Bill Allombert on Fri, 25 Oct 2002 23:24:25 +0200

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Re: polredabs(,16) for quadhilbertreal

On Mon, Oct 21, 2002 at 11:50:13AM -0400, Igor Schein wrote:
> Right now, for example, galoisinit() does lazy factorization by
> default.  I don't know if there're exist cases where that failes, or
> when the size of automorphisms is unnecessarily large because it just
> needed 1 more smallish factor.  Bill surely can clear the fog for me
> here.  However, I can speak confidently for polredabs().

galoisinit do not use lazy factorisation but partial factorisation.
This is safe.

The only case where a slight gain could be obtained if we were able
to compute the complete factorisation is when the unfactored part is not a
perfect power, but this never happen in practice.

Also this would not change the size of the automorphisms which is independant
of the algorithm used, only the bound used for the hensel lift, which is
very fast anyhow.