Karim BELABAS on Tue, 22 Oct 2002 19:48:04 +0200 (MEST) |
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Re: polredabs(,16) for quadhilbertreal |
On Mon, 21 Oct 2002, Igor Schein wrote: > On Sat, Oct 19, 2002 at 06:42:20PM +0200, Bill Allombert wrote: >> quadhilbertreal call polredabs0 via makescind via rnfpolredabs. >> >> Should it be possible to use polredabs(,16) to avoid hanging on the factorization ? Yes, I have made the necessary changes [ I had not implemented the relevant portions of rnfpolredabs ]. > Based on my experience, as of current implementation, I wouldn't want > to see it as a default, as long as it's not a default for polredabs() > itself. I've see polynomials where polredabs(,16) is a noop until > you, say, increase primelimit. So maybe, make lazy factorization a > default for all related functions, but leave an option to do a > complete one with a certain flag. Or, even make lazy factorization a > global default(). As long as there's consistency, I have no > problem. I think this is irrelevant for quadhilbert. The problem with partial (lazy) factorisation is when a "large" prime actually divides the field discriminant. In general (assume K = Q[X]/(P)), you write disc(P) = D * f^2, and you know that v_p(disc(K)) <= v_p(D) for all p, with equality if p <= factorization bound polredabs then LLL-reduces an order of discriminant D. If D >> disc(K), you get little or no reduction. For quadhilbert the ramification is under control, by definition, so the fields which arise will have smooth discriminants and the above should never occur [ until bnrstark() is able to treat huge conductors... ]. I've added the relevant nf_PARTIALFACT flags. Any regression ? Karim. -- Karim Belabas Tel: (+33) (0)1 69 15 57 48 Dép. de Mathematiques, Bat. 425 Fax: (+33) (0)1 69 15 60 19 Université Paris-Sud Email: Karim.Belabas@math.u-psud.fr F-91405 Orsay (France) http://www.math.u-psud.fr/~belabas/ -- PARI/GP Home Page: http://www.parigp-home.de/