Kevin Ryde on Sat, 21 Jul 2018 10:42:36 +0200

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generating function solution to poly

 To: pariusers@pari.math.ubordeaux.fr
 Subject: generating function solution to poly
 From: Kevin Ryde <user42_kevin@yahoo.com.au>
 Date: Sat, 21 Jul 2018 18:38:30 +1000
 Deliverydate: Sat, 21 Jul 2018 10:42:36 +0200
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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 + (1x+2*x^2)*g  x^2 == 0
Is there an easy or good way to have gp solve that for series g?
I know how to work upwards to get g term by term (after deciding lowest
should be 0), but maybe gp already has it. I wondered only for interest
or generality though, since this one comes from recurrences which are
easy to calculate. I attempted serreverse() without joy (change
variables to solve in x, but I may have confused myself).