The answer is, I believe, yes. Should it rely on the check flag to  
decide whether or not to try and factor?

- Robert


On Oct 31, 2007, at 11:58 PM, William Stein wrote:

>
> Robert,
>
> You massively sped up quadratic field arithmetic, which is really  
> awesome.
> Unfortunately the following is now slow:
>
>     sage: p = next_prime(10^24); q = next_prime(10^26); D = p*q; D
>     sage: K.<b> = NumberField(x^2 - D, check=False)
>
> because in the quadratic field constructor you factor the D no matter
> waht in order to compute the discriminant.  Is that really necessary?
> It makes arithmetic in quadratic fields of large discriminant  
> impossible.
> Is there any way to easily change your quadratic fields code so it
> doesn't require explicitly having the discriminant?  (I strongly  
> suspect
> yes, but it's complicated code, so I'll let you decide for now.)
>
> Anyway, this is trac #1043, and it came up when I was preparing for  
> Math 583
> today:
>             http://trac.sagemath.org/sage_trac/ticket/1043
>
>   -- William
>
> -- 
> William Stein
> Associate Professor of Mathematics
> University of Washington
> http://wstein.org
>
> >


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