Bill Allombert on Fri, 15 Apr 2016 17:57:45 +0200 |
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Re: factoring in non-maximal orders. |
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.