Re: Cube roots mod prime powers

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

* Charles Greathouse [2014-11-07 06:04]:
> Is there a way to find cube roots mod prime powers, rather than just
> primes? Modular roots are handled by gen_Shanks_sqrtn, which is quite
> specific to primes, but I don't know if there's away to do Hensel lifting
> other than 'by hand'.

  ?  t = lift(sqrtn(2 + O(31^5), 3, &z))
  %1 = 21483438
  ? (t + O(31^5))^3
  %2 = 2 + O(31^5)

> Also, is there a way to get Fp_sqrtn's *zeta from gp?

  ? z
  %3 = 25 + 16*31 + 6*31^2 + 22*31^3 + 12*31^4 + O(31^5)

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 69 50
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