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zalm_pair.jl
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zalm_pair.jl
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function cf(Ns, n)
return sqrt((Ns.^n)./(Ns+1).^(n+1))
end
function cascaded_source_photonic(Ns, eAs, eBs, eD, Pd, VisF)
c0 = cf(Ns, 0)
c1 = cf(Ns, 1)
c2 = cf(Ns, 2)
v1 = [(1/4)*((-1)+Pd)^2*(4*c0^8*Pd^2+4*c1^8*((-1)+eAs)
^2*((-1)+eBs)^2*((-1)+eD)^2*(eD+Pd+(-2)*eD*Pd)^2+
4*c0^6*Pd*(2*c2^2*(2+(-2)*eAs+eAs^2+(-2)*eBs+
eBs^2)*((-1)+eD)*((-1)*Pd+eD*((-1)+2*Pd))+c1^2*((-2)
+eAs+eBs)*((-2)*Pd+eD*((-1)+3*Pd)))+4*c0^2*c1^4*((
-1)+eAs)*((-1)+eBs)*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd))
*(c1^2*((-2)+eAs+eBs)*((-1)*Pd+eD*((-1)+2*Pd))+
c2^2*((-1)+eAs)*((-1)+eBs)*((-1)+eD)*((-2)*Pd+eD*((
-3)+5*Pd)))+c0^4*(8*c2^4*((-1)+eAs)^2*((-1)+eBs)
^2*((-1)+eD)^2*(4*eD*(1+(-2)*Pd)*Pd+2*Pd^2+eD^2*
(1+(-6)*Pd+7*Pd^2))+4*c1^2*c2^2*((-1)+eAs)*((-1)+
eBs)*((-2)+eAs+eBs)*((-1)+eD)*(2*eD*(3+(-7)*Pd)*Pd+
4*Pd^2+eD^2*(1+(-8)*Pd+11*Pd^2))+c1^4*(4*(6+
eAs^2+(-6)*eBs+eBs^2+eAs*((-6)+4*eBs))*Pd^2+(-4)*(6+
eAs^2+(-6)*eBs+eBs^2+eAs*((-6)+4*eBs))*eD*Pd*((-1)+
3*Pd)+eD^2*(4+eAs^2*(1+(-3)*Pd)^2+eBs^2*(1+(-3)*
Pd)^2+(-32)*Pd+52*Pd^2+(-4)*eBs*(1+(-8)*Pd+13*Pd^2)
+2*eAs*((-2)+eBs+16*Pd+(-10)*eBs*Pd+(-26)*Pd^2+17*
eBs*Pd^2))))),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]
v2 = [0,(-1/4)*eBs*((-1)+Pd)^2*(4*
c1^8*((-1)+eAs)^2*((-1)+eBs)*((-1)+eD)^2*(eD+Pd+(-2)
*eD*Pd)^2+2*c0^6*Pd*(4*c2^2*((-1)+eBs)*((-1)+eD)
*((-1)*Pd+eD*((-1)+2*Pd))+c1^2*((-2)*Pd+eD*((-1)+3*
Pd)))+2*c0^2*c1^4*((-1)+eAs)*((-1)+eD)*((-2)*Pd+eD*
((-1)+3*Pd))*(c1^2*((-3)+eAs+2*eBs)*((-1)*Pd+eD*((
-1)+2*Pd))+2*c2^2*((-1)+eAs)*((-1)+eBs)*((-1)+eD)*((
-2)*Pd+eD*((-3)+5*Pd)))+c0^4*(8*c2^4*((-1)+eAs)^2*
((-1)+eBs)*((-1)+eD)^2*(4*eD*(1+(-2)*Pd)*Pd+2*Pd^2+
eD^2*(1+(-6)*Pd+7*Pd^2))+2*c1^2*c2^2*((-1)+eAs)*(
(-3)+eAs+2*eBs)*((-1)+eD)*(2*eD*(3+(-7)*Pd)*Pd+4*
Pd^2+eD^2*(1+(-8)*Pd+11*Pd^2))+c1^4*(4*((-3)+2*
eAs+eBs)*Pd^2+(-4)*((-3)+2*eAs+eBs)*eD*Pd*((-1)+3*
Pd)+eD^2*((-2)+eBs*(1+(-3)*Pd)^2+16*Pd+(-26)*Pd^2+
eAs*(1+(-10)*Pd+17*Pd^2))))),0,0,0,0,(1/4)*c0^2*
c1^2*eD*((-1)+Pd)^3*(2*c0^4*eAs^(1/2)*eBs^(1/2)*
Pd+(-4)*c0^3*c2*((1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)
*eAs)^(1/2)*eBs^(1/2)+eAs^(1/2)*(1+(-1)*eBs)^(1/2)*
((-1)*((-1)+eBs)*eBs)^(1/2))*((-1)+eD)*Pd+2*c1^4*((
-1)+eAs)*eAs^(1/2)*((-1)+eBs)*eBs^(1/2)*((-1)+eD)*((
-1)*Pd+eD*((-1)+2*Pd))+(-2)*c0*c1^2*c2*((-1)*(1+(
-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*eBs^(1/2)
+(1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*
eBs^(3/2)+((-1)+eAs)*eAs^(1/2)*(1+(-1)*eBs)^(1/2)*((
-1)*((-1)+eBs)*eBs)^(1/2))*((-1)+eD)*((-2)*Pd+eD*((
-1)+3*Pd))+c0^2*(8*c2^2*(1+(-1)*eAs)^(1/2)*((-1)*(
(-1)+eAs)*eAs)^(1/2)*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+
eBs)*eBs)^(1/2)*((-1)+eD)^2*Pd+c1^2*eAs^(1/2)*
eBs^(1/2)*((-2)+eAs+eBs)*((-2)*Pd+eD*((-1)+3*Pd)))),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]
v3 = [0,0,
(1/4)*c0^2*c2^2*eBs^2*((-1)+eD)*((-1)+Pd)^2*(4*
c0^4*Pd*((-1)*Pd+eD*((-1)+2*Pd))+c1^4*((-1)+eAs)
^2*((-1)+eD)*(8*eD*(1+(-2)*Pd)*Pd+4*Pd^2+eD^2*(3+
(-14)*Pd+15*Pd^2))+2*c0^2*((-1)+eAs)*(2*c2^2*((-1)
+eAs)*((-1)+eD)*(4*eD*(1+(-2)*Pd)*Pd+2*Pd^2+eD^2*(
1+(-6)*Pd+7*Pd^2))+c1^2*(2*eD*(3+(-7)*Pd)*Pd+4*
Pd^2+eD^2*(1+(-8)*Pd+11*Pd^2)))),0,0,0,0,(-1/2)*2^(
-1/2)*c0^3*c1^2*c2*eBs^(1/2)*(eBs^2)^(1/2)*((-1)+
eD)*eD*((-1)+Pd)^3*(2*c0*(c0*eAs^(1/2)+(-2)*c2*(1+
(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*((-1)+eD)
)*Pd+c1^2*((-1)+eAs)*eAs^(1/2)*((-2)*Pd+eD*((-1)+3*
Pd))),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]
v4 = [0,0,0,(-1/4)*eBs*((-1)+Pd)^2*(4*c1^8*((-1)+eAs)
^2*((-1)+eBs)*((-1)+eD)^2*(eD+Pd+(-2)*eD*Pd)^2+2*
c0^6*Pd*(4*c2^2*((-1)+eBs)*((-1)+eD)*((-1)*Pd+eD*(
(-1)+2*Pd))+c1^2*((-2)*Pd+eD*((-1)+3*Pd)))+2*c0^2*
c1^4*((-1)+eAs)*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd))*(
c1^2*((-3)+eAs+2*eBs)*((-1)*Pd+eD*((-1)+2*Pd))+2*
c2^2*((-1)+eAs)*((-1)+eBs)*((-1)+eD)*((-2)*Pd+eD*((
-3)+5*Pd)))+c0^4*(8*c2^4*((-1)+eAs)^2*((-1)+eBs)*((
-1)+eD)^2*(4*eD*(1+(-2)*Pd)*Pd+2*Pd^2+eD^2*(1+(-6)
*Pd+7*Pd^2))+2*c1^2*c2^2*((-1)+eAs)*((-3)+eAs+2*
eBs)*((-1)+eD)*(2*eD*(3+(-7)*Pd)*Pd+4*Pd^2+eD^2*(
1+(-8)*Pd+11*Pd^2))+c1^4*(4*((-3)+2*eAs+eBs)*Pd^2+(
-4)*((-3)+2*eAs+eBs)*eD*Pd*((-1)+3*Pd)+eD^2*((-2)+
eBs*(1+(-3)*Pd)^2+16*Pd+(-26)*Pd^2+eAs*(1+(-10)*Pd+
17*Pd^2))))),0,0,0,0,0,0,0,0,0,0,0,0,0,0,(1/4)*c0^2*
c1^2*eD*((-1)+Pd)^3*(2*c0^4*eAs^(1/2)*eBs^(1/2)*
Pd+(-4)*c0^3*c2*((1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)
*eAs)^(1/2)*eBs^(1/2)+eAs^(1/2)*(1+(-1)*eBs)^(1/2)*
((-1)*((-1)+eBs)*eBs)^(1/2))*((-1)+eD)*Pd+2*c1^4*((
-1)+eAs)*eAs^(1/2)*((-1)+eBs)*eBs^(1/2)*((-1)+eD)*((
-1)*Pd+eD*((-1)+2*Pd))+(-2)*c0*c1^2*c2*((-1)*(1+(
-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*eBs^(1/2)
+(1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*
eBs^(3/2)+((-1)+eAs)*eAs^(1/2)*(1+(-1)*eBs)^(1/2)*((
-1)*((-1)+eBs)*eBs)^(1/2))*((-1)+eD)*((-2)*Pd+eD*((
-1)+3*Pd))+c0^2*(8*c2^2*(1+(-1)*eAs)^(1/2)*((-1)*(
(-1)+eAs)*eAs)^(1/2)*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+
eBs)*eBs)^(1/2)*((-1)+eD)^2*Pd+c1^2*eAs^(1/2)*
eBs^(1/2)*((-2)+eAs+eBs)*((-2)*Pd+eD*((-1)+3*Pd)))),0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
v5 = [0,0,0,0,(1/4)*c1^4*
eBs^2*((-1)+Pd)^2*(4*c1^4*((-1)+eAs)^2*((-1)+eD)
^2*(eD+Pd+(-2)*eD*Pd)^2+c0^4*((-2)*Pd+eD*((-1)+3*
Pd))^2+2*c0^2*((-1)+eAs)*((-1)+eD)*((-2)*Pd+eD*((-1)
+3*Pd))*(c1^2*((-2)*Pd+eD*((-2)+4*Pd))+c2^2*((-1)+
eAs)*((-1)+eD)*((-2)*Pd+eD*((-3)+5*Pd)))),0,0,0,0,(
-1/4)*c0^2*c1^4*eBs^(3/2)*eD*((-1)+Pd)^3*(2*
c1^2*((-1)+eAs)*eAs^(1/2)*((-1)+eD)*((-1)*Pd+eD*((
-1)+2*Pd))+c0^2*eAs^(1/2)*((-2)*Pd+eD*((-1)+3*Pd))+(
-2)*c0*c2*(1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)
^(1/2)*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd))),0,0,0,0,0,
0,0,0,0,(-1/4)*c0^2*c1^4*eBs^(3/2)*eD*((-1)+Pd)^3*
(2*c1^2*((-1)+eAs)*eAs^(1/2)*((-1)+eD)*((-1)*Pd+eD*
((-1)+2*Pd))+c0^2*eAs^(1/2)*((-2)*Pd+eD*((-1)+3*Pd))
+(-2)*c0*c2*(1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)
^(1/2)*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd))),0,0,0,0,(
1/4)*c0^4*c1^4*eAs*eBs*eD^2*((-1)+Pd)^4*VisF,0,0,
0,0,0,0,0,0,0,0,0]
v6 = [0,0,0,0,0,(1/4)*c0^2*c2^2*eBs^2*((
-1)+eD)*((-1)+Pd)^2*(4*c0^4*Pd*((-1)*Pd+eD*((-1)+
2*Pd))+c1^4*((-1)+eAs)^2*((-1)+eD)*(8*eD*(1+(-2)*
Pd)*Pd+4*Pd^2+eD^2*(3+(-14)*Pd+15*Pd^2))+2*c0^2*(
(-1)+eAs)*(2*c2^2*((-1)+eAs)*((-1)+eD)*(4*eD*(1+(-2)
*Pd)*Pd+2*Pd^2+eD^2*(1+(-6)*Pd+7*Pd^2))+c1^2*(2*
eD*(3+(-7)*Pd)*Pd+4*Pd^2+eD^2*(1+(-8)*Pd+11*Pd^2))
)),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,(-1/2)*2^(-1/2)*c0^3*
c1^2*c2*eBs^(1/2)*(eBs^2)^(1/2)*((-1)+eD)*eD*((-1)
+Pd)^3*(2*c0*(c0*eAs^(1/2)+(-2)*c2*(1+(-1)*eAs)^(
1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*((-1)+eD))*Pd+c1^2*
((-1)+eAs)*eAs^(1/2)*((-2)*Pd+eD*((-1)+3*Pd))),0,0,0,
0,0,0,0,0,0,0,0,0,0,0]
v7 = [0,(1/4)*c0^2*c1^2*eD*(((-1)+Pd)
^3)*(2*c0^4*eAs^(1/2)*eBs^(1/2)*Pd+(-4)*c0^3*c2*
((1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*
eBs^(1/2)+eAs^(1/2)*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+
eBs)*eBs)^(1/2))*((-1)+eD)*Pd+2*c1^4*((-1)+eAs)*
eAs^(1/2)*((-1)+eBs)*eBs^(1/2)*((-1)+eD)*((-1)*Pd+
eD*((-1)+2*Pd))+(-2)*c0*c1^2*c2*((-1)*(1+(-1)*eAs)
^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*eBs^(1/2)+(1+(-1)
*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*eBs^(3/2)+((
-1)+eAs)*eAs^(1/2)*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+
eBs)*eBs)^(1/2))*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd))+
c0^2*(8*c2^2*(1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*
eAs)^(1/2)*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+eBs)*eBs)
^(1/2)*((-1)+eD)^2*Pd+c1^2*eAs^(1/2)*eBs^(1/2)*((
-2)+eAs+eBs)*((-2)*Pd+eD*((-1)+3*Pd)))),0,0,0,0,(-1/4)*
eAs*((-1)+Pd)^2*(4*c1^8*((-1)+eAs)*((-1)+eBs)^2*((
-1)+eD)^2*(eD+Pd+(-2)*eD*Pd)^2+2*c0^6*Pd*(4*
c2^2*((-1)+eAs)*((-1)+eD)*((-1)*Pd+eD*((-1)+2*Pd))+
c1^2*((-2)*Pd+eD*((-1)+3*Pd)))+2*c0^2*c1^4*((-1)+
eBs)*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd))*(c1^2*((-3)+
2*eAs+eBs)*((-1)*Pd+eD*((-1)+2*Pd))+2*c2^2*((-1)+
eAs)*((-1)+eBs)*((-1)+eD)*((-2)*Pd+eD*((-3)+5*Pd)))+
c0^4*(8*c2^4*((-1)+eAs)*((-1)+eBs)^2*((-1)+eD)^2*(
4*eD*(1+(-2)*Pd)*Pd+2*Pd^2+eD^2*(1+(-6)*Pd+7*
Pd^2))+2*c1^2*c2^2*((-1)+eBs)*((-3)+2*eAs+eBs)*((
-1)+eD)*(2*eD*(3+(-7)*Pd)*Pd+4*Pd^2+eD^2*(1+(-8)*
Pd+11*Pd^2))+c1^4*(4*((-3)+eAs+2*eBs)*Pd^2+(-4)*((
-3)+eAs+2*eBs)*eD*Pd*((-1)+3*Pd)+eD^2*((-2)+eBs+eAs*
(1+(-3)*Pd)^2+16*Pd+(-10)*eBs*Pd+(-26)*Pd^2+17*eBs*
Pd^2)))),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]
v8 = [0,0,(-1/2)*2^(-1/2)*c0^3*c1^2*c2*eBs^(1/2)\
*(eBs^2)^(1/2)*((-1)+eD)*eD*((-1)+Pd)^3*(2*c0*(
c0*eAs^(1/2)+(-2)*c2*(1+(-1)*eAs)^(1/2)*((-1)*((-1)+
eAs)*eAs)^(1/2)*((-1)+eD))*Pd+c1^2*((-1)+eAs)*eAs^(
1/2)*((-2)*Pd+eD*((-1)+3*Pd))),0,0,0,0,(1/2)*eAs*eBs*
((-1)+eD)*((-1)+Pd)^2*(2*c1^8*((-1)+eAs)*((-1)+eBs)*
((-1)+eD)*(eD+Pd+(-2)*eD*Pd)^2+c0^2*c1^4*((-2)*Pd+
eD*((-1)+3*Pd))*(c1^2*((-2)+eAs+eBs)*((-1)*Pd+eD*((
-1)+2*Pd))+2*c2^2*((-1)+eAs)*((-1)+eBs)*((-1)+eD)*((
-2)*Pd+eD*((-3)+5*Pd)))+2*c0^4*Pd*(c1^4*((-1)*Pd+
eD*((-1)+2*Pd))+4*c2^4*((-1)+eAs)*((-1)+eBs)*((-1)+
eD)^2*((-1)*Pd+eD*((-2)+3*Pd))+c1^2*c2^2*((-2)+eAs+
eBs)*((-1)+eD)*((-2)*Pd+eD*((-3)+5*Pd)))),0,0,0,0,(
-1/2)*2^(-1/2)*c0^3*c1^2*c2*eAs^(1/2)*(eAs^2)^(
1/2)*((-1)+eD)*eD*((-1)+Pd)^3*(2*c0*(c0*eBs^(1/2)+(
-2)*c2*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+eBs)*eBs)^(
1/2)*((-1)+eD))*Pd+c1^2*((-1)+eBs)*eBs^(1/2)*((-2)*
Pd+eD*((-1)+3*Pd))),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0]
v9 = [0,0,0,0,0,0,0,0,(-1/4)*c0^2*c2^2*eAs*eBs^2*(
(-1)+eD)^2*((-1)+Pd)^2*(8*c0^2*c2^2*((-1)+eAs)*((
-1)+eD)*Pd*((-1)*Pd+eD*((-2)+3*Pd))+2*c0^2*c1^2*
Pd*((-2)*Pd+eD*((-3)+5*Pd))+c1^4*((-1)+eAs)*(8*eD*(
1+(-2)*Pd)*Pd+4*Pd^2+eD^2*(3+(-14)*Pd+15*Pd^2))),0,
0,0,0,c0^4*c1^2*c2^2*eAs^(1/2)*(eAs^2)^(1/2)*
eBs^(1/2)*(eBs^2)^(1/2)*((-1)+eD)^2*eD*(((-1)+Pd)
^3)*Pd,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
v10 = [0,0,0,0,
(-1/4)*c0^2*c1^4*eBs^(3/2)*eD*((-1)+Pd)^3*(2*
c1^2*((-1)+eAs)*eAs^(1/2)*((-1)+eD)*((-1)*Pd+eD*((
-1)+2*Pd))+c0^2*eAs^(1/2)*((-2)*Pd+eD*((-1)+3*Pd))+(
-2)*c0*c2*(1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)
^(1/2)*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd))),0,0,0,0,(
1/4)*eAs*eBs*((-1)+Pd)^2*(4*c1^8*((-1)+eAs)*((-1)+
eBs)*((-1)+eD)^2*(eD+Pd+(-2)*eD*Pd)^2+c0^4*(4*
c2^2*((-1)+eAs)*((-1)+eD)*((-1)*Pd+eD*((-1)+2*Pd))+
c1^2*((-2)*Pd+eD*((-1)+3*Pd)))*(4*c2^2*((-1)+eBs)*
((-1)+eD)*((-1)*Pd+eD*((-1)+2*Pd))+c1^2*((-2)*Pd+eD*
((-1)+3*Pd)))+2*c0^2*c1^4*((-1)+eD)*((-2)*Pd+eD*((
-1)+3*Pd))*(c1^2*((-2)+eAs+eBs)*((-1)*Pd+eD*((-1)+2*
Pd))+2*c2^2*((-1)+eAs)*((-1)+eBs)*((-1)+eD)*((-2)*Pd+
eD*((-3)+5*Pd)))),0,0,0,0,0,0,0,0,0,(1/4)*c0^2*c1^4*
eAs^(1/2)*eBs^(1/2)*(c0*eAs^(1/2)+(-4)*c2*(1+(-1)*
eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*((-1)+eD))*(
c0*eBs^(1/2)+(-4)*c2*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+
eBs)*eBs)^(1/2)*((-1)+eD))*eD^2*((-1)+Pd)^4*VisF,0,
0,0,0,(-1/4)*c0^2*c1^4*eAs^(3/2)*eD*((-1)+Pd)^3*(
2*c1^2*((-1)+eBs)*eBs^(1/2)*((-1)+eD)*((-1)*Pd+eD*(
(-1)+2*Pd))+c0^2*eBs^(1/2)*((-2)*Pd+eD*((-1)+3*Pd))+
(-2)*c0*c2*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+eBs)*eBs)
^(1/2)*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd))),0,0,0,0,0,
0,0,0,0,0,0]
v11 = [0,0,0,0,0,0,0,0,0,0,(-1/2)*c1^4*eAs*eBs^2*
((-1)+eD)*((-1)+Pd)^2*(2*c1^4*((-1)+eAs)*((-1)+eD)*(
eD+Pd+(-2)*eD*Pd)^2+c0^2*((-2)*Pd+eD*((-1)+3*Pd))*(
c1^2*((-1)*Pd+eD*((-1)+2*Pd))+c2^2*((-1)+eAs)*((-1)+
eD)*((-2)*Pd+eD*((-3)+5*Pd)))),0,0,0,0,(1/2)*(2^(-1/2))*c0^3*c1^4*c2*eAs^(1/2)*((eAs^2)^(1/2))*eBs^(3/2)\
*((-1)+eD)*eD*((-1)+Pd)^3*((-2)*Pd+eD*((-1)+3*Pd)),
0,0,0,0,(1/2)*2^(-1/2)*c0^2*c1^4*c2*eAs^(1/2)*
eBs*(eBs^2)^(1/2)*((-1)*c0*eAs^(1/2)+4*c2*(1+(-1)*
eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*((-1)+eD))*((
-1)+eD)*eD^2*((-1)+Pd)^4,0,0,0,0,(1/2)*c0^2*c1^6*
eAs^(3/2)*eBs^(3/2)*((-1)+eD)*eD*((-1)+Pd)^3*((-1)*
Pd+eD*((-1)+2*Pd)),0,0,0,0,0,0,0,0,0,0]
v12 = [0,0,0,0,0,0,0,0,0,
0,0,(-1/4)*c0^2*c2^2*eAs*eBs^2*((-1)+eD)*(((-1)+Pd)
^2)*(c1^4*((-1)+eAs)*((-1)+eD)*(8*eD*(1+(-2)*Pd)*
Pd+4*Pd^2+eD^2*(3+(-14)*Pd+15*Pd^2))+2*c0^2*((-1)
*Pd+eD*((-1)+2*Pd))*(4*c2^2*((-1)+eAs)*((-1)+eD)*((
-1)*Pd+eD*((-1)+2*Pd))+c1^2*((-2)*Pd+eD*((-1)+3*Pd))
)),0,0,0,0,0,0,0,0,0,0,(1/2)*2^(-1/2)*c0^2*c1^4*c2*
eAs^(1/2)*eBs*(eBs^2)^(1/2)*((-1)*c0*eAs^(1/2)+4*
c2*(1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*((
-1)+eD))*((-1)+eD)*eD^2*((-1)+Pd)^4,0,0,0,0,(1/2)*2^(
-1/2)*c0^3*c1^4*c2*eAs^(3/2)*eBs^(1/2)*(eBs^2)^(
1/2)*((-1)+eD)*eD*((-1)+Pd)^3*((-2)*Pd+eD*((-1)+3*
Pd)),0,0,0,0,0,0,0,0]
v13 = [0,0,0,0,0,0,0,(-1/2)*2^(-1/2)*
c0^3*c1^2*c2*eAs^(1/2)*(eAs^2)^(1/2)*((-1)+eD)*
eD*((-1)+Pd)^3*(2*c0*(c0*eBs^(1/2)+(-2)*c2*(1+(-1)
*eBs)^(1/2)*((-1)*((-1)+eBs)*eBs)^(1/2)*((-1)+eD))*
Pd+c1^2*((-1)+eBs)*eBs^(1/2)*((-2)*Pd+eD*((-1)+3*Pd)
)),0,0,0,0,(1/4)*c0^2*c2^2*eAs^2*((-1)+eD)*(((-1)+Pd)
^2)*(4*c0^4*Pd*((-1)*Pd+eD*((-1)+2*Pd))+c1^4*((-1)
+eBs)^2*((-1)+eD)*(8*eD*(1+(-2)*Pd)*Pd+4*Pd^2+
eD^2*(3+(-14)*Pd+15*Pd^2))+2*c0^2*((-1)+eBs)*(2*
c2^2*((-1)+eBs)*((-1)+eD)*(4*eD*(1+(-2)*Pd)*Pd+2*
Pd^2+eD^2*(1+(-6)*Pd+7*Pd^2))+c1^2*(2*eD*(3+(-7)*
Pd)*Pd+4*Pd^2+eD^2*(1+(-8)*Pd+11*Pd^2)))),0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
v14 = [0,0,0,0,0,0,0,0,c0^4*
c1^2*c2^2*eAs^(1/2)*(eAs^2)^(1/2)*eBs^(1/2)*(
eBs^2)^(1/2)*((-1)+eD)^2*eD*((-1)+Pd)^3*Pd,0,0,0,0,(
-1/4)*c0^2*c2^2*eAs^2*eBs*((-1)+eD)^2*(((-1)+Pd)
^2)*(8*c0^2*c2^2*((-1)+eBs)*((-1)+eD)*Pd*((-1)*Pd+
eD*((-2)+3*Pd))+2*c0^2*c1^2*Pd*((-2)*Pd+eD*((-3)+
5*Pd))+c1^4*((-1)+eBs)*(8*eD*(1+(-2)*Pd)*Pd+4*
Pd^2+eD^2*(3+(-14)*Pd+15*Pd^2))),0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0]
v15 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,c0^4*
c2^4*eAs^2*eBs^2*((-1)+eD)^3*((-1)+Pd)^2*Pd*((-1)
*Pd+eD*((-2)+3*Pd)),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0]
v16 = [0,0,0,0,0,0,0,0,0,0,(1/2)*2^(-1/2)*c0^3*c1^4*
c2*eAs^(1/2)*(eAs^2)^(1/2)*eBs^(3/2)*((-1)+eD)*eD*
((-1)+Pd)^3*((-2)*Pd+eD*((-1)+3*Pd)),0,0,0,0,(-1/4)*
c0^2*c2^2*eAs^2*eBs*((-1)+eD)*((-1)+Pd)^2*(c1^4*
((-1)+eBs)*((-1)+eD)*(8*eD*(1+(-2)*Pd)*Pd+4*Pd^2+
eD^2*(3+(-14)*Pd+15*Pd^2))+2*c0^2*((-1)*Pd+eD*((
-1)+2*Pd))*(4*c2^2*((-1)+eBs)*((-1)+eD)*((-1)*Pd+
eD*((-1)+2*Pd))+c1^2*((-2)*Pd+eD*((-1)+3*Pd)))),0,0,
0,0,0,0,0,0,0,(1/2)*2^(-1/2)*c0^2*c1^4*c2*eAs*(
eAs^2)^(1/2)*eBs^(1/2)*((-1)*c0*eBs^(1/2)+4*c2*(1+
(-1)*eBs)^(1/2)*((-1)*((-1)+eBs)*eBs)^(1/2)*((-1)+eD)
)*((-1)+eD)*eD^2*((-1)+Pd)^4,0,0,0,0,0,0,0,0,0,0]
v17 = [0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,(1/4)*c0^2*c1^4*c2^2*
eAs^2*eBs^2*((-1)+eD)^2*((-1)+Pd)^2*(8*eD*(1+(-2)
*Pd)*Pd+4*Pd^2+eD^2*(3+(-14)*Pd+15*Pd^2)),0,0,0,0,
0,0,0,0,0,(1/2)*c0^2*c1^4*c2^2*eAs*(eAs^2)^(1/2)*
eBs*(eBs^2)^(1/2)*((-1)+eD)^2*eD^2*((-1)+Pd)^4,0,0,
0,0,0,0,0,0,0]
v18 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,c0^4*
c2^4*eAs^2*eBs^2*((-1)+eD)^2*((-1)+Pd)^2*(eD+Pd+(
-2)*eD*Pd)^2,0,0,0,0,0,0,0,0,0,0,(1/2)*c0^2*c1^4*
c2^2*eAs*(eAs^2)^(1/2)*eBs*(eBs^2)^(1/2)*(((-1)+eD)
^2)*eD^2*((-1)+Pd)^4,0,0,0,0,0,0,0]
v19 = [0,0,0,(1/4)*c0^2*
c1^2*eD*((-1)+Pd)^3*(2*c0^4*eAs^(1/2)*eBs^(1/2)*
Pd+(-4)*c0^3*c2*((1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)
*eAs)^(1/2)*eBs^(1/2)+eAs^(1/2)*(1+(-1)*eBs)^(1/2)*
((-1)*((-1)+eBs)*eBs)^(1/2))*((-1)+eD)*Pd+2*c1^4*((
-1)+eAs)*eAs^(1/2)*((-1)+eBs)*eBs^(1/2)*((-1)+eD)*((
-1)*Pd+eD*((-1)+2*Pd))+(-2)*c0*c1^2*c2*((-1)*(1+(
-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*eBs^(1/2)
+(1+(-1)*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*
eBs^(3/2)+((-1)+eAs)*eAs^(1/2)*(1+(-1)*eBs)^(1/2)*((
-1)*((-1)+eBs)*eBs)^(1/2))*((-1)+eD)*((-2)*Pd+eD*((
-1)+3*Pd))+c0^2*(8*c2^2*(1+(-1)*eAs)^(1/2)*((-1)*(
(-1)+eAs)*eAs)^(1/2)*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+
eBs)*eBs)^(1/2)*((-1)+eD)^2*Pd+c1^2*eAs^(1/2)*
eBs^(1/2)*((-2)+eAs+eBs)*((-2)*Pd+eD*((-1)+3*Pd)))),0,
0,0,0,0,0,0,0,0,0,0,0,0,0,(-1/4)*eAs*((-1)+Pd)^2*(4*
c1^8*((-1)+eAs)*((-1)+eBs)^2*((-1)+eD)^2*(eD+Pd+(-2)
*eD*Pd)^2+2*c0^6*Pd*(4*c2^2*((-1)+eAs)*((-1)+eD)
*((-1)*Pd+eD*((-1)+2*Pd))+c1^2*((-2)*Pd+eD*((-1)+3*
Pd)))+2*c0^2*c1^4*((-1)+eBs)*((-1)+eD)*((-2)*Pd+eD*
((-1)+3*Pd))*(c1^2*((-3)+2*eAs+eBs)*((-1)*Pd+eD*((
-1)+2*Pd))+2*c2^2*((-1)+eAs)*((-1)+eBs)*((-1)+eD)*((
-2)*Pd+eD*((-3)+5*Pd)))+c0^4*(8*c2^4*((-1)+eAs)*((
-1)+eBs)^2*((-1)+eD)^2*(4*eD*(1+(-2)*Pd)*Pd+2*
Pd^2+eD^2*(1+(-6)*Pd+7*Pd^2))+2*c1^2*c2^2*((-1)+
eBs)*((-3)+2*eAs+eBs)*((-1)+eD)*(2*eD*(3+(-7)*Pd)*
Pd+4*Pd^2+eD^2*(1+(-8)*Pd+11*Pd^2))+c1^4*(4*((-3)+
eAs+2*eBs)*Pd^2+(-4)*((-3)+eAs+2*eBs)*eD*Pd*((-1)+
3*Pd)+eD^2*((-2)+eBs+eAs*(1+(-3)*Pd)^2+16*Pd+(-10)*
eBs*Pd+(-26)*Pd^2+17*eBs*Pd^2)))),0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0]
v20 = [0,0,0,0,(-1/4)*c0^2*c1^4*eBs^(3/2)*eD*
((-1)+Pd)^3*(2*c1^2*((-1)+eAs)*eAs^(1/2)*((-1)+eD)*
((-1)*Pd+eD*((-1)+2*Pd))+c0^2*eAs^(1/2)*((-2)*Pd+
eD*((-1)+3*Pd))+(-2)*c0*c2*(1+(-1)*eAs)^(1/2)*((-1)
*((-1)+eAs)*eAs)^(1/2)*((-1)+eD)*((-2)*Pd+eD*((-1)+
3*Pd))),0,0,0,0,(1/4)*c0^2*c1^4*eAs^(1/2)*eBs^(1/2)*(c0*eAs^(1/2)+(-4)*c2*(1+(-1)*eAs)^(1/2)*((-1)*((
-1)+eAs)*eAs)^(1/2)*((-1)+eD))*(c0*eBs^(1/2)+(-4)*
c2*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+eBs)*eBs)^(1/2)*((
-1)+eD))*eD^2*((-1)+Pd)^4*VisF,0,0,0,0,0,0,0,0,0,(1/4)*eAs*eBs*((-1)+Pd)^2*(4*c1^8*((-1)+eAs)*((-1)+eBs)
*((-1)+eD)^2*(eD+Pd+(-2)*eD*Pd)^2+c0^4*(4*c2^2*((
-1)+eAs)*((-1)+eD)*((-1)*Pd+eD*((-1)+2*Pd))+c1^2*((
-2)*Pd+eD*((-1)+3*Pd)))*(4*c2^2*((-1)+eBs)*((-1)+eD)
*((-1)*Pd+eD*((-1)+2*Pd))+c1^2*((-2)*Pd+eD*((-1)+3*
Pd)))+2*c0^2*c1^4*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd)
)*(c1^2*((-2)+eAs+eBs)*((-1)*Pd+eD*((-1)+2*Pd))+2*
c2^2*((-1)+eAs)*((-1)+eBs)*((-1)+eD)*((-2)*Pd+eD*((
-3)+5*Pd)))),0,0,0,0,(-1/4)*c0^2*c1^4*eAs^(3/2)*eD*
((-1)+Pd)^3*(2*c1^2*((-1)+eBs)*eBs^(1/2)*((-1)+eD)*
((-1)*Pd+eD*((-1)+2*Pd))+c0^2*eBs^(1/2)*((-2)*Pd+
eD*((-1)+3*Pd))+(-2)*c0*c2*(1+(-1)*eBs)^(1/2)*((-1)
*((-1)+eBs)*eBs)^(1/2)*((-1)+eD)*((-2)*Pd+eD*((-1)+
3*Pd))),0,0,0,0,0,0,0,0,0,0,0]
v21 = [0,0,0,0,0,0,0,0,0,0,(1/2)*
2^(-1/2)*c0^2*c1^4*c2*eAs^(1/2)*eBs*(eBs^2)^(
1/2)*((-1)*c0*eAs^(1/2)+4*c2*(1+(-1)*eAs)^(1/2)*((
-1)*((-1)+eAs)*eAs)^(1/2)*((-1)+eD))*((-1)+eD)*eD^2*
((-1)+Pd)^4,0,0,0,0,0,0,0,0,0,(-1/4)*c0^2*c2^2*eAs*
eBs^2*((-1)+eD)*((-1)+Pd)^2*(c1^4*((-1)+eAs)*((-1)+
eD)*(8*eD*(1+(-2)*Pd)*Pd+4*Pd^2+eD^2*(3+(-14)*Pd+
15*Pd^2))+2*c0^2*((-1)*Pd+eD*((-1)+2*Pd))*(4*
c2^2*((-1)+eAs)*((-1)+eD)*((-1)*Pd+eD*((-1)+2*Pd))+
c1^2*((-2)*Pd+eD*((-1)+3*Pd)))),0,0,0,0,(1/2)*2^(
-1/2)*c0^3*c1^4*c2*eAs^(3/2)*eBs^(1/2)*(eBs^2)^(
1/2)*((-1)+eD)*eD*((-1)+Pd)^3*((-2)*Pd+eD*((-1)+3*
Pd)),0,0,0,0,0,0,0,0,0,0]
v22 = [0,0,0,0,0,(-1/2)*2^(-1/2)*
c0^3*c1^2*c2*eBs^(1/2)*(eBs^2)^(1/2)*((-1)+eD)*
eD*((-1)+Pd)^3*(2*c0*(c0*eAs^(1/2)+(-2)*c2*(1+(-1)
*eAs)^(1/2)*((-1)*((-1)+eAs)*eAs)^(1/2)*((-1)+eD))*
Pd+c1^2*((-1)+eAs)*eAs^(1/2)*((-2)*Pd+eD*((-1)+3*Pd)
)),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,(1/2)*eAs*eBs*((-1)+eD)*((-1)+Pd)^2*(2*c1^8*((-1)+eAs)*((-1)+eBs)*((-1)+eD)
*(eD+Pd+(-2)*eD*Pd)^2+c0^2*c1^4*((-2)*Pd+eD*((-1)+
3*Pd))*(c1^2*((-2)+eAs+eBs)*((-1)*Pd+eD*((-1)+2*Pd))
+2*c2^2*((-1)+eAs)*((-1)+eBs)*((-1)+eD)*((-2)*Pd+eD*
((-3)+5*Pd)))+2*c0^4*Pd*(c1^4*((-1)*Pd+eD*((-1)+2*
Pd))+4*c2^4*((-1)+eAs)*((-1)+eBs)*((-1)+eD)^2*((-1)*
Pd+eD*((-2)+3*Pd))+c1^2*c2^2*((-2)+eAs+eBs)*((-1)+eD)
*((-2)*Pd+eD*((-3)+5*Pd)))),0,0,0,0,0,0,0,0,(-1/2)*2^(
-1/2)*c0^3*c1^2*c2*eAs^(1/2)*(eAs^2)^(1/2)*((-1)+
eD)*eD*((-1)+Pd)^3*(2*c0*(c0*eBs^(1/2)+(-2)*c2*(1+
(-1)*eBs)^(1/2)*((-1)*((-1)+eBs)*eBs)^(1/2)*((-1)+eD)
)*Pd+c1^2*((-1)+eBs)*eBs^(1/2)*((-2)*Pd+eD*((-1)+3*
Pd))),0,0,0,0,0]
v23 = [0,0,0,0,0,0,0,0,0,0,0,(1/2)*2^(-1/2)*
c0^2*c1^4*c2*eAs^(1/2)*eBs*(eBs^2)^(1/2)*((-1)*
c0*eAs^(1/2)+4*c2*(1+(-1)*eAs)^(1/2)*((-1)*((-1)+
eAs)*eAs)^(1/2)*((-1)+eD))*((-1)+eD)*eD^2*(((-1)+Pd)
^4),0,0,0,0,0,0,0,0,0,0,(-1/2)*c1^4*eAs*eBs^2*((-1)+
eD)*((-1)+Pd)^2*(2*c1^4*((-1)+eAs)*((-1)+eD)*(eD+Pd+
(-2)*eD*Pd)^2+c0^2*((-2)*Pd+eD*((-1)+3*Pd))*(
c1^2*((-1)*Pd+eD*((-1)+2*Pd))+c2^2*((-1)+eAs)*((-1)+
eD)*((-2)*Pd+eD*((-3)+5*Pd)))),0,0,0,0,(1/2)*c0^2*
c1^6*eAs^(3/2)*eBs^(3/2)*((-1)+eD)*eD*((-1)+Pd)^3*
((-1)*Pd+eD*((-1)+2*Pd)),0,0,0,(1/2)*2^(-1/2)*c0^3*
c1^4*c2*eAs^(1/2)*(eAs^2)^(1/2)*eBs^(3/2)*((-1)+
eD)*eD*((-1)+Pd)^3*((-2)*Pd+eD*((-1)+3*Pd)),0,0,0,0]
v24 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,(-1/4)*
c0^2*c2^2*eAs*eBs^2*((-1)+eD)^2*((-1)+Pd)^2*(8*
c0^2*c2^2*((-1)+eAs)*((-1)+eD)*Pd*((-1)*Pd+eD*((-2)
+3*Pd))+2*c0^2*c1^2*Pd*((-2)*Pd+eD*((-3)+5*Pd))+
c1^4*((-1)+eAs)*(8*eD*(1+(-2)*Pd)*Pd+4*Pd^2+eD^2*
(3+(-14)*Pd+15*Pd^2))),0,0,0,0,0,0,0,0,0,c0^4*c1^2*
c2^2*eAs^(1/2)*(eAs^2)^(1/2)*eBs^(1/2)*(eBs^2)^(
1/2)*((-1)+eD)^2*eD*((-1)+Pd)^3*Pd,0,0]
v25 = [0,0,0,0,(1/4)*
c0^4*c1^4*eAs*eBs*eD^2*((-1)+Pd)^4*VisF,0,0,0,0,(
-1/4)*c0^2*c1^4*eAs^(3/2)*eD*((-1)+Pd)^3*(2*
c1^2*((-1)+eBs)*eBs^(1/2)*((-1)+eD)*((-1)*Pd+eD*((
-1)+2*Pd))+c0^2*eBs^(1/2)*((-2)*Pd+eD*((-1)+3*Pd))+(
-2)*c0*c2*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+eBs)*eBs)
^(1/2)*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd))),0,0,0,0,0,
0,0,0,0,(-1/4)*c0^2*c1^4*eAs^(3/2)*eD*((-1)+Pd)^3*
(2*c1^2*((-1)+eBs)*eBs^(1/2)*((-1)+eD)*((-1)*Pd+eD*
((-1)+2*Pd))+c0^2*eBs^(1/2)*((-2)*Pd+eD*((-1)+3*Pd))
+(-2)*c0*c2*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+eBs)*eBs)
^(1/2)*((-1)+eD)*((-2)*Pd+eD*((-1)+3*Pd))),0,0,0,0,(
1/4)*c1^4*eAs^2*((-1)+Pd)^2*(4*c1^4*((-1)+eBs)
^2*((-1)+eD)^2*(eD+Pd+(-2)*eD*Pd)^2+c0^4*((-2)*Pd+
eD*((-1)+3*Pd))^2+2*c0^2*((-1)+eBs)*((-1)+eD)*((-2)
*Pd+eD*((-1)+3*Pd))*(c1^2*((-2)*Pd+eD*((-2)+4*Pd))+
c2^2*((-1)+eBs)*((-1)+eD)*((-2)*Pd+eD*((-3)+5*Pd)))),
0,0,0,0,0,0,0,0,0,0,0]
v26 = [0,0,0,0,0,0,0,0,0,0,(1/2)*c0^2*
c1^6*eAs^(3/2)*eBs^(3/2)*((-1)+eD)*eD*((-1)+Pd)^3*
((-1)*Pd+eD*((-1)+2*Pd)),0,0,0,0,(1/2)*2^(-1/2)*
c0^2*c1^4*c2*eAs*(eAs^2)^(1/2)*eBs^(1/2)*((-1)*
c0*eBs^(1/2)+4*c2*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+
eBs)*eBs)^(1/2)*((-1)+eD))*((-1)+eD)*eD^2*(((-1)+Pd)
^4),0,0,0,0,(1/2)*2^(-1/2)*c0^3*c1^4*c2*eAs^(3/2)*
eBs^(1/2)*(eBs^2)^(1/2)*((-1)+eD)*eD*((-1)+Pd)^3*((
-2)*Pd+eD*((-1)+3*Pd)),0,0,0,0,(-1/2)*c1^4*eAs^2*
eBs*((-1)+eD)*((-1)+Pd)^2*(2*c1^4*((-1)+eBs)*((-1)+
eD)*(eD+Pd+(-2)*eD*Pd)^2+c0^2*((-2)*Pd+eD*((-1)+3*
Pd))*(c1^2*((-1)*Pd+eD*((-1)+2*Pd))+c2^2*((-1)+eBs)
*((-1)+eD)*((-2)*Pd+eD*((-3)+5*Pd)))),0,0,0,0,0,0,0,0,
0,0]
v27 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,(1/2)*c0^2*c1^4*
c2^2*eAs*(eAs^2)^(1/2)*eBs*(eBs^2)^(1/2)*(((-1)+eD)
^2)*eD^2*((-1)+Pd)^4,0,0,0,0,0,0,0,0,0,(1/4)*c0^2*
c1^4*c2^2*eAs^2*eBs^2*((-1)+eD)^2*((-1)+Pd)^2*(
8*eD*(1+(-2)*Pd)*Pd+4*Pd^2+eD^2*(3+(-14)*Pd+15*
Pd^2)),0,0,0,0,0,0,0,0,0]
v28 = [0,0,0,0,0,0,0,0,0,0,0,(1/2)*2^(
-1/2)*c0^3*c1^4*c2*eAs^(3/2)*eBs^(1/2)*(eBs^2)^(
1/2)*((-1)+eD)*eD*((-1)+Pd)^3*((-2)*Pd+eD*((-1)+3*
Pd)),0,0,0,0,0,0,0,0,0,0,(1/2)*c0^2*c1^6*eAs^(3/2)*
eBs^(3/2)*((-1)+eD)*eD*((-1)+Pd)^3*((-1)*Pd+eD*((-1)
+2*Pd)),0,0,0,0,(-1/2)*c1^4*eAs^2*eBs*((-1)+eD)*((
-1)+Pd)^2*(2*c1^4*((-1)+eBs)*((-1)+eD)*(eD+Pd+(-2)*
eD*Pd)^2+c0^2*((-2)*Pd+eD*((-1)+3*Pd))*(c1^2*((-1)
*Pd+eD*((-1)+2*Pd))+c2^2*((-1)+eBs)*((-1)+eD)*((-2)*
Pd+eD*((-3)+5*Pd)))),0,0,0,(1/2)*2^(-1/2)*c0^2*
c1^4*c2*eAs*(eAs^2)^(1/2)*eBs^(1/2)*((-1)*c0*
eBs^(1/2)+4*c2*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+eBs)*
eBs)^(1/2)*((-1)+eD))*((-1)+eD)*eD^2*((-1)+Pd)^4,0,0,
0,0]
v29 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,(1/2)*c0^2*c1^4*
c2^2*eAs*(eAs^2)^(1/2)*eBs*(eBs^2)^(1/2)*(((-1)+eD)
^2)*eD^2*((-1)+Pd)^4,0,0,0,0,0,0,0,0,0,0,c1^8*eAs^2*
eBs^2*((-1)+eD)^2*((-1)+Pd)^2*(eD+Pd+(-2)*eD*Pd)^2,
0,0,0,(1/2)*c0^2*c1^4*c2^2*eAs*(eAs^2)^(1/2)*
eBs*(eBs^2)^(1/2)*((-1)+eD)^2*eD^2*((-1)+Pd)^4,0,0,
0]
v30 = [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,
(1/4)*c0^2*c1^4*c2^2*eAs^2*eBs^2*((-1)+eD)^2*((
-1)+Pd)^2*(8*eD*(1+(-2)*Pd)*Pd+4*Pd^2+eD^2*(3+(
-14)*Pd+15*Pd^2)),0,0,0,0,(1/2)*c0^2*c1^4*c2^2*
eAs*(eAs^2)^(1/2)*eBs*(eBs^2)^(1/2)*((-1)+eD)^2*
eD^2*((-1)+Pd)^4,0]
v31 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,(-1/2)*2^(-1/2)*c0^3*c1^2*c2*eAs^(1/2)*(
eAs^2)^(1/2)*((-1)+eD)*eD*((-1)+Pd)^3*(2*c0*(c0*
eBs^(1/2)+(-2)*c2*(1+(-1)*eBs)^(1/2)*((-1)*((-1)+eBs)
*eBs)^(1/2)*((-1)+eD))*Pd+c1^2*((-1)+eBs)*eBs^(1/2)
*((-2)*Pd+eD*((-1)+3*Pd))),0,0,0,0,0,0,0,0,(1/4)*
c0^2*c2^2*eAs^2*((-1)+eD)*((-1)+Pd)^2*(4*c0^4*
Pd*((-1)*Pd+eD*((-1)+2*Pd))+c1^4*((-1)+eBs)^2*((-1)+
eD)*(8*eD*(1+(-2)*Pd)*Pd+4*Pd^2+eD^2*(3+(-14)*Pd+
15*Pd^2))+2*c0^2*((-1)+eBs)*(2*c2^2*((-1)+eBs)*((
-1)+eD)*(4*eD*(1+(-2)*Pd)*Pd+2*Pd^2+eD^2*(1+(-6)*
Pd+7*Pd^2))+c1^2*(2*eD*(3+(-7)*Pd)*Pd+4*Pd^2+
eD^2*(1+(-8)*Pd+11*Pd^2)))),0,0,0,0,0]
v32 = [0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,(1/2)*2^(-1/2)*c0^3*c1^4*
c2*eAs^(1/2)*(eAs^2)^(1/2)*eBs^(3/2)*((-1)+eD)*eD*
((-1)+Pd)^3*((-2)*Pd+eD*((-1)+3*Pd)),0,0,0,0,(1/2)*
2^(-1/2)*c0^2*c1^4*c2*eAs*(eAs^2)^(1/2)*eBs^(
1/2)*((-1)*c0*eBs^(1/2)+4*c2*(1+(-1)*eBs)^(1/2)*((
-1)*((-1)+eBs)*eBs)^(1/2)*((-1)+eD))*((-1)+eD)*eD^2*
((-1)+Pd)^4,0,0,0,(-1/4)*c0^2*c2^2*eAs^2*eBs*((-1)+
eD)*((-1)+Pd)^2*(c1^4*((-1)+eBs)*((-1)+eD)*(8*eD*(
1+(-2)*Pd)*Pd+4*Pd^2+eD^2*(3+(-14)*Pd+15*Pd^2))+2*
c0^2*((-1)*Pd+eD*((-1)+2*Pd))*(4*c2^2*((-1)+eBs)*(
(-1)+eD)*((-1)*Pd+eD*((-1)+2*Pd))+c1^2*((-2)*Pd+eD*(
(-1)+3*Pd)))),0,0,0,0]
v33 = [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,(1/2)*c0^2*c1^4*c2^2*eAs*(
eAs^2)^(1/2)*eBs*(eBs^2)^(1/2)*((-1)+eD)^2*eD^2*(
(-1)+Pd)^4,0,0,0,c0^4*c2^4*eAs^2*eBs^2*(((-1)+eD)
^2)*((-1)+Pd)^2*(eD+Pd+(-2)*eD*Pd)^2,0,0,0]
v34 = [0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,c0^4*c1^2*c2^2*
eAs^(1/2)*(eAs^2)^(1/2)*eBs^(1/2)*(eBs^2)^(1/2)*((
-1)+eD)^2*eD*((-1)+Pd)^3*Pd,0,0,0,0,0,0,0,0,0,(-1/4)*
c0^2*c2^2*eAs^2*eBs*((-1)+eD)^2*((-1)+Pd)^2*(8*
c0^2*c2^2*((-1)+eBs)*((-1)+eD)*Pd*((-1)*Pd+eD*((-2)
+3*Pd))+2*c0^2*c1^2*Pd*((-2)*Pd+eD*((-3)+5*Pd))+
c1^4*((-1)+eBs)*(8*eD*(1+(-2)*Pd)*Pd+4*Pd^2+eD^2*
(3+(-14)*Pd+15*Pd^2))),0,0]
v35 = [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,(1/2)*c0^2*c1^4*c2^2*
eAs*(eAs^2)^(1/2)*eBs*(eBs^2)^(1/2)*((-1)+eD)^2*
eD^2*((-1)+Pd)^4,0,0,0,0,(1/4)*c0^2*c1^4*c2^2*
eAs^2*eBs^2*((-1)+eD)^2*((-1)+Pd)^2*(8*eD*(1+(-2)
*Pd)*Pd+4*Pd^2+eD^2*(3+(-14)*Pd+15*Pd^2)),0]
v36 = [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,c0^4*c2^4*eAs^2*eBs^2*((-1)+eD)^3*(((-1)+Pd)
^2)*Pd*((-1)*Pd+eD*((-2)+3*Pd))]
hcat(v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17,
v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36)'
end
function cascaded_source_spin(Ns,gA,gB,eAm,eBm,eAs,eBs,eD,Pd,Pdo1,Pdo2,VisF)
m11=ret_c11(Ns,gA,gB,eAm,eBm,eAs,eBs,eD,Pd,Pdo1,Pdo2,VisF)
m22=ret_c22(Ns,gA,gB,eAm,eBm,eAs,eBs,eD,Pd,Pdo1,Pdo2,VisF)
m33=ret_c33(Ns,gA,gB,eAm,eBm,eAs,eBs,eD,Pd,Pdo1,Pdo2,VisF)
m44=ret_c44(Ns,gA,gB,eAm,eBm,eAs,eBs,eD,Pd,Pdo1,Pdo2,VisF)
m23=ret_c23(Ns,gA,gB,eAm,eBm,eAs,eBs,eD,Pd,Pdo1,Pdo2,VisF)
return [m11 0 0 0 ; 0 m22 m23 0 ; 0 m23' m33 0 ; 0 0 0 m44]
end
"""
$TYPEDEF
Fields:
$FIELDS
Generate symbolic object for the unnormalized spin-spin density matrix for a
cascaded source swapped with emissive spin memories. Since the matrix is 'weighted' by the probability for
success, it is suffixed with a W to distinguish it from the normalized object `ZALMSpinPair`. The cascaded
source from papers [prajit2022heralded](@cite) and [kevin2023zero](@cite)
is stored in spin memories as discussed in [prajit2023entangling](@cite).
It takes the following parameters:
- Ns: mean photon number per mode of the cascaded source model
- gA: qubit initialization parameter on Alice's side
- gB: qubit initialization parameter on Bob's side
- eAm: memory out-coupling efficiency for Alice's side (Allowed range: [0,1])
- eBm: memory out-coupling efficiency for Bob's side (Allowed range: [0,1])
- eAs: source out-coupling efficiency for Alice's side (Allowed range: [0,1])
- eBs: source out-coupling efficiency for Bob's side (Allowed range: [0,1])
- eD: detector efficiency (Allowed range: [0,1])
- Pd: dark click probability per photonic mode on source's swap
- Pdo1: dark click probability per photonic mode on Alice side swap
- Pdo2: dark click probability per photonic mode on Bob side swap
- VisF: product of visibilities of all three interferometers (Allowed range: [0,1])
```jldoctest
julia> r = Register(2)
julia> initialize!(r[1:2], ZALMSpinPairW(1e-3, 0.5, 0.5, 1, 1, 1, 1, 0.9, 1e-8, 1e-8, 1e-8, 0.99))
juilia> observable(r[1:2], Z⊗Z)
```
"""
@withmetadata struct ZALMSpinPairW <: AbstractTwoQubitState
Ns::Float64
gA::Float64
gB::Float64
eAm::Float64
eBm::Float64
eAs::Float64
eBs::Float64
eD::Float64
Pd::Float64
Pdo1::Float64
Pdo2::Float64
VisF::Float64
end
symbollabel(x::ZALMSpinPairW) = "ρᶻᵃˡᵐᵂ"
"""
$TYPEDEF
Fields:
$FIELDS
Generate symbolic object for the normalized spin-spin density matrix for a
cascaded source swapped with emissive spin memories. The cascaded
source from papers [prajit2022heralded](@cite) and [kevin2023zero](@cite)
is stored in spin memories as discussed in [prajit2023entangling](@cite).
It takes the following parameters:
- Ns: mean photon number per mode of the cascaded source model
- gA: qubit initialization parameter on Alice's side
- gB: qubit initialization parameter on Bob's side
- eAm: memory out-coupling efficiency for Alice's side (Allowed range: [0,1])
- eBm: memory out-coupling efficiency for Bob's side (Allowed range: [0,1])
- eAs: source out-coupling efficiency for Alice's side (Allowed range: [0,1])
- eBs: source out-coupling efficiency for Bob's side (Allowed range: [0,1])
- eD: detector efficiency (Allowed range: [0,1])
- Pd: dark click probability per photonic mode on source's swap
- Pdo1: dark click probability per photonic mode on Alice side swap
- Pdo2: dark click probability per photonic mode on Bob side swap
- VisF: product of visibilities of all three interferometers (Allowed range: [0,1])
```jldoctest
julia> r = Register(2)
julia> initialize!(r[1:2], ZALMSpinPair(1e-3, 0.5, 0.5, 1, 1, 1, 1, 0.9, 1e-8, 1e-8, 1e-8, 0.99))
juilia> observable(r[1:2], Z⊗Z)
```
"""
@withmetadata struct ZALMSpinPair <: AbstractTwoQubitState
Ns::Float64
gA::Float64
gB::Float64
eAm::Float64
eBm::Float64
eAs::Float64
eBs::Float64
eD::Float64
Pd::Float64
Pdo1::Float64
Pdo2::Float64
VisF::Float64
end
symbollabel(x::ZALMSpinPair) = "ρᶻᵃˡᵐ"
## express
function express_nolookup(x::ZALMSpinPairW, ::QuantumOpticsRepr)
data = cascaded_source_spin(x.Ns, x.gA, x.gB, x.eAm, x.eBm, x.eAs, x.eBs, x.eD, x.Pd, x.Pdo1, x.Pdo2, x.VisF)
return SparseOperator(_bspin⊗_bspin, Complex.(data))
end
function express_nolookup(x::ZALMSpinPair, ::QuantumOpticsRepr)
data = cascaded_source_spin(x.Ns, x.gA, x.gB, x.eAm, x.eBm, x.eAs, x.eBs, x.eD, x.Pd, x.Pdo1, x.Pdo2, x.VisF)
return SparseOperator(_bspin⊗_bspin, Complex.(data/tr(data)))
end
## Symbolic trace
tr(::ZALMSpinPair) = 1