) f (F^3) g (r^2) (2 L+Lr r)+16 a (E^(A (r^2)+T)) (8 B (E^((a^2) B+A (r^2)+S+T)) L+f F ((E^(A (r^2)+T)) Lr r-4 (E^((a^2) B+S)) L (-1+A (r^2))))),-((E^(-S-T)) f (256 (E^((a^2) B+2 A (r^2)+2 S+3 T)) f Lr r+512 (E^(2 (a^2) B+2 A (r^2)+2 S+3 T)) f Lr r+128 a (E^(2 (a^2) B+3 S+T)) F g La (r^2)+128 (E^((a^2) B+A (r^2)+2 (S+T))) F (-a ga L+g ((-2+4 (a^2) B) L+a La)) (r^2)+16 (a^2) (E^(A (r^2)+S+2 T)) f (F^2) g Lr (r^3)-64 (a^2) (E^((a^2) B+A (r^2)+S+2 T)) f (F^2) g Lr (r^3)+2 (a^4) (E^T) f (F^4) (g^2) Lr (r^5)+256 (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) (2 f L+2 fr L r+f Lr r)-32 (a^2) (E^((a^2) B+A (r^2)+2 S+T)) (F^2) g (r^2) (2 f L+2 fr L r+f Lr r)+(a^4) (E^S) (F^4) (g^2) (r^4) (2 f L+2 fr L r+f Lr r)+16 (a^2) (E^((a^2) B+2 S+T)) (F^2) g (r^2) (4 f L-2 fr L r+3 f Lr r)-256 (E^(2 (a^2) B+A (r^2)+3 S+2 T)) (-2 fr L r+f (Lr r+4 L (-1+A (r^2))))))/(8 (L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),((E^(-S)) f (1024 (E^(3 (a^2) B+2 A (r^2)+3 S+2 T)) (2 g L+a ga L+a g La)+1024 (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) (-a ga L+g (-2 L+(a^2) B L-2 a La))+256 (a^2) (E^(2 ((a^2) B+A (r^2)+S+T))) f F g Lr r+128 (a^2) (E^((a^2) B+2 (A (r^2)+S+T))) f F g Lr r+32 (a^3) (E^(2 (a^2) B+3 S)) (F^2) (g^2) La (r^2)-128 (a^2) (E^(2 (a^2) B+A (r^2)+2 S+T)) (F^2) g (2 g L+a ga L+a g La) (r^2)+32 (a^2) (E^((a^2) B+A (r^2)+2 S+T)) (F^2) g (8 g L+4 a ga L+7 a g La) (r^2)-32 (a^4) (E^((a^2) B+A (r^2)+S+T)) f (F^3) (g^2) Lr (r^3)-4 (a^4) (E^S) (F^4) (g^2) (2 g L+a ga L+a g La) (r^4)+4 (a^4) (E^((a^2) B+S)) (F^4) (g^2) (2 g L+a ga L+a g La) (r^4)+(a^6) f (F^5) (g^3) Lr (r^5)+8 (a^4) (E^((a^2) B+2 S)) f (F^3) (g^2) (r^2) (2 L+Lr r)-512 (a^2) (E^(2 (a^2) B+A (r^2)+3 S+T)) f F g L (-1+A (r^2))))/(4 (a^2) g (L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),((E^(-T)) (-512 (E^((a^2) B+2 A (r^2)+S+3 T)) F (2 (-1+(a^2) B) g-a ga) L (r^2)+256 a (E^(2 ((a^2) B+A (r^2)+S+T))) F g La (r^2)+256 a (E^(2 (a^2) B+A (r^2)+2 (S+T))) F g La (r^2)+64 (a^2) (E^(2 A (r^2)+3 T)) f (F^2) g Lr (r^3)-32 (a^3) (E^((a^2) B+A (r^2)+S+T)) (F^3) (g^2) La (r^4)+16 (a^2) (E^(A (r^2)+2 T)) (F^3) g (2 g L+a ga L+a g La) (r^4)+(a^5) (F^5) (g^3) La (r^6)+1024 (E^(2 (a^2) B+3 A (r^2)+2 S+3 T)) (2 f L+2 fr L r+f Lr r)-128 (a^2) (E^((a^2) B+2 A (r^2)+S+2 T)) (F^2) g (r^2) (2 f L+2 fr L r+f Lr r)-4 (a^4) (E^T) (F^4) (g^2) (r^4) (2 f L+2 fr L r+f Lr r)+4 (a^4) (E^(A (r^2)+T)) (F^4) (g^2) (r^4) (2 f L+2 fr L r+f Lr r)+64 (a^2) (E^((a^2) B+A (r^2)+S+2 T)) (F^2) g (r^2) (4 f L+4 fr L r+5 f Lr r)+1024 (E^(2 (a^2) B+2 A (r^2)+2 S+3 T)) (-2 fr L r+f (-3 Lr r+2 L (-1+A (r^2))))))/(8 a (L^2) (r^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),(1/(a (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)))2 (E^(A (r^2)+T)) r (-32 (E^((a^2) B+A (r^2)+S+T)) F (2 (-1+(a^2) B) g-a ga) L r+16 a (E^(2 ((a^2) B+S))) F g La r+12 (a^2) (E^((a^2) B+S)) f (F^2) g Lr (r^2)+4 (a^2) (E^(A (r^2)+T)) f (F^2) g Lr (r^2)+(a^2) (F^3) g (2 g L+a ga L+a g La) (r^3)-128 (E^(2 (a^2) B+A (r^2)+2 S+T)) f (Lr-A L r)),((2 a (E^((a^2) B+S)) (64 (E^(3 (A (r^2)+T))) f Lr+64 (E^((a^2) B+2 A (r^2)+S+2 T)) f Lr+16 (E^(2 (A (r^2)+T))) F (2 g L+a ga L+a g La) r+(a^3) (F^3) (g^2) La (r^3)+8 (a^2) (E^(A (r^2)+T)) f (F^2) g L r (-2+3 A (r^2))))/((L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),-((E^(-S-T)) (256 a (E^(2 (a^2) B+A (r^2)+3 S+2 T)) g La+256 a (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) g La+512 (E^(2 (a^2) B+2 A (r^2)+2 S+3 T)) (2 g L+a ga L+a g La)-256 (E^((a^2) B+2 A (r^2)+2 S+3 T)) (-3 a ga L+g (4 (-1+(a^2) B) L+a La))+128 (a^2) (E^(2 A (r^2)+S+3 T)) f F g Lr r+16 (a^3) (E^((a^2) B+2 S+T)) (F^2) (g^2) La (r^2)-32 (a^3) (E^((a^2) B+A (r^2)+2 S+T)) (F^2) (g^2) La (r^2)-64 (a^2) (E^((a^2) B+A (r^2)+S+2 T)) (F^2) g (2 g L+a ga L+a g La) (r^2)+16 (a^2) (E^(A (r^2)+S+2 T)) (F^2) g (4 g L+a ga L+3 a g La) (r^2)+(a^5) (E^S) (F^4) (g^3) La (r^4)+2 (a^4) (E^T) (F^4) (g^2) (2 g L+a ga L+a g La) (r^4)+128 (a^2) (E^((a^2) B+A (r^2)+2 (S+T))) f F g (Lr r+L (-2+4 A (r^2)))))/(8 a (L^2) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),((E^(-S)) (-512 (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) f Lr+512 (E^((a^2) B+3 A (r^2)+2 S+3 T)) f Lr+1024 (E^(2 (a^2) B+3 A (r^2)+2 S+3 T)) f Lr+256 (E^(2 ((a^2) B+A (r^2)+S+T))) F (2 g L+a ga L+a g La) r+128 (E^((a^2) B+2 (A (r^2)+S+T))) F (2 g L+a ga L+a g La) r-128 (a^2) (E^((a^2) B+2 A (r^2)+S+2 T)) f (F^2) g Lr (r^2)+8 (a^3) (E^((a^2) B+2 S)) (F^3) (g^2) La (r^3)-32 (a^2) (E^((a^2) B+A (r^2)+S+T)) (F^3) g (2 g L+a ga L+a g La) (r^3)-4 (a^4) (E^S) f (F^4) (g^2) Lr (r^4)+4 (a^4) (E^(A (r^2)+T)) f (F^4) (g^2) Lr (r^4)+(a^4) (F^5) (g^2) (2 g L+a ga L+a g La) (r^5)+64 (a^2) (E^((a^2) B+A (r^2)+2 S+T)) f (F^2) g r (2 Lr r+L (-2+3 A (r^2)))))/(4 a (L^2) r (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))},{0,0,0,0,-(1/(8 (L^2) (16 (E^((a^2) B+A (r^2)+S+T)) r-(a^2) (F^2) g (r^3))))(E^(-S-T)) f (16 (E^(A (r^2)+S+2 T)) f Lr r+32 (E^((a^2) B+A (r^2)+S+2 T)) f Lr r+16 (E^((a^2) B+2 S+T)) (2 fr L-f Lr) r+8 a (E^(S+T)) F g La (r^2)-2 (a^2) (E^T) f (F^2) g Lr (r^3)+16 (E^((a^2) B+A (r^2)+2 S+T)) (2 f L+2 fr L r+f Lr r)-(a^2) (E^S) (F^2) g (r^2) (2 f L+2 fr L r+f Lr r)),0,0,0,0,(1/(8 (L^2) (16 a (E^((a^2) B+A (r^2)+S+T))-(a^3) (F^2) g (r^2))))(E^(-S-T)) (-16 a (E^((a^2) B+2 S+T)) g La-16 a (E^((a^2) B+A (r^2)+2 S+T)) g La-16 a (E^(A (r^2)+S+2 T)) (ga L-g La)-32 (E^((a^2) B+A (r^2)+S+2 T)) (2 g L+a ga L+a g La)-8 (a^2) (E^(S+T)) f F g Lr r+(a^3) (E^S) (F^2) (g^2) La (r^2)+2 (a^2) (E^T) (F^2) g (2 g L+a ga L+a g La) (r^2))}};

newcoeffderiv2={{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-(((a^2) (E^(-A (r^2)-T)) (f^2) (F^2) g (-64 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))/(8 L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),((8 (E^((a^2) B+S)) (f^2) (8 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),((4 (a^4) (E^((a^2) B+S)) (f^2) (F^2) g)/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),-((16 (a^2) (E^((a^2) B+S)) (f^2) F g)/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),((4 (a^2) (E^((a^2) B+S)) (f^2) (F^2) g)/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),-((2 (a^3) f (F^3) (g^2) r)/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),-((2 (a^3) f (F^3) (g^2) (r^3))/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),0,((2 (a^3) f (F^2) (g^2) r)/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),0,((4 (E^((a^2) B+S)) (f^2) (r^2) (8 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),((4 (a^4) (E^((a^2) B+S)) (f^2) (F^2) g (r^2))/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),-((16 (a^2) (E^((a^2) B+S)) (f^2) F g (r^2))/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),((4 (a^2) (E^((a^2) B+S)) (f^2) (F^2) g (r^2))/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),-((2 (a^3) f (F^3) (g^2) (r^3))/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),-((2 (a^3) f (F^3) (g^2) (r^5))/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),0,((2 (a^3) f (F^2) (g^2) (r^3))/(L (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2))),0,-((32 (a^4) (E^(2 (a^2) B+A (r^2)+2 S+T)) (f^2))/(L (((-16 (E^((a^2) B+A (r^2)+S+T)) r+(a^2) (F^2) g (r^3)))^2))),0,-((64 (a^2) (E^(2 (a^2) B+A (r^2)+2 S+T)) (f^2))/(L (((-16 (E^((a^2) B+A (r^2)+S+T)) r+(a^2) (F^2) g 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La (r^2)+4 (a^2) (E^T) F g (r^2) (-F g L La (r^2)+4 (E^S) (fr L La r+f (L La+2 La Lr r-L Lra r)))-(a^3) (F^2) g (r^2) (2 (E^T) r (La (ga L+g La) r+2 f fr L Lr r+(f^2) Lr (2 L+Lr r))+(E^S) ((4 (fr^2) (L^2)+g (La^2)) (r^2)+4 f fr L r (2 L+Lr r)+(f^2) (((2 L+Lr r))^2))+16 (E^(S+T)) (L^3) (r^2) Λ)+16 a (E^(S+T)) (2 (E^((a^2) B+A (r^2)+T)) r (La (ga L+g La) r+2 f fr L Lr r+(f^2) Lr (2 L+Lr r))+(E^(A (r^2)+T)) r ((ga L La-3 g (La^2)+2 g L Laa) r+2 f fr L Lr r+(f^2) Lr (2 L+Lr r))+(E^((a^2) B+A (r^2)+S)) ((4 (fr^2) (L^2)+g (La^2)) (r^2)+4 f fr L r (2 L+Lr r)+(f^2) (((2 L+Lr r))^2))+(E^((a^2) B+S)) (g (La^2) (r^2)+4 f (L^2) r (fr+frr r)-(f^2) (4 (L^2)+3 (Lr^2) (r^2)+2 L r (Lr-Lrr r)))+16 (E^((a^2) B+A (r^2)+S+T)) (L^3) (r^2) Λ))+(1/(a (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)))(E^(-A (r^2))) (-2048 (E^(2 (a^2) B+3 A (r^2)+2 S+4 T)) g L La (r^2)-(a^6) f (F^5) (g^2) ((E^S) g (-2 La Lr+L Lra)-2 (E^T) (ga L Lr+2 g La Lr-g L Lra)) (r^7)-8 (a^4) (E^T) (F^3) g (r^4) (4 (E^((a^2) B+A (r^2)+2 S)) f g (2 La Lr-L Lra) r+8 (E^((a^2) B+A (r^2)+S+T)) f (ga L Lr+2 g La Lr-g L Lra) r+(E^(A (r^2)+T)) F (g^2) L La (r^2)+2 (E^((a^2) B+2 S)) f g (2 L La+2 La Lr r-L Lra r)-2 (E^(A (r^2)+S+T)) f (g (2 La Lr-L Lra) r+ga L (-2 L-Lr r+2 A L (r^2))))-256 (a^2) (E^((a^2) B+A (r^2)+S+2 T)) F (r^2) (-(E^((a^2) B+A (r^2)+2 S)) f g (2 La Lr-L Lra) r-2 (E^((a^2) B+A (r^2)+S+T)) f (ga L Lr+2 g La Lr-g L Lra) r-(E^(A (r^2)+T)) F (g^2) L La (r^2)-(E^((a^2) B+2 S)) f g r (-L Lra+2 La (Lr+A L r))-(E^(A (r^2)+S+T)) f (ga L Lr r+g (-2 L La-2 La Lr r+L Lra r+2 A L La (r^2))))-2 (a^5) (E^T) (F^4) (g^2) (r^4) (-2 f F g L Lr (r^3)+2 (E^(A (r^2)+T)) (r^2) (ga L La+g (La^2)+f (2 fr L Lr-3 f (Lr^2)+2 f L Lrr+2 A f L Lr r))+(E^S) (8 f fr (L^2) r+4 (fr^2) (L^2) (r^2)+(f^2) (4 (L^2)+11 (Lr^2) (r^2)-4 L r (-2 Lr+Lrr r)))+(E^(A (r^2)+S)) (g (La^2) (r^2)+4 f (L^2) r (fr+frr r+A fr (r^2))+(f^2) (-3 (Lr^2) (r^2)+4 (L^2) (-1+A (r^2))+2 L r (-Lr+Lrr r+A Lr (r^2))))+16 (E^(A (r^2)+S+T)) (L^3) (r^2) Λ)-512 a (E^((a^2) B+2 A (r^2)+2 S+3 T)) (-f F g L Lr (r^3)-2 (E^((a^2) B)) f F g L Lr (r^3)+2 (E^((a^2) B+A (r^2)+T)) (r^2) (ga L La+g (La^2)+f (2 fr L Lr-3 f (Lr^2)+2 f L Lrr+2 A f L Lr r))+(E^(A (r^2)+T)) (r^2) (ga L La+g (-3 (La^2)+2 L Laa)+f (2 fr L Lr-3 f (Lr^2)+2 f L Lrr+2 A f L Lr r))+(E^((a^2) B+A (r^2)+S)) (g (La^2) (r^2)+4 f (L^2) r (fr+frr r+A fr (r^2))+(f^2) (-3 (Lr^2) (r^2)+4 (L^2) (-1+A (r^2))+2 L r (-Lr+Lrr r+A Lr (r^2))))+(E^((a^2) B+S)) ((4 (fr^2) (L^2)+g (La^2)) (r^2)+4 f fr L r (Lr r+L (2+A (r^2)))+(f^2) (4 (Lr^2) (r^2)-2 L Lr r (-2+A (r^2))+(L^2) (4+4 A (r^2)-4 (A^2) (r^4))))+16 (E^((a^2) B+A (r^2)+S+T)) (L^3) (r^2) Λ)+32 (a^3) (E^(A (r^2)+S+2 T)) (F^2) g (r^2) (-4 (E^((a^2) B)) f F g L Lr (r^3)+4 (E^((a^2) B+A (r^2)+T)) (r^2) (ga L La+g (La^2)+f (2 fr L Lr-3 f (Lr^2)+2 f L Lrr+2 A f L Lr r))+f F g L (r^2) (-Lr r+2 L (-1+A (r^2)))+2 (E^((a^2) B+A (r^2)+S)) (g (La^2) (r^2)+4 f (L^2) r (fr+frr r+A fr (r^2))+(f^2) (-3 (Lr^2) (r^2)+4 (L^2) (-1+A (r^2))+2 L r (-Lr+Lrr r+A Lr (r^2))))+(E^(A (r^2)+T)) r ((ga L La-3 g (La^2)+2 g L Laa) r+2 f fr L Lr r+(f^2) (-3 (Lr^2) r+2 L (-2 Lr+Lrr r+3 A Lr (r^2))))+(E^((a^2) B+S)) ((8 (fr^2) (L^2)+g (La^2)) (r^2)+4 f fr L r (Lr r+L (4+A (r^2)))+(f^2) (15 (Lr^2) (r^2)+2 L r (4 Lr-2 Lrr r+A Lr (r^2))+4 (L^2) (3-3 A (r^2)+2 (A^2) (r^4))))+32 (E^((a^2) B+A (r^2)+S+T)) (L^3) (r^2) Λ))),((E^(-(a^2) B-2 S-T)) (-1024 a (E^(3 (a^2) B+A (r^2)+4 S+2 T)) (g^2) (-2 a (La^2)+L ((-1+(a^2) B) La+a Laa))-1024 a (E^(3 (a^2) B+2 A (r^2)+4 S+2 T)) (g^2) (-2 a (La^2)+L ((-1+(a^2) B) La+a Laa))+512 (E^(2 (a^2) B+2 A (r^2)+3 (S+T))) (-3 (a^2) (ga^2) (L^2)-2 a g L (-a gaa L+ga (3 L+(a^2) B L+2 a La))+(g^2) (4 (-3-(a^2) B+(a^4) (B^2)) (L^2)-7 (a^2) (La^2)+2 a L (-5 La+(a^2) B La+a Laa)))-2048 (E^(3 (a^2) B+2 A (r^2)+3 (S+T))) ((4+2 (-2+(a^2) B) (g^2)-(a^2) (ga^2)+a g (-ga+(a^2) B ga+a gaa)) (L^2)-2 (a^2) (g^2) (La^2)+a g L (-a ga La+g (-3 La+(a^2) B La+a Laa)))+512 (a^3) (E^(2 (a^2) B+2 A (r^2)+2 S+3 T)) f F (g^2) (2 La Lr-L Lra) r+256 (a^3) (E^((a^2) B+2 A (r^2)+2 S+3 T)) f F (g^2) (2 a B L Lr+2 La Lr-L Lra) r+128 (a^3) (E^(2 (a^2) B+A (r^2)+3 S+T)) (F^2) (g^3) (-2 a (La^2)+L ((-1+(a^2) B) La+a Laa)) (r^2)+64 (a^2) (E^((a^2) B+A (r^2)+2 (S+T))) (F^2) g (3 (a^2) (ga^2) (L^2)+a g L (-a gaa L+ga (9 L-3 (a^2) B L+3 a La))+(g^2) (2 (6-3 (a^2) B+2 (a^4) (B^2)) (L^2)+9 (a^2) (La^2)+a L (9 La+(a^2) B La-3 a Laa))) (r^2)+256 (a^2) (E^(2 (a^2) B+A (r^2)+2 (S+T))) (F^2) g ((4+2 (-2+(a^2) B) (g^2)-(a^2) (ga^2)+a g (-ga+(a^2) B ga+a gaa)) (L^2)-2 (a^2) (g^2) (La^2)+a g L (-a ga La+g (-3 La+(a^2) B La+a Laa))) (r^2)+64 (a^3) (E^(2 (a^2) B+3 S+T)) (F^2) (g^2) (-a ga L La+g (-2 a (La^2)+L (-3 La+3 (a^2) B La+a Laa))) (r^2)-64 (a^5) (E^((a^2) B+A (r^2)+S+2 T)) f (F^3) (g^3) (2 La Lr-L Lra) (r^3)+16 (a^4) (E^(A (r^2)+S+2 T)) f (F^3) (g^2) (-a ga L Lr+g (-2 L Lr-2 a La Lr+a L Lra)) (r^3)-4 (a^5) (E^((a^2) B+2 S)) (F^4) (g^4) (-2 a (La^2)+L ((-1+(a^2) B) La+a Laa)) (r^4)+2 (a^4) (E^(S+T)) (F^4) (g^2) (-2 (a^2) (ga^2) (L^2)-4 a g ga L (2 L+a La)-(g^2) (8 (L^2)+11 (a^2) (La^2)-4 a L (-3 La+a Laa))) (r^4)-8 (a^4) (E^((a^2) B+S+T)) (F^4) (g^2) ((4+2 (-2+(a^2) B) (g^2)-(a^2) (ga^2)+a g (-ga+(a^2) B ga+a gaa)) (L^2)-2 (a^2) (g^2) (La^2)+a g L (-a ga La+g (-3 La+(a^2) B La+a Laa))) (r^4)+2 (a^7) (E^T) f (F^5) (g^4) (2 La Lr-L Lra) (r^5)+256 (a^3) (E^(2 (a^2) B+A (r^2)+3 S+2 T)) f F (g^2) (2 La Lr r+L (2 La+2 a B Lr r-Lra r))+256 (a^3) (E^(2 (a^2) B+2 A (r^2)+3 S+2 T)) F (g^2) (2 fr L La r+f (2 L La+2 La Lr r-L Lra r))-32 (a^5) (E^((a^2) B+A (r^2)+2 S+T)) (F^3) (g^3) (r^2) (2 fr L La r+f (2 L La+2 La Lr r-L Lra r))+(a^7) (E^S) (F^5) (g^4) (r^4) (2 fr L La r+f (2 L La+2 La Lr r-L Lra r))+16 (a^4) (E^((a^2) B+2 S+T)) f (F^3) (g^2) (r^2) (-a ga L (2 L+Lr r)+g (4 (-1+(a^2) B) (L^2)-2 a La Lr r+L (-2 a La-2 Lr r+a Lra r)))))/(16 (a^4) g (L^3) (((-16 (E^((a^2) B+A (r^2)+S+T))+(a^2) (F^2) g (r^2)))^2)),((E^(-S-T)) (4096 (E^(2 (a^2) B+2 A (r^2)+3 (S+T))) (-1+(E^((a^2) B))) f g L Lr r-(a^5) (F^3) (g^2) (r^4) (-32 B (E^((a^2) B+2 S+T)) g L La+F (-4 (E^((a^2) B+2 S)) f g (2 La Lr-L Lra) r-8 (E^(A (r^2)+2 T)) f g (2 La Lr-L Lra) r-8 (E^((a^2) B+S+T)) f (ga L Lr+2 g La Lr-g L Lra) r+(E^S) F (g^2) L La (r^2)+2 (E^T) F g L (3 ga L+g La) (r^2)+4 (E^(S+T)) (2 f g L La+2 fr g L La r+2 f ga L Lr r+3 f g La Lr r)-4 (E^(A (r^2)+S+T)) g (2 f L La+2 fr L La r+2 f La Lr r-f L Lra r)))+16 (a^3) (E^(S+T)) F g (r^2) (32 B (E^((a^2) B+2 A (r^2)+S+2 T)) L (ga L+g La)+F (-8 (E^(2 (a^2) B+A (r^2)+2 S)) f g (2 La Lr-L Lra) r-16 (E^((a^2) B+2 A (r^2)+2 T)) f g (2 La Lr-L Lra) r-4 (E^(2 (A (r^2)+T))) f (ga L Lr+2 g La Lr-g L Lra) r-16 (E^(2 (a^2) B+A (r^2)+S+T)) f (ga L Lr+2 g La Lr-g L Lra) r-(E^((a^2) B+S)) F (g^2) L La (r^2)+2 (E^((a^2) B+A (r^2)+S)) F (g^2) L La (r^2)+4 (E^((a^2) B+A (r^2)+T)) F g L (3 ga L+g La) (r^2)-(E^(A (r^2)+T)) F g L (ga L+3 g La) (r^2)-4 (E^(2 ((a^2) B+S))) f g (2 L La+2 La Lr r-L Lra r)-8 (E^((a^2) B+2 A (r^2)+S+T)) g (2 fr L La r+f (2 L La+2 La Lr r-L Lra r))+4 (E^((a^2) B+A (r^2)+S+T)) (4 fr g L La r+f (2 g (L La+5 La Lr r-L Lra r)+ga L (2 L+3 Lr r-4 A L (r^2))))))-256 a (E^((a^2) B+A (r^2)+2 (S+T))) (-4 (E^(2 (a^2) B+A (r^2)+2 S)) f g (2 La Lr-L Lra) r-4 (E^(2 (A (r^2)+T))) f g (2 La Lr-L Lra) r-8 (E^((a^2) B+2 A (r^2)+2 T)) f g (2 La Lr-L Lra) r-8 (E^(2 (a^2) B+A (r^2)+S+T)) f (ga L Lr+2 g La Lr-g L Lra) r+(E^((a^2) B+S)) F (g^2) L La (r^2)+(E^((a^2) B+A (r^2)+S)) F (g^2) L La (r^2)-(E^(A (r^2)+T)) F g L (-3 ga L+g La) (r^2)+2 (E^((a^2) B+A (r^2)+T)) F g L (3 ga L+g La) (r^2)-4 (E^(2 ((a^2) B+S))) f g r (-L Lra+2 La (Lr+A L r))-4 (E^((a^2) B+2 A (r^2)+S+T)) g (2 fr L La r+f (2 L La+2 La Lr r-L Lra r))+(E^((a^2) B+A (r^2)+S+T)) (8 fr g L La r+f (8 ga L Lr r+g (28 La Lr r-8 L (-La+Lra r+A La (r^2))))))-(a^6) (F^5) (g^3) (r^5) (2 (E^T) ((gaa (L^2)+ga L La-g (La^2)+g L Laa) r+f fr L Lr r+(f^2) (L Lr-(Lr^2) r+L Lrr r))+(E^S) ((ga L La-g (La^2)+g L Laa) r+f L (4 fr L+2 frr L r+fr Lr r)+(f^2) (L Lr-(Lr^2) r+L Lrr r))+16 (E^(S+T)) (L^3) r Λ)+64 (a^2) (E^(A (r^2)+S+2 T)) g r (32 B (E^((a^2) B+2 A (r^2)+S+2 T)) f L Lr-8 (E^(2 (a^2) B+S)) f (F^2) g L Lr (r^2)-2 (E^(A (r^2)+T)) f (F^2) g L Lr (r^2)-(F^3) (g^2) (L^2) (r^3)-2 (E^((a^2) B+S)) f (F^2) g L r (-3 Lr r+L (-2+4 A (r^2)))-8 (E^(2 (a^2) B+A (r^2)+S+T)) F ((gaa (L^2)+ga L La-g (La^2)+g L Laa) r+f fr L Lr r+(f^2) (-(Lr^2) r+L (Lr+Lrr r)))-4 (E^((a^2) B+A (r^2)+S+T)) F ((-4 B g (L^2)+gaa (L^2)+ga L La-5 g (La^2)+3 g L Laa) r+f fr L Lr r+(f^2) (-(Lr^2) r+L (Lr+Lrr r)))-4 (E^(2 (a^2) B+A (r^2)+2 S)) F ((ga L La-g (La^2)+g L Laa) r+f L (4 fr L+2 frr L r+fr Lr r)+(f^2) (-(Lr^2) r+L (Lr+Lrr r)))+4 (E^(2 ((a^2) B+S))) F (-(ga L La-g (La^2)+g L Laa) r-f fr L (2 L+3 Lr r)+(f^2) (4 A (L^2) r+5 (Lr^2) r+L (Lr-3 Lrr r+2 A Lr (r^2))))+32 (E^(2 (a^2) B+A (r^2)+2 S+T)) L (B f Lr-2 F (L^2) r Λ))+16 (a^4) (E^(S+T)) (F^2) g (r^2) (16 B (E^((a^2) B+A (r^2)+S+T)) f g (L^2) (-2+3 A (r^2))+F (-f F (g^2) L Lr (r^3)+(E^((a^2) B)) f F (g^2) L Lr (r^3)+(E^((a^2) B+S)) g (g (-(La^2)+L Laa) (r^2)+f fr L r (2 L+3 Lr r)-(f^2) (4 (L^2)+5 (Lr^2) (r^2)+3 L r (Lr-Lrr r)))+4 (E^((a^2) B+A (r^2)+T)) g r ((gaa (L^2)+ga L La-g (La^2)+g L Laa) r+f fr L Lr r+(f^2) (-(Lr^2) r+L (Lr+Lrr r)))+2 (E^((a^2) B+A (r^2)+S)) g r ((ga L La-g (La^2)+g L Laa) r+f L (4 fr L+2 frr L r+fr Lr r)+(f^2) (-(Lr^2) r+L (Lr+Lrr r)))+(E^(A (r^2)+T)) r ((-(ga^2) (L^2)+g (gaa (L^2)-5 g (La^2)+3 g L Laa)) r+f fr g L Lr r+(f^2) g (-(Lr^2) r+L (-Lr+Lrr r+2 A Lr (r^2))))+32 (E^((a^2) B+A (r^2)+S+T)) g (L^3) (r^2) Λ))))/(8 g (L^3) (((-16 a (E^((a^2) B+A (r^2)+S+T)) r+(a^3) (F^2) g (r^3)))^2)),((E^(-S-T)) (-64 (E^(A (r^2)+S+2 T)) (-(g^2)+2 (E^((a^2) B)) (-2+(g^2))) (L^2) r-32 a (E^(S+T)) g L ((E^((a^2) B+S)) g La+(E^((a^2) B+A (r^2)+S)) g La+(E^(A (r^2)+T)) (ga L-g La)+4 (E^((a^2) B+A (r^2)+T)) (ga L+g La)) r+2 (a^3) F g (r^2) (-4 (E^(S+T)) f (ga L Lr+4 g La Lr-2 g L Lra)+(E^S) F (g^2) L La r+4 (E^T) F g L (ga L+g La) r)+(a^4) (F^2) g (r^2) (2 (E^T) ((ga^2) (L^2)+2 g ga L La+g (g (La^2)+(f^2) (Lr^2))) r+(E^S) g (La (ga L+g La) r+2 f fr L Lr r+(f^2) Lr (2 L+Lr r))+16 (E^(S+T)) g (L^3) r Λ)-8 (a^2) (E^T) (4 (E^((a^2) B+A (r^2)+S+T)) ((ga^2) (L^2)+2 g ga L La+g (g (La^2)+(f^2) (Lr^2))) r-2 (E^(A (r^2)+S+T)) ((ga^2) (L^2)-g (2 gaa (L^2)-3 g (La^2)+2 g L Laa+(f^2) (Lr^2))) r+2 (E^((a^2) B+2 S)) g (ga L La+g (La^2)+f (2 fr L Lr-3 f (Lr^2)+2 f L Lrr)) r+2 (E^S) f F (g^2) L Lr (r^2)-(F^2) g (-2+(g^2)) (L^2) (r^3)+2 (E^((a^2) B+A (r^2)+2 S)) g (La (ga L+g La) r+2 f fr L Lr r+(f^2) Lr (2 L+Lr r))+32 (E^((a^2) B+A (r^2)+2 S+T)) g (L^3) r Λ)))/(8 (a^2) g (L^3) r (16 (E^((a^2) B+A (r^2)+S+T))-(a^2) (F^2) g (r^2)))};

Linearize

newcoeffrrT=Simplify[D[newcoeffrr,T]];

newcoeffrrA=Simplify[D[newcoeffrr,A]];

newcoeffrrB=Simplify[D[newcoeffrr,B]];

newcoeffrrF=Simplify[D[newcoeffrr,F]];

newcoeffrrS=Simplify[D[newcoeffrr,S]];

newcoeffaaT=Simplify[D[newcoeffaa,T]];

newcoeffaaA=Simplify[D[newcoeffaa,A]];

newcoeffaaB=Simplify[D[newcoeffaa,B]];

newcoeffaaF=Simplify[D[newcoeffaa,F]];

newcoeffaaS=Simplify[D[newcoeffaa,S]];

newcoeffraT=Simplify[D[newcoeffra,T]];

newcoeffraA=Simplify[D[newcoeffra,A]];

newcoeffraB=Simplify[D[newcoeffra,B]];

newcoeffraF=Simplify[D[newcoeffra,F]];

newcoeffraS=Simplify[D[newcoeffra,S]];

newcoeffderiv1T=Simplify[D[newcoeffderiv1,T]];

newcoeffderiv1A=Simplify[D[newcoeffderiv1,A]];

newcoeffderiv1B=Simplify[D[newcoeffderiv1,B]];

newcoeffderiv1F=Simplify[D[newcoeffderiv1,F]];

newcoeffderiv1S=Simplify[D[newcoeffderiv1,S]];

newcoeffderiv2T=Simplify[D[newcoeffderiv2,T]];

newcoeffderiv2A=Simplify[D[newcoeffderiv2,A]];

newcoeffderiv2B=Simplify[D[newcoeffderiv2,B]];

newcoeffderiv2F=Simplify[D[newcoeffderiv2,F]];

newcoeffderiv2S=Simplify[D[newcoeffderiv2,S]];

newcoeffnoderivT=Simplify[D[newcoeffnoderiv,T]];

newcoeffnoderivA=Simplify[D[newcoeffnoderiv,A]];

newcoeffnoderivB=Simplify[D[newcoeffnoderiv,B]];

newcoeffnoderivF=Simplify[D[newcoeffnoderiv,F]];

newcoeffnoderivS=Simplify[D[newcoeffnoderiv,S]];

Process

EqX=newcoeffrr.dlistrr+newcoeffaa.dlistaa+newcoeffra.dlistra+newcoeffderiv1.dlist+newcoeffderiv2.dlist2+newcoeffnoderiv;

coeffrr=newcoeffrr[[1,1]]

coeffaa=newcoeffaa[[1,1]]

coeffra=newcoeffra[[1,1]]

newcoeffrr/coeffrr

newcoeffaa/coeffaa

newcoeffra/coeffra

dlist[[1;;5]]

dEqdXr=Transpose[Table[
var=dlist[[ii]];
newcoeffderiv1.D[dlist,var]+newcoeffderiv2.D[dlist2,var]
,{ii,1,5}]];

dlist[[6;;10]]

dEqdXa=Transpose[Table[
var=dlist[[ii]];
newcoeffderiv1.D[dlist,var]+newcoeffderiv2.D[dlist2,var]
,{ii,6,10}]];

dEqdT=newcoeffrrT.dlistrr+newcoeffaaT.dlistaa+newcoeffraT.dlistra+newcoeffderiv1T.dlist+newcoeffderiv2T.dlist2+newcoeffnoderivT;

dEqdA=newcoeffrrA.dlistrr+newcoeffaaA.dlistaa+newcoeffraA.dlistra+newcoeffderiv1A.dlist+newcoeffderiv2A.dlist2+newcoeffnoderivA;

dEqdB=newcoeffrrB.dlistrr+newcoeffaaB.dlistaa+newcoeffraB.dlistra+newcoeffderiv1B.dlist+newcoeffderiv2B.dlist2+newcoeffnoderivB;

dEqdF=newcoeffrrF.dlistrr+newcoeffaaF.dlistaa+newcoeffraF.dlistra+newcoeffderiv1F.dlist+newcoeffderiv2F.dlist2+newcoeffnoderivF;

dEqdS=newcoeffrrS.dlistrr+newcoeffaaS.dlistaa+newcoeffraS.dlistra+newcoeffderiv1S.dlist+newcoeffderiv2S.dlist2+newcoeffnoderivS;

Dimensions[dEqdXr]

Writeout

repl={Exp[x_]->exp[x],r^2->r2,a^2->a2,Λ->Lambda};

SetDirectory["~/Work/SpecTest6/"]

string="\n\n";

Do[
stringtmp=ToString[CForm[EqX[[ii]]//.repl]];
stringtmp="EqX["<>ToString[ii-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp;
,{ii,1,5}]

string=string<>"\n";

Export["Eqn.c",string,"Text"];

string="\n\n";

string=string<>"coeffrr = "<>ToString[CForm[coeffrr//.repl]]<>" ; \n";

string=string<>"coeffaa = "<>ToString[CForm[coeffaa//.repl]]<>" ; \n";

string=string<>"coeffra = "<>ToString[CForm[coeffra//.repl]]<>" ; \n\n";

Do[
stringtmp=ToString[CForm[dEqdXr[[ii,jj]]//.repl]];
stringtmp="dEqXr["<>ToString[ii-1]<>"]["<>ToString[jj-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp;
,{ii,1,5},{jj,1,5}]

string=string<>"\n";

Do[
stringtmp=ToString[CForm[dEqdXa[[ii,jj]]//.repl]];
stringtmp="dEqXa["<>ToString[ii-1]<>"]["<>ToString[jj-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp;
,{ii,1,5},{jj,1,5}]

string=string<>"\n";

Do[
stringtmp=ToString[CForm[dEqdT[[ii]]//.repl]];
stringtmp="dEqT["<>ToString[ii-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp;
,{ii,1,5}]

string=string<>"\n";

Do[
stringtmp=ToString[CForm[dEqdA[[ii]]//.repl]];
stringtmp="dEqA["<>ToString[ii-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp;
,{ii,1,5}]

string=string<>"\n";

Do[
stringtmp=ToString[CForm[dEqdB[[ii]]//.repl]];
stringtmp="dEqB["<>ToString[ii-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp;
,{ii,1,5}]

string=string<>"\n";

Do[
stringtmp=ToString[CForm[dEqdF[[ii]]//.repl]];
stringtmp="dEqF["<>ToString[ii-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp;
,{ii,1,5}]

string=string<>"\n";

Do[
stringtmp=ToString[CForm[dEqdS[[ii]]//.repl]];
stringtmp="dEqS["<>ToString[ii-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp;
,{ii,1,5}]

string=string<>"\n";

Export["Licheq.c",string,"Text"];

dlist

newcoeffderiv1[[1,4]]

Simplify[dEqdXr[[1,4]]/.{F->0,A->0,T->0,S->0,B->0,Fr->0,Aa->0}]

Invariants

Ricci=Simplify[Ricci];

R2=Simplify[R2];

R4=Simplify[R4];

Clear[C4]

MT[C4,4,{d,d,d,d}];

Do[
C4=ST[C4,{{i1,d},{i2,d},{i3,d},{i4,d}},
GT[R4,{{i1,d},{i2,d},{i3,d},{i4,d}}]-(1/3)(Gd[[i1,i3]]GT[R2,{{i2,d},{i4,d}}]-Gd[[i1,i4]]GT[R2,{{i2,d},{i3,d}}]-Gd[[i2,i3]]GT[R2,{{i1,d},{i4,d}}]+Gd[[i2,i4]]GT[R2,{{i1,d},{i3,d}}])+(1/(4*3))Ricci(Gd[[i1,i3]]Gd[[i2,i4]]-Gd[[i1,i4]]Gd[[i2,i3]])
];,
{i1,1,Nind},{i2,1,Nind},{i3,1,Nind},{i4,1,Nind}];

repl={T[l,r,a]->T,Derivative[1,0,0][T][l,r,a]->Tl,Derivative[0,1,0][T][l,r,a]->Tr,Derivative[0,0,1][T][l,r,a]->Ta,Derivative[0,2,0][T][l,r,a]->Trr,Derivative[0,0,2][T][l,r,a]->Taa,Derivative[0,1,1][T][l,r,a]->Tra,A[l,r,a]->A,Derivative[1,0,0][A][l,r,a]->Al,Derivative[0,1,0][A][l,r,a]->Ar,Derivative[0,0,1][A][l,r,a]->Aa,Derivative[0,2,0][A][l,r,a]->Arr,Derivative[0,0,2][A][l,r,a]->Aaa,Derivative[0,1,1][A][l,r,a]->Ara,B[l,r,a]->B,Derivative[1,0,0][B][l,r,a]->Bl,Derivative[0,1,0][B][l,r,a]->Br,Derivative[0,0,1][B][l,r,a]->Ba,Derivative[0,2,0][B][l,r,a]->Brr,Derivative[0,0,2][B][l,r,a]->Baa,Derivative[0,1,1][B][l,r,a]->Bra,F[l,r,a]->F,Derivative[1,0,0][F][l,r,a]->Fl,Derivative[0,1,0][F][l,r,a]->Fr,Derivative[0,0,1][F][l,r,a]->Fa,Derivative[0,2,0][F][l,r,a]->Frr,Derivative[0,0,2][F][l,r,a]->Faa,Derivative[0,1,1][F][l,r,a]->Fra,S[l,r,a]->S,Derivative[1,0,0][S][l,r,a]->Sl,Derivative[0,1,0][S][l,r,a]->Sr,Derivative[0,0,1][S][l,r,a]->Sa,Derivative[0,2,0][S][l,r,a]->Srr,Derivative[0,0,2][S][l,r,a]->Saa,Derivative[0,1,1][S][l,r,a]->Sra,Δ[r,a]->L,Derivative[1,0][Δ][r,a]->Lr,Derivative[2,0][Δ][r,a]->Lrr,Derivative[0,1][Δ][r,a]->La,Derivative[0,2][Δ][r,a]->Laa,Derivative[1,1][Δ][r,a]->Lra,f[r]->f,f'[r]->fr,f''[r]->frr,g[a]->g,g'[a]->ga,g''[a]->gaa,Exp[x_]->expl[x],θ1->theta};

SetDirectory["~/Work/SpecTest2/"]

string="\n\n";

Do[

stringtmp=ToString[CForm[Gd[[ii,jj]]//.repl]];
stringtmp="gd["<>ToString[ii-1]<>"]["<>ToString[jj-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp<>"\n";

,{ii,1,Nind},{jj,1,Nind}]

string=string<>"\n";

Do[

stringtmp=ToString[CForm[Gu[[ii,jj]]//.repl]];
stringtmp="gu["<>ToString[ii-1]<>"]["<>ToString[jj-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp<>"\n";

,{ii,1,Nind},{jj,1,Nind}]

string=string<>"\n";

Do[

stringtmp=ToString[CForm[R2[[2]][[ii,jj]]//.repl]];
stringtmp="R2["<>ToString[ii-1]<>"]["<>ToString[jj-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp<>"\n";

,{ii,1,Nind},{jj,1,Nind}]

string=string<>"\n";

Do[

stringtmp=ToString[CForm[C4[[2]][[ii,jj,kk,ll]]//.repl]];
stringtmp="C4["<>ToString[ii-1]<>"]["<>ToString[jj-1]<>"]["<>ToString[kk-1]<>"]["<>ToString[ll-1]<>"] = "<>stringtmp<>" ;\n";
string=string<>stringtmp<>"\n";

,{ii,1,Nind},{jj,1,Nind},{kk,1,Nind},{ll,1,Nind}]

string=string<>"\n";

Export["Curv.c",string,"Text"];