Karim Belabas on Mon, 22 Jul 2013 20:46:08 +0200

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Re: Bug in bnfcertify?


* Stephan Ehlen [2013-07-22 19:49]:
> I tried to compute class numbers of Hilbert class fields of several
> imaginary quadratic fields, originally using sage but sage basically
> interfaces pari/gp for this purpose. In one particular example, the
> computation took very long, so I tried to find out what was going on.
> If I perform bnfinit() in pari/gp with the polynomial that defines the
> Hilbert class field in this case, the process terminates after less
> than a minute or so on my laptop. It is the bnfcertify that takes so
> long. Well, in order to see if we end up in an infinite loop or so, I
> turned on debugging and was a bit surprised to see that pari continued
> with the function testprimes beyond the Minkowski bound in this case.

(Actually, Zimmert's twin class bound)

> Looking at the source code only briefly, it seems that the second for
> loop in 'testprimes' in the file buch2.c does never terminate.

In 'master' (2.6.1, development git-6446ba6), the computation stops for
p = 1015919 as expected (with default primelimit).

In 'stable' (2.5.4), the second loop in testprimes() indeed does not
terminate :-(. The attached patch fixes this.

2.6.0 and later are not affected because all loops over consecutive primes
have been rewritten (and simplified) using the new forprime_next() iterator.

2.3.* and earlier are not affected because a loop over primes larger than
primelimit in this function simply raised an exception.


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/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]

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