Karim BELABAS on Wed, 7 Aug 2002 03:20:00 +0200 (MEST)

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Re: rnfkummer-induced bug

On Sun, 4 Aug 2002, Igor Schein wrote:
> ? setrand(1);rnfkummer(bnrinit(bnfinit(quadpoly(-8,y)),11,1),[5,2;0,1]);
>   ***   impossible inverse modulo: Mod(0, 11).

It's gone now [typo].

1) I've axed further useless (and quite complicated) code in kummer.c, so
that rnfkummersimple (ell-th root of 1 already in K) re-uses the general
code (which had become much more efficient). The changes are non trivial
so I may have broken something in rnfkummersimple in the process.

2) rnfkummer(bnr, , deg) [output all extensions of degree deg] didn't work in
the general case (it was only implemented in rnfkummersimple). It does work
in general now. In any case, the documentation was quite misleading:  what
this variant does is to output all extension _of exact conductor f_
( assuming bnr = bnrinit(bnf, f, 1) ). _Not_ all extensions included in the
ray class field mod f.

Changing that behaviour to conform to the docs is rather tedious [I can loop
over divisors of the initial conductor, but that would be highly
inefficient]. I'd rather fix the documentation so that it corresponds to the
current code [ which is entirely trivial: it amounts to skipping the last
test = computation of the Artin norm group ]

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/
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