Re: polredbest() and polredabs()

On Tue, 25 Sep 2018 at 14:09, Karim Belabas <Karim.Belabas@math.u-bordeaux.fr> wrote:

* J E Cremona [2018-09-25 13:49]:
> According to http://pari.math.u-bordeaux.fr/dochtml/html-stable/ the
> function polredbest() "computes an LLL-reduced basis for the ring of
> integers of ℚ[X]/(T), then ..." which seems to imply that some expensive
> work, including factorization of the discriminant, is being done.

> Is the documentation wrong? Or does polredbest() indeed do the hard work?

Yes, this is imprecise. The documentation should read "LLL-reduced basis
for an order in Q[X]/(T)...". [ It now does, in 'master'. ]

The function correctly states that it runs in polynomial time (wrt. the
size of its input).

Thanks -- that agrees with what I have always understood to be the case.

John

Cheers,

K.B.
--
Karim Belabas, IMB (UMR 5251) Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux Fax: (+33) (0)5 40 00 21 23
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Prof J E Cremona
Warwick Mathematics Institute
University of Warwick
http://www2.warwick.ac.uk/fac/sci/maths/people/staff/john_cremona/