Re: polrootsmod(f,p) with f%p==0

[Max Alekseyev <maxale@gmail.com>]

Hi Karim,

Ok, I understand. 

On a related note, - why does polrootsmod() not allow prime powers as a modulus? 

I see that there is polhensellift() which does Helsel lifting for a given (whole) factorization, and it's natural to expect that there should be a "simplified" version of it that takes care only about roots (i.e., linear factors). It seems that polrootsmod() could do that internally, but it does not. 

Regards,

Max

On Sat, Mar 25, 2023 at 5:27 PM Karim Belabas <Karim.Belabas@math.u-bordeaux.fr> wrote:

Hi Max,

  first, please show your code: there must be a better solution.

Second, there are a number of drawbacks to what you propose:
- to avoid the error, you can easily trap this exception or test for the
  0 polynomial yourself in a user function, say POLROOTSMOD with the
  semantic you expect. So we have easy and efficient workarounds.

- all polroots* function currently raise an exception on the 0 polynomial;
  polrootsmod handling a finite ring is the only one for which we
  *could* make an exception [together with the obsolete polrootsff]).
  Consistency is nice.

- by "chance" we don't provide root multiplicities in polrootsmod
  [in which case the proposed change wouldn't make sense].
  But polrootsmod and polrootspadic are actually inconsistent with polroots
  and polrootsreal ! (the former don't take multiplicities into account,
  the latter do) It has been requested in the past to fix that
  inconsistency and provide a way to obtain multiplicities [rejected on
  grounds of backward compatibility but it was a close decision].
  This becomes impossible if we make the proposed change.

- the delicate situation is not when you get a memory error but have
  p about parisizemax, the latter being large. Then your machine is going to
  start swapping. For unlucky values of p, this may essentially kill
  your session (huge result gets stored in a variable or history entry and
  then, you get memory errors whenever you try anything new)

All in all, the balance is not is favour of changing this.

Cheers,

      K.B.

* Max Alekseyev [2023-03-25 19:57]:
> Well, there will be a memory allocation error in this case, but it'll work
> fine in many other cases with small p.
> I'd prefer to see a memory error in the case of large p rather than the
> "zero polynomial in FpX_roots" error unconditionally.
> Regards,
> Max
>
> On Sat, Mar 25, 2023 at 2:36 PM Bill Allombert <
> Bill.Allombert@math.u-bordeaux.fr> wrote:
>
> > On Sat, Mar 25, 2023 at 12:46:49PM -0400, Max Alekseyev wrote:
> > > Shouldn't polrootsmod(f,p) for a prime p and f%p==0 simply return
> > > vector(p,i,Mod(i-1,p)) instead of the error?
> >
> > Given that p can be arbitrarily large, this is not practical...
> > Just consider polrootsmod(0*x,2^127-1)
> >
> > Cheers,
> > Bill
> >
> >

    K.B.
--
Pr Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/