>	restart:grtw();

 

 

 

 

 

 

	(1)

 

>	l:=1:grload(AdS,`/home/grumil/projects/BHfreeCCTMG/AdS3lccx.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for AdS (0.004000 sec.)
	(2)

 

>	hdp:=-h-hp:

 

>	bhdp:=-bh-bhp:

 

>	grload(log1,`/home/grumil/projects/BHfreeCCTMG/Logasymptotic.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for log1 (0.000000 sec.)
	(3)

 

>	grdef(`Psi1{a b}:=g<2>{a b}`);

 

Created definition for Psi1(dn,dn)

 

>	grcalc(2=log1,Psi1(dn,dn));

 

 

Calculated Psi1(dn,dn) for log1 (0.004000 sec.)
	(4)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`Psi1U{a ^b}:=Psi1{a c}*g{^c ^b}`);

 

Created definition for Psi1U(dn,up)

 

>	grdef(`Psi1UU{^a ^b}:=Psi1U{c ^b}*g{^c ^a}`);

 

Created definition for Psi1UU(up,up)

 

>	grdef(`deChr1{^a b c}:=g{^a ^d}*(Psi1{d b ;c}+Psi1{d c ;b}-Psi1{b c ;d})/2`);

 

Created a definition for Psi1(dn,dn,cdn) Created definition for deChr1(up,dn,dn)

 

>	grload(log2,`/home/grumil/projects/BHfreeCCTMG/Logasymptoticprime.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for log2 (0.000000 sec.)
	(5)

 

>	grdef(`Psi2{a b}:=g<3>{a b}`);

 

Created definition for Psi2(dn,dn)

 

>	grcalc(3=log2,Psi2(dn,dn));

 

 

Calculated Psi2(dn,dn) for log2 (0.000000 sec.)
	(6)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`Psi2U{a ^b}:=Psi2{a c}*g{^c ^b}`);

 

Created definition for Psi2U(dn,up)

 

>	grdef(`Psi2UU{^a ^b}:=Psi2U{c ^b}*g{^c ^a}`);

 

Created definition for Psi2UU(up,up)

 

>	grdef(`deChr2{^a b c}:=g{^a ^d}*(Psi2{d b ;c}+Psi2{d c ;b}-Psi2{b c ;d})/2`);

 

Created a definition for Psi2(dn,dn,cdn) Created definition for deChr2(up,dn,dn)

 

>	grload(left,`/home/grumil/projects/BHfreeCCTMG/Lasymptoticdoubleprime.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for left (0.000000 sec.)
	(7)

 

>	grdef(`PsiL{a b}:=g<4>{a b}`);

 

Created definition for PsiL(dn,dn)

 

>	grcalc(4=left,PsiL(dn,dn));

 

 

Calculated PsiL(dn,dn) for left (0.000000 sec.)
	(8)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`PsiLU{a ^b}:=PsiL{a c}*g{^c ^b}`);

 

Created definition for PsiLU(dn,up)

 

>	grdef(`PsiLUU{^a ^b}:=PsiLU{c ^b}*g{^c ^a}`);

 

Created definition for PsiLUU(up,up)

 

>	grdef(`deChrL{^a b c}:=g{^a ^d}*(PsiL{d b ;c}+PsiL{d c ;b}-PsiL{b c ;d})/2`);

 

Created a definition for PsiL(dn,dn,cdn) Created definition for deChrL(up,dn,dn)

 

>	grload(left1,`/home/grumil/projects/BHfreeCCTMG/Lasymptotic.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for left1 (0.000000 sec.)
	(9)

 

>	grdef(`PsiL1{a b}:=g<5>{a b}`);

 

Created definition for PsiL1(dn,dn)

 

>	grcalc(5=left1,PsiL1(dn,dn));

 

 

Calculated PsiL1(dn,dn) for left1 (0.000000 sec.)
	(10)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`PsiL1U{a ^b}:=PsiL1{a c}*g{^c ^b}`);

 

Created definition for PsiL1U(dn,up)

 

>	grdef(`PsiL1UU{^a ^b}:=PsiL1U{c ^b}*g{^c ^a}`);

 

Created definition for PsiL1UU(up,up)

 

>	grload(left2,`/home/grumil/projects/BHfreeCCTMG/Lasymptoticprime.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for left2 (0.000000 sec.)
	(11)

 

>	grdef(`PsiL2{a b}:=g<6>{a b}`);

 

Created definition for PsiL2(dn,dn)

 

>	grcalc(6=left2,PsiL2(dn,dn));

 

 

Calculated PsiL2(dn,dn) for left2 (0.000000 sec.)
	(12)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`PsiL2U{a ^b}:=PsiL2{a c}*g{^c ^b}`);

 

Created definition for PsiL2U(dn,up)

 

>	grdef(`PsiL2UU{^a ^b}:=PsiL2U{c ^b}*g{^c ^a}`);

 

Created definition for PsiL2UU(up,up)

 

>	grdef(`deRiem1{^a b c d}:=deChr1{^a b d ;c}-deChr1{^a b c ;d}`);grdef(`deRiem2{^a b c d}:=deChr2{^a b d ;c}-deChr2{^a b c ;d}`);grdef(`deRiemL{^a b c d}:=deChrL{^a b d ;c}-deChrL{^a b c ;d}`);

 

Created a definition for deChr1(up,dn,dn,cdn) Created definition for deRiem1(up,dn,dn,dn) Created a definition for deChr2(up,dn,dn,cdn) Created definition for deRiem2(up,dn,dn,dn)

 

Created a definition for deChrL(up,dn,dn,cdn) Created definition for deRiemL(up,dn,dn,dn)

 

>

grdef(`deRic2{(a b)}:=PsiLU{c ^d}*deRiem2{^c (a b) d}+(2*PsiLU{a ^c ;d}*Psi2{c b ;e}*g{^d ^e}-2*PsiLU{a ^c ;d}*Psi2U{b ^d ;c}+PsiLUU{^c ^d ;a}*Psi2{c d ;b})/4+Psi2U{c ^d}*deRiemL{^c (a b) d}+(2*Psi2U{a ^c ;d}*PsiL{c b ;e}*g{^d ^e}-2*Psi2U{a ^c ;d}*PsiLU{b ^d ;c}+Psi2UU{^c ^d ;a}*PsiL{c d ;b})/4`);grdef(`deRic1{(a b)}:=PsiLU{c ^d}*deRiem1{^c (a b) d}+(2*PsiLU{a ^c ;d}*Psi1{c b ;e}*g{^d ^e}-2*PsiLU{a ^c ;d}*Psi1U{b ^d ;c}+PsiLUU{^c ^d ;a}*Psi1{c d ;b})/4+Psi1U{c ^d}*deRiemL{^c (a b) d}+(2*Psi1U{a ^c ;d}*PsiL{c b ;e}*g{^d ^e}-2*Psi1U{a ^c ;d}*PsiLU{b ^d ;c}+Psi1UU{^c ^d ;a}*PsiL{c d ;b})/4`);

 

Created a definition for PsiLU(dn,up,cdn) Created a definition for Psi2U(dn,up,cdn) Created a definition for PsiLUU(up,up,cdn) Created a definition for Psi2UU(up,up,cdn) Created definition for deRic2(dn,dn) Created a definition for Psi1U(dn,up,cdn) Created a definition for Psi1UU(up,up,cdn) Created definition for deRic1(dn,dn)

 

>

grdef(`De12{(a b)}:=(-(Psi2U{a ^c}*PsiL1{c b})+(PsiL1{c d}*LevC{a ^c ^e}*deChr2{^d b e})-(Psi1U{a ^c}*PsiL2{c b})+(PsiL2{c d}*LevC{a ^c ^e}*deChr1{^d b e}))`);grdef(`De2{(a b)}:=-(PsiLU{a ^c}*PsiL2{c b})+(PsiL2{c d}*LevC{a ^c ^e}*deChrL{^d b e})`);grdef(`De1{(a b)}:=-(PsiLU{a ^c}*PsiL1{c b})+(PsiL1{c d}*LevC{a ^c ^e}*deChrL{^d b e})`);

 

Created definition for LevC(dn,up,up)

 

Created definition for De12(dn,dn) Created definition for De2(dn,dn) Created definition for De1(dn,dn)

 

>

grcalcalter(detg,simplify);grcalcalter(g(up,up),simplify);grcalcalter(Psi1(dn,dn),simplify);grcalcalter(Psi1U(dn,up),simplify);grcalcalter(Psi1UU(up,up),simplify);grcalcalter(Psi2(dn,dn),simplify);grcalcalter(Psi2U(dn,up),simplify);grcalcalter(Psi2UU(up,up),simplify);grcalcalter(PsiL1(dn,dn),simplify);grcalcalter(PsiL1U(dn,up),simplify);grcalcalter(PsiL1UU(up,up),simplify);grcalcalter(PsiL2(dn,dn),simplify);grcalcalter(PsiL2U(dn,up),simplify);grcalcalter(PsiL2UU(up,up),simplify);grcalcalter(Chr(dn,dn,dn),simplify);grcalcalter(Chr(dn,dn,up),simplify);grcalcalter(deChr1(up,dn,dn),simplify);grcalcalter(deChr2(up,dn,dn),simplify);grcalcalter(deChrL(up,dn,dn),simplify);grcalcalter(De12(dn,dn),simplify);grcalcalter(De1(dn,dn),simplify);grcalcalter(De2(dn,dn),simplify);

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Simplification will be applied during calculation. Applying routine simplify to object detg Calculated detg for AdS (0.000000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object g(up,up) Calculated g(up,up) for AdS (0.000000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi1(dn,dn) Calculated Psi1(dn,dn) for AdS (0.028000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi1U(dn,up) Calculated Psi1U(dn,up) for AdS (0.036000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi1UU(up,up) Calculated Psi1UU(up,up) for AdS (0.048000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi2(dn,dn) Calculated Psi2(dn,dn) for AdS (0.016000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi2U(dn,up) Calculated Psi2U(dn,up) for AdS (0.044000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi2UU(up,up) Calculated Psi2UU(up,up) for AdS (0.040000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL1(dn,dn) Calculated PsiL1(dn,dn) for AdS (0.008000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL1U(dn,up) Calculated PsiL1U(dn,up) for AdS (0.020000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL1UU(up,up) Calculated PsiL1UU(up,up) for AdS (0.020000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL2(dn,dn) Calculated PsiL2(dn,dn) for AdS (0.008000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL2U(dn,up) Calculated PsiL2U(dn,up) for AdS (0.012000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL2UU(up,up) Calculated PsiL2UU(up,up) for AdS (0.016000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object g(dn,dn,pdn) Calculated g(dn,dn,pdn) for AdS (0.000000 sec.) Applying routine simplify to object Chr(dn,dn,dn) Calculated Chr(dn,dn,dn) for AdS (0.000000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Chr(dn,dn,up) Calculated Chr(dn,dn,up) for AdS (0.004000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi1(dn,dn,cdn) Calculated Psi1(dn,dn,cdn) for AdS (0.180000 sec.) Applying routine simplify to object deChr1(up,dn,dn) Calculated deChr1(up,dn,dn) for AdS (0.408000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi2(dn,dn,cdn) Calculated Psi2(dn,dn,cdn) for AdS (0.176000 sec.) Applying routine simplify to object deChr2(up,dn,dn) Calculated deChr2(up,dn,dn) for AdS (0.376000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL(dn,dn) Calculated PsiL(dn,dn) for AdS (0.008000 sec.) Applying routine simplify to object PsiL(dn,dn,cdn) Calculated PsiL(dn,dn,cdn) for AdS (0.084000 sec.) Applying routine simplify to object deChrL(up,dn,dn) Calculated deChrL(up,dn,dn) for AdS (0.200000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object LevC(up,up,up) Calculated LevC(up,up,up) for AdS (0.000000 sec.) Applying routine simplify to object LevC(dn,up,up) Calculated LevC(dn,up,up) for AdS (0.004000 sec.) Applying routine simplify to object De12(dn,dn)
Calculated De12(dn,dn) for AdS (3.572000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiLU(dn,up) Calculated PsiLU(dn,up) for AdS (0.028000 sec.) Applying routine simplify to object De1(dn,dn)
Calculated De1(dn,dn) for AdS (1.004000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object De2(dn,dn)
Calculated De2(dn,dn) for AdS (1.048000 sec.)
	(13)

 

>	grcalcalter(deRiem1(up,dn,dn,dn),simplify);grcalcalter(deRiem2(up,dn,dn,dn),simplify);grcalcalter(deRiemL(up,dn,dn,dn),simplify);grcalcalter(deRic2(dn,dn),simplify);grcalcalter(deRic1(dn,dn),simplify);

 

 

Simplification will be applied during calculation. Applying routine simplify to object deChr1(up,dn,dn,cdn)

 

Calculated deChr1(up,dn,dn,cdn) for AdS (3.016000 sec.) Applying routine simplify to object deRiem1(up,dn,dn,dn)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculated deRiem1(up,dn,dn,dn) for AdS (1.892000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object deChr2(up,dn,dn,cdn)
Calculated deChr2(up,dn,dn,cdn) for AdS (3.028000 sec.) Applying routine simplify to object deRiem2(up,dn,dn,dn)
Calculated deRiem2(up,dn,dn,dn) for AdS (1.937000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object deChrL(up,dn,dn,cdn)
Calculated deChrL(up,dn,dn,cdn) for AdS (1.904000 sec.) Applying routine simplify to object deRiemL(up,dn,dn,dn)
Calculated deRiemL(up,dn,dn,dn) for AdS (1.532000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiLU(dn,up,cdn)
Calculated PsiLU(dn,up,cdn) for AdS (0.252000 sec.) Applying routine simplify to object Psi2U(dn,up,cdn)
Calculated Psi2U(dn,up,cdn) for AdS (0.368000 sec.) Applying routine simplify to object PsiLUU(up,up) Calculated PsiLUU(up,up) for AdS (0.036000 sec.) Applying routine simplify to object PsiLUU(up,up,cdn)
Calculated PsiLUU(up,up,cdn) for AdS (0.188000 sec.) Applying routine simplify to object Psi2UU(up,up,cdn)
Calculated Psi2UU(up,up,cdn) for AdS (0.324000 sec.) Applying routine simplify to object deRic2(dn,dn)
Calculated deRic2(dn,dn) for AdS (74.689000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi1U(dn,up,cdn)
Calculated Psi1U(dn,up,cdn) for AdS (0.424000 sec.) Applying routine simplify to object Psi1UU(up,up,cdn)
Calculated Psi1UU(up,up,cdn) for AdS (0.328000 sec.) Applying routine simplify to object deRic1(dn,dn)
Calculated deRic1(dn,dn) for AdS (75.040000 sec.)
	(14)

 

>	grdef(`Corpart1:=2*c*PsiL1UU{^a ^b}*deRic2{(a b)}+2*c*Psi1UU{^a ^b}*De2{(a b)}`);

 

Created definition for Corpart1

 

>	grdef(`Corpart2:=2*c*PsiL2UU{^a ^b}*deRic1{(a b)}+2*c*Psi2UU{^a ^b}*De1{(a b)}`);

 

Created definition for Corpart2

 

>	grdef(`Corpart3:=2*c*PsiLUU{^a ^b}*De12{(a b)}`);

 

Created definition for Corpart3

 

>	grcalcalter(Corpart1,simplify);

 

 

Simplification will be applied during calculation. Applying routine simplify to object Corpart1

 

Calculated Corpart1 for AdS (158.482000 sec.)
	(15)

 

>	grcalcalter(Corpart2,simplify);

 

 

Simplification will be applied during calculation.

 

Applying routine simplify to object Corpart2

 

Calculated Corpart2 for AdS (163.070000 sec.)
	(16)

 

>	grcalcalter(Corpart3,simplify);

 

 

Simplification will be applied during calculation. Applying routine simplify to object Corpart3

 

Calculated Corpart3 for AdS (30.006000 sec.)
	(17)

 

>	integrandCorpart1:=series(simplify(subs(u=t+phi,(subs(v=t-phi,(grcomponent(Corpart1))*2*Pi/8)))),xx=infinity,10);

 

(18)

 

>	integrandCorpart2:=series(simplify(subs(u=t+phi,(subs(v=t-phi,(grcomponent(Corpart2))*2*Pi/8)))),xx=infinity,10);

 

(19)

 

>	integrandCorpart3:=series(simplify(subs(u=t+phi,(subs(v=t-phi,(grcomponent(Corpart3))*2*Pi/8)))),xx=infinity,10);

 

(20)

 

>	fullintegrand:=collect(collect(simplify(integrandCorpart1+integrandCorpart2+integrandCorpart3),log(xx)),xx);

 

(21)

 

>	series(subs(h=a*h,subs(bh=a*bh,subs(hp=a*hp,subs(bhp=a*bhp,fullintegrand)))),a=infinity,5);

 

(22)

 

>

a4logx:=simplify(-(-288*c^2*Pi*bh^2*h^2*hp^3*bhp^2+160*c^2*Pi*bh^2*h*hp^4*bhp^2+160*c^2*Pi*bh^2*h^4*hp*bhp^2+224*c^2*Pi*bh^2*h^5*bhp^2-256*c^2*Pi*bh*h^5*bhp^3-768*c^2*Pi*bh^3*h*hp^4*bhp+224*c^2*Pi*bh^2*bhp^2*hp^5-256*c^2*Pi*bh^3*hp^5*bhp-672*c^2*Pi*h^3*bh*hp^2*bhp^3-768*c^2*Pi*h^4*bh*hp*bhp^3-288*c^2*Pi*h^3*bh^2*hp^2*bhp^2-672*c^2*Pi*bh^3*h^2*hp^3*bhp)/bh^2/bhp^2/(bh+bhp));

 

(23)

 

>

collect(collect(collect(simplify(-(((2368*I)*c^2*Pi*bh^2*hp^3*bhp^2*h^2*t+(1600*I)*c^2*Pi*hp^5*bhp^2*bh^2*t+(640*I)*c^2*Pi*hp^5*bhp*bh^3*t+576*c^2*Pi*hp^5*ln(-a^2*hp*bhp)*bhp*bh^3+576*c^2*Pi*h^5*ln(-a^2*h*bh)*bh*bhp^3+1472*c^2*Pi*bhp^2*hp^3*ln(-a^2*hp*bhp)*h^2*bh^2+1472*c^2*Pi*bh^3*hp^3*ln(-a^2*hp*bhp)*bhp*h^2+1472*c^2*Pi*bhp^3*ln(-a^2*h*bh)*bh*h^3*hp^2+576*c^2*Pi*h^5*ln(-a^2*h*bh)*bh^2*bhp^2+1664*c^2*Pi*h^4*ln(-a^2*h*bh)*bh*bhp^3*hp+1664*c^2*Pi*bh^3*hp^4*ln(-a^2*hp*bhp)*bhp*h+576*c^2*Pi*hp^5*ln(-a^2*hp*bhp)*bhp^2*bh^2+1664*c^2*Pi*bh^2*h^4*ln(-a^2*h*bh)*hp*bhp^2+1472*c^2*Pi*bhp^2*ln(-a^2*h*bh)*bh^2*h^3*hp^2+1664*c^2*Pi*hp^4*ln(-a^2*hp*bhp)*bhp^2*bh^2*h+(1600*I)*c^2*Pi*bh^2*h^5*bhp^2*t+(1792*I)*c^2*Pi*bh^3*hp^4*bhp*h*t+(1600*I)*c^2*Pi*bh^3*hp^3*bhp*h^2*t+(1600*I)*c^2*Pi*bh*h^3*bhp^3*hp^2*t+288*c^2*Pi*bh^3*hp^5*bhp+896*c^2*Pi*bh^3*h*hp^4*bhp-128*c^2*Pi*bh^2*h^5*bhp^2-128*c^2*Pi*bh^2*bhp^2*hp^5-224*c^2*Pi*bh^2*h*hp^4*bhp^2+832*c^2*Pi*bh^3*h^2*hp^3*bhp+288*c^2*Pi*bh*h^5*bhp^3+896*c^2*Pi*h^4*bh*hp*bhp^3-448*c^2*Pi*h^3*bh^2*hp^2*bhp^2+832*c^2*Pi*h^3*bh*hp^2*bhp^3-448*c^2*Pi*bh^2*h^2*hp^3*bhp^2-224*c^2*Pi*bh^2*h^4*hp*bhp^2+(2368*I)*c^2*Pi*bh^2*bhp^2*hp^2*h^3*t+(1792*I)*c^2*Pi*bh*h^4*bhp^3*hp*t+(640*I)*c^2*Pi*bhp^3*bh*h^5*t+(3648*I)*c^2*Pi*bh^2*bhp^2*h*hp^4*t+(3648*I)*c^2*Pi*bh^2*bhp^2*h^4*hp*t)/(bhp^2*bh^2*(bh+bhp)))),t),log(-a^2*h*bh)),log(-a^2*hp*bhp));

 

(24)

 

>	a4t:=simplify(-(32*Pi*c^2*((74*I)*bh*bhp*hp^2*h^3+(20*I)*bhp^2*h^5+(114*I)*bh*bhp*h^4*hp+(20*I)*hp^5*bh^2+(50*I)*hp^5*bhp*bh+(50*I)*bh*h^5*bhp+(50*I)*bh^2*hp^3*h^2+(74*I)*bh*hp^3*bhp*h^2+(114*I)*bh*bhp*h*hp^4+(56*I)*bh^2*hp^4*h+(50*I)*h^3*bhp^2*hp^2+(56*I)*h^4*bhp^2*hp)*t/(bhp*bh*(bh+bhp))));

 

(25)

 

>	a4logweight:=simplify(-(32*Pi*c^2*(18*h^5*bhp^2+18*bh*h^5*bhp+46*h^3*hp^2*bhp^2+52*h^4*hp*bhp^2+52*bh*h^4*hp*bhp+46*h^3*bh*hp^2*bhp)*ln(-a^2*h*bh)/(bhp*bh*(bh+bhp))));

 

(26)

 

>	a4logweightprime:=simplify(-(32*Pi*c^2*(18*bh^2*hp^5+46*bh*h^2*hp^3*bhp+46*bh^2*h^2*hp^3+52*bh^2*h*hp^4+18*bh*bhp*hp^5+52*bh*h*hp^4*bhp)*ln(-a^2*hp*bhp)/(bhp*bh*(bh+bhp))));

 

(27)

 

>	a4rat:=simplify(-(32*Pi*c^2*(-7*bh*h*hp^4*bhp-7*bh*h^4*hp*bhp-4*bh*h^5*bhp+26*h^3*hp^2*bhp^2+28*h^4*hp*bhp^2-4*bh*bhp*hp^5+9*bh^2*hp^5+28*bh^2*h*hp^4-14*bh*h^2*hp^3*bhp-14*h^3*bh*hp^2*bhp+26*bh^2*h^2*hp^3+9*h^5*bhp^2)/(bhp*bh*(bh+bhp))));

 

(28)

 

>

 

>