Bill Allombert on Fri, 30 Jan 2004 17:47:21 +0100

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Re: Preparing PARI 2.3

On Fri, Jan 30, 2004 at 04:50:15PM +0100, Karim Belabas wrote:
> 1) an existing p-adic root of A (in Qp), given to relative accuracy r ?
> [ consistent with polroots() ]
> 2) the roots of A in Z / p^r ?
> As for 2), polrootspadic currently does this for the roots which are not  0
> mod p (because of the phenomenon described in the comment above). No other
> routine does it and it would be straightforward to implement it consistently
> (including 0 mod p !). We have a minor problem when A has non-p-integral
> coefficients but one can always raise an error.

In my experience, implementing 2) properly is rather difficult and lead
to an unwieldly interface due to the number of special cases. I have the
code for the square root somewhere if you need it. Generally, solving
equations in rings that are not domains is asking for trouble.