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Series of a Root object


Dear MathUsers,

I would like to know why the following program, meant to expand the Root
object r in serie of g and s up to the second order, fails to give an
answer.

Thanks a lot
Ferruccio Renzoni


r = Root[-8*b*g^4*s^2 + 8*b^2*g^4*s^2 - 4*g^4*#1 + 8*b*g^4*#1 + 
    4*b^3*g^2*s^2*#1 - 16*g^4*s^2*#1 + 24*b*g^4*s^2*#1 + 16*b*g^4*s^4*#1
- 
    2*b*g^2*#1^2 + 6*b^2*g^2*#1^2 + 16*g^4*#1^2 + 20*b^2*g^2*s^2*#1^2 + 
    32*g^4*s^2*#1^2 + 16*g^4*s^4*#1^2 + b^3*#1^3 - 4*g^2*#1^3 + 
    22*b*g^2*#1^3 + 36*b*g^2*s^2*#1^3 + 5*b^2*#1^4 + 20*g^2*#1^4 + 
    20*g^2*s^2*#1^4 + 8*b*#1^5 + 4*#1^6 & , 3];

f00 = Simplify @ Limit[Limit[r,s->0],g->0] 

Ds = D[r,s]; Dg = D[r,g];
ds = Limit[ Limit[Ds, s->0],g-> 0]
dg = Limit[ Limit[Dg, s->0],g-> 0]
dss = Limit[ Limit[ D[Ds,s],s->0], g->0] dgg = Limit[ Limit[
D[Dg,g],s->0], g->0] dsg = Limit[ Limit[ D[Ds,g],s->0], g->0]

taylor = f00 + ds s + dg g + 1/2 (dss s^2 + dgg g^2 + 2 dsg s g) 





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