Re: isfundamental() suggestion

[Igor Schein <igor@txc.com>]

On Wed, Dec 22, 2004 at 07:01:37PM +0100, Karim Belabas wrote:
> * Igor Schein [2004-12-22 18:53]:
> > (12:44:26) gp> N=-3^2000-2;
> > (12:44:28) gp> isfundamental(N)
> >   *** isfundamental: user interrupt after 4,610 ms.
> > (12:44:39) gp> nfdisc(quadpoly(N),1)==N
> > %141 = 1
> 
> This may or may not be correct [ I didn't try to factor N... ]
> 
> > For consistency, I think it makes sense to add flag=1 option to
> > isfundamental(). 
> 
> What would be the point ?

Practical value of it is questionable, I agree.  I was only thinking
in terms of being consistent, i.e. whenever rigorous answer depends on
a complete factorization, a function should have a flag to skip
complete factorization. 

> 
> > BTW, are there any known cases where nfdisc(pol,1)!=nfdisc(pol) ?
> 
> Plenty.
> 
> (18:57) gp > pol = x^2 - nextprime(10^7)*nextprime(10^6)^2
> (18:57) gp > nfdisc(pol)
> %1 = 40000076
> (18:57) gp > nfdisc(pol,1)
> %2 = 40000316000816000684

I didn't realize it's that easy.

Thanks

Igor