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. Cheers, Bill.