Karim Belabas on Fri, 16 Sep 2011 23:24:10 +0200

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Re: class group without units or grh

* John Jones [2011-09-16 23:08]:
> Is it possible to have pari compute the class group of a number field
> without assuming grh and without computing units?

As stated, no. The sequence

 K = bnfinit(pol);
will compute class group and units, without assuming GRH. I don't know
any way to check correctness of the class group without knowing 
(a finite index subgroup of) the units.

Caveat: strictly speaking, bnfinit is not guaranteed to finish in finite
time, nor to output a correct result, even under GRH. Whether bnfinit's
output is indeed correct or not, bnfcertify may not halt either. What is
true is that (barring bugs in the implementation), IF both bnfinit and
bnfcertify succeed, then class groups and units contained in K
are unconditionally correct.


Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~belabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]