Re: nfinit(,4)

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

On Tue, 5 Nov 2002, Igor Schein wrote:
[ to me, apparently not to the list, I'm repeating the relevant bits ]

> On Wed, Nov 06, 2002 at 01:08:32AM +0100, Karim BELABAS wrote:
> > On Tue, 5 Nov 2002, Igor Schein wrote:
> > > nfinit(,4) is not doing partial polred like it's supposed to according
> > > to the documentation.
> >
> > Err, could you be a bit more specific ?
> >
> > I hit a SEGV in nfinit(x^2-4*3, 4), due to a stupid typo which I fixed. But
> > besides that, I see nothing wrong.
>
> setrand(1);
> p=x^24+62*x^12+1;
> for(k=1,3,p=poltschirnhaus(p));
> \g5
> nfinit(p,4);
>
> You can see that it's trying to completely factor the discriminant.  However,
>
> ? ?nfinit
> [snip]
> 4: as 2 but use a partial polred;

The documentation is too vague: it means "partial polred" in the sense of

  "look only at the first vectors in the reduced basis"

(as opposed to _all_ basis vectors), not

  "use a partial factorization of the discriminant".


This is IMHO a confusing and completely useless feature of nfinit:

* you get much more control using polredabs / polred and their specific
flags.

* the time-critical operation is the discriminant factorization, not the
computation of a few characteristic polynomials. So your interpretation is
in fact the logical one.

I'd rather "undocument" nfinit flags 4 and 5 (warning that these flags are
deprecated).

    Karim.
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