Re: factoring in non-maximal orders.

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

On Fri, Apr 15, 2016 at 04:21:57PM +0100, Kevin Buzzard wrote:
> n=nfinit([f,[p]]);
> X=idealfactor(n,p);
> P1=nfmodprinit(n,X[1,1])
> nfeltreducemodpr(n,t,P1)
> 
> Is this code likely to work?

Yes it should. However most of the time, as long as p <= 10^7, it is
better to do simply n=nfinit([f,10^7]); This will result with a nf which
is minimal at all primes <= 10^7, which will lead to a smaller integral
basis, and thus will speed up further computation (and reduce the risk
of hitting an implementation bug...)

Note that it is often the case that the discriminant of the field can be
factored while the discriminant of the polynomial cannot.

Cheers,
Bill.