Re: [Fwd: Re: bnrisprincipal to slow]

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

On 9 Dec 2003, Markus Endres wrote:
>> First make absolutely sure you are using the CVS version of PARI....
>
> Ok, now I use the CVS version and it is really faster, fast enough for my
> examples. Thanks.
>
> But I now I have some other questions. In the CVS version the output of
> some routines are different form the old ones.

Indeed. We're trying to minimize this, but some (usually implicit) choices
made in older versions had to be reversed for the sake of correctness or
efficiency, and sometimes plain consistency.

[ see for instance the painful problem with polgalois() output format in the
CVS docs ]

> So I get a 'strange' result from 'rnfidealup'. How to interprete this
> result?

The CHANGES file reads:

2- rnfidealreltoabs, rnfidealup: now return a Z-basis as a vector of
   elements in the relative extension, instead of a meaningless HNF matrix
   wrt an unknown basis. Was especially dangerous if the extension also
   existed in nfinit form, since the HNF matrices were _not_ ideals wrt
   this nf structure. [ also consistent with rnfeltreltoabs ]

The COMPAT files and user's manual had not been properly updated. They now
(in CVS !) read the same as above, plus:

    Use the following construction instead, referring to an explicit NF
    structure:

    \\ return y = rnfidealup(rnf,...) as an ideal in HNF form associated to
    \\ nf = nfinit(rnf.pol);
    idealgentoHNF(nf, y) =
    {
      local(z); z = nfalgtobasis(nf, y);
      z[1] = Mat(z[1]); mathnf( concat(z) );
    }

> I did an idealfactor with the result from rnfidealup and this works fine in
> the old version. But now, that isn't possible. Why?

In the stable version, rnfidealup returns a matrix in HNF with respect to an
unspecified basis, which turns out to be the correct one if you compute an
'nf' using nfinit on the right component of the 'rnf' (undocumented feature).

One of the (many) reasons why the development version is so much faster is
that the integral basis associated to an 'nf' is no longer in HNF wrt the
power basis, but LLL-reduced. In short, it is no longer canonical, and
the old (shaky) construction now broke in all cases.

Hope this helps,

    Karim.
-- 
Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dép. de Mathématiques, Bât. 425   Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://pari.math.u-bordeaux.fr/  [PARI/GP]