Igor Schein on Sun, 6 Apr 2003 21:16:40 -0400

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Re: polredabs() again

On Fri, Apr 04, 2003 at 12:18:34AM +0200, Karim BELABAS wrote:
> Let me describe precisely the current algorithm (for future reference, and to
> spur ideas:-).
>  1) Compute an (T2-)LLL-reduced basis for the maximal order
>     [ fast and reliable nowadays, compared even to stable version. This is
>     especially efficient when the field is totally real. In this case, the
>     T2 matrix is integral, and Schnorr-Euchner strategy is used on an
>     _exact_ matrix, at the lowest possible accuracy. So one sees many
>     "precision increase" at \g4, but it's a feature of the algorithm, and
>     the signe we are making good progress: whenever precision remains
>     "stuck", we are in a quandary ]

I have a question about this step.  Let's say I first run polred(,1)
on a large polynomial, because I know it'll finish in finite time, and
it returns polynomials large than the input one.  So now I wanna run
polredabs() and hope it'll finish in reasonable time.  The annoyance
is that it has to repeat step 1, which is usually a couple of hours
for polynomials I'm currently working with.  I thought maybe it's
possible to modularize step 1 common to polred() and polredabs(), so
that it can be computed once and reused if needed. 

I'm not sure though if it'll be easier than just reworking polredabs()
to be more flexible, like it's discussed in this thread.