Re: observation: high-precision L-function values of ray class field

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Sat, Dec 11, 2021 at 01:00:02PM +0100, Markus Grassl wrote:
> Hello,
> 
> I would like to share an observation that took me some time to identify.
> Given ray class fields over real quadratic field, I am computing
> high-precision numerical values of the first derivative of L-functions at
> zero.
> 
> The implementation in PARI/GP benefits from multi-threading.
> 
> There is a big difference in total running time whether the default
> precision is changed at the very beginning of the program, i.e., before
> constructing the ray class field, or just before calling 'lfun'.

Yes, this is expected...

The reason is that bnrisprincipal() is used to compute the ideal class, and
this function behaviour depend on the precision of the bnf.
However the result should not depend on the precision of the bnf.

We recommend you use the flag 1 to bnfinit to avoid precision issue
with bnrisprincipal():
K=bnfinit(y^2-4493,1);

Cheers,
Bill