Re: Class groups in Pari and Magma

[Gerhard Niklasch <nikl@mathematik.tu-muenchen.de>]

In response to:
> Message-Id: <9806171641.AA00289@rhrz.uni-bonn.de>
> From: Michael Stoll <Michael_Stoll@math.uni-bonn.de>
> Date: 	Wed, 17 Jun 1998 18:41:48 +0200
> To: magma@maths.usyd.edu.au, pari-dev@list.cr.yp.to
[...]
> here are two examples of class group computations which show that
> there is room for improvement in both programs.

Which should surprise no-one...

> (2) On the other hand, take the field generated by X^4 + 5*239*X^2 + 5*239^2.
>     Pari keeps doubling the stack [...]
>     whereas Magma finds the class group in 54 seconds.

Anybody know which version of the PARI kernel would be included in that
version of MAGMA?

And whether the result computed by MAGMA is in fact correct? :)

> gp (18:18)> bnfclgp(x^4 + 5*239*x^2 + 5*239^2)

>From running this with verbose diagnostics turned on (default(debug) is
your friend, if you can read fast :^),  it seems the thing keeps doubling
the size of its ideal factor base since after each iteration it still
sees a factor-of-2 discrepancy between the class number-so-far times the
regulator-so-far and the zeta function residue.  (So far I can't say
whether this discrepancy is real, or whether it gets one of those numbers
wrong.  Several other fields defined by similar polynomials are handled
quickly by pari-between-2.0.9.alpha-and-2.0.10... e.g. when 239 is replaced
by 199, 229, 269;  with 349, it takes two factor base doublings to arrive
at a result.)

You may want to play around with the `tech' optional argument to see
whether you can coax it into returning a result in reasonable time
(and look at the diagnostic output to get an indication of what changes).
I'll be chasing some other booboos in the meantime... :^)

Cheers, Gerhard