Re: generating function solution to poly

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Kevin Ryde [2018-07-21 10:42]:
> I have a generating function (and more terms too)
> 
>     g = x^2 + x^3 + x^4 + 3*x^5 + 6*x^6 + 12*x^7 + 29*x^8 + 67*x^9 + O(x^10);
> 
> which satisfies a cubic
> 
>     (1+x)*g^3 - 2*g^2 + (1-x+2*x^2)*g - x^2 == 0
> 
> Is there an easy or good way to have gp solve that for series g?

? g = subst(g,x,y)
%1 = y^2 + y^3 + y^4 + 3*y^5 + 6*y^6 + 12*y^7 + 29*y^8 + 67*y^9 + O(y^10)
? seralgdep(g,3,2)
%2 = (y + 1)*x^3 - 2*x^2 + (2*y^2 - y + 1)*x - y^2

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
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